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Sample records for geometrical optics approach

  1. Light scattering in porous materials: Geometrical optics and stereological approach

    International Nuclear Information System (INIS)

    Malinka, Aleksey V.

    2014-01-01

    Porous material has been considered from the point of view of stereology (geometrical statistics), as a two-phase random mixture of solid material and air. Considered are the materials having the refractive index with the real part that differs notably from unit and the imaginary part much less than unit. Light scattering in such materials has been described using geometrical optics. These two – the geometrical optics laws and the stereological approach – allow one to obtain the inherent optical properties of such a porous material, which are basic in the radiative transfer theory: the photon survival probability, the scattering phase function, and the polarization properties (Mueller matrix). In this work these characteristics are expressed through the refractive index of the material and the random chord length distribution. The obtained results are compared with the traditional approach, modeling the porous material as a pack of particles of different shapes. - Highlights: • Porous material has been considered from the point of view of stereology. • Properties of a two-phase random mixture of solid material and air are considered. • Light scattering in such materials has been described using geometrical optics. • The inherent optical properties of such a porous material have been obtained

  2. A Wave-Optics Approach to Paraxial Geometrical Laws Based on Continuity at Boundaries

    Science.gov (United States)

    Linares, J.; Nistal, M. C.

    2011-01-01

    We present a derivation of the paraxial geometrical laws starting from a wave-optics approach, in particular by using simple continuity conditions of paraxial spherical waves at boundaries (discontinuities) between optical media. Paraxial geometrical imaging and magnification laws, under refraction and reflection at boundaries, are derived for…

  3. Geometrical optical illusionists.

    Science.gov (United States)

    Wade, Nicholas J

    2014-01-01

    Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.

  4. A practical guide to experimental geometrical optics

    CERN Document Server

    Garbovskiy, Yuriy A

    2017-01-01

    A concise, yet deep introduction to experimental, geometrical optics, this book begins with fundamental concepts and then develops the practical skills and research techniques routinely used in modern laboratories. Suitable for students, researchers and optical engineers, this accessible text teaches readers how to build their own optical laboratory and to design and perform optical experiments. It uses a hands-on approach which fills a gap between theory-based textbooks and laboratory manuals, allowing the reader to develop their practical skills in this interdisciplinary field, and also explores the ways in which this knowledge can be applied to the design and production of commercial optical devices. Including supplementary online resources to help readers track and evaluate their experimental results, this text is the ideal companion for anyone with a practical interest in experimental geometrical optics.

  5. Vergence, Vision, and Geometric Optics

    Science.gov (United States)

    Keating, Michael P.

    1975-01-01

    Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…

  6. Optical traps with geometric aberrations

    International Nuclear Information System (INIS)

    Roichman, Yael; Waldron, Alex; Gardel, Emily; Grier, David G.

    2006-01-01

    We assess the influence of geometric aberrations on the in-plane performance of optical traps by studying the dynamics of trapped colloidal spheres in deliberately distorted holographic optical tweezers. The lateral stiffness of the traps turns out to be insensitive to moderate amounts of coma, astigmatism, and spherical aberration. Moreover holographic aberration correction enables us to compensate inherent shortcomings in the optical train, thereby adaptively improving its performance. We also demonstrate the effects of geometric aberrations on the intensity profiles of optical vortices, whose readily measured deformations suggest a method for rapidly estimating and correcting geometric aberrations in holographic trapping systems

  7. Renormgroup symmetries in problems of nonlinear geometrical optics

    International Nuclear Information System (INIS)

    Kovalev, V.F.

    1996-01-01

    Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)

  8. Geometrical optics approach in liquid crystal films with three-dimensional director variations.

    Science.gov (United States)

    Panasyuk, G; Kelly, J; Gartland, E C; Allender, D W

    2003-04-01

    A formal geometrical optics approach (GOA) to the optics of nematic liquid crystals whose optic axis (director) varies in more than one dimension is described. The GOA is applied to the propagation of light through liquid crystal films whose director varies in three spatial dimensions. As an example, the GOA is applied to the calculation of light transmittance for the case of a liquid crystal cell which exhibits the homeotropic to multidomainlike transition (HMD cell). Properties of the GOA solution are explored, and comparison with the Jones calculus solution is also made. For variations on a smaller scale, where the Jones calculus breaks down, the GOA provides a fast, accurate method for calculating light transmittance. The results of light transmittance calculations for the HMD cell based on the director patterns provided by two methods, direct computer calculation and a previously developed simplified model, are in good agreement.

  9. Plasma geometric optics analysis and computation

    International Nuclear Information System (INIS)

    Smith, T.M.

    1983-01-01

    Important practical applications in the generation, manipulation, and diagnosis of laboratory thermonuclear plasmas have created a need for elaborate computational capabilities in the study of high frequency wave propagation in plasmas. A reduced description of such waves suitable for digital computation is provided by the theory of plasma geometric optics. The existing theory is beset by a variety of special cases in which the straightforward analytical approach fails, and has been formulated with little attention to problems of numerical implementation of that analysis. The standard field equations are derived for the first time from kinetic theory. A discussion of certain terms previously, and erroneously, omitted from the expansion of the plasma constitutive relation is given. A powerful but little known computational prescription for determining the geometric optics field in the neighborhood of caustic singularities is rigorously developed, and a boundary layer analysis for the asymptotic matching of the plasma geometric optics field across caustic singularities is performed for the first time with considerable generality. A proper treatment of birefringence is detailed, wherein a breakdown of the fundamental perturbation theory is identified and circumvented. A general ray tracing computer code suitable for applications to radiation heating and diagnostic problems is presented and described

  10. A geometric morphometric assessment of the optic cup in glaucoma.

    Science.gov (United States)

    Sanfilippo, Paul G; Cardini, Andrea; Sigal, Ian A; Ruddle, Jonathan B; Chua, Brian E; Hewitt, Alex W; Mackey, David A

    2010-09-01

    The morphologic appearance of the optic disc is of interest in glaucoma. In contrast to descriptive classification systems that are currently used, a quantitative approach to the analysis of optic disc morphology is required. Our goal was to determine the optimal method for quantifying optic cup shape by comparing traditional (ovality, form-factor and neuroretinal rim (NRR) width ratio) and geometric morphometric approaches. Left optic disc stereophotographs of 160 (80 normal and 80 glaucomatous (stratified by severity)) subjects were examined. The optic cup margins were stereoscopically delineated with a custom tracing system and saved as a series of discrete points. The geometric morphometric methods of elliptic Fourier analysis (EFA) and sliding semi-landmark analysis (SSLA) were used to eliminate variation unrelated to shape (e.g. size) and yield a series of shape variables. Differences in optic cup shape between normal and glaucoma groups were investigated. Discriminant functions were computed and the sensitivity and specificity of each technique determined. Receiver operator characteristic (ROC) curves were calculated for all methods and evaluated in their potential to discriminate between normal and glaucomatous eyes based on the shape variables. All geometric morphometric methods revealed differences between normal and glaucomatous eyes in optic cup shape, in addition to the traditional parameters of ovality, form-factor and NRR width ratio (pgeometric morphometric approach for discriminating between normal and glaucomatous eyes in optic cup shape is superior to that provided by traditional single parameter shape measures. Such analytical techniques could be incorporated into future automated optic disc screening modalities. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

  11. Depth-of-field effects in wiggler radiation sources: Geometrical versus wave optics

    Directory of Open Access Journals (Sweden)

    Richard P. Walker

    2017-02-01

    Full Text Available A detailed analysis is carried out of the optical properties of synchrotron radiation emitted by multipole wigglers, concentrating on the effective source size and brightness and the so-called “depth of field” effects, concerning which there has been some controversy in the literature. By comparing calculations made with both geometrical optics and wave optics methods we demonstrate that the two approaches are not at variance, and that the wave optics results tend towards those of geometrical optics under well-defined conditions.

  12. Geometrical optics and the diffraction phenomenon

    International Nuclear Information System (INIS)

    Timofeev, Aleksandr V

    2005-01-01

    This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)

  13. Advanced Geometric Optics on a Programmable Pocket Calculator.

    Science.gov (United States)

    Nussbaum, Allen

    1979-01-01

    Presents a ray-tracing procedure based on some ideas of Herzberger and the matrix approach to geometrical optics. This method, which can be implemented on a programmable pocket calculator, applies to any conic surface, including paraboloids, spheres, and planes. (Author/GA)

  14. On geometric optics and surface waves for light scattering by spheres

    International Nuclear Information System (INIS)

    Liou, K.N.; Takano, Y.; Yang, P.

    2010-01-01

    A geometric optics approach including surface wave contributions has been developed for homogeneous and concentrically coated spheres. In this approach, a ray-by-ray tracing program was used for efficient computation of the extinction and absorption cross sections. The present geometric-optics surface-wave (GOS) theory for light scattering by spheres considers the surface wave contribution along the edge of a particle as a perturbation term to the geometric-optics core that includes Fresnel reflection-refraction and Fraunhofer diffraction. Accuracies of the GOS approach for spheres have been assessed through comparison with the results determined from the exact Lorenz-Mie (LM) theory in terms of the extinction efficiency, single-scattering albedo, and asymmetry factor in the size-wavelength ratio domain. In this quest, we have selected a range of real and imaginary refractive indices representative of water/ice and aerosol species and demonstrated close agreement between the results computed by GOS and LM. This provides the foundation to conduct physically reliable light absorption and scattering computations based on the GOS approach for aerosol aggregates associated with internal and external mixing states employing spheres as building blocks.

  15. Generalization of the geometric optical series approach for nonadiabatic scattering problems

    International Nuclear Information System (INIS)

    Herman, M.F.

    1982-01-01

    The geometric optical series approach of Bremmer is generalized for multisurface nonadiabatic scattering problems. This method yields the formal solution of the Schroedinger equation as an infinite series of multiple integrals. The zeroth order term corresponds to WKB propagation on a single adiabatic surface, while the general Nth order term involves N reflections and/or transitions between surfaces accompanied by ''free,'' single surface semiclassical propagation between the points of reflection and transition. Each term is integrated over all possible transition and reflection points. The adiabatic and diabatic limits of this expression are discussed. Numerical results, in which all reflections are ignored, are presented for curve crossing and noncrossing problems. These results are compared to exact quantum results and are shown to be highly accurate

  16. Controlling lightwave in Riemann space by merging geometrical optics with transformation optics.

    Science.gov (United States)

    Liu, Yichao; Sun, Fei; He, Sailing

    2018-01-11

    In geometrical optical design, we only need to choose a suitable combination of lenses, prims, and mirrors to design an optical path. It is a simple and classic method for engineers. However, people cannot design fantastical optical devices such as invisibility cloaks, optical wormholes, etc. by geometrical optics. Transformation optics has paved the way for these complicated designs. However, controlling the propagation of light by transformation optics is not a direct design process like geometrical optics. In this study, a novel mixed method for optical design is proposed which has both the simplicity of classic geometrical optics and the flexibility of transformation optics. This mixed method overcomes the limitations of classic optical design; at the same time, it gives intuitive guidance for optical design by transformation optics. Three novel optical devices with fantastic functions have been designed using this mixed method, including asymmetrical transmissions, bidirectional focusing, and bidirectional cloaking. These optical devices cannot be implemented by classic optics alone and are also too complicated to be designed by pure transformation optics. Numerical simulations based on both the ray tracing method and full-wave simulation method are carried out to verify the performance of these three optical devices.

  17. Thomas Young's contributions to geometrical optics.

    Science.gov (United States)

    Atchison, David A; Charman, W Neil

    2011-07-01

    In addition to his work on physical optics, Thomas Young (1773-1829) made several contributions to geometrical optics, most of which received little recognition in his time or since. We describe and assess some of these contributions: Young's construction (the basis for much of his geometric work), paraxial refraction equations, oblique astigmatism and field curvature, and gradient-index optics. © 2011 The Authors. Clinical and Experimental Optometry © 2011 Optometrists Association Australia.

  18. Optical rectification using geometrical field enhancement in gold nano-arrays

    Science.gov (United States)

    Piltan, S.; Sievenpiper, D.

    2017-11-01

    Conversion of photons to electrical energy has a wide variety of applications including imaging, solar energy harvesting, and IR detection. A rectenna device consists of an antenna in addition to a rectifying element to absorb the incident radiation within a certain frequency range. We designed, fabricated, and measured an optical rectifier taking advantage of asymmetrical field enhancement for forward and reverse currents due to geometrical constraints. The gold nano-structures as well as the geometrical parameters offer enhanced light-matter interaction at 382 THz. Using the Taylor expansion of the time-dependent current as a function of the external bias and oscillating optical excitation, we obtained responsivities close to quantum limit of operation. This geometrical approach can offer an efficient, broadband, and scalable solution for energy conversion and detection in the future.

  19. Modeling bidirectional reflectance of forests and woodlands using Boolean models and geometric optics

    Science.gov (United States)

    Strahler, Alan H.; Jupp, David L. B.

    1990-01-01

    Geometric-optical discrete-element mathematical models for forest canopies have been developed using the Boolean logic and models of Serra. The geometric-optical approach is considered to be particularly well suited to describing the bidirectional reflectance of forest woodland canopies, where the concentration of leaf material within crowns and the resulting between-tree gaps make plane-parallel, radiative-transfer models inappropriate. The approach leads to invertible formulations, in which the spatial and directional variance provides the means for remote estimation of tree crown size, shape, and total cover from remotedly sensed imagery.

  20. Geometrical aspects in optical wave-packet dynamics.

    Science.gov (United States)

    Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto

    2006-12-01

    We construct a semiclassical theory for propagation of an optical wave packet in a nonconducting medium with a periodic structure of dielectric permittivity and magnetic permeability, i.e., a nonconducting photonic crystal. We employ a quantum-mechanical formalism in order to clarify its link to those of electronic systems. It involves the geometrical phase, i.e., Berry's phase, in a natural way, and describes an interplay between orbital motion and internal rotation. Based on the above theory, we discuss the geometrical aspects of the optical Hall effect. We also consider a reduction of the theory to a system without periodic structure and apply it to the transverse shift of an optical beam at an interface reflection or refraction. For a generic incident beam with an arbitrary polarization, an identical result for the transverse shift of each reflected or transmitted beam is given by the following different approaches: (i) analytic evaluation of wave-packet dynamics, (ii) total angular momentum (TAM) conservation for individual photons, and (iii) numerical simulation of wave-packet dynamics. It is consistent with a result by classical electrodynamics. This means that the TAM conservation for individual photons is already taken into account in wave optics, i.e., classical electrodynamics. Finally, we show an application of our theory to a two-dimensional photonic crystal, and propose an optimal design for the enhancement of the optical Hall effect in photonic crystals.

  1. A Practical Guide to Experimental Geometrical Optics

    Science.gov (United States)

    Garbovskiy, Yuriy A.; Glushchenko, Anatoliy V.

    2017-12-01

    Preface; 1. Markets of optical materials, components, accessories, light sources and detectors; 2. Introduction to optical experiments: light producing, light managing, light detection and measuring; 3. Light detectors based on semiconductors: photoresistors, photodiodes in a photo-galvanic regime. Principles of operation and measurements; 4. Linear light detectors based on photodiodes; 5. Basic laws of geometrical optics: experimental verification; 6. Converging and diverging thin lenses; 7. Thick lenses; 8. Lens systems; 9. Simple optical instruments I: the eye and the magnifier, eyepieces and telescopes; 10. Simple optical instruments II: light illuminators and microscope; 11. Spherical mirrors; 12. Introduction to optical aberrations; 13. Elements of optical radiometry; 14. Cylindrical lenses and vials; 15. Methods of geometrical optics to measure refractive index; 16. Dispersion of light and prism spectroscope; 17. Elements of computer aided optical design; Index.

  2. An efficient approach for computing the geometrical optics field reflected from a numerically specified surface

    Science.gov (United States)

    Mittra, R.; Rushdi, A.

    1979-01-01

    An approach for computing the geometrical optic fields reflected from a numerically specified surface is presented. The approach includes the step of deriving a specular point and begins with computing the reflected rays off the surface at the points where their coordinates, as well as the partial derivatives (or equivalently, the direction of the normal), are numerically specified. Then, a cluster of three adjacent rays are chosen to define a 'mean ray' and the divergence factor associated with this mean ray. Finally, the ampilitude, phase, and vector direction of the reflected field at a given observation point are derived by associating this point with the nearest mean ray and determining its position relative to such a ray.

  3. Simple and practical approach for computing the ray Hessian matrix in geometrical optics.

    Science.gov (United States)

    Lin, Psang Dain

    2018-02-01

    A method is proposed for simplifying the computation of the ray Hessian matrix in geometrical optics by replacing the angular variables in the system variable vector with their equivalent cosine and sine functions. The variable vector of a boundary surface is similarly defined in such a way as to exclude any angular variables. It is shown that the proposed formulations reduce the computation time of the Hessian matrix by around 10 times compared to the previous method reported by the current group in Advanced Geometrical Optics (2016). Notably, the method proposed in this study involves only polynomial differentiation, i.e., trigonometric function calls are not required. As a consequence, the computation complexity is significantly reduced. Five illustrative examples are given. The first three examples show that the proposed method is applicable to the determination of the Hessian matrix for any pose matrix, irrespective of the order in which the rotation and translation motions are specified. The last two examples demonstrate the use of the proposed Hessian matrix in determining the axial and lateral chromatic aberrations of a typical optical system.

  4. Active Learning Environment with Lenses in Geometric Optics

    Science.gov (United States)

    Tural, Güner

    2015-01-01

    Geometric optics is one of the difficult topics for students within physics discipline. Students learn better via student-centered active learning environments than the teacher-centered learning environments. So this study aimed to present a guide for middle school teachers to teach lenses in geometric optics via active learning environment…

  5. Field guide to geometrical optics

    CERN Document Server

    Greivenkamp, John E

    2004-01-01

    This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.

  6. Geometrical optics in general relativity

    OpenAIRE

    Loinger, A.

    2006-01-01

    General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.

  7. Geometrical co-calibration of a tomographic optical system with CT for intrinsically co-registered imaging

    Energy Technology Data Exchange (ETDEWEB)

    Cao Liji; Breithaupt, Mathies; Peter, Joerg [Division of Medical Physics in Radiology, German Cancer Research Center, Im Neuenheimer Feld 280, 69120 Heidelberg (Germany)], E-mail: l.cao@dkfz.de

    2010-03-21

    A mathematical approach for geometric co-calibration of a dual-modal small-animal imaging system is presented. The system comprises an optical imaging setup for in vivo bioluminescence and fluorescence detection, as well as an x-ray CT, both mounted on a common rotatable gantry enabling fully simultaneous imaging at axially overlapping fields-of-view. Geometric co-calibration is performed once by imaging a single cylindrical light-emitting source with both modalities over 360 deg. at two axial positions, respectively. Given the three-dimensional coordinates of the source positions in the reconstructed CT volume data along with their two-dimensional locations projected at the optical detector plane, the following intrinsic system parameters are calculated: (i) the intrinsic geometric parameters of the optical detection system-five parameters for each view and (ii) the relative positional relationship between the optical and CT systems-two parameters for each view. After co-calibration is performed, experimental studies using phantoms demonstrate the high degree of intrinsic positional accuracy between the optical and CT measurements. The most important advantage of this approach is that dual-modal data fusion is accomplished without any post-registration strategies.

  8. Invisibility Cloaking Based on Geometrical Optics for Visible Light

    Science.gov (United States)

    Ichikawa, H.; Oura, M.; Taoda, T.

    2013-06-01

    Optical cloaking has been one of unattainable dreams and just a subject in fiction until recently. Several different approaches to cloaking have been proposed and demonstrated: stealth technology, active camouflage and transformation optics. The last one would be the most formal approach modifying electromagnetic field around an object to be cloaked with metamaterials. While cloaking based on transformation optics, though valid only at single frequency, is experimentally demonstrated in microwave region, its operation in visible spectrum is still distant from realisation mainly owing to difficulty in fabricating metamaterial structure whose elements are much smaller than wavelength of light. Here we show that achromatic optical cloaking in visible spectrum is possible with the mere principle based on geometrical optics. In combining a pair of polarising beam splitters and right-angled prisms, rays of light to be obstructed by an object can make a detour to an observer, while unobstructed rays go straight through two polarising beam splitters. What is observed eventually through the device is simply background image as if nothing exists in between.

  9. Calculation of far-field scattering from nonspherical particles using a geometrical optics approach

    Science.gov (United States)

    Hovenac, Edward A.

    1991-01-01

    A numerical method was developed using geometrical optics to predict far-field optical scattering from particles that are symmetric about the optic axis. The diffractive component of scattering is calculated and combined with the reflective and refractive components to give the total scattering pattern. The phase terms of the scattered light are calculated as well. Verification of the method was achieved by assuming a spherical particle and comparing the results to Mie scattering theory. Agreement with the Mie theory was excellent in the forward-scattering direction. However, small-amplitude oscillations near the rainbow regions were not observed using the numerical method. Numerical data from spheroidal particles and hemispherical particles are also presented. The use of hemispherical particles as a calibration standard for intensity-type optical particle-sizing instruments is discussed.

  10. Stress measurement in thin films by geometrical optics

    Science.gov (United States)

    Rossnagel, S. M.; Gilstrap, P.; Rujkorakarn, R.

    1982-01-01

    A variation of Newton's rings experiment is proposed for measuring film stress. The procedure described, the geometrical optics method, is used to measure radii of curvature for a series of film depositions with Ta, Al, and Mo films. The method has a sensitivity of 1 x 10 to the 9th dyn/sq cm, corresponding to the practical radius limit of about 50 m, and a repeatability usually within five percent. For the purposes of comparison, radii are also measured by Newton's rings method and the Talysurf method; all results are found to be in general agreement. Measurement times are also compared: the geometrical optics method requires only 1/2-1 minute. It is concluded that the geometrical optics method provides an inexpensive, fast, and a reasonably correct technique with which to measure stresses in film.

  11. Resonant inelastic scattering by use of geometrical optics.

    Science.gov (United States)

    Schulte, Jörg; Schweiger, Gustav

    2003-02-01

    We investigate the inelastic scattering on spherical particles that contain one concentric inclusion in the case of input and output resonances, using a geometrical optics method. The excitation of resonances is included in geometrical optics by use of the concept of tunneled rays. To get a quantitative description of optical tunneling on spherical surfaces, we derive appropriate Fresnel-type reflection and transmission coefficients for the tunneled rays. We calculate the inelastic scattering cross section in the case of input and output resonances and investigate the influence of the distribution of the active material in the particle as well as the influence of the inclusion on inelastic scattering.

  12. Comparisons between geometrical optics and Lorenz-Mie theory

    Science.gov (United States)

    Ungut, A.; Grehan, G.; Gouesbet, G.

    1981-01-01

    Both the Lorenz-Mie and geometrical optics theories are used in calculating the scattered light patterns produced by transparent spherical particles over a wide range of diameters, between 1.0 and 100 microns, and for the range of forward scattering angles from zero to 20 deg. A detailed comparison of the results shows the greater accuracy of the geometrical optics theory in the forward direction. Emphasis is given to the simultaneous sizing and velocimetry of particles by means of pedestal calibration methods.

  13. A fast method for linear waves based on geometrical optics

    NARCIS (Netherlands)

    Stolk, C.C.

    2009-01-01

    We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the

  14. Black-hole quasinormal resonances: Wave analysis versus a geometric-optics approximation

    International Nuclear Information System (INIS)

    Hod, Shahar

    2009-01-01

    It has long been known that null unstable geodesics are related to the characteristic modes of black holes--the so-called quasinormal resonances. The basic idea is to interpret the free oscillations of a black hole in the eikonal limit in terms of null particles trapped at the unstable circular orbit and slowly leaking out. The real part of the complex quasinormal resonances is related to the angular velocity at the unstable null geodesic. The imaginary part of the resonances is related to the instability time scale (or the inverse Lyapunov exponent) of the orbit. While this geometric-optics description of the black-hole quasinormal resonances in terms of perturbed null rays is very appealing and intuitive, it is still highly important to verify the validity of this approach by directly analyzing the Teukolsky wave equation which governs the dynamics of perturbation waves in the black-hole spacetime. This is the main goal of the present paper. We first use the geometric-optics technique of perturbing a bundle of unstable null rays to calculate the resonances of near-extremal Kerr black holes in the eikonal approximation. We then directly solve the Teukolsky wave equation (supplemented by the appropriate physical boundary conditions) and show that the resultant quasinormal spectrum obtained directly from the wave analysis is in accord with the spectrum obtained from the geometric-optics approximation of perturbed null rays.

  15. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle.

    Science.gov (United States)

    Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu

    2006-07-10

    The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.

  16. Geometric Phase Generated Optical Illusion.

    Science.gov (United States)

    Yue, Fuyong; Zang, Xiaofei; Wen, Dandan; Li, Zile; Zhang, Chunmei; Liu, Huigang; Gerardot, Brian D; Wang, Wei; Zheng, Guoxing; Chen, Xianzhong

    2017-09-12

    An optical illusion, such as "Rubin's vase", is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of "Rubin faces" with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a 'vase' is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.

  17. Experimental and Theoretical Investigations on the Validity of Geometrical Optics Model for Calculating the Stability of Optical Traps

    NARCIS (Netherlands)

    Bakker schut, T.C.; Bakker Schut, Tom C.; Hesselink, Gerlo; Hesselink, Gerlo; de Grooth, B.G.; Greve, Jan

    1991-01-01

    We have developed a computer program based on the geometrical optics approach proposed by Roosen to calculate the forces on dielectric spheres in focused laser beams. We have explicitly taken into account the polarization of the laser light and thd divergence of the laser beam. The model can be used

  18. A geometrical optics polarimetric bidirectional reflectance distribution function for dielectric and metallic surfaces.

    Science.gov (United States)

    Hyde, M W; Schmidt, J D; Havrilla, M J

    2009-11-23

    A polarimetric bidirectional reflectance distribution function (pBRDF), based on geometrical optics, is presented. The pBRDF incorporates a visibility (shadowing/masking) function and a Lambertian (diffuse) component which distinguishes it from other geometrical optics pBRDFs in literature. It is shown that these additions keep the pBRDF bounded (and thus a more realistic physical model) as the angle of incidence or observation approaches grazing and better able to model the behavior of light scattered from rough, reflective surfaces. In this paper, the theoretical development of the pBRDF is shown and discussed. Simulation results of a rough, perfect reflecting surface obtained using an exact, electromagnetic solution and experimental Mueller matrix results of two, rough metallic samples are presented to validate the pBRDF.

  19. Geometrical optics in the near field: local plane-interface approach with evanescent waves.

    Science.gov (United States)

    Bose, Gaurav; Hyvärinen, Heikki J; Tervo, Jani; Turunen, Jari

    2015-01-12

    We show that geometrical models may provide useful information on light propagation in wavelength-scale structures even if evanescent fields are present. We apply a so-called local plane-wave and local plane-interface methods to study a geometry that resembles a scanning near-field microscope. We show that fair agreement between the geometrical approach and rigorous electromagnetic theory can be achieved in the case where evanescent waves are required to predict any transmission through the structure.

  20. Life Science-Related Physics Laboratory on Geometrical Optics

    Science.gov (United States)

    Edwards, T. H.; And Others

    1975-01-01

    Describes a laboratory experiment on geometrical optics designed for life science majors in a noncalculus introductory physics course. The thin lens equation is used by the students to calculate the focal length of the lens necessary to correct a myopic condition in an optical bench simulation of a human eye. (Author/MLH)

  1. Geometrical charged-particle optics

    CERN Document Server

    Rose, Harald

    2012-01-01

    This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...

  2. Application of complex geometrical optics to determination of thermal, transport, and optical parameters of thin films by the photothermal beam deflection technique.

    Science.gov (United States)

    Korte, Dorota; Franko, Mladen

    2015-01-01

    In this work, complex geometrical optics is, for what we believe is the first time, applied instead of geometrical or wave optics to describe the probe beam interaction with the field of the thermal wave in photothermal beam deflection (photothermal deflection spectroscopy) experiments on thin films. On the basis of this approach the thermal (thermal diffusivity and conductivity), optical (energy band gap), and transport (carrier lifetime) parameters of the semiconductor thin films (pure TiO2, N- and C-doped TiO2, or TiO2/SiO2 composites deposited on a glass or aluminum support) were determined with better accuracy and simultaneously during one measurement. The results are in good agreement with results obtained by the use of other methods and reported in the literature.

  3. Coated sphere scattering by geometric optics approximation.

    Science.gov (United States)

    Mengran, Zhai; Qieni, Lü; Hongxia, Zhang; Yinxin, Zhang

    2014-10-01

    A new geometric optics model has been developed for the calculation of light scattering by a coated sphere, and the analytic expression for scattering is presented according to whether rays hit the core or not. The ray of various geometric optics approximation (GOA) terms is parameterized by the number of reflections in the coating/core interface, the coating/medium interface, and the number of chords in the core, with the degeneracy path and repeated path terms considered for the rays striking the core, which simplifies the calculation. For the ray missing the core, the various GOA terms are dealt with by a homogeneous sphere. The scattering intensity of coated particles are calculated and then compared with those of Debye series and Aden-Kerker theory. The consistency of the results proves the validity of the method proposed in this work.

  4. Geometric-optical illusions at isoluminance.

    Science.gov (United States)

    Hamburger, Kai; Hansen, Thorsten; Gegenfurtner, Karl R

    2007-12-01

    The idea of a largely segregated processing of color and form was initially supported by observations that geometric-optical illusions vanish under isoluminance. However, this finding is inconsistent with some psychophysical studies and also with physiological evidence showing that color and luminance are processed together by largely overlapping sets of neurons in the LGN, in V1, and in extrastriate areas. Here we examined the strength of nine geometric-optical illusions under isoluminance (Delboeuf, Ebbinghaus, Hering, Judd, Müller-Lyer, Poggendorff, Ponzo, Vertical, Zöllner). Subjects interactively manipulated computer-generated line drawings to counteract the illusory effect. In all cases, illusions presented under isoluminance (both for colors drawn from the cardinal L-M or S-(L+M) directions of DKL color space) were as effective as the luminance versions (both for high and low contrast). The magnitudes of the illusion effects were highly correlated across subjects for the different conditions. In two additional experiments we determined that the strong illusions observed under isoluminance were not due to individual deviations from the photometric point of isoluminance or due to chromatic aberrations. Our findings show that our conscious percept is affected similarly for both isoluminance and luminance conditions, suggesting that the joint processing for chromatic and luminance defined contours may extend well beyond early visual areas.

  5. Light propagation and transmission in hybrid-aligned nematic liquid crystal cells: Geometrical optics calculations

    Science.gov (United States)

    Mendoza, Carlos I.; Reyes, J. Adrian

    2006-08-01

    The authors present a geometrical approach to calculate the transmission of light in a hybrid-aligned nematic cell under the influence of an applied electric field. Using the framework of geometrical optics they present results for the ray tracing as well as the transmission of light as a function of the applied low frequency voltage. Dispersion effects are included through a wavelength dependent dielectric function. Their results for the transmittance as a function of the applied voltage show oscillations that are in good qualitative agreement with previously obtained experimental measurements.

  6. The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

    OpenAIRE

    Maj, Omar

    2004-01-01

    The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also disc...

  7. Flat-field response and geometric distortion measurements of optical streak cameras

    International Nuclear Information System (INIS)

    Montgomery, D.S.; Drake, R.P.; Jones, B.A.; Wiedwald, J.D.

    1987-08-01

    To accurately measure pulse amplitude, shape, and relative time histories of optical signals with an optical streak camera, it is necessary to correct each recorded image for spatially-dependent gain nonuniformity and geometric distortion. Gain nonuniformities arise from sensitivity variations in the streak-tube photocathode, phosphor screen, image-intensifier tube, and image recording system. These nonuniformities may be severe, and have been observed to be on the order of 100% for some LLNL optical streak cameras. Geometric distortion due to optical couplings, electron-optics, and sweep nonlinearity not only affects pulse position and timing measurements, but affects pulse amplitude and shape measurements as well. By using a 1.053-μm, long-pulse, high-power laser to generate a spatially and temporally uniform source as input to the streak camera, the combined effects of flat-field response and geometric distortion can be measured under the normal dynamic operation of cameras with S-1 photocathodes. Additionally, by using the same laser system to generate a train of short pulses that can be spatially modulated at the input of the streak camera, we can effectively create a two-dimensional grid of equally-spaced pulses. This allows a dynamic measurement of the geometric distortion of the streak camera. We will discuss the techniques involved in performing these calibrations, will present some of the measured results for LLNL optical streak cameras, and will discuss software methods to correct for these effects. 6 refs., 6 figs

  8. Advances on geometric flux optical design method

    Science.gov (United States)

    García-Botella, Ángel; Fernández-Balbuena, Antonio Álvarez; Vázquez, Daniel

    2017-09-01

    Nonimaging optics is focused on the study of methods to design concentrators or illuminators systems. It can be included in the area of photometry and radiometry and it is governed by the laws of geometrical optics. The field vector method, which starts with the definition of the irradiance vector E, is one of the techniques used in nonimaging optics. Called "Geometrical flux vector" it has provide ideal designs. The main property of this model is, its ability to estimate how radiant energy is transferred by the optical system, from the concepts of field line, flux tube and pseudopotential surface, overcoming traditional raytrace methods. Nevertheless this model has been developed only at an academic level, where characteristic optical parameters are ideal not real and the studied geometries are simple. The main objective of the present paper is the application of the vector field method to the analysis and design of real concentration and illumination systems. We propose the development of a calculation tool for optical simulations by vector field, using algorithms based on Fermat`s principle, as an alternative to traditional tools for optical simulations by raytrace, based on reflection and refraction law. This new tool provides, first, traditional simulations results: efficiency, illuminance/irradiance calculations, angular distribution of light- with lower computation time, photometrical information needs about a few tens of field lines, in comparison with million rays needed nowadays. On the other hand the tool will provides new information as vector field maps produced by the system, composed by field lines and quasipotential surfaces. We show our first results with the vector field simulation tool.

  9. Geometric phases in astigmatic optical modes of arbitrary order

    International Nuclear Information System (INIS)

    Habraken, Steven J. M.; Nienhuis, Gerard

    2010-01-01

    The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.

  10. Geometrical optics in general relativity: A study of the higher order corrections

    International Nuclear Information System (INIS)

    Anile, A.M.

    1976-01-01

    The higher order corrections to geometrical optics are studied in general relativity for an electromagnetic test wave. An explicit expression is found for the average energy--momentum tensor which takes into account the first-order corrections. Finally the first-order corrections to the well-known area-intensity law of geometrical optics are derived

  11. Applicability of geometrical optics to in-plane liquid-crystal configurations

    NARCIS (Netherlands)

    Sluijter, M.; Xu, M.; Urbach, H.P.; De Boer, D.K.G.

    2010-01-01

    We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices no=1.5 and ne=1.7. To this end, we compare the results of advanced ray- and wave-optics simulations

  12. Geometrical-optics code for computing the optical properties of large dielectric spheres.

    Science.gov (United States)

    Zhou, Xiaobing; Li, Shusun; Stamnes, Knut

    2003-07-20

    Absorption of electromagnetic radiation by absorptive dielectric spheres such as snow grains in the near-infrared part of the solar spectrum cannot be neglected when radiative properties of snow are computed. Thus a new, to our knowledge, geometrical-optics code is developed to compute scattering and absorption cross sections of large dielectric particles of arbitrary complex refractive index. The number of internal reflections and transmissions are truncated on the basis of the ratio of the irradiance incident at the nth interface to the irradiance incident at the first interface for a specific optical ray. Thus the truncation number is a function of the angle of incidence. Phase functions for both near- and far-field absorption and scattering of electromagnetic radiation are calculated directly at any desired scattering angle by using a hybrid algorithm based on the bisection and Newton-Raphson methods. With these methods a large sphere's absorption and scattering properties of light can be calculated for any wavelength from the ultraviolet to the microwave regions. Assuming that large snow meltclusters (1-cm order), observed ubiquitously in the snow cover during summer, can be characterized as spheres, one may compute absorption and scattering efficiencies and the scattering phase function on the basis of this geometrical-optics method. A geometrical-optics method for sphere (GOMsphere) code is developed and tested against Wiscombe's Mie scattering code (MIE0) and a Monte Carlo code for a range of size parameters. GOMsphere can be combined with MIE0 to calculate the single-scattering properties of dielectric spheres of any size.

  13. Geometrical optics of dense aerosols: forming dense plasma slabs.

    Science.gov (United States)

    Hay, Michael J; Valeo, Ernest J; Fisch, Nathaniel J

    2013-11-01

    Assembling a freestanding, sharp-edged slab of homogeneous material that is much denser than gas, but much more rarefied than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed field, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the finite particle density reduces the effective Stokes number of the flow, a critical result for controlled focusing.

  14. Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

    International Nuclear Information System (INIS)

    Bi Lei; Yang Ping; Kattawar, George W.; Hu Yongxiang; Baum, Bryan A.

    2011-01-01

    A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a 'benchmark' within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.

  15. Geometrical-optics approximation of forward scattering by coated particles.

    Science.gov (United States)

    Xu, Feng; Cai, Xiaoshu; Ren, Kuanfang

    2004-03-20

    By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 degrees-60 degrees) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10 degrees or so.

  16. Two-dimensional fast marching for geometrical optics.

    Science.gov (United States)

    Capozzoli, Amedeo; Curcio, Claudio; Liseno, Angelo; Savarese, Salvatore

    2014-11-03

    We develop an approach for the fast and accurate determination of geometrical optics solutions to Maxwell's equations in inhomogeneous 2D media and for TM polarized electric fields. The eikonal equation is solved by the fast marching method. Particular attention is paid to consistently discretizing the scatterers' boundaries and matching the discretization to that of the computational domain. The ray tracing is performed, in a direct and inverse way, by using a technique introduced in computer graphics for the fast and accurate generation of textured images from vector fields. The transport equation is solved by resorting only to its integral form, the transport of polarization being trivial for the considered geometry and polarization. Numerical results for the plane wave scattering of two perfectly conducting circular cylinders and for a Luneburg lens prove the accuracy of the algorithm. In particular, it is shown how the approach is capable of properly accounting for the multiple scattering occurring between the two metallic cylinders and how inverse ray tracing should be preferred to direct ray tracing in the case of the Luneburg lens.

  17. Generation of equal-intensity coherent optical beams by binary geometrical phase on metasurface

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Zheng-Han; Jiang, Shang-Chi; Xiong, Xiang; Peng, Ru-Wen, E-mail: rwpeng@nju.edu.cn, E-mail: muwang@nju.edu.cn; Wang, Mu, E-mail: rwpeng@nju.edu.cn, E-mail: muwang@nju.edu.cn [National Laboratory of Solid State Microstructures and School of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China)

    2016-06-27

    We report here the design and realization of a broadband, equal-intensity optical beam splitter with a dispersion-free binary geometric phase on a metasurface with unit cell consisting of two mirror-symmetric elements. We demonstrate experimentally that two identical beams can be efficiently generated with incidence of any polarization. The efficiency of the device reaches 80% at 1120 nm and keeps larger than 70% in the range of 1000–1400 nm. We suggest that this approach for generating identical, coherent beams have wide applications in diffraction optics and in entangled photon light source for quantum communication.

  18. Geometrical optics in correlated imaging systems

    International Nuclear Information System (INIS)

    Cao Dezhong; Xiong Jun; Wang Kaige

    2005-01-01

    We discuss the geometrical optics of correlated imaging for two kinds of spatial correlations corresponding, respectively, to a classical thermal light source and a quantum two-photon entangled source. Due to the different features in the second-order spatial correlation, the two sources obey different imaging equations. The quantum entangled source behaves as a mirror, whereas the classical thermal source looks like a phase-conjugate mirror in the correlated imaging

  19. Geometrical-optics approximation of forward scattering by gradient-index spheres.

    Science.gov (United States)

    Li, Xiangzhen; Han, Xiang'e; Li, Renxian; Jiang, Huifen

    2007-08-01

    By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.

  20. Geometric and potential dynamics interpretation of the optic ring resonator bistability

    Science.gov (United States)

    Chiangga, S.; Chittha, T.; Frank, T. D.

    2015-07-01

    The optical bistability is a fundamental nonlinear feature of the ring resonator. A geometric and potential dynamics interpretation of the bistability is given. Accordingly, the bistability of the nonlinear system is shown to be a consequence of geometric laws of vector calculus describing the resonator ring. In contrast, the so-called transcendental relations that have been obtained in the literature in order to describe the optical wave are interpreted in terms of potential dynamical systems. The proposed novel interpretation provides new insights into the nature of the ring resonator optical bistability. The fundamental work by Rukhlenko, Premaratne and Agrawal (2010) as well as a more recent study by Chiangga, Pitakwongsaporn, Frank and Yupapin (2013) are considered.

  1. Geometric optical transfer function and tis computation method

    International Nuclear Information System (INIS)

    Wang Qi

    1992-01-01

    Geometric Optical Transfer Function formula is derived after expound some content to be easily ignored, and the computation method is given with Bessel function of order zero and numerical integration and Spline interpolation. The method is of advantage to ensure accuracy and to save calculation

  2. Applicability of geometrical optics to in-plane liquid-crystal configurations.

    Science.gov (United States)

    Sluijter, M; Xu, M; Urbach, H P; de Boer, D K G

    2010-02-15

    We study the applicability of geometrical optics to inhomogeneous dielectric nongyrotropic optically anisotropic media typically found in in-plane liquid-crystal configurations with refractive indices n(o)=1.5 and n(e)=1.7. To this end, we compare the results of advanced ray- and wave-optics simulations of the propagation of an incident plane wave to a special anisotropic configuration. Based on the results, we conclude that for a good agreement between ray and wave optics, a maximum change in optical properties should occur over a distance of at least 20 wavelengths.

  3. Geometrical optics and optimal transport.

    Science.gov (United States)

    Rubinstein, Jacob; Wolansky, Gershon

    2017-10-01

    The Fermat principle is generalized to a system of rays. It is shown that all the ray mappings that are compatible with two given intensities of a monochromatic wave, measured at two planes, are stationary points of a canonical functional, which is the weighted average of the actions of all the rays. It is further shown that there exist at least two stationary points for this functional, implying that in the geometrical optics regime the phase from intensity problem has inherently more than one solution. The caustic structures of all the possible ray mappings are analyzed. A number of simulations illustrate the theoretical considerations.

  4. Real-Time Correction By Optical Tracking with Integrated Geometric Distortion Correction for Reducing Motion Artifacts in fMRI

    Science.gov (United States)

    Rotenberg, David J.

    Artifacts caused by head motion are a substantial source of error in fMRI that limits its use in neuroscience research and clinical settings. Real-time scan-plane correction by optical tracking has been shown to correct slice misalignment and non-linear spin-history artifacts, however residual artifacts due to dynamic magnetic field non-uniformity may remain in the data. A recently developed correction technique, PLACE, can correct for absolute geometric distortion using the complex image data from two EPI images, with slightly shifted k-space trajectories. We present a correction approach that integrates PLACE into a real-time scan-plane update system by optical tracking, applied to a tissue-equivalent phantom undergoing complex motion and an fMRI finger tapping experiment with overt head motion to induce dynamic field non-uniformity. Experiments suggest that including volume by volume geometric distortion correction by PLACE can suppress dynamic geometric distortion artifacts in a phantom and in vivo and provide more robust activation maps.

  5. Flat-field response and geometric distortion measurements of optical streak cameras

    International Nuclear Information System (INIS)

    Montgomery, D.S.; Drake, R.P.; Jones, B.A.; Wiedwald, J.D.

    1987-01-01

    To accurately measure pulse amplitude, shape, and relative time histories of optical signals with an optical streak camera, it is necessary to correct each recorded image for spatially-dependent gain nonuniformity and geometric distortion. Gain nonuniformities arise from sensitivity variations in the streak-tube photocathode, phosphor screen, image-intensifier tube, and image recording system. By using a 1.053-μm, long-pulse, high-power laser to generate a spatially and temporally uniform source as input to the streak camera, the combined effects of flat-field response and geometric distortion can be measured under the normal dynamic operation of cameras with S-1 photocathodes. Additionally, by using the same laser system to generate a train of short pulses that can be spatially modulated at the input of the streak camera, the authors can create a two-dimensional grid of equally-spaced pulses. This allows a dynamic measurement of the geometric distortion of the streak camera. The author discusses the techniques involved in performing these calibrations, present some of the measured results for LLNL optical streak cameras, and will discuss software methods to correct for these effects

  6. Aspects of the geometrical approach to supermanifolds

    International Nuclear Information System (INIS)

    Rogers, A.

    1984-01-01

    Various topics in the theory and application of the geometrical approach to supermanifolds are discussed. The construction of the superspace used in supergravity over an arbitrary spacetime manifold is described. Super Lie groups and their relation to graded Lie algebras (and more general structures referred to as 'graded Lie modules') are discussed, with examples. Certain supermanifolds, allowed in the geometric approach (using the fine topology), but having no analogue in the algebraic approach, are discussed. Finally lattice supersymmetry, and its relation to the differential geometry of supermanifolds, is discussed. (orig.)

  7. Exploiting Auto-Collimation for Real-Time Onboard Monitoring of Space Optical Camera Geometric Parameters

    Science.gov (United States)

    Liu, W.; Wang, H.; Liu, D.; Miu, Y.

    2018-05-01

    Precise geometric parameters are essential to ensure the positioning accuracy for space optical cameras. However, state-of-the-art onorbit calibration method inevitably suffers from long update cycle and poor timeliness performance. To this end, in this paper we exploit the optical auto-collimation principle and propose a real-time onboard calibration scheme for monitoring key geometric parameters. Specifically, in the proposed scheme, auto-collimation devices are first designed by installing collimated light sources, area-array CCDs, and prisms inside the satellite payload system. Through utilizing those devices, the changes in the geometric parameters are elegantly converted into changes in the spot image positions. The variation of geometric parameters can be derived via extracting and processing the spot images. An experimental platform is then set up to verify the feasibility and analyze the precision index of the proposed scheme. The experiment results demonstrate that it is feasible to apply the optical auto-collimation principle for real-time onboard monitoring.

  8. A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

    Science.gov (United States)

    Constantinides, E. D.; Marhefka, R. J.

    1994-01-01

    A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly

  9. Homogenous isotropic invisible cloak based on geometrical optics.

    Science.gov (United States)

    Sun, Jingbo; Zhou, Ji; Kang, Lei

    2008-10-27

    Invisible cloak derived from the coordinate transformation requires its constitutive material to be anisotropic. In this work, we present a cloak of graded-index isotropic material based on the geometrical optics theory. The cloak is realized by concentric multilayered structure with designed refractive index to achieve the low-scattering and smooth power-flow. Full-wave simulations on such a design of a cylindrical cloak are performed to demonstrate the cloaking ability to incident wave of any polarization. Using normal nature material with isotropy and low absorption, the cloak shows light on a practical path to stealth technology, especially that in the optical range.

  10. Establishment of Imaging Spectroscopy of Nuclear Gamma-Rays based on Geometrical Optics.

    Science.gov (United States)

    Tanimori, Toru; Mizumura, Yoshitaka; Takada, Atsushi; Miyamoto, Shohei; Takemura, Taito; Kishimoto, Tetsuro; Komura, Shotaro; Kubo, Hidetoshi; Kurosawa, Shunsuke; Matsuoka, Yoshihiro; Miuchi, Kentaro; Mizumoto, Tetsuya; Nakamasu, Yuma; Nakamura, Kiseki; Parker, Joseph D; Sawano, Tatsuya; Sonoda, Shinya; Tomono, Dai; Yoshikawa, Kei

    2017-02-03

    Since the discovery of nuclear gamma-rays, its imaging has been limited to pseudo imaging, such as Compton Camera (CC) and coded mask. Pseudo imaging does not keep physical information (intensity, or brightness in Optics) along a ray, and thus is capable of no more than qualitative imaging of bright objects. To attain quantitative imaging, cameras that realize geometrical optics is essential, which would be, for nuclear MeV gammas, only possible via complete reconstruction of the Compton process. Recently we have revealed that "Electron Tracking Compton Camera" (ETCC) provides a well-defined Point Spread Function (PSF). The information of an incoming gamma is kept along a ray with the PSF and that is equivalent to geometrical optics. Here we present an imaging-spectroscopic measurement with the ETCC. Our results highlight the intrinsic difficulty with CCs in performing accurate imaging, and show that the ETCC surmounts this problem. The imaging capability also helps the ETCC suppress the noise level dramatically by ~3 orders of magnitude without a shielding structure. Furthermore, full reconstruction of Compton process with the ETCC provides spectra free of Compton edges. These results mark the first proper imaging of nuclear gammas based on the genuine geometrical optics.

  11. Complementary Huygens principle for geometrical and nongeometrical optics

    International Nuclear Information System (INIS)

    Luis, Alfredo

    2007-01-01

    We develop a fundamental principle depicting the generalized ray formulation of optics provided by the Wigner function. This principle is formally identical to the Huygens-Fresnel principle but in terms of opposite concepts, rays instead of waves, and incoherent superpositions instead of coherent ones. This ray picture naturally includes diffraction and interference, and provides a geometrical picture of the degree of coherence

  12. The Zoom Lens: A Case Study in Geometrical Optics.

    Science.gov (United States)

    Cheville, Alan; Scepanovic, Misa

    2002-01-01

    Introduces a case study on a motion picture company considering the purchase of a newly developed zoom lens in which students act as the engineers designing the zoom lens based on the criteria of company's specifications. Focuses on geometrical optics. Includes teaching notes and classroom management strategies. (YDS)

  13. Linear and nonlinear optical properties of multilayered spherical quantum dots: Effects of geometrical size, hydrogenic impurity, hydrostatic pressure and temperature

    International Nuclear Information System (INIS)

    Karimi, M.J.; Rezaei, G.; Nazari, M.

    2014-01-01

    Based on the effective mass and parabolic one band approximations, simultaneous effects of the geometrical size, hydrogenic impurity, hydrostatic pressure, and temperature on the intersubband optical absorption coefficients and refractive index changes in multilayered spherical quantum dots are studied. Energy eigenvalues and eigenvectors are calculated using the fourth-order Runge–Kutta method and optical properties are obtained using the compact density matrix approach. The results indicate that the hydrogenic impurity, hydrostatic pressure, temperature and geometrical parameters such as the well and barrier widths have a great influence on the linear, the third-order nonlinear and the total optical absorption coefficients and refractive index changes. -- Highlights: • Hydrogenic impurity effects on the optical properties of a MSQD are investigated. • Hydrostatic pressure and temperature effects are also studied. • Hydrogenic impurity has a great influence on the linear and nonlinear ACs and RICs. • Hydrostatic pressure and temperature change the linear and nonlinear ACs and RICs

  14. Scaling-based forest structural change detection using an inverted geometric-optical model in the Three Gorges region of China

    NARCIS (Netherlands)

    Zeng, Y.; Schaepman, M.E.; Wu, B.; Clevers, J.G.P.W.; Bregt, A.K.

    2008-01-01

    We use the Li-Strahler geometric-optical model combined with a scaling-based approach to detect forest structural changes in the Three Gorges region of China. The physical-based Li-Strahler model can be inverted to retrieve forest structural properties. One of the main input variables for the

  15. Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus effect

    International Nuclear Information System (INIS)

    Bliokh, K.Yu.; Bliokh, Yu.P.

    2004-01-01

    We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Applying this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes an increase of the Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed

  16. Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect.

    Science.gov (United States)

    Bliokh, K Yu; Bliokh, Yu P

    2004-08-01

    We present a modification of the geometrical optics method, which allows one to properly separate the complex amplitude and the phase of the wave solution. Appling this modification to a smoothly inhomogeneous isotropic medium, we show that in the first geometrical optics approximation the medium is weakly anisotropic. The refractive index, being dependent on the direction of the wave vector, contains the correction, which is proportional to the Berry geometric phase. Two independent eigenmodes of right-hand and left-hand circular polarizations exist in the medium. Their group velocities and phase velocities differ. The difference in the group velocities results in the shift of the rays of different polarizations (the optical Magnus effect). The difference in the phase velocities causes an increase of the Berry phase along with the interference of two modes leading to the familiar Rytov law about the rotation of the polarization plane of a wave. The theory developed suggests that both the optical Magnus effect and the Berry phase are accompanying nonlocal topological effects. In this paper the Hamilton ray equations giving a unified description for both of these phenomena have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted. Specific examples are also discussed.

  17. Geometrical optics modeling of the grating-slit test.

    Science.gov (United States)

    Liang, Chao-Wen; Sasian, Jose

    2007-02-19

    A novel optical testing method termed the grating-slit test is discussed. This test uses a grating and a slit, as in the Ronchi test, but the grating-slit test is different in that the grating is used as the incoherent illuminating object instead of the spatial filter. The slit is located at the plane of the image of a sinusoidal intensity grating. An insightful geometrical-optics model for the grating-slit test is presented and the fringe contrast ratio with respect to the slit width and object-grating period is obtained. The concept of spatial bucket integration is used to obtain the fringe contrast ratio.

  18. Geometric characteristics of aberrations of plane-symmetric optical systems

    International Nuclear Information System (INIS)

    Lu Lijun; Deng Zhiyong

    2009-01-01

    The geometric characteristics of aberrations of plane-symmetric optical systems are studied in detail with a wave-aberration theory. It is dealt with as an extension of the Seidel aberrations to realize a consistent aberration theory from axially symmetric to plane-symmetric systems. The aberration distribution is analyzed with the spot diagram of a ray and an aberration curve. Moreover, the root-mean-square value and the centroid of aberration distribution are discussed. The numerical results are obtained with the focusing optics of a toroidal mirror at grazing incidence.

  19. Cross-Grade Comparison of Students' Conceptual Understanding with Lenses in Geometric Optics

    Science.gov (United States)

    Tural, G.

    2015-01-01

    Students commonly find the field of physics difficult. Therefore, they generally have learning problems. One of the subjects with which they have difficulties is optics within a physics discipline. This study aims to determine students' conceptual understanding levels at different education levels relating to lenses in geometric optics. A…

  20. Analyser-based phase contrast image reconstruction using geometrical optics.

    Science.gov (United States)

    Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A

    2007-07-21

    Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser.

  1. Digital polarization holography advancing geometrical phase optics.

    Science.gov (United States)

    De Sio, Luciano; Roberts, David E; Liao, Zhi; Nersisyan, Sarik; Uskova, Olena; Wickboldt, Lloyd; Tabiryan, Nelson; Steeves, Diane M; Kimball, Brian R

    2016-08-08

    Geometrical phase or the fourth generation (4G) optics enables realization of optical components (lenses, prisms, gratings, spiral phase plates, etc.) by patterning the optical axis orientation in the plane of thin anisotropic films. Such components exhibit near 100% diffraction efficiency over a broadband of wavelengths. The films are obtained by coating liquid crystalline (LC) materials over substrates with patterned alignment conditions. Photo-anisotropic materials are used for producing desired alignment conditions at the substrate surface. We present and discuss here an opportunity of producing the widest variety of "free-form" 4G optical components with arbitrary spatial patterns of the optical anisotropy axis orientation with the aid of a digital spatial light polarization converter (DSLPC). The DSLPC is based on a reflective, high resolution spatial light modulator (SLM) combined with an "ad hoc" optical setup. The most attractive feature of the use of a DSLPC for photoalignment of nanometer thin photo-anisotropic coatings is that the orientation of the alignment layer, and therefore of the fabricated LC or LC polymer (LCP) components can be specified on a pixel-by-pixel basis with high spatial resolution. By varying the optical magnification or de-magnification the spatial resolution of the photoaligned layer can be adjusted to an optimum for each application. With a simple "click" it is possible to record different optical components as well as arbitrary patterns ranging from lenses to invisible labels and other transparent labels that reveal different images depending on the side from which they are viewed.

  2. Geometrical optics model of Mie resonances

    Science.gov (United States)

    Roll; Schweiger

    2000-07-01

    The geometrical optics model of Mie resonances is presented. The ray path geometry is given and the resonance condition is discussed with special emphasis on the phase shift that the rays undergo at the surface of the dielectric sphere. On the basis of this model, approximate expressions for the positions of first-order resonances are given. Formulas for the cavity mode spacing are rederived in a simple manner. It is shown that the resonance linewidth can be calculated regarding the cavity losses. Formulas for the mode density of Mie resonances are given that account for the different width of resonances and thus may be adapted to specific experimental situations.

  3. One step geometrical calibration method for optical coherence tomography

    International Nuclear Information System (INIS)

    Díaz, Jesús Díaz; Ortmaier, Tobias; Stritzel, Jenny; Rahlves, Maik; Reithmeier, Eduard; Roth, Bernhard; Majdani, Omid

    2016-01-01

    We present a novel one-step calibration methodology for geometrical distortion correction for optical coherence tomography (OCT). A calibration standard especially designed for OCT is introduced, which consists of an array of inverse pyramidal structures. The use of multiple landmarks situated on four different height levels on the pyramids allow performing a 3D geometrical calibration. The calibration procedure itself is based on a parametric model of the OCT beam propagation. It is validated by experimental results and enables the reduction of systematic errors by more than one order of magnitude. In future, our results can improve OCT image reconstruction and interpretation for medical applications such as real time monitoring of surgery. (paper)

  4. Fresnel Lens Solar Concentrator Design Based on Geometric Optics and Blackbody Radiation Equations

    Science.gov (United States)

    Watson, Michael D.; Jayroe, Robert, Jr.

    1999-01-01

    Fresnel lenses have been used for years as solar concentrators in a variety of applications. Several variables effect the final design of these lenses including: lens diameter, image spot distance from the lens, and bandwidth focused in the image spot. Defining the image spot as the geometrical optics circle of least confusion and applying blackbody radiation equations the spot energy distribution can be determined. These equations are used to design a fresnel lens to produce maximum flux for a given spot size, lens diameter, and image distance. This approach results in significant increases in solar efficiency over traditional single wavelength designs.

  5. A New (?) Physiological Effect in a Demonstration Experiment in Geometrical Optics

    Science.gov (United States)

    Ganci, S.

    2018-01-01

    A surprising phenomenology from a traditional demonstration experiment in Geometrical Optics reveals here an interesting matter of discussion and analysis. Hence, the main focus of this paper is to observe and discuss such an innovative phenomenology.

  6. RADIANCE AND PHOTON NOISE: Imaging in geometrical optics, physical optics, quantum optics and radiology.

    Science.gov (United States)

    Barrett, Harrison H; Myers, Kyle J; Caucci, Luca

    2014-08-17

    A fundamental way of describing a photon-limited imaging system is in terms of a Poisson random process in spatial, angular and wavelength variables. The mean of this random process is the spectral radiance. The principle of conservation of radiance then allows a full characterization of the noise in the image (conditional on viewing a specified object). To elucidate these connections, we first review the definitions and basic properties of radiance as defined in terms of geometrical optics, radiology, physical optics and quantum optics. The propagation and conservation laws for radiance in each of these domains are reviewed. Then we distinguish four categories of imaging detectors that all respond in some way to the incident radiance, including the new category of photon-processing detectors. The relation between the radiance and the statistical properties of the detector output is discussed and related to task-based measures of image quality and the information content of a single detected photon.

  7. On geometric approach to Lie symmetries of differential-difference equations

    International Nuclear Information System (INIS)

    Li Hongjing; Wang Dengshan; Wang Shikun; Wu Ke; Zhao Weizhong

    2008-01-01

    Based upon Cartan's geometric formulation of differential equations, Harrison and Estabrook proposed a geometric approach for the symmetries of differential equations. In this Letter, we extend Harrison and Estabrook's approach to analyze the symmetries of differential-difference equations. The discrete exterior differential technique is applied in our approach. The Lie symmetry of (2+1)-dimensional Toda equation is investigated by means of our approach

  8. Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem

    DEFF Research Database (Denmark)

    Delbary, Fabrice; Knudsen, Kim

    2014-01-01

    to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...

  9. Analyser-based phase contrast image reconstruction using geometrical optics

    International Nuclear Information System (INIS)

    Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A

    2007-01-01

    Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (<100 μm), whilst quantitative phase and attenuation information can be extracted using just two images when the approximations of geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser

  10. Optical approximation in the theory of geometric impedance

    International Nuclear Information System (INIS)

    Stupakov, G.; Bane, K.L.F.; Zagorodnov, I.

    2007-02-01

    In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually equivalent to the approximation of geometric optics in electromagnetic theory. Using this approximation, we derive equations for the longitudinal impedance for arbitrary offsets, with respect to a reference orbit, of source and test particles. With the help of the Panofsky-Wenzel theorem we also obtain expressions for the transverse impedance (also for arbitrary offsets). We further simplify these expressions for the case of the small offsets that are typical for practical applications. Our final expressions for the impedance, in the general case, involve two dimensional integrals over various cross-sections of the transition. We further demonstrate, for several known axisymmetric examples, how our method is applied to the calculation of impedances. Finally, we discuss the accuracy of the optical approximation and its relation to the diffraction regime in the theory of impedance. (orig.)

  11. Investigation of the geometrical barrier in Bi-2212 using the magneto-optical technique

    International Nuclear Information System (INIS)

    Lin, Z.W.

    2000-01-01

    It has been found that the penetration of vortices into a weak pinning crystal is governed by a geometrical barrier and they form a dome-shaped flux profile across the crystal. Using the powerful magneto-optical technique, we investigated this geometrical barrier in a high-purity Bi 2 Sr 2 CaCu 2 O 8+x single-crystal platelet. Our results show that over the temperature range 20-70 K the dome-shaped profile is observed. Also, the influences of the edge shape and the roughness on the geometrical barrier are discussed. (author)

  12. Impact of Simulator-Based Instruction on Diagramming in Geometrical Optics by Introductory Physics Students.

    Science.gov (United States)

    Reiner, Miriam; And Others

    1995-01-01

    Observations of high school physics students in an instructional experiment with an interactive learning environment in geometrical optics indicated that students in the Optics Dynagrams Project went through major conceptual developments as reflected in the diagrams they constructed. (Author/MKR)

  13. Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

    Science.gov (United States)

    Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

    2008-12-01

    Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

  14. Effects of coating on the optical trapping efficiency of microspheres via geometrical optics approximation.

    Science.gov (United States)

    Park, Bum Jun; Furst, Eric M

    2014-09-23

    We present the optical trapping forces that are generated when a single laser beam strongly focuses on a coated dielectric microsphere. On the basis of geometrical optics approximation (GOA), in which a particle intercepts all of the rays that make up a single laser beam, we calculate the trapping forces with varying coating thickness and refractive index values. To increase the optical trapping efficiency, the refractive index (n(b)) of the coating is selected such that n(a) < n(b) < n(c), where na and nc are the refractive indices of the medium and the core material, respectively. The thickness of the coating also increases trapping efficiency. Importantly, we find that trapping forces for the coated particles are predominantly determined by two rays: the incident ray and the first refracted ray to the medium.

  15. Evaluation of Geometrical Modulation Transfer Function in Optical Lens System

    Directory of Open Access Journals (Sweden)

    Cheng-Mu Tsai

    2015-01-01

    Full Text Available This paper presents ray tracing algorithms to evaluate the geometrical modulation transfer function (GMTF of optical lens system. There are two kinds of ray tracings methods that can be applied to help simulate the point spread function (PSF in the image plane, for example, paraxial optics and real ray tracings. The paraxial optics ray tracing is used to calculate the first-order properties such as the effective focal length (EFL and the entrance pupil position through less cost of computation. However, the PSF could have a large tolerance by only using paraxial optics ray tracing for simulation. Some formulas for real ray tracing are applied in the sagittal and tangential line spread function (LSF. The algorithms are developed to demonstrate the simulation of LSF. Finally, the GMTF is evaluated after the fast Fourier transform (FFT of the LSF.

  16. Diffraction, self-focusing, and the geometrical optics limit in laser produced plasmas

    International Nuclear Information System (INIS)

    Marchand, R.; Rankin, R.; Capjack, C.E.; Birnboim, A.

    1987-01-01

    The effect of diffraction on the self-modulation of an intense laser beam in an initially uniform hydrogen plasma is investigated. A formalism is used in which the diffraction term in the paraxial wave equation can be arbitrarily reduced by the use of a weight factor iota. In the limit where iota approaches zero, it is shown that the paraxial wave equation correctly reduces to the geometrical optics limit and that the problem then becomes formally equivalent to solving the ray-tracing equations. When iota = 1, the paraxial wave equation takes its usual form and diffraction is fully accounted for. This formalism is applied to the simulation of self-modulation of an intense laser beam in a hydrogen plasma, for which diffraction is shown to be significant

  17. Geometrical-optics solution to light scattering by droxtal ice crystals.

    Science.gov (United States)

    Zhang, Zhibo; Yang, Ping; Kattawar, George W; Tsay, Si-Chee; Baum, Bryan A; Hu, Yongxiang; Heymsfield, Andrew J; Reichardt, Jens

    2004-04-20

    We investigate the phase matrices of droxtals at wavelengths of 0.66 and 11 microm by using an improved geometrical-optics method. An efficient method is developed to specify the incident rays and the corresponding impinging points on the particle surface necessary to initialize the ray-tracing computations. At the 0.66-microm wavelength, the optical properties of droxtals are different from those of hexagonal ice crystals. At the 11-microm wavelength, the phase functions for droxtals are essentially featureless because of strong absorption within the particles, except for ripple structures that are caused by the phase interference of the diffracted wave.

  18. Expression of the degree of polarization based on the geometrical optics pBRDF model.

    Science.gov (United States)

    Wang, Kai; Zhu, Jingping; Liu, Hong; Du, Bingzheng

    2017-02-01

    An expression of the degree of polarization (DOP) based on the geometrical optics polarimetric bidirectional reflectance distribution function model is presented. In this expression, the DOP is related to the surface roughness and decreases at different reflection angles because diffuse reflection is taken into consideration. A shadowing/masking function introduced into the specular reflection expression makes the DOP values decrease as the angle of incidence or observation approaches grazing. Different kinds of materials were measured to validate the accuracy of this DOP expression. The measured results suggest that the errors of the DOP are reduced significantly, and the polarized reflection characteristics can be described more reasonably and accurately.

  19. The relationship between wave and geometrical optics models of coded aperture type x-ray phase contrast imaging systems.

    Science.gov (United States)

    Munro, Peter R T; Ignatyev, Konstantin; Speller, Robert D; Olivo, Alessandro

    2010-03-01

    X-ray phase contrast imaging is a very promising technique which may lead to significant advancements in medical imaging. One of the impediments to the clinical implementation of the technique is the general requirement to have an x-ray source of high coherence. The radiation physics group at UCL is currently developing an x-ray phase contrast imaging technique which works with laboratory x-ray sources. Validation of the system requires extensive modelling of relatively large samples of tissue. To aid this, we have undertaken a study of when geometrical optics may be employed to model the system in order to avoid the need to perform a computationally expensive wave optics calculation. In this paper, we derive the relationship between the geometrical and wave optics model for our system imaging an infinite cylinder. From this model we are able to draw conclusions regarding the general applicability of the geometrical optics approximation.

  20. Geometrical charged-particle optics. 2. ed.

    International Nuclear Information System (INIS)

    Rose, Harald

    2013-01-01

    Provides a unique theoretical treatment of charged-particle optics. Displays novel unpublished results on several topics. Provides insight into the properties of charged-particle devices. Treats wave optical properties of the electron. Presents the resolution limit of electron microscopes and novel theoretical treatment of the Stern-Gerlach effect. This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are discussed extensively. Beam properties such as emittance, brightness, transmissivity and the formation of caustics are outlined. Relativistic motion and spin precession of the electron are treated in a covariant way by introducing the Lorentz-invariant universal time and by extending Hamilton's principle from three to four spatial dimensions where the laboratory time is considered as the fourth pseudo-spatial coordinate. Using this procedure and introducing the self action of the electron, its accompanying electromagnetic field and its radiation field are calculated for arbitrary motion. In addition, the Stern

  1. Two solvable problems of planar geometrical optics.

    Science.gov (United States)

    Borghero, Francesco; Bozis, George

    2006-12-01

    In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f(x,y)=c of any definite color and satisfying a differential condition, all the refractive index profiles n=n(x,y) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n=n(x,y) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.

  2. Geometrical approach to fluid models

    International Nuclear Information System (INIS)

    Kuvshinov, B.N.; Schep, T.J.

    1997-01-01

    Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notion of invariance is introduced in terms of Lie derivatives and a general procedure for the construction of local and integral fluid invariants is presented. The solutions of the equations for invariant fields can be written in terms of Lagrange variables. A generalization of the Hamiltonian formalism for finite-dimensional systems to continuous media is proposed. Analogously to finite-dimensional systems, Hamiltonian fluids are introduced as systems that annihilate an exact two-form. It is shown that Euler and ideal, charged fluids satisfy this local definition of a Hamiltonian structure. A new class of scalar invariants of Hamiltonian fluids is constructed that generalizes the invariants that are related with gauge transformations and with symmetries (Noether). copyright 1997 American Institute of Physics

  3. Geometric optics theory and design of astronomical optical systems using Mathematica

    CERN Document Server

    Romano, Antonio

    2016-01-01

    This text, now in its second edition, presents the mathematical background needed to design many optical combinations that are used in astronomical telescopes and cameras. It uses a novel approach to third-order aberration theory based on Fermat’s principle and the use of particular optical paths (called stigmatic paths) instead of rays, allowing for easier derivation of third-order formulae. Each optical combination analyzed is accompanied by a downloadable Mathematica® notebook that automates its third-order design, eliminating the need for lengthy calculations. The essential aspects of an optical system with an axis of rotational symmetry are introduced first, along with a development of Gaussian optics from Fermat’s principal. A simpler approach to third-order monochromatic aberrations based on both Fermat’s principle and stigmatic paths is then described, followed by a new chapter on fifth-order aberrations and their classification. Several specific optical devices are discussed and analyzed, incl...

  4. Geometrical superresolved imaging using nonperiodic spatial masking.

    Science.gov (United States)

    Borkowski, Amikam; Zalevsky, Zeev; Javidi, Bahram

    2009-03-01

    The resolution of every imaging system is limited either by the F-number of its optics or by the geometry of its detection array. The geometrical limitation is caused by lack of spatial sampling points as well as by the shape of every sampling pixel that generates spectral low-pass filtering. We present a novel approach to overcome the low-pass filtering that is due to the shape of the sampling pixels. The approach combines special algorithms together with spatial masking placed in the intermediate image plane and eventually allows geometrical superresolved imaging without relation to the actual shape of the pixels.

  5. VIRTOPSY--scientific documentation, reconstruction and animation in forensic: individual and real 3D data based geo-metric approach including optical body/object surface and radiological CT/MRI scanning.

    Science.gov (United States)

    Thali, Michael J; Braun, Marcel; Buck, Ursula; Aghayev, Emin; Jackowski, Christian; Vock, Peter; Sonnenschein, Martin; Dirnhofer, Richard

    2005-03-01

    Until today, most of the documentation of forensic relevant medical findings is limited to traditional 2D photography, 2D conventional radiographs, sketches and verbal description. There are still some limitations of the classic documentation in forensic science especially if a 3D documentation is necessary. The goal of this paper is to demonstrate new 3D real data based geo-metric technology approaches. This paper present approaches to a 3D geo-metric documentation of injuries on the body surface and internal injuries in the living and deceased cases. Using modern imaging methods such as photogrammetry, optical surface and radiological CT/MRI scanning in combination it could be demonstrated that a real, full 3D data based individual documentation of the body surface and internal structures is possible in a non-invasive and non-destructive manner. Using the data merging/fusing and animation possibilities, it is possible to answer reconstructive questions of the dynamic development of patterned injuries (morphologic imprints) and to evaluate the possibility, that they are matchable or linkable to suspected injury-causing instruments. For the first time, to our knowledge, the method of optical and radiological 3D scanning was used to document the forensic relevant injuries of human body in combination with vehicle damages. By this complementary documentation approach, individual forensic real data based analysis and animation were possible linking body injuries to vehicle deformations or damages. These data allow conclusions to be drawn for automobile accident research, optimization of vehicle safety (pedestrian and passenger) and for further development of crash dummies. Real 3D data based documentation opens a new horizon for scientific reconstruction and animation by bringing added value and a real quality improvement in forensic science.

  6. The Young-Laplace equation links capillarity with geometrical optics

    International Nuclear Information System (INIS)

    Rodriguez-Valverde, M A; Cabrerizo-Vilchez, M A; Hidalgo-Alvarez, R

    2003-01-01

    Analogies in physics are unusual coincidences that can be very useful to solve problems and to clarify some theoretical concepts. Apart from their own curiosity, analogies are attractive tools because they reduce the abstraction of some complex phenomena in such a way that these can be understood by means of other phenomena closer to daily experience. Usually, two analogous systems share a common aspect, like the movement of particles or transport of matter. On account of this, the analogy presented is exceptional since the involved phenomena are a priori disjoined. The most important equation of capillarity, the Young-Laplace equation, has the same structure as the Gullstrand equation of geometrical optics, which relates the optic power of a thick lens to its geometry and the properties of the media

  7. Geometric mechanics of ray optics as particle dynamics: refraction index with cylindrical symmetry

    Science.gov (United States)

    Cortés, Emilio; Ruiz, Melina

    2017-09-01

    Starting from the Fermat principle of geometrical optics, we analyse the ray dynamics in a graded refractive index system device with cylindrical symmetry and a refractive index that decreases parabolically with the radial coordinate. By applying Hamiltonian dynamics to the study of the ray path we obtain the strict equivalence of this optical system with the dynamics of a particle with an equivalent mass moving in a potential function that may exhibit a well, depending on the value of some associated parameters. We analyse the features of this potential function as well as the energy values and the symmetries of the system and see that both the azimuthal and axial components of the optical conjugate momentum are two constants of motion. The phase space relation for the momentum radial component is obtained analytically, and then we can obtain the components of the momentum vector at any point, given the value of the radial coordinate, and from this we have the direction of the ray. We discuss the optical path length as an action functional and we can evaluate this stationary path, with initial and final arbitrary points, as a line integral of the optical momentum, by showing that this momentum is a conservative vector field. We integrate the equations of motion numerically and obtain different ray paths which depend on the initial conditions. We believe that with this work the physics student will appreciate very clearly the close connection between geometrical optics and particle Hamiltonian dynamics.

  8. Graphene geometric diodes for terahertz rectennas

    International Nuclear Information System (INIS)

    Zhu Zixu; Joshi, Saumil; Grover, Sachit; Moddel, Garret

    2013-01-01

    We demonstrate a new thin-film graphene diode called a geometric diode that relies on geometric asymmetry to provide rectification at 28 THz. The geometric diode is coupled to an optical antenna to form a rectenna that rectifies incoming radiation. This is the first reported graphene-based antenna-coupled diode working at 28 THz, and potentially at optical frequencies. The planar structure of the geometric diode provides a low RC time constant, on the order of 10 −15 s, required for operation at optical frequencies, and a low impedance for efficient power transfer from the antenna. Fabricated geometric diodes show asymmetric current–voltage characteristics consistent with Monte Carlo simulations for the devices. Rectennas employing the geometric diode coupled to metal and graphene antennas rectify 10.6 µm radiation, corresponding to an operating frequency of 28 THz. The graphene bowtie antenna is the first demonstrated functional antenna made using graphene. Its response indicates that graphene is a suitable terahertz resonator material. Applications for this terahertz diode include terahertz-wave and optical detection, ultra-high-speed electronics and optical power conversion. (paper)

  9. Designing and Using an Open Graphic Interface for Instruction in Geometrical Optics.

    Science.gov (United States)

    Ronen, Miky; And Others

    1993-01-01

    Discusses conceptual difficulties in the field of geometrical optics and describes RAY, a microcomputer-based graphic interface that was designed to serve as a teaching aid and as a learning environment. The ability to combine theory and formal representations with real demonstrations and experiments is discussed. (Contains seven references.) (LRW)

  10. Design of an ultra-thin near-eye display with geometrical waveguide and freeform optics.

    Science.gov (United States)

    Cheng, Dewen; Wang, Yongtian; Xu, Chen; Song, Weitao; Jin, Guofan

    2014-08-25

    Small thickness and light weight are two important requirements for a see-through near-eye display which are achieved in this paper by using two advanced technologies: geometrical waveguide and freeform optics. A major problem associated with the geometrical waveguide is the stray light which can severely degrade the display quality. The causes and solutions to this problem are thoroughly studied. A mathematical model of the waveguide is established and a non-sequential ray tracing algorithm is developed, which enable us to carefully examine the stray light of the planar waveguide and explore a global searching method to find an optimum design with the least amount of stray light. A projection optics using freeform surfaces on a wedge shaped prism is also designed. The near-eye display integrating the projection optics and the waveguide has a field of view of 28°, an exit pupil diameter of 9.6mm and an exit pupil distance of 20mm. In our final design, the proportion of the stray light energy over the image output energy of the waveguide is reduced to 2%, the modulation transfer function values across the entire field of the eyepiece are above 0.5 at 30 line pairs/mm (lps/mm). A proof-of-concept prototype of the proposed geometrical waveguide near-eye display is developed and demonstrated.

  11. Analysis of specular resonance in dielectric bispheres using rigorous and geometrical-optics theories.

    Science.gov (United States)

    Miyazaki, Hideki T; Miyazaki, Hiroshi; Miyano, Kenjiro

    2003-09-01

    We have recently identified the resonant scattering from dielectric bispheres in the specular direction, which has long been known as the specular resonance, to be a type of rainbow (a caustic) and a general phenomenon for bispheres. We discuss the details of the specular resonance on the basis of systematic calculations. In addition to the rigorous theory, which precisely describes the scattering even in the resonance regime, the ray-tracing method, which gives the scattering in the geometrical-optics limit, is used. Specular resonance is explicitly defined as strong scattering in the direction of the specular reflection from the symmetrical axis of the bisphere whose intensity exceeds that of the scattering from noninteracting bispheres. Then the range of parameters for computing a particular specular resonance is specified. This resonance becomes prominent in a wide range of refractive indices (from 1.2 to 2.2) in a wide range of size parameters (from five to infinity) and for an arbitrarily polarized light incident within an angle of 40 degrees to the symmetrical axis. This particular scattering can stay evident even when the spheres are not in contact or the sizes of the spheres are different. Thus specular resonance is a common and robust phenomenon in dielectric bispheres. Furthermore, we demonstrate that various characteristic features in the scattering from bispheres can be explained successfully by using intuitive and simple representations. Most of the significant scatterings other than the specular resonance are also understandable as caustics in geometrical-optics theory. The specular resonance becomes striking at the smallest size parameter among these caustics because its optical trajectory is composed of only the refractions at the surfaces and has an exceptionally large intensity. However, some characteristics are not accounted for by geometrical optics. In particular, the oscillatory behaviors of their scattering intensity are well described by

  12. Quantum renormalization group approach to geometric phases in spin chains

    International Nuclear Information System (INIS)

    Jafari, R.

    2013-01-01

    A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size

  13. From the Snell-Descartes refraction law, to the Hamilton equations in the phase space of geometrical optics

    International Nuclear Information System (INIS)

    Lopez Moreno, E.; Wolf, K.B.

    1989-01-01

    Starting from the Snell-Descartes' refraction law, we obtain in a brief and direct way the Hamilton equations of Geometrical Optics. We show the global structure of phase space and compare it with that used in paraxial optics. (Author)

  14. Geometrical and wave optics of paraxial beams.

    Science.gov (United States)

    Meron, M; Viccaro, P J; Lin, B

    1999-06-01

    Most calculational techniques used to evaluate beam propagation are geared towards either fully coherent or fully incoherent beams. The intermediate partial-coherence regime, while in principle known for a long time, has received comparably little attention so far. The resulting shortage of adequate calculational techniques is currently being felt in the realm of x-ray optics where, with the advent of third generation synchrotron light sources, partially coherent beams become increasingly common. The purpose of this paper is to present a calculational approach which, utilizing a "variance matrix" representation of paraxial beams, allows for a straightforward evaluation of wave propagation through an optical system. Being capable of dealing with an arbitrary degree of coherence, this approach covers the whole range from wave to ray optics, in a seamless fashion.

  15. Macroscopic polarization in crystalline dielectrics: the geometric phase approach

    International Nuclear Information System (INIS)

    Resta, R.

    1994-01-01

    The macroscopic electric polarization of a crystal is often defined as the dipole of a unit cell. In fact, such a dipole moment is ill defined, and the above definition is incorrect. Looking more closely, the quantity generally measured is differential polarization, defined with respect to a ''reference state'' of the same material. Such differential polarizations include either derivatives of the polarization (dielectric permittivity, Born effective charges, piezoelectricity, pyroelectricity) or finite differences (ferroelectricity). On the theoretical side, the differential concept is basic as well. Owing to continuity, a polarization difference is equivalent to a macroscopic current, which is directly accessible to the theory as a bulk property. Polarization is a quantum phenomenon and cannot be treated with a classical model, particularly whenever delocalized valence electrons are present in the dielectric. In a quantum picture, the current is basically a property of the phase of the wave functions, as opposed to the charge, which is a property of their modulus. An elegant and complete theory has recently been developed by King-Smith and Vanderbilt, in which the polarization difference between any two crystal states--in a null electric field--takes the form of a geometric quantum phase. This gives a comprehensive account of this theory, which is relevant for dealing with transverse-optic phonons, piezoelectricity, and ferroelectricity. Its relation to the established concepts of linear-response theory is also discussed. Within the geometric phase approach, the relevant polarization difference occurs as the circuit integral of a Berry connection (or ''vector potential''), while the corresponding curvature (or ''magnetic field'') provides the macroscopic linear response

  16. Uncertainty in visual processes predicts geometrical optical illusions.

    Science.gov (United States)

    Fermüller, Cornelia; Malm, Henrik

    2004-03-01

    It is proposed in this paper that many geometrical optical illusions, as well as illusory patterns due to motion signals in line drawings, are due to the statistics of visual computations. The interpretation of image patterns is preceded by a step where image features such as lines, intersections of lines, or local image movement must be derived. However, there are many sources of noise or uncertainty in the formation and processing of images, and they cause problems in the estimation of these features; in particular, they cause bias. As a result, the locations of features are perceived erroneously and the appearance of the patterns is altered. The bias occurs with any visual processing of line features; under average conditions it is not large enough to be noticeable, but illusory patterns are such that the bias is highly pronounced. Thus, the broader message of this paper is that there is a general uncertainty principle which governs the workings of vision systems, and optical illusions are an artifact of this principle.

  17. Comparison of three optical models and analysis of geometric parameters for parabolic trough solar collectors

    International Nuclear Information System (INIS)

    Liang, Hongbo; You, Shijun; Zhang, Huan

    2016-01-01

    A PTC (parabolic trough solar collector) focuses direct solar radiation reflected by the reflector onto a receiver located on its focal line. The solar flux distribution on the absorber is non-uniform generally, thus it needs to carry out optical simulation to analyze the concentrated flux density and optical performance. In this paper, three different optical models based on ray tracing for a PTC were proposed and compared in detail. They were proved to be feasible and reliable in comparison with other literature. Model 1 was based on MCM (Monte Carlo Method). Model 2 initialized photon distribution with FVM (Finite Volume Method), and calculated reflection, transmission, and absorption by means of MCM. Model 3 utilized FVM to determine ray positions initially, while it changed the photon energy by multiplying reflectivity, transmissivity and absorptivity. The runtime and computation effort of Model 3 were approximately 40% and 60% of that of Model 1 in the present work. Moreover, the simulation result of Model 3 was not affected by the algorithm for generating random numbers, however, it needed to take account of suitable grid configurations for different sections of the system. Additionally, effects of varying the geometric parameters for a PTC on optical efficiency were estimated. Effect of offsetting the absorber in width direction of aperture was greater than that in its normal direction at the same offset distance, which was more obvious with offset distance increasing. Furthermore, absorber offset at the opposite direction of tracking error was beneficial for improving optical performance. The larger rim angle (≤90°) was, the less sensitive optical efficiency was to tracking error for the same aperture width of a PTC. In contrast, a larger aperture width was more sensitive to tracking error for a certain rim angle. - Highlights: • Three different optical models for parabolic trough solar collectors were derived. • Their running time, computation

  18. Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

    Science.gov (United States)

    Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

    2006-06-01

    We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

  19. Refraction at a curved dielectric interface - Geometrical optics solution

    Science.gov (United States)

    Lee, S.-W.; Sheshadri, M. S.; Mittra, R.; Jamnejad, V.

    1982-01-01

    The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.

  20. A geometrical approach to free-field quantization

    International Nuclear Information System (INIS)

    Tabensky, R.; Valle, J.W.F.

    1977-01-01

    A geometrical approach to the quantization of free relativistic fields is given. Complex probability amplitudes are assigned to the solutions of the classical evolution equation. It is assumed that the evolution is stricly classical, according to the scalar unitary representation of the Poincare group in a functional space. The theory is equivalent to canonical quantization [pt

  1. Johann Joseph on Geometrical-Optical Illusions: A Translation and Commentary.

    Science.gov (United States)

    Wade, Nicholas J; Todorović, Dejan; Phillips, David; Lingelbach, Bernd

    2017-01-01

    The term geometrical-optical illusions was coined by Johann Joseph Oppel (1815-1894) in 1855 in order to distinguish spatial distortions of size and orientation from the broader illusions of the senses. We present a translation of Oppel's article and a commentary on the material described in it. Oppel did much more than give a name to a class of visual spatial distortions. He examined a variety of figures and phenomena that were precursors of later, named illusions, and attempted to quantify and interpret them.

  2. General analysis of slab lasers using geometrical optics.

    Science.gov (United States)

    Chung, Te-yuan; Bass, Michael

    2007-02-01

    A thorough and general geometrical optics analysis of a slab-shaped laser gain medium is presented. The length and thickness ratio is critical if one is to achieve the maximum utilization of absorbed pump power by the laser light in such a medium; e.g., the fill factor inside the slab is to be maximized. We point out that the conditions for a fill factor equal to 1, laser light entering and exiting parallel to the length of the slab, and Brewster angle incidence on the entrance and exit faces cannot all be satisfied at the same time. Deformed slabs are also studied. Deformation along the width direction of the largest surfaces is shown to significantly reduce the fill factor that is possible.

  3. Quantum trajectory approach to the geometric phase: open bipartite systems

    International Nuclear Information System (INIS)

    Yi, X X; Liu, D P; Wang, W

    2005-01-01

    Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other and then are entangled in the evolution. The geometric phase due to the quantum jump for both the bipartite system and its subsystems is calculated and analysed. As an example, we present two coupled spin-1/2 particles to detail the calculations

  4. Geometrical optics, electrostatics, and nanophotonic resonances in absorbing nanowire arrays.

    Science.gov (United States)

    Anttu, Nicklas

    2013-03-01

    Semiconductor nanowire arrays have shown promise for next-generation photovoltaics and photodetection, but enhanced understanding of the light-nanowire interaction is still needed. Here, we study theoretically the absorption of light in an array of vertical InP nanowires by moving continuously, first from the electrostatic limit to the nanophotonic regime and then to the geometrical optics limit. We show how the absorption per volume of semiconductor material in the array can be varied by a factor of 200, ranging from 10 times weaker to 20 times stronger than in a bulk semiconductor sample.

  5. Rayleigh's hypothesis and the geometrical optics limit.

    Science.gov (United States)

    Elfouhaily, Tanos; Hahn, Thomas

    2006-09-22

    The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.

  6. Illusions in the spatial sense of the eye: geometrical-optical illusions and the neural representation of space.

    Science.gov (United States)

    Westheimer, Gerald

    2008-09-01

    Differences between the geometrical properties of simple configurations and their visual percept are called geometrical-optical illusions. They can be differentiated from illusions in the brightness or color domains, from ambiguous figures and impossible objects, from trompe l'oeil and perspective drawing with perfectly valid views, and from illusory contours. They were discovered independently by several scientists in a short time span in the 1850's. The clear distinction between object and visual space that they imply allows the question to be raised whether the transformation between the two spaces can be productively investigated in terms of differential geometry and metrical properties. Perceptual insight and psychophysical research prepares the ground for investigation of the neural representation of space but, because visual attributes are processed separately in parallel, one looks in vain for a neural map that is isomorphic with object space or even with individual forms it contains. Geometrical-optical illusions help reveal parsing rules for sensory signals by showing how conflicts are resolved when there is mismatch in the output of the processing modules for various primitives as a perceptual pattern's unitary structure is assembled. They point to a hierarchical ordering of spatial primitives: cardinal directions and explicit contours predominate over oblique orientation and implicit contours (Poggendorff illusion); rectilinearity yields to continuity (Hering illusion), point position and line length to contour orientation (Ponzo). Hence the geometrical-optical illusions show promise as analytical tools in unraveling neural processing in vision.

  7. On the geometrical approach to the relativistic string theory

    International Nuclear Information System (INIS)

    Barbashov, B.M.; Nesterenko, V.V.

    1978-01-01

    In a geometrical approach to the string theory in the four-dimensional Minkowski space the relativistic invariant gauge proposed earlier for the string moving in three-dimensional space-time is used. In contrast to the results of previous paper the system of equations for the coefficients of the fundamental forms of the string model world sheet can be reduced now to one nonlinear Lionville equation again but for a complex valued function u. It is shown that in the case of space-time with arbitrary dimension there are such string motions which are described by one non-linear equation with a real function u. And as a consequence the soliton solutions investigated earlier take place in a geometrical approach to the string theory in any dimensional space-time

  8. Impact of geometrical parameters on the optical properties of negative curvature hollow-core fibers

    International Nuclear Information System (INIS)

    Alagashev, G K; Pryamikov, A D; Kosolapov, A F; Kolyadin, A N; Lukovkin, A Yu; Biriukov, A S

    2015-01-01

    We analyze the impact of geometrical parameters on such important optical characteristics of negative curvature hollow-core fibers (NCHCFs) as waveguide dispersion, waveguide losses and the structure of transmission bands. We consider both theoretically and experimentally the resonance effects and formation of band edges under bending in NCHCFs. (paper)

  9. Effect of the geometrical parameters of an optical integrator on the unformity of the radiation flux distribution

    International Nuclear Information System (INIS)

    Vishnyakova, T.P.; Klychev, Sh.I.

    1992-01-01

    The use of optical mixers in the optical irradiators of simulators of direct and concentrated solar radiation has been proposed. In this paper, the parameters of an optical mixer are calculated geometrically, and the effect of the parameters of the optical mixer on the unformity of the irradiance distribution η of the radiation flux on the detector is investigated. These investigations show that the light distribution from an optical mixer is close to the characteristics of an ideal uniform emitter within the region from 0 to the limit of α. 5 refs., 4 figs

  10. Geometrical-confinement effects on excitons in quantum disks

    International Nuclear Information System (INIS)

    Song, J.; Ulloa, S.E.

    1995-01-01

    Excitons confined to flat semiconductor quantum dots with elliptical cross sections are considered as we study geometrical effects on exciton binding energy, electron-hole separation, and the resulting linear optical properties. We use numerical matrix diagonalization techniques with appropriately large and optimized basis sets in an effective-mass Hamiltonian approach. The linear optical susceptibilities of GaAs and InAs dots for several different size ratios are discussed and compared to experimental photoluminescence spectra obtained on GaAs/Al x Ga 1-x As and InAs/GaAs quantum dots. For quantum dots of several nm in size, there is a strong blueshift of the luminescence due to geometrical-confinement effects. Also, transition peaks are split and shifted towards higher energy, in comparison with dots with circular cross sections

  11. Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system

    International Nuclear Information System (INIS)

    Kawabe, Tetsuji

    2003-01-01

    Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system. By analyzing a close relation between the sectional curvature and the Gaussian curvature, we point out that the Toda-Brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition

  12. Using geometric algebra to understand pattern rotations in multiple mirror optical systems

    International Nuclear Information System (INIS)

    Hanlon, J.; Ziock, H.

    1997-01-01

    Geometric Algebra (GA) is a new formulation of Clifford Algebra that includes vector analysis without notation changes. Most applications of Ga have been in theoretical physics, but GA is also a very good analysis tool for engineering. As an example, the authors use GA to study pattern rotation in optical systems with multiple mirror reflections. The common ways to analyze pattern rotations are to use rotation matrices or optical ray trace codes, but these are often inconvenient. The authors use GA to develop a simple expression for pattern rotation that is useful for designing or tolerancing pattern rotations in a multiple mirror optical system by inspection. Pattern rotation is used in many optical engineering systems, but it is not normally covered in optical system engineering texts. Pattern rotation is important in optical systems such as: (1) the 192 beam National ignition Facility (NIF), which uses square laser beams in close packed arrays to cut costs; (2) visual optical systems, which use pattern rotation to present the image to the observer in the appropriate orientation, and (3) the UR90 unstable ring resonator, which uses pattern rotation to fill a rectangular laser gain region and provide a filled-in laser output beam

  13. Accretion disc boundary layers - geometrically and optically thin case

    International Nuclear Information System (INIS)

    Regev, Oded; Hougerat, A.A.

    1988-01-01

    The method of matched asymptotic expansions is applied to an optically and geometrically thin boundary layer between an accretion disc and the accreting star. Analytical solutions are presented for a particular viscosity prescription in the boundary layer. For a typical example we find that the disc closely resembles standard steady-disc theory. It is identical to it everywhere save a narrow boundary layer, where the temperature increases rapidly inward (by an order of magnitude), the angular velocity achieves maximum and decreases to its surface value and other variables also undergo rapid changes. This and previous work can now be used to calculate the emission from accretion discs including the boundary layers for a wide range of parameters. (author)

  14. A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics

    NARCIS (Netherlands)

    Lith, van B.S.; Thije Boonkkamp, ten J.H.M.; IJzerman, W.L.; Tukker, T.W.

    2015-01-01

    We compute numerical solutions of Liouville's equation with a discontinuous Hamiltonian. We assume that the underlying Hamiltonian system has a well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell's law or

  15. A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics

    NARCIS (Netherlands)

    van Lith, B.S.; ten Thije Boonkkamp, J.H.M.; IJzerman, W.L.; Tukker, T.W.

    A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity

  16. Geometrical effect characterization of femtosecond-laser manufactured glass microfluidic chips based on optical manipulation of submicroparticles

    Science.gov (United States)

    Kotsifaki, Domna G.; Mackenzie, Mark D.; Polydefki, Georgia; Kar, Ajoy K.; Makropoulou, Mersini; Serafetinides, Alexandros A.

    2017-12-01

    Microfluidic devices provide a platform with wide ranging applications from environmental monitoring to disease diagnosis. They offer substantive advantages but are often not optimized or designed to be used by nonexpert researchers. Microchannels of a microanalysis platform and their geometrical characterization are of eminent importance when designing such devices. We present a method that is used to optimize each microchannel within a device using high-throughput particle manipulation. For this purpose, glass-based microfluidic devices, with three-dimensional channel networks of several geometrical sizes, were fabricated by employing laser fabrication techniques. The effect of channel geometry was investigated by employing an optical tweezer. The optical trapping force depends on the flow velocity that is associated with the dimensions of the microchannel. We observe a linear dependence of the trapping efficiency and of the fluid flow velocity, with the channel dimensions. We determined that the highest trapping efficiency was achieved for microchannels with aspect ratio equal to one. Numerical simulation validated the impact of the device design dimensions on the trapping efficiency. This investigation indicates that the geometrical characteristics, the flow velocity, and trapping efficiency are crucial and should be considered when fabricating microfluidic devices for cell studies.

  17. A Didactic Sequence of Elementary Geometric Optics Informed by History and Philosophy of Science

    Science.gov (United States)

    Maurício, Paulo; Valente, Bianor; Chagas, Isabel

    2017-01-01

    The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic process without a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the…

  18. Tunable orbital angular momentum mode filter based on optical geometric transformation.

    Science.gov (United States)

    Huang, Hao; Ren, Yongxiong; Xie, Guodong; Yan, Yan; Yue, Yang; Ahmed, Nisar; Lavery, Martin P J; Padgett, Miles J; Dolinar, Sam; Tur, Moshe; Willner, Alan E

    2014-03-15

    We present a tunable mode filter for spatially multiplexed laser beams carrying orbital angular momentum (OAM). The filter comprises an optical geometric transformation-based OAM mode sorter and a spatial light modulator (SLM). The programmable SLM can selectively control the passing/blocking of each input OAM beam. We experimentally demonstrate tunable filtering of one or multiple OAM modes from four multiplexed input OAM modes with vortex charge of ℓ=-9, -4, +4, and +9. The measured output power suppression ratio of the propagated modes to the blocked modes exceeds 14.5 dB.

  19. Symmetry analysis of talus bone: A Geometric morphometric approach.

    Science.gov (United States)

    Islam, K; Dobbe, A; Komeili, A; Duke, K; El-Rich, M; Dhillon, S; Adeeb, S; Jomha, N M

    2014-01-01

    The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139-45.

  20. Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states

    International Nuclear Information System (INIS)

    Tong, D.M.; Oh, C.H.; Sjoeqvist, Erik; Filipp, Stefan; Kwek, L.C.

    2005-01-01

    Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed states. We further extend the mixed-state concept proposed in [Phys. Rev. Lett. 90, 050403 (2003)] to degenerate density operators. The first- and second-order off-diagonal geometric phases are analyzed for unitarily evolving pairs of pseudopure states

  1. Errors in the universal and sufficient heuristic criteria of estimating validity limits of geometric optics and of the geometric theory of diffraction

    International Nuclear Information System (INIS)

    Borovikov, V.A.; Kinber, B.E.

    1988-01-01

    The heuristic criteria (HC) of validity of geometric optics (GO) and of the geometric theory of diffraction (GTD), suggested in [2-7, 13, 14] and based on identifying the physical volume occupied by the ray with the Fresnel volume (FV) introduced in these papers (i.e., the envelope of the first Fresnel zone), are analyzed. Numerous examples of HC invalidity are given, as well as the reasons. In particular, HC provide an incorrect answer for all GO problems with caustics, since in these problems there always exists a ray, whose FV is nonlocal and covers the FV of other rays. The HC are shown to be unsuitable for multiple ray GTD problems, as well as for the simplest problems of diffraction of a cylindrical wave by a half-plane and of a plane wave by a curved half-plane

  2. Topological charge on the lattice: a field theoretical view of the geometrical approach

    International Nuclear Information System (INIS)

    Rastelli, L.; Rossi, P.; Vicari, E.

    1997-01-01

    We construct sequences of ''field theoretical'' lattice topological charge density operators which formally approach geometrical definitions in 2D CP N-1 models and 4D SU(N) Yang-Mills theories. The analysis of these sequences of operators suggests a new way of looking at the geometrical method, showing that geometrical charges can be interpreted as limits of sequences of field theoretical (analytical) operators. In perturbation theory, renormalization effects formally tend to vanish along such sequences. But, since the perturbative expansion is asymptotic, this does not necessarily lead to well-behaved geometrical limits. It indeed leaves open the possibility that non-perturbative renormalizations survive. (orig.)

  3. A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter

    NARCIS (Netherlands)

    Brigo, D.; Hanzon, B.; LeGland, F.

    1998-01-01

    This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is

  4. A new approach to estimate the geometrical factors, solid angle approximation, geometrical efficiency and their use in basic interaction cross section measurements

    CERN Document Server

    Rao, D V; Brunetti, A; Gigante, G E; Takeda, T; Itai, Y; Akatsuka, T

    2002-01-01

    A new approach is developed to estimate the geometrical factors, solid angle approximation and geometrical efficiency for a system with experimental arrangements using X-ray tube and secondary target as an excitation source in order to produce the nearly monoenergetic K alpha radiation to excite the sample. The variation of the solid angle is studied by changing the radius and length of the collimators towards and away from the source and sample. From these values the variation of the total solid angle and geometrical efficiency is deduced and the optimum value is used for the experimental work. (authors)

  5. A new approach to estimate the geometrical factors, solid angle approximation, geometrical efficiency and their use in basic interaction cross section measurements

    Energy Technology Data Exchange (ETDEWEB)

    Rao, D.V.; Cesareo, R.; Brunetti, A. [Sassari University, Istituto di Matematica e Fisica (Italy); Gigante, G.E. [Roma Universita, Dipt. di Fisica (Italy); Takeda, T.; Itai, Y. [Tsukuba Univ., Ibaraki (Japan). Inst. of Clinical Medicine; Akatsuka, T. [Yamagata Univ., Yonezawa (Japan). Faculty of Engineering

    2002-10-01

    A new approach is developed to estimate the geometrical factors, solid angle approximation and geometrical efficiency for a system with experimental arrangements using X-ray tube and secondary target as an excitation source in order to produce the nearly monoenergetic K{alpha} radiation to excite the sample. The variation of the solid angle is studied by changing the radius and length of the collimators towards and away from the source and sample. From these values the variation of the total solid angle and geometrical efficiency is deduced and the optimum value is used for the experimental work. (authors)

  6. A new approach to estimate the geometrical factors, solid angle approximation, geometrical efficiency and their use in basic interaction cross section measurements

    Science.gov (United States)

    Rao, D. V.; Cesareo, R.; Brunetti, A.; Gigante, G. E.; Takeda, T.; Itai, Y.; Akatsuka, T.

    2002-10-01

    A new approach is developed to estimate the geometrical factors, solid angle approximation and geometrical efficiency for a system with experimental arrangements using X-ray tube and secondary target as an excitation source in order to produce the nearly monoenergetic Kα radiation to excite the sample. The variation of the solid angle is studied by changing the radius and length of the collimators towards and away from the source and sample. From these values the variation of the total solid angle and geometrical efficiency is deduced and the optimum value is used for the experimental work.

  7. Geometric and Optic Characterization of a Hemispherical Dome Port for Underwater Photogrammetry

    Directory of Open Access Journals (Sweden)

    Fabio Menna

    2016-01-01

    Full Text Available The popularity of automatic photogrammetric techniques has promoted many experiments in underwater scenarios leading to quite impressive visual results, even by non-experts. Despite these achievements, a deep understanding of camera and lens behaviors as well as optical phenomena involved in underwater operations is fundamental to better plan field campaigns and anticipate the achievable results. The paper presents a geometric investigation of a consumer grade underwater camera housing, manufactured by NiMAR and equipped with a 7′′ dome port. After a review of flat and dome ports, the work analyzes, using simulations and real experiments, the main optical phenomena involved when operating a camera underwater. Specific aspects which deal with photogrammetric acquisitions are considered with some tests in laboratory and in a swimming pool. Results and considerations are shown and commented.

  8. The algebraic versus geometric approach to quantum field theory

    International Nuclear Information System (INIS)

    Schroer, B.

    1990-06-01

    Some recent developments in algebraic QFT are reviewed and confronted with results obtained by geometric methods. In particular a critical evaluation of the present status of the quantum symmetry discussion is given and the possible relation of the (Gepner-Witten) modularity in conformal QFT 2 and the Tomita modularity (existence of quantum reflections) of the algebraic approach is commented on. (author) 34 refs

  9. Design of all-optical, hot-electron current-direction-switching device based on geometrical asymmetry.

    Science.gov (United States)

    Kumarasinghe, Chathurangi S; Premaratne, Malin; Gunapala, Sarath D; Agrawal, Govind P

    2016-02-18

    We propose a nano-scale current-direction-switching device(CDSD) that operates based on the novel phenomenon of geometrical asymmetry between two hot-electron generating plasmonic nanostructures. The proposed device is easy to fabricate and economical to develop compared to most other existing designs. It also has the ability to function without external wiring in nano or molecular circuitry since it is powered and controlled optically. We consider a such CDSD made of two dissimilar nanorods separated by a thin but finite potential barrier and theoretically derive the frequency-dependent electron/current flow rate. Our analysis takes in to account the quantum dynamics of electrons inside the nanorods under a periodic optical perturbation that are confined by nanorod boundaries, modelled as finite cylindrical potential wells. The influence of design parameters, such as geometric difference between the two nanorods, their volumes and the barrier width on quality parameters such as frequency-sensitivity of the current flow direction, magnitude of the current flow, positive to negative current ratio, and the energy conversion efficiency is discussed by considering a device made of Ag/TiO2/Ag. Theoretical insight and design guidelines presented here are useful for customizing our proposed CDSD for applications such as self-powered logic gates, power supplies, and sensors.

  10. ASYMPTOTICAL CALCULATION OF ELECTROMAGNETIC WAVES SCATTERED FROM A DIELECTRIC COATED CYLINDRICAL SURFACE WITH PHYSICAL OPTICS APPROACH

    Directory of Open Access Journals (Sweden)

    Uğur YALÇIN

    2004-02-01

    Full Text Available In this study, quasi-optical scattering of finite source electromagnetic waves from a dielectric coated cylindrical surface is analysed with Physical Optics (PO approach. A linear electrical current source is chosen as the finite source. Reflection coefficient of the cylindrical surface is derived by using Geometrical Theory of Diffraction (GTD. Then, with the help of this coefficient, fields scattered from the surface are obtained. These field expressions are used in PO approach and surface scattering integral is determined. Evaluating this integral asymptotically, fields reflected from the surface and surface divergence coefficient are calculated. Finally, results obtained in this study are evaluated numerically and effects of the surface impedance to scattered fields are analysed. The time factor is taken as j te? in this study.

  11. Femtosecond pulse shaping using the geometric phase.

    Science.gov (United States)

    Gökce, Bilal; Li, Yanming; Escuti, Michael J; Gundogdu, Kenan

    2014-03-15

    We demonstrate a femtosecond pulse shaper that utilizes polarization gratings to manipulate the geometric phase of an optical pulse. This unique approach enables circular polarization-dependent shaping of femtosecond pulses. As a result, it is possible to create coherent pulse pairs with orthogonal polarizations in a 4f pulse shaper setup, something until now that, to our knowledge, was only achieved via much more complex configurations. This approach could be used to greatly simplify and enhance the functionality of multidimensional spectroscopy and coherent control experiments, in which multiple coherent pulses are used to manipulate quantum states in materials of interest.

  12. Application of semiclassical and geometrical optics theories to resonant modes of a coated sphere.

    Science.gov (United States)

    Bambino, Túlio M; Breitschaft, Ana Maria S; Barbosa, Valmar C; Guimarães, Luiz G

    2003-03-01

    This work deals with some aspects of the resonant scattering of electromagnetic waves by a metallic sphere covered by a dielectric layer, in the weak-absorption approximation. We carry out a geometrical optics treatment of the scattering and develop semiclassical formulas to determine the positions and widths of the system resonances. In addition, we show that the mean lifetime of broad resonances is strongly dependent on the polarization of the incident light.

  13. The optical levitation of spheres

    International Nuclear Information System (INIS)

    Roosen, G.

    1979-01-01

    In this article we are dealing with optical levitation, that is the possibility of maintaining particles in a stable equilibrium position in air or vacuum by means of laser beams. In the first part, we review the methods used to calculate the force exerted on a sphere by a laser beam. The axial and transverse force components could be obtained either by applying Debye theory to laser beams which have a non-uniform energy distribution or by using, in the case of large spheres, a geometrical optics approach. From the results achieved with the geometrical optics approach, we derive, in a second part, the required stable equilibrium conditions for a sphere placed either in a vertical beam or in two horizontal ones having the same axis but opposite direction. In the last part, we describe in detail the levitation experiments carried out using either a vertical or two horizontal beams. In conclusion, we point out some applications of optical levitation, emphasizing especially the suspension by optical levitation of the targets used in laser fusion experiments. (author) [fr

  14. Theoretical approach for plasma series resonance effect in geometrically symmetric dual radio frequency plasma

    International Nuclear Information System (INIS)

    Bora, B.; Bhuyan, H.; Favre, M.; Wyndham, E.; Chuaqui, H.

    2012-01-01

    Plasma series resonance (PSR) effect is well known in geometrically asymmetric capacitively couple radio frequency plasma. However, plasma series resonance effect in geometrically symmetric plasma has not been properly investigated. In this work, a theoretical approach is made to investigate the plasma series resonance effect and its influence on Ohmic and stochastic heating in geometrically symmetric discharge. Electrical asymmetry effect by means of dual frequency voltage waveform is applied to excite the plasma series resonance. The results show considerable variation in heating with phase difference between the voltage waveforms, which may be applicable in controlling the plasma parameters in such plasma.

  15. Determining the direction of a geometrical/optical reference axis in the coordinate system of a triaxial magnetometer sensor

    DEFF Research Database (Denmark)

    Primdahl, Fritz; Brauer, Peter; Merayo, José M.G.

    2002-01-01

    optical or geometrical axes in order to be able to determine the precise orientation of the magnetic coordinate axes in an external reference system. Two methods for determining a reference axis in the sensor coordinates are discussed: (1) using a triaxial coil facility to measure the sensor orientation...

  16. Size and direction of distortion in geometric-optical illusions: conciliation between the Müller-Lyer and Titchener configurations.

    Science.gov (United States)

    Nemati, Farshad

    2009-01-01

    Over the past few decades, different theories have been advanced to explain geometric-optical illusions based on various perceptual processes such as assimilation and/or contrast. Consistent with the contradictory effects of assimilation and contrast, Pressey's assimilation theory provided an explanation for the Müller-Lyer illusion, but failed to account for the Titchener (Ebbinghaus) illusion. A model that explains both Müller-Lyer and Titchener illusions according to a common underlying process may outline a unified explanation for a variety of geometric-optical illusions. In order to develop such a model, the concept of empty space is introduced as an area of the illusory figure that is not filled by line drawings. It was predicted that the magnitude of illusion would increase with the area of the empty space around the illusory figures. The effect of empty space on the magnitude of perceptual distortion was measured in Müller-Lyer figures, with outward arrowheads of different length. The results indicated an overestimation of the target stimulus in all of the figures. Nevertheless, consistent with the prediction of the present model, the horizontal line in the Müller-Lyer figure with the longest arrowheads appeared shorter than that with the shortest arrowheads, although the size contrast of these figures was the same. According to the analysis proposed in the present study, the area of empty space not only affects the magnitude of illusion but also serves as a contextual cue for the perceptual system to determine the direction of illusion (orientation). The functional relationships between the size contrast and empty space provide a common explanation for the Müller-Lyer, Titchener, and a variety of other geometric-optical illusions.

  17. Optical design of grazing incidence toroidal grating monochromator

    International Nuclear Information System (INIS)

    Pouey, M.; Howells, M.R.; Takacs, P.Z.

    1982-01-01

    Design rules using geometrical optics and physical optics associated with the phase balancing method are discussed for stigmatic toroidal grazing incidence monochromators. To determine the optical performance of devices involving mirrirs and/or gratings, ray tracing programs using exact geometry are quite widely used. It is then desirable to have some way to infer the practical performance of an instrument from a spot diagram created by tracing a limited number of rays. We propose a first approach to this problem involving an estimation of the geometrical intensity distribution in the image plane and the corresponding line spread function. (orig.)

  18. Construction of Ray Diagrams in Geometrical Optics: A Media-Focused Approach

    Science.gov (United States)

    Santana, Alejandro; Rodriguez, Yohany; Gomez, Edgar A.

    2012-01-01

    Ray diagrams offer a powerful framework for understanding and characterizing many properties of optical systems, such as images and magnifications. However, this construction also introduces many conceptual hurdles for students. The idea of representing the propagation of waves by means of a light ray, which is a line or curve perpendicular to the…

  19. Geometrical approach to tumor growth.

    Science.gov (United States)

    Escudero, Carlos

    2006-08-01

    Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells and particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former paper [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyze the unexplored three-dimensional case, for which interesting conclusions on tumor growth are derived.

  20. Active Learning of Geometrical Optics in High School: The ALOP Approach

    Science.gov (United States)

    Alborch, Alejandra; Pandiella, Susana; Benegas, Julio

    2017-01-01

    A group comparison experiment of two high school classes with pre and post instruction testing has been carried out to study the suitability and advantages of using the active learning of optics and photonics (ALOP) curricula in high schools of developing countries. Two parallel, mixed gender, 12th grade classes of a high school run by the local…

  1. 3D geometric modeling and simulation of laser propagation through turbulence with plenoptic functions

    Science.gov (United States)

    Wu, Chensheng; Nelson, William; Davis, Christopher C.

    2014-10-01

    Plenoptic functions are functions that preserve all the necessary light field information of optical events. Theoretical work has demonstrated that geometric based plenoptic functions can serve equally well in the traditional wave propagation equation known as the "scalar stochastic Helmholtz equation". However, in addressing problems of 3D turbulence simulation, the dominant methods using phase screen models have limitations both in explaining the choice of parameters (on the transverse plane) in real-world measurements, and finding proper correlations between neighboring phase screens (the Markov assumption breaks down). Though possible corrections to phase screen models are still promising, the equivalent geometric approach based on plenoptic functions begins to show some advantages. In fact, in these geometric approaches, a continuous wave problem is reduced to discrete trajectories of rays. This allows for convenience in parallel computing and guarantees conservation of energy. Besides the pairwise independence of simulated rays, the assigned refractive index grids can be directly tested by temperature measurements with tiny thermoprobes combined with other parameters such as humidity level and wind speed. Furthermore, without loss of generality one can break the causal chain in phase screen models by defining regional refractive centers to allow rays that are less affected to propagate through directly. As a result, our work shows that the 3D geometric approach serves as an efficient and accurate method in assessing relevant turbulence problems with inputs of several environmental measurements and reasonable guesses (such as Cn 2 levels). This approach will facilitate analysis and possible corrections in lateral wave propagation problems, such as image de-blurring, prediction of laser propagation over long ranges, and improvement of free space optic communication systems. In this paper, the plenoptic function model and relevant parallel algorithm computing

  2. The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

    Science.gov (United States)

    Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

    2018-04-01

    The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

  3. Geometrical interpretation of optical absorption

    Energy Technology Data Exchange (ETDEWEB)

    Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain); Montesinos-Amilibia, J. M. [Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, E-28040 Madrid (Spain)

    2011-08-15

    We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.

  4. Geometric allocation approaches in Markov chain Monte Carlo

    International Nuclear Information System (INIS)

    Todo, S; Suwa, H

    2013-01-01

    The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the selection of candidate states, the optimization of transition kernel, algorithm for choosing a configuration according to the transition probabilities. We show that the unconventional approaches based on the geometric allocation of probabilities or weights can improve the dynamics and scaling of the Monte Carlo simulation in several aspects. Particularly, the approach using the irreversible kernel can reduce or sometimes completely eliminate the rejection of trial move in the Markov chain. We also discuss how the space-time interchange technique together with Walker's method of aliases can reduce the computational time especially for the case where the number of candidates is large, such as models with long-range interactions

  5. Geometric phase modulation for stellar interferometry

    International Nuclear Information System (INIS)

    Roy, M.; Boschung, B.; Tango, W.J.; Davis, J.

    2002-01-01

    Full text: In a long baseline optical interferometer, the fringe visibility is normally measured by modulation of the optical path difference between the two arms of the instruments. To obtain accurate measurements, the spectral bandwidth must be narrow, limiting the sensitivity of the technique. The application of geometric phase modulation technique to stellar interferometry has been proposed by Tango and Davis. Modulation of the geometric phase has the potential for improving the sensitivity of optical interferometers, and specially the Sydney University Stellar Interferometer (SUSI), by allowing broad band modulation of the light signals. This is because a modulator that changes the geometric phase of the signal is, in principle, achromatic. Another advantage of using such a phase modulator is that it can be placed in the common path traversed by the two orthogonally polarized beams emerging from the beam combiner in a stellar interferometer. Thus the optical components of the modulator do not have to be interferometric quality and could be relatively easily introduced into SUSI. We have investigated the proposed application in a laboratory-based experiment using a Mach-Zehnder interferometer with white-light source. This can be seen as a small model of an amplitude stellar interferometer where the light source takes the place of the distant star and two corner mirrors replaces the entrance pupils of the stellar interferometer

  6. Geometrical approach to central molecular chirality: a chirality selection rule

    OpenAIRE

    Capozziello, S.; Lattanzi, A.

    2004-01-01

    Chirality is of primary importance in many areas of chemistry and has been extensively investigated since its discovery. We introduce here the description of central chirality for tetrahedral molecules using a geometrical approach based on complex numbers. According to this representation, for a molecule having n chiral centres, it is possible to define an index of chirality. Consequently a chirality selection rule has been derived which allows the characterization of a molecule as achiral, e...

  7. Physical optics

    International Nuclear Information System (INIS)

    Kim Il Gon; Lee, Seong Su; Jang, Gi Wan

    2012-07-01

    This book indicates physical optics with properties and transmission of light, mathematical expression of wave like harmonic wave and cylindrical wave, electromagnetic theory and light, transmission of light with Fermat principle and Fresnel equation, geometrical optics I, geometrical optics II, optical instrument such as stops, glasses and camera, polarized light like double refraction by polarized light, interference, interference by multiple reflections, diffraction, solid optics, crystal optics such as Faraday rotation and Kerr effect and measurement of light. Each chapter has an exercise.

  8. Physical optics

    Energy Technology Data Exchange (ETDEWEB)

    Kim Il Gon; Lee, Seong Su; Jang, Gi Wan

    2012-07-15

    This book indicates physical optics with properties and transmission of light, mathematical expression of wave like harmonic wave and cylindrical wave, electromagnetic theory and light, transmission of light with Fermat principle and Fresnel equation, geometrical optics I, geometrical optics II, optical instrument such as stops, glasses and camera, polarized light like double refraction by polarized light, interference, interference by multiple reflections, diffraction, solid optics, crystal optics such as Faraday rotation and Kerr effect and measurement of light. Each chapter has an exercise.

  9. Determination of scattering center of multipath signals using geometric optics and Fresnel zone concepts

    Directory of Open Access Journals (Sweden)

    Kamil Yavuz Kapusuz

    2014-06-01

    Full Text Available In this study, a method for determining scattering center (or center of scattering points of a multipath is proposed, provided that the direction of arrival of the multipath is known by the receiver. The method is based on classical electromagnetic wave principles in order to determine scattering center over irregular terrain. Geometrical optics (GO along with Fresnel zone concept is employed, as the receiver, the transmitter positions and irregular terrain data are assumed to be provided. The proposed method could be used at UHF bands, especially, operations of radars and electronic warfare applications.

  10. Fundamentals and techniques of nonimaging optics research

    Science.gov (United States)

    Winston, R.; Ogallagher, J.

    1987-07-01

    Nonimaging Optics differs from conventional approaches in its relaxation of unnecessary constraints on energy transport imposed by the traditional methods for optimizing image formation and its use of more broadly based analytical techniques such as phase space representations of energy flow, radiative transfer analysis, thermodynamic arguments, etc. Based on these means, techniques for designing optical elements which approach and in some cases attain the maximum concentration permitted by the Second Law of Thermodynamics were developed. The most widely known of these devices are the family of Compound Parabolic Concentrators (CPC's) and their variants and the so called Flow-Line or trumpet concentrator derived from the geometric vector flux formalism developed under this program. Applications of these and other such ideal or near-ideal devices permits increases of typically a factor of four (though in some cases as much as an order of magnitude) in the concentration above that possible with conventional means. Present efforts can be classed into two main areas: (1) classical geometrical nonimaging optics, and (2) logical extensions of nonimaging concepts to the physical optics domain.

  11. Time-and-frequency domains approach to data processing in multiwavelength optical scatterometry of dielectric gratings

    KAUST Repository

    Granet, Gé rard; Melezhik, Petr N.; Sirenko, Kostyantyn; Yashina, Nataliya P.

    2013-01-01

    This paper focuses on scatterometry problems arising in lithography production of periodic gratings. Namely, the paper introduces a theoretical and numerical-modeling-oriented approach to scatterometry problems and discusses its capabilities. The approach allows for reliable detection of deviations in gratings' critical dimensions (CDs) during the manufacturing process. The core of the approach is the one-to-one correspondence between the electromagnetic (EM) characteristics and the geometric/material properties of gratings. The approach is based on highly accurate solutions of initial boundary-value problems describing EM waves' interaction on periodic gratings. The advantage of the approach is the ability to perform simultaneously and interactively both in frequency and time domains under conditions of possible resonant scattering of EM waves by infinite or finite gratings. This allows a detection of CDs for a wide range of gratings, and, thus is beneficial for the applied scatterometry. (C) 2013 Optical Society of America

  12. Time-and-frequency domains approach to data processing in multiwavelength optical scatterometry of dielectric gratings

    KAUST Repository

    Granet, Gérard

    2013-01-01

    This paper focuses on scatterometry problems arising in lithography production of periodic gratings. Namely, the paper introduces a theoretical and numerical-modeling-oriented approach to scatterometry problems and discusses its capabilities. The approach allows for reliable detection of deviations in gratings\\' critical dimensions (CDs) during the manufacturing process. The core of the approach is the one-to-one correspondence between the electromagnetic (EM) characteristics and the geometric/material properties of gratings. The approach is based on highly accurate solutions of initial boundary-value problems describing EM waves\\' interaction on periodic gratings. The advantage of the approach is the ability to perform simultaneously and interactively both in frequency and time domains under conditions of possible resonant scattering of EM waves by infinite or finite gratings. This allows a detection of CDs for a wide range of gratings, and, thus is beneficial for the applied scatterometry. (C) 2013 Optical Society of America

  13. Geometrical approach to the dynamics of the relativistic string

    International Nuclear Information System (INIS)

    Barbashov, B.M.; Koshkarov, A.L.

    1979-01-01

    The dynamics of the relativistic string is considered from the point of view of the gaussian theory of two-dimensional surfaces in the three-dimensional pseudoeuclidean space-epsilon 3 1 according to which the surface is characterized by its first and second quadratic forms. The geometrical approach possesses an advantage which gives the possibility to solve manifestly additional conditions on the vector describing the coordinates of the string world surface. The equations of motion and boundary conditions are written out for the cases of a string with massive ends and a closed string. The basic equations are formulated for the coefficients of the first and second quadratic forms of the string world surface, which represent the known geometric conditions of integration of Gauss and Weingarten derivation formulas. By means of integration of the derivation formulas the representation is obtained for the form of the string world surface in a certain basis, which satisfies the equations of motion as well as additional conditions. A new relativistic invariant gauge is suggested which fixes the second quadratic form of the surface. This representation can be extended to the case of arbitrary dimensional space

  14. Geometric screening of core/shell hydrogel microcapsules using a tapered microchannel with interdigitated electrodes.

    Science.gov (United States)

    Niu, Ye; Qi, Lin; Zhang, Fen; Zhao, Yi

    2018-07-30

    Core/shell hydrogel microcapsules attract increasing research attention due to their potentials in tissue engineering, food engineering, and drug delivery. Current approaches for generating core/shell hydrogel microcapsules suffer from large geometric variations. Geometrically defective core/shell microcapsules need to be removed before further use. High-throughput geometric characterization of such core/shell microcapsules is therefore necessary. In this work, a continuous-flow device was developed to measure the geometric properties of microcapsules with a hydrogel shell and an aqueous core. The microcapsules were pumped through a tapered microchannel patterned with an array of interdigitated microelectrodes. The geometric parameters (the shell thickness and the diameter) were derived from the displacement profiles of the microcapsules. The results show that this approach can successfully distinguish all unencapsulated microparticles. The geometric properties of core/shell microcapsules can be determined with high accuracy. The efficacy of this method was demonstrated through a drug releasing experiment where the optimization of the electrospray process based on geometric screening can lead to controlled and extended drug releasing profiles. This method does not require high-speed optical systems, simplifying the system configuration and making it an indeed miniaturized device. The throughput of up to 584 microcapsules per minute was achieved. This study provides a powerful tool for screening core/shell hydrogel microcapsules and is expected to facilitate the applications of these microcapsules in various fields. Copyright © 2018 Elsevier B.V. All rights reserved.

  15. Subreflector extension for improved efficiencies in Cassegrain antennas - GTD/PO analysis. [Geometrical Theory of Diffraction/Physical Optics

    Science.gov (United States)

    Rahmat-Samii, Yahya

    1986-01-01

    Both offset and symmetric Cassegrain reflector antennas are used in satellite and ground communication systems. It is known that the subreflector diffraction can degrade the performance of these reflectors. A geometrical theory of diffraction/physical optics analysis technique is used to investigate the effects of the extended subreflector, beyond its optical rim, on the reflector efficiency and far-field patterns. Representative numerical results are shown for an offset Cassegrain reflector antenna with different feed illumination tapers and subreflector extensions. It is observed that for subreflector extensions as small as one wavelength, noticeable improvements in the overall efficiencies can be expected. Useful design data are generated for the efficiency curves and far-field patterns.

  16. Modeling of solar transmission through multilayer glazing facade using shading blinds with arbitrary geometrical and surface optical properties

    International Nuclear Information System (INIS)

    Luo, Yongqiang; Zhang, Ling; Wu, Jing; Wang, Xiliang; Liu, Zhongbing; Wu, Zhenghong

    2017-01-01

    A system model that can accurately simulate the instantaneous solar transmittance through multilayer glazing façade (MGF) and shading device can provide a solid foundation for the thermal and daylighting performance calculation of MGF as well as indoor visual comfort evaluation. Traditional optical models for venetian blind and glazing façade meet with their limitations to analyze new prototype of shading blind like photovoltaic (PV) blind which has quite different surface optical properties compared with conventional venetian blind. The present study proposed a new system model for MGF using shading blind with arbitrary geometrical and optical features which is suitable for a wide range of applications. Three major calculation types for modeling of shading blinds cover all the possible situations in application. Guess Integer-Valued Function is adopted for delivering a general description on direct radiation transport. The direct-direct, direct-diffuse and diffuse-diffuse radiation transports are separately considered. A series of experiments were carried out to validate the model under various parameter settings and different weather conditions. Parametric study revealed some new findings in the evaluations of influence of ambient radiation situations, geometrical and optical features of blind space on both solar transmittance and solar absorption by blind layer. - Highlights: • Solar transport through glazing façades with PV blind with arbitrary geometry is simulated. • Ray-tracing and radiosity method are coupled in calculation. • Guess Integer-Valued Function is used in calculation of direct radiation transport. • Experiment and simulated data are compared for model validation. • Parametric study is conducted for evaluating the impact of different factors on the system.

  17. Error performance analysis in K-tier uplink cellular networks using a stochastic geometric approach

    KAUST Repository

    Afify, Laila H.; Elsawy, Hesham; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim

    2015-01-01

    -in-Distribution approach that utilizes stochastic geometric tools to account for the network geometry in the performance characterization. Different from the other stochastic geometry models adopted in the literature, the developed analysis accounts for important

  18. Implementation and efficiency of two geometric stiffening approaches

    International Nuclear Information System (INIS)

    Lugris, Urbano; Naya, Miguel A.; Perez, Jose A.; Cuadrado, Javier

    2008-01-01

    When the modeling of flexible bodies is required in multibody systems, the floating frame of reference formulations are probably the most efficient methods available. In the case of beams undergoing high speed rotations, the geometric stiffening effect can appear due to geometric nonlinearities, and it is often not captured by the aforementioned methods, since it is common to linearize the elastic forces assuming small deformations. The present work discusses the implementation of different existing methods developed to consider such geometric nonlinearities within a floating frame of reference formulation in natural coordinates, making emphasis on the relation between efficiency and accuracy of the resulting algorithms, seeking to provide practical criteria of use

  19. A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE

    International Nuclear Information System (INIS)

    Puschmann, K. G.; Ruiz Cobo, B.; MartInez Pillet, V.

    2010-01-01

    Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.

  20. Active learning of geometrical optics in high school: the ALOP approach

    Science.gov (United States)

    Alborch, Alejandra; Pandiella, Susana; Benegas, Julio

    2017-09-01

    A group comparison experiment of two high school classes with pre and post instruction testing has been carried out to study the suitability and advantages of using the active learning of optics and photonics (ALOP) curricula in high schools of developing countries. Two parallel, mixed gender, 12th grade classes of a high school run by the local university were chosen. One course was randomly selected to follow the experimental instruction, based on teacher and student activities contained in the ALOP Manual. The other course followed the traditional, teacher-centered, instruction previously practiced. Conceptual knowledge of the characteristics of image formation by plane mirrors and single convergent and divergent lenses was measured by applying, in both courses, the multiple-choice test, light and optics conceptual evaluation (LOCE). Measurement before instruction showed that initial knowledge was almost null, and therefore equivalent, in both courses. After instruction testing showed that the conceptual knowledge of students following the ALOP curricula more than doubled that achieved by students in the control course, a situation maintained throughout the six conceptual dimensions tested by the 34 questions of the LOCE test used in this experiment. Using a 60% performance level on the LOCE test as the threshold of satisfactory performance, most (about 90%) of the experimental group achieved this level—independent of initial knowledge, while no student following traditional instruction reached this level of understanding. Some considerations and recommendations for prospective users are also included.

  1. Problems in Geometrical Optics

    Science.gov (United States)

    Joyce, L. S.

    1973-01-01

    Ten laboratory exercises on optics are described to clarify concepts involving point objects and converging lenses producing real images. Mathematical treatment is kept to a minimum to stress concepts involved. (PS)

  2. Geometric Lagrangian approach to the physical degree of freedom count in field theory

    Science.gov (United States)

    Díaz, Bogar; Montesinos, Merced

    2018-05-01

    To circumvent some technical difficulties faced by the geometric Lagrangian approach to the physical degree of freedom count presented in the work of Díaz, Higuita, and Montesinos [J. Math. Phys. 55, 122901 (2014)] that prevent its direct implementation to field theory, in this paper, we slightly modify the geometric Lagrangian approach in such a way that its resulting version works perfectly for field theory (and for particle systems, of course). As in previous work, the current approach also allows us to directly get the Lagrangian constraints, a new Lagrangian formula for the counting of the number of physical degrees of freedom, the gauge transformations, and the number of first- and second-class constraints for any action principle based on a Lagrangian depending on the fields and their first derivatives without performing any Dirac's canonical analysis. An advantage of this approach over the previous work is that it also allows us to handle the reducibility of the constraints and to get the off-shell gauge transformations. The theoretical framework is illustrated in 3-dimensional generalized general relativity (Palatini and Witten's exotic actions), Chern-Simons theory, 4-dimensional BF theory, and 4-dimensional general relativity given by Palatini's action with a cosmological constant.

  3. An introduction to geometrical physics

    CERN Document Server

    Aldrovandi, R

    1995-01-01

    This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level o

  4. An information geometric approach to least squares minimization

    Science.gov (United States)

    Transtrum, Mark; Machta, Benjamin; Sethna, James

    2009-03-01

    Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems.

  5. Statistics of optical and geometrical properties of cirrus cloud over tibetan plateau measured by lidar and radiosonde

    Directory of Open Access Journals (Sweden)

    Dai Guangyao

    2018-01-01

    Full Text Available Cirrus clouds affect the energy budget and hydrological cycle of the earth’s atmosphere. The Tibetan Plateau (TP plays a significant role in the global and regional climate. Optical and geometrical properties of cirrus clouds in the TP were measured in July-August 2014 by lidar and radiosonde. The statistics and temperature dependences of the corresponding properties are analyzed. The cirrus cloud formations are discussed with respect to temperature deviation and dynamic processes.

  6. Random Process Theory Approach to Geometric Heterogeneous Surfaces: Effective Fluid-Solid Interaction

    Science.gov (United States)

    Khlyupin, Aleksey; Aslyamov, Timur

    2017-06-01

    Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric roughness. We provide the general theory of effective coarse-grained fluid-solid potential by proper averaging of the free energy of fluid molecules which interact with the solid media. This procedure is largely based on the theory of random processes. We apply first passage time probability problem and assume the local Markov properties of random surfaces. General expression of effective fluid-solid potential is obtained. In the case of small surface irregularities analytical approximation for effective potential is proposed. Both amorphous materials with large surface roughness and crystalline solids with several types of fcc lattices are considered. It is shown that the wider the lattice spacing in terms of molecular diameter of the fluid, the more obtained potentials differ from classical ones. A comparison with published Monte-Carlo simulations was discussed. The work provides a promising approach to explore how the random geometric heterogeneity affects on thermodynamic properties of the fluids.

  7. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence.

    Science.gov (United States)

    Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi

    2006-07-10

    On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.

  8. Demystifying the memory effect: A geometrical approach to understanding speckle correlations

    Science.gov (United States)

    Prunty, Aaron C.; Snieder, Roel K.

    2017-05-01

    The memory effect has seen a surge of research into its fundamental properties and applications since its discovery by Feng et al. [Phys. Rev. Lett. 61, 834 (1988)]. While the wave trajectories for which the memory effect holds are hidden implicitly in the diffusion probability function [Phys. Rev. B 40, 737 (1989)], the physical intuition of why these trajectories satisfy the memory effect has often been masked by the derivation of the memory correlation function itself. In this paper, we explicitly derive the specific trajectories through a random medium for which the memory effect holds. Our approach shows that the memory effect follows from a simple conservation argument, which imposes geometrical constraints on the random trajectories that contribute to the memory effect. We illustrate the time-domain effects of these geometrical constraints with numerical simulations of pulse transmission through a random medium. The results of our derivation and numerical simulations are consistent with established theory and experimentation.

  9. Geometrical theory of nonlinear phase distortion of intense laser beams

    International Nuclear Information System (INIS)

    Glaze, J.A.; Hunt, J.T.; Speck, D.R.

    1975-01-01

    Phase distortion arising from whole beam self-focusing of intense laser pulses with arbitrary spatial profiles is treated in the limit of geometrical optics. The constant shape approximation is used to obtain the phase and angular distribution of the geometrical rays in the near field. Conditions for the validity of this approximation are discussed. Geometrical focusing of the aberrated beam is treated for the special case of a beam with axial symmetry. Equations are derived that show both the shift of the focus and the distortion of the intensity distribution that are caused by the nonlinear index of refraction of the optical medium. An illustrative example treats the case of beam distortion in a Nd:Glass amplifier

  10. Accurate single-scattering simulation of ice cloud using the invariant-imbedding T-matrix method and the physical-geometric optics method

    Science.gov (United States)

    Sun, B.; Yang, P.; Kattawar, G. W.; Zhang, X.

    2017-12-01

    The ice cloud single-scattering properties can be accurately simulated using the invariant-imbedding T-matrix method (IITM) and the physical-geometric optics method (PGOM). The IITM has been parallelized using the Message Passing Interface (MPI) method to remove the memory limitation so that the IITM can be used to obtain the single-scattering properties of ice clouds for sizes in the geometric optics regime. Furthermore, the results associated with random orientations can be analytically achieved once the T-matrix is given. The PGOM is also parallelized in conjunction with random orientations. The single-scattering properties of a hexagonal prism with height 400 (in units of lambda/2*pi, where lambda is the incident wavelength) and an aspect ratio of 1 (defined as the height over two times of bottom side length) are given by using the parallelized IITM and compared to the counterparts using the parallelized PGOM. The two results are in close agreement. Furthermore, the integrated single-scattering properties, including the asymmetry factor, the extinction cross-section, and the scattering cross-section, are given in a completed size range. The present results show a smooth transition from the exact IITM solution to the approximate PGOM result. Because the calculation of the IITM method has reached the geometric regime, the IITM and the PGOM can be efficiently employed to accurately compute the single-scattering properties of ice cloud in a wide spectral range.

  11. Effects of source shape on the numerical aperture factor with a geometrical-optics model.

    Science.gov (United States)

    Wan, Der-Shen; Schmit, Joanna; Novak, Erik

    2004-04-01

    We study the effects of an extended light source on the calibration of an interference microscope, also referred to as an optical profiler. Theoretical and experimental numerical aperture (NA) factors for circular and linear light sources along with collimated laser illumination demonstrate that the shape of the light source or effective aperture cone is critical for a correct NA factor calculation. In practice, more-accurate results for the NA factor are obtained when a linear approximation to the filament light source shape is used in a geometric model. We show that previously measured and derived NA factors show some discrepancies because a circular rather than linear approximation to the filament source was used in the modeling.

  12. A geometric approach for fault detection and isolation of stator short circuit failure in a single asynchronous machine

    KAUST Repository

    Khelouat, Samir

    2012-06-01

    This paper deals with the problem of detection and isolation of stator short-circuit failure in a single asynchronous machine using a geometric approach. After recalling the basis of the geometric approach for fault detection and isolation in nonlinear systems, we will study some structural properties which are fault detectability and isolation fault filter existence. We will then design filters for residual generation. We will consider two approaches: a two-filters structure and a single filter structure, both aiming at generating residuals which are sensitive to one fault and insensitive to the other faults. Some numerical tests will be presented to illustrate the efficiency of the method.

  13. Comparison of stresses on homogeneous spheroids in the optical stretcher computed with geometrical optics and generalized Lorenz-Mie theory.

    Science.gov (United States)

    Boyde, Lars; Ekpenyong, Andrew; Whyte, Graeme; Guck, Jochen

    2012-11-20

    We present two electromagnetic frameworks to compare the surface stresses on spheroidal particles in the optical stretcher (a dual-beam laser trap that can be used to capture and deform biological cells). The first model is based on geometrical optics (GO) and limited in its applicability to particles that are much greater than the incident wavelength. The second framework is more sophisticated and hinges on the generalized Lorenz-Mie theory (GLMT). Despite the difference in complexity between both theories, the stress profiles computed with GO and GLMT are in good agreement with each other (relative errors are on the order of 1-10%). Both models predict a diminishing of the stresses for larger wavelengths and a strong increase of the stresses for shorter laser-cell distances. Results indicate that surface stresses on a spheroid with an aspect ratio of 1.2 hardly differ from the stresses on a sphere of similar size. Knowledge of the surface stresses and whether or not they redistribute during the stretching process is of crucial importance in real-time applications of the stretcher that aim to discern the viscoelastic properties of cells for purposes of cell characterization, sorting, and medical diagnostics.

  14. Present State of the Art of Composite Fabric Forming: Geometrical and Mechanical Approaches

    Science.gov (United States)

    Cherouat, Abel; Borouchaki, Houman

    2009-01-01

    Continuous fibre reinforced composites are now firmly established engineering materials for the manufacture of components in the automotive and aerospace industries. In this respect, composite fabrics provide flexibility in the design manufacture. The ability to define the ply shapes and material orientation has allowed engineers to optimize the composite properties of the parts. The formulation of new numerical models for the simulation of the composite forming processes must allow for reduction in the delay in manufacturing and an optimization of costs in an integrated design approach. We propose two approaches to simulate the deformation of woven fabrics: geometrical and mechanical approaches.

  15. Intercomparison of the GOS approach, superposition T-matrix method, and laboratory measurements for black carbon optical properties during aging

    International Nuclear Information System (INIS)

    He, Cenlin; Takano, Yoshi; Liou, Kuo-Nan; Yang, Ping; Li, Qinbin; Mackowski, Daniel W.

    2016-01-01

    We perform a comprehensive intercomparison of the geometric-optics surface-wave (GOS) approach, the superposition T-matrix method, and laboratory measurements for optical properties of fresh and coated/aged black carbon (BC) particles with complex structures. GOS and T-matrix calculations capture the measured optical (i.e., extinction, absorption, and scattering) cross sections of fresh BC aggregates, with 5–20% differences depending on particle size. We find that the T-matrix results tend to be lower than the measurements, due to uncertainty in theoretical approximations of realistic BC structures, particle property measurements, and numerical computations in the method. On the contrary, the GOS results are higher than the measurements (hence the T-matrix results) for BC radii 100 nm. We find good agreement (differences 100 nm. We find small deviations (≤10%) in asymmetry factors computed from the two methods for most BC coating structures and sizes, but several complex structures have 10–30% differences. This study provides the foundation for downstream application of the GOS approach in radiative transfer and climate studies. - Highlights: • The GOS and T-matrix methods capture laboratory measurements of BC optical properties. • The GOS results are consistent with the T-matrix results for BC optical properties. • BC optical properties vary remarkably with coating structures and sizes during aging.

  16. Entanglement capacity of nonlocal Hamiltonians: A geometric approach

    International Nuclear Information System (INIS)

    Lari, Behzad; Hassan, Ali Saif M.; Joag, Pramod S.

    2009-01-01

    We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for N-qubit pure states [Ali Saif M. Hassan and Pramod S. Joag, Phys. Rev. A 77, 062334 (2008)]. This geometric method has the distinct advantage that it gives the experimentally implementable criteria to ensure the optimal entanglement production rate without requiring a detailed knowledge of the state of the two qubit system. For the production of entanglement in practice, we need criteria for optimal entanglement production, which can be checked in situ without any need to know the state, as experimentally finding out the state of a quantum system is generally a formidable task. Further, we use our method to quantify the entanglement capacity in higher level and multipartite systems. We quantify the entanglement capacity for two qutrits and find the maximal entanglement generation rate and the corresponding state for the general isotropic interaction between qutrits, using the entanglement measure of N-qudit pure states proposed by us [Ali Saif M. Hassan and Pramod S. Joag, Phys. Rev. A 80, 042302 (2009)]. Next we quantify the genuine three qubit entanglement capacity for a general interaction between qubits. We obtain the maximum entanglement generation rate and the corresponding three qubit state for a general isotropic interaction between qubits. The state maximizing the entanglement generation rate is of the Greenberger-Horne-Zeilinger class. To the best of our knowledge, the entanglement capacities for two qutrit and three qubit systems have not been reported earlier.

  17. Mobile Watermarking against Geometrical Distortions

    Directory of Open Access Journals (Sweden)

    Jing Zhang

    2015-08-01

    Full Text Available Mobile watermarking robust to geometrical distortions is still a great challenge. In mobile watermarking, efficient computation is necessary because mobile devices have very limited resources due to power consumption. In this paper, we propose a low-complexity geometrically resilient watermarking approach based on the optimal tradeoff circular harmonic function (OTCHF correlation filter and the minimum average correlation energy Mellin radial harmonic (MACE-MRH correlation filter. By the rotation, translation and scale tolerance properties of the two kinds of filter, the proposed watermark detector can be robust to geometrical attacks. The embedded watermark is weighted by a perceptual mask which matches very well with the properties of the human visual system. Before correlation, a whitening process is utilized to improve watermark detection reliability. Experimental results demonstrate that the proposed watermarking approach is computationally efficient and robust to geometrical distortions.

  18. A geometric approach to multiperiod mean variance optimization of assets and liabilities

    OpenAIRE

    Leippold, Markus; Trojani, Fabio; Vanini, Paolo

    2005-01-01

    We present a geometric approach to discrete time multiperiod mean variance portfolio optimization that largely simplifies the mathematical analysis and the economic interpretation of such model settings. We show that multiperiod mean variance optimal policies can be decomposed in an orthogonal set of basis strategies, each having a clear economic interpretation. This implies that the corresponding multi period mean variance frontiers are spanned by an orthogonal basis of dynamic returns. Spec...

  19. [Retrieval of crown closure of moso bamboo forest using unmanned aerial vehicle (UAV) remotely sensed imagery based on geometric-optical model].

    Science.gov (United States)

    Wang, Cong; Du, Hua-qiang; Zhou, Guo-mo; Xu, Xiao-jun; Sun, Shao-bo; Gao, Guo-long

    2015-05-01

    This research focused on the application of remotely sensed imagery from unmanned aerial vehicle (UAV) with high spatial resolution for the estimation of crown closure of moso bamboo forest based on the geometric-optical model, and analyzed the influence of unconstrained and fully constrained linear spectral mixture analysis (SMA) on the accuracy of the estimated results. The results demonstrated that the combination of UAV remotely sensed imagery and geometric-optical model could, to some degrees, achieve the estimation of crown closure. However, the different SMA methods led to significant differentiation in the estimation accuracy. Compared with unconstrained SMA, the fully constrained linear SMA method resulted in higher accuracy of the estimated values, with the coefficient of determination (R2) of 0.63 at 0.01 level, against the measured values acquired during the field survey. Root mean square error (RMSE) of approximate 0.04 was low, indicating that the usage of fully constrained linear SMA could bring about better results in crown closure estimation, which was closer to the actual condition in moso bamboo forest.

  20. A network approach to the geometric structure of shallow cloud fields

    Science.gov (United States)

    Glassmeier, F.; Feingold, G.

    2017-12-01

    The representation of shallow clouds and their radiative impact is one of the largest challenges for global climate models. While the bulk properties of cloud fields, including effects of organization, are a very active area of research, the potential of the geometric arrangement of cloud fields for the development of new parameterizations has hardly been explored. Self-organized patterns are particularly evident in the cellular structure of Stratocumulus (Sc) clouds so readily visible in satellite imagery. Inspired by similar patterns in biology and physics, we approach pattern formation in Sc fields from the perspective of natural cellular networks. Our network analysis is based on large-eddy simulations of open- and closed-cell Sc cases. We find the network structure to be neither random nor characteristic to natural convection. It is independent of macroscopic cloud fields properties like the Sc regime (open vs closed) and its typical length scale (boundary layer height). The latter is a consequence of entropy maximization (Lewis's Law with parameter 0.16). The cellular pattern is on average hexagonal, where non-6 sided cells occur according to a neighbor-number distribution variance of about 2. Reflecting the continuously renewing dynamics of Sc fields, large (many-sided) cells tend to neighbor small (few-sided) cells (Aboav-Weaire Law with parameter 0.9). These macroscopic network properties emerge independent of the Sc regime because the different processes governing the evolution of closed as compared to open cells correspond to topologically equivalent network dynamics. By developing a heuristic model, we show that open and closed cell dynamics can both be mimicked by versions of cell division and cell disappearance and are biased towards the expansion of smaller cells. This model offers for the first time a fundamental and universal explanation for the geometric pattern of Sc clouds. It may contribute to the development of advanced Sc parameterizations

  1. Geometrical approach to tumor growth

    OpenAIRE

    Escudero, Carlos

    2006-01-01

    Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells/particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former article [C. Escudero, Phys. Rev. E 73, 020902(R) (200...

  2. Linear versus geometric morphometric approaches for the analysis of head shape dimorphism in lizards.

    Science.gov (United States)

    Fabre, Anne-Claire; Cornette, Raphäel; Huyghe, Katleen; Andrade, Denis V; Herrel, Anthony

    2014-09-01

    Differences between the sexes may arise because of differences in reproductive strategy, with females investing more in traits related to reproductive output and males investing more in traits related to resource holding capacity and territory defence. Sexual dimorphism is widespread in lizards and in many species males and females also differ in head shape. Males typically have bigger heads than females resulting in intersexual differences in bite force. Whereas most studies documenting differences in head dimensions between sexes use linear dimensions, the use of geometric morphometrics has been advocated as more appropriate to characterize such differences. This method may allow the characterization of local shape differences that may have functional consequences, and provides unbiased indicators of shape. Here, we explore whether the two approaches provide similar results in an analyses of head shape in Tupinambis merianae. The Argentine black and white tegu differs dramatically in body size, head size, and bite force between the sexes. However, whether the intersexual differences in bite force are simply the result of differences in head size or whether more subtle modifications (e.g., in muscle insertion areas) are involved remains currently unknown. Based on the crania and mandibles of 19 lizards with known bite force, we show intersexual differences in the shape of the cranium and mandible using both linear and geometric morphometric approaches. Although both types of analyses showed generally similar results for the mandible, this was not the case for the cranium. Geometric morphometric approaches provided better insights into the underlying functional relationships between the cranium and the jaw musculature, as illustrated by shape differences in muscle insertion areas not detected using linear morphometric data. © 2014 Wiley Periodicals, Inc.

  3. Geometric phases and quantum computation

    International Nuclear Information System (INIS)

    Vedral, V.

    2005-01-01

    Full text: In my lectures I will talk about the notion of the geometric phase and explain its relevance for both fundamental quantum mechanics as well as quantum computation. The phase will be at first introduced via the idea of Pancharatnam which involves interference of three or more light beams. This notion will then be generalized to the evolving quantum systems. I will discuss both pure and mixed states as well as unitary and non-unitary evolutions. I will also show how the concept of the vacuum induced geometric phase arises in quantum optics. A simple measurement scheme involving a Mach Zehnder interferometer will be presented and will be used to illustrate all the concepts in the lecture. Finally, I will expose a simple generalization of the geometric phase to evolving degenerate states. This will be seen to lead to the possibility of universal quantum computation using geometric effects only. Moreover, this contains a promise of intrinsically fault tolerant quantum information processing, whose prospects will be outlined at the end of the lecture. (author)

  4. Inexpensive demonstration set for teaching geometrical optics made by 3D printer

    Science.gov (United States)

    Havlíček, Karel; Ryston, Matěj

    2018-03-01

    Good sets for teaching geometric optics are relatively expensive to buy and difficult to make on your own, which often forces teachers to use less than ideal instruments and methods. This is a great shame, since this is a visually appealing topic that can motivate students. For this reason, we have designed a set that is relatively cheap, easy to use and can therefore (in some cases) remedy this situation. Our set is manufactured using 3D printing technology, which limits its users to those that have access to it; however, 3D printing technology is becoming more and more accessible every day (even in schools). On the other hand, 3D printing allows us to let the machines do the majority of the manufacturing work, making the process of building the set almost as simple as ‘download and press print’. This article presents this set, what it consists of, how it is done and where can you find all the necessary files and instructions.

  5. Geometric phases for nonlinear coherent and squeezed states

    International Nuclear Information System (INIS)

    Yang Dabao; Chen Ying; Chen Jingling; Zhang Fulin

    2011-01-01

    The geometric phases for standard coherent states which are widely used in quantum optics have attracted considerable attention. Nevertheless, few physicists consider the counterparts of nonlinear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated, respectively. Moreover, some of their common properties are discussed, such as gauge invariance, non-locality and nonlinear effects. The nonlinear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have an application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r → ∞, the limiting value of the geometric phase is also determined by a nonlinear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states may be regarded as a geometric criterion.

  6. Geometric optimisation of an accurate cosine correcting optic fibre coupler for solar spectral measurement

    Science.gov (United States)

    Cahuantzi, Roberto; Buckley, Alastair

    2017-09-01

    Making accurate and reliable measurements of solar irradiance is important for understanding performance in the photovoltaic energy sector. In this paper, we present design details and performance of a number of fibre optic couplers for use in irradiance measurement systems employing remote light sensors applicable for either spectrally resolved or broadband measurement. The angular and spectral characteristics of different coupler designs are characterised and compared with existing state-of-the-art commercial technology. The new coupler designs are fabricated from polytetrafluorethylene (PTFE) rods and operate through forward scattering of incident sunlight on the front surfaces of the structure into an optic fibre located in a cavity to the rear of the structure. The PTFE couplers exhibit up to 4.8% variation in scattered transmission intensity between 425 nm and 700 nm and show minimal specular reflection, making the designs accurate and reliable over the visible region. Through careful geometric optimization near perfect cosine dependence on the angular response of the coupler can be achieved. The PTFE designs represent a significant improvement over the state of the art with less than 0.01% error compared with ideal cosine response for angles of incidence up to 50°.

  7. Geometric optimisation of an accurate cosine correcting optic fibre coupler for solar spectral measurement.

    Science.gov (United States)

    Cahuantzi, Roberto; Buckley, Alastair

    2017-09-01

    Making accurate and reliable measurements of solar irradiance is important for understanding performance in the photovoltaic energy sector. In this paper, we present design details and performance of a number of fibre optic couplers for use in irradiance measurement systems employing remote light sensors applicable for either spectrally resolved or broadband measurement. The angular and spectral characteristics of different coupler designs are characterised and compared with existing state-of-the-art commercial technology. The new coupler designs are fabricated from polytetrafluorethylene (PTFE) rods and operate through forward scattering of incident sunlight on the front surfaces of the structure into an optic fibre located in a cavity to the rear of the structure. The PTFE couplers exhibit up to 4.8% variation in scattered transmission intensity between 425 nm and 700 nm and show minimal specular reflection, making the designs accurate and reliable over the visible region. Through careful geometric optimization near perfect cosine dependence on the angular response of the coupler can be achieved. The PTFE designs represent a significant improvement over the state of the art with less than 0.01% error compared with ideal cosine response for angles of incidence up to 50°.

  8. Analysis of NN amplitudes up to 2.5 GeV: an optical model and geometric interpretation

    International Nuclear Information System (INIS)

    Geramb, H.V. von; Universitaet Hamburg, Hamburg,; Amos, K.A.; Labes, H.; Sander, M.

    1998-01-01

    We analyse the SM97 partial wave amplitudes for nucleon-nucleon (NN) scattering to 2.5 GeV, in which resonance and meson production effects are evident for energies above pion production threshold. Our analyses are based upon boson exchange or quantum inversion potentials with which the sub-threshold data are fit perfectly. Above 300 MeV they are extrapolations, to which complex short ranged Gaussian potentials are added in the spirit of the optical models of nuclear physics and of diffraction models of high energy physics. The data to 2.5 GeV are all well fit. The energy dependences of these Gaussians are very smooth save for precise effects caused by the known Δ and N* resonances. With this approach, we confirm that the geometrical implications of the profile function found from diffraction scattering are pertinent in the regime 300 MeV to 2.5 GeV and that the overwhelming part of meson production comes from the QCD sector of the nucleons when they have a separation of their centres of 1 to 1.2 fm. This analysis shows that the elastic NN scattering data above 300 MeV can be understood with a local potential operator as well as has the data below 300 MeV

  9. Cartesian oval representation of freeform optics in illumination systems.

    Science.gov (United States)

    Michaelis, D; Schreiber, P; Bräuer, A

    2011-03-15

    The geometrical method for constructing optical surfaces for illumination purpose developed by Oliker and co-workers [Trends in Nonlinear Analysis (Springer, 2003)] is generalized in order to obtain freeform designs in arbitrary optical systems. The freeform is created by a set of primitive surface elements, which are generalized Cartesian ovals adapted to the given optical system. Those primitives are determined by Hamiltonian theory of ray optics. The potential of this approach is demonstrated by some examples, e.g., freeform lenses with collimating front elements.

  10. Geometrically unrestricted, topologically constrained control of liquid crystal defects using simultaneous holonomic magnetic and holographic optical manipulation

    Science.gov (United States)

    Varney, Michael C. M.; Jenness, Nathan J.; Smalyukh, Ivan I.

    2014-02-01

    Despite the recent progress in physical control and manipulation of various condensed matter, atomic, and particle systems, including individual atoms and photons, our ability to control topological defects remains limited. Recently, controlled generation, spatial translation, and stretching of topological point and line defects have been achieved using laser tweezers and liquid crystals as model defect-hosting systems. However, many modes of manipulation remain hindered by limitations inherent to optical trapping. To overcome some of these limitations, we integrate holographic optical tweezers with a magnetic manipulation system, which enables fully holonomic manipulation of defects by means of optically and magnetically controllable colloids used as "handles" to transfer forces and torques to various liquid crystal defects. These colloidal handles are magnetically rotated around determined axes and are optically translated along three-dimensional pathways while mechanically attached to defects, which, combined with inducing spatially localized nematic-isotropic phase transitions, allow for geometrically unrestricted control of defects, including previously unrealized modes of noncontact manipulation, such as the twisting of disclination clusters. These manipulation capabilities may allow for probing topological constraints and the nature of defects in unprecedented ways, providing the foundation for a tabletop laboratory to expand our understanding of the role defects play in fields ranging from subatomic particle physics to early-universe cosmology.

  11. Differential algebraic method for arbitrary order curvilinear-axis combined geometric-chromatic aberration analysis

    International Nuclear Information System (INIS)

    Cheng Min; Tang Tiantong; Lu Yilong; Yao Zhenhua

    2003-01-01

    The principle of differential algebra is applied to analyse and calculate arbitrary order curvilinear-axis combined geometric-chromatic aberrations of electron optical systems. Expressions of differential algebraic form of high order combined aberrations are obtained and arbitrary order combined aberrations can be calculated numerically. As an example, a typical wide electron beam focusing system with curved optical axes named magnetic immersion lens has been studied. All the second-order and third-order combined geometric-chromatic aberrations of the lens have been calculated, and the patterns of the corresponding geometric aberrations and combined aberrations have been given as well

  12. Geometric metamorphosis.

    Science.gov (United States)

    Niethammer, Marc; Hart, Gabriel L; Pace, Danielle F; Vespa, Paul M; Irimia, Andrei; Van Horn, John D; Aylward, Stephen R

    2011-01-01

    Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient.

  13. Geometric Approaches to Quadratic Equations from Other Times and Places.

    Science.gov (United States)

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  14. Lidar inelastic multiple-scattering parameters of cirrus particle ensembles determined with geometrical-optics crystal phase functions.

    Science.gov (United States)

    Reichardt, J; Hess, M; Macke, A

    2000-04-20

    Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5-0.7 followed by a gradual and monotonic decrease to 0.1-0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect hexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height, and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.

  15. Asymptotic and geometrical quantization

    International Nuclear Information System (INIS)

    Karasev, M.V.; Maslov, V.P.

    1984-01-01

    The main ideas of geometric-, deformation- and asymptotic quantizations are compared. It is shown that, on the one hand, the asymptotic approach is a direct generalization of exact geometric quantization, on the other hand, it generates deformation in multiplication of symbols and Poisson brackets. Besides investigating the general quantization diagram, its applications to the calculation of asymptotics of a series of eigenvalues of operators possessing symmetry groups are considered

  16. Fundamentals and techniques of nonimaging optics research at the University of Chicago

    Science.gov (United States)

    Winston, R.; Ogallagher, J.

    1986-11-01

    Nonimaging Optics differs from conventional approaches in its relaxation of unnecessary constraints on energy transport imposed by the traditional methods for optimizing image formation and its use of more broadly based analytical techniques such as phase space representations of energy flow, radiative transfer analysis, thermodynamic arguments, etc. Based on these means, techniques for designing optical elements which approach and in some cases attain the maximum concentration permitted by the Second Law of Thermodynamics were developed. The most widely known of these devices are the family of Compound Parabolic Concentrators (CPC's) and their variants and the so called Flow-Line concentrator derived from the geometric vector flux formalism developed under this program. Applications of these and other such ideal or near-ideal devices permits increases of typically a factor of four (though in some cases as much as an order of magnitude) in the concentration above that possible with conventional means. In the most recent phase, our efforts can be classed into two main areas; (a) ''classical'' geometrical nonimaging optics; and (b) logical extensions of nonimaging concepts to the physical optics domain.

  17. Optics and geometric characterization of cirrus from Lille lidar measurements over the period 2008-2013

    International Nuclear Information System (INIS)

    Nohra, R.; Parol, F.; Dubuisson

    2015-01-01

    The aim of this work is the detection and characterization of cirrus clouds from ground-based lidar measurements acquired at 532 nm wave length. An inversion method has been developed during this work to realize a climatologyof cirrus clouds over Lille, France (50.65°N, 3.08ºE) from 2008 to 2013. The mid-cloud height is generally observed between 7 and 13 km, and a mean thickness is found to be 1.4 ±0.8 km. Visibleclouds, characterized by anoptical thickness between 0.03 and 0.3, present 68 % of the total observed cirrus clouds. The methodology used in this work andthe retrieved geometrical and optical parameters of cirrus clouds are presented in this article. (author)

  18. Geometric approach to soliton equations

    International Nuclear Information System (INIS)

    Sasaki, R.

    1979-09-01

    A class of nonlinear equations that can be solved in terms of nxn scattering problem is investigated. A systematic geometric method of exploiting conservation laws and related equations, the so-called prolongation structure, is worked out. The nxn problem is reduced to nsub(n-1)x(n-1) problems and finally to 2x2 problems, which have been comprehensively investigated recently by the author. A general method of deriving the infinite numbers of polynomial conservation laws for an nxn problem is presented. The cases of 3x3 and 2x2 problems are discussed explicitly. (Auth.)

  19. Non-geometrical optics investigation of mode conversion in weakly relativistic inhomogeneous plasmas

    International Nuclear Information System (INIS)

    Imre, K.

    1985-06-01

    Electron cyclotron resonance heating of plasmas by waves incident to the fundamental and second harmonic layer is investigated. When the wave propagation is nearly perpendicular to the equilibrium field in a weakly inhomogeneous plasma the standard geometrical optics breaks down and the relativistic corrections become significant at the resonance layer. Unlike the previous studies of this problem, the governing equations are derived from the linearized relativistic Vlasov equation coupled with Maxwell's equations, rather than using the uniform field dispersion relation to construct equations by replacing the refractive index by some spatial differential operations. We employ a boundary layer analysis at the resonance region and match the inner and outer solutions in the usual manner. We obtain not only the full wave solution of the problem, but also the set of physical parameters and their ranges in which the analysis is valid. Although we obtain analytic results for the asymptotic solutions, our analysis usually requires a numerical procedure when the relativistic and/or nonzero parallel refractive index are included

  20. Calculating the bidirectional reflectance of natural vegetation covers using Boolean models and geometric optics

    Science.gov (United States)

    Strahler, Alan H.; Li, Xiao-Wen; Jupp, David L. B.

    1991-01-01

    The bidirectional radiance or reflectance of a forest or woodland can be modeled using principles of geometric optics and Boolean models for random sets in a three dimensional space. This model may be defined at two levels, the scene includes four components; sunlight and shadowed canopy, and sunlit and shadowed background. The reflectance of the scene is modeled as the sum of the reflectances of the individual components as weighted by their areal proportions in the field of view. At the leaf level, the canopy envelope is an assemblage of leaves, and thus the reflectance is a function of the areal proportions of sunlit and shadowed leaf, and sunlit and shadowed background. Because the proportions of scene components are dependent upon the directions of irradiance and exitance, the model accounts for the hotspot that is well known in leaf and tree canopies.

  1. A Circumzenithal Arc to Study Optics Concepts with Geometrical Optics

    Science.gov (United States)

    Isik, Hakan

    2017-01-01

    This paper describes the formation of a circumzenithal arc for the purpose of teaching light and optics. A circumzenithal arc, an optic formation rarely witnessed by people, is formed in this study using a water-filled cylindrical glass illuminated by sunlight. Sunlight refracted at the top and side surfaces of the glass of water is dispersed into…

  2. Different optical properties in different periodic slot cavity geometrical morphologies

    Science.gov (United States)

    Zhou, Jing; Shen, Meng; Du, Lan; Deng, Caisong; Ni, Haibin; Wang, Ming

    2016-09-01

    In this paper, optical properties of two-dimensional periodic annular slot cavity arrays in hexagonal close-packing on a silica substrate are theoretically characterized by finite difference time domain (FDTD) simulation method. By simulating reflectance spectra, electric field distribution, and charge distribution, we confirm that multiple cylindrical surface plasmon resonances can be excited in annular inclined slot cavities by linearly polarized light, in which the four reflectance dips are attributed to Fabry-Perot cavity resonances in the coaxial cavity. A coaxial waveguide mode TE11 will exist in these annular cavities, and the wavelengths of these reflectance dips are effectively tailored by changing the geometrical pattern of slot cavity and the dielectric materials filled in the cavities. These resonant wavelengths are localized in annular cavities with large electric field enhancement and dissipate gradually due to metal loss. The formation of an absorption peak can be explained from the aspect of phase matching conditions. We observed that the proposed structure can be tuned over the broad spectral range of 600-4000 nm by changing the outer and inner radii of the annular gaps, gap surface topography. Meanwhile, different lengths of the cavity may cause the shift of resonance dips. Also, we study the field enhancement at different vertical locations of the slit. In addition, dielectric materials filling in the annular gaps will result in a shift of the resonance wavelengths, which make the annular cavities good candidates for refractive index sensors. The refractive index sensitivity of annular cavities can also be tuned by the geometry size and the media around the cavity. Annular cavities with novel applications can be implied as surface enhanced Raman spectra substrates, refractive index sensors, nano-lasers, and optical trappers. Project supported by the National Natural Science Foundation of China (Grant No. 61178044), the Natural Science Foundation

  3. Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

    International Nuclear Information System (INIS)

    Ichinose, Shoichi

    2010-01-01

    A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean coordinate system (X i ,τ) as the quantum statistical system of N quantum (statistical) variables (X τ ) and one Euclidean time variable (t). Introducing paths (lines or hypersurfaces) in this space (X τ ,t), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the mechanical system. The system Hamiltonian appears as the area. We show quantization is realized by the minimal area principle in the present geometric approach. When we take a line as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a hyper-surface as the path, the system Hamiltonian is given by the area of the hyper-surface which is defined as a closed-string configuration in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.

  4. Transmission properties of a single metallic slit: from the subwavelength regime to the geometrical-optics limit.

    Science.gov (United States)

    Bravo-Abad, J; Martín-Moreno, L; García-Vidal, F J

    2004-02-01

    In this work we explore the transmission properties of a single slit in a metallic screen. We analyze the dependence of these properties on both slit width and angle of incident radiation. We study in detail the crossover between the subwavelength regime and the geometrical-optics limit. In the subwavelength regime, resonant transmission linked to the excitation of waveguide resonances is analyzed. Linewidth of these resonances and their associated electric-field intensities are controlled by just the width of the slit. More complex transmission spectra appear when the wavelength of light is comparable to the slit width. Rapid oscillations associated with the emergence of different propagating modes inside the slit are the main features appearing in this regime.

  5. Geometric approach to the design of an imaging probe to evaluate the iridocorneal angle structures

    Science.gov (United States)

    Hong, Xun Jie Jeesmond; V. K., Shinoj; Murukeshan, V. M.; Baskaran, M.; Aung, Tin

    2017-06-01

    Photographic imaging methods allow the tracking of anatomical changes in the iridocorneal angle structures and the monitoring of treatment responses overtime. In this work, we aim to design an imaging probe to evaluate the iridocorneal angle structures using geometrical optics. We first perform an analytical analysis on light propagation from the anterior chamber of the eye to the exterior medium using Snell's law. This is followed by adopting a strategy to achieve uniform near field irradiance, by simplifying the complex non-rotational symmetric irradiance distribution of LEDs tilted at an angle. The optimization is based on the geometric design considerations of an angled circular ring array of 4 LEDs (or a 2 × 2 square LED array). The design equation give insights on variable parameters such as the illumination angle of the LEDs, ring array radius, viewing angle of the LEDs, and the working distance. A micro color CCD video camera that has sufficient resolution to resolve the iridocorneal angle structures at the required working distance is then chosen. The proposed design aspects fulfil the safety requirements recommended by the International Commission on Non-ionizing Radiation Protection.

  6. Geometrical methods for power network analysis

    Energy Technology Data Exchange (ETDEWEB)

    Bellucci, Stefano; Tiwari, Bhupendra Nath [Istituto Nazioneale di Fisica Nucleare, Frascati, Rome (Italy). Lab. Nazionali di Frascati; Gupta, Neeraj [Indian Institute of Technology, Kanpur (India). Dept. of Electrical Engineering

    2013-02-01

    Uses advanced geometrical methods to analyse power networks. Provides a self-contained and tutorial introduction. Includes a fully worked-out example for the IEEE 5 bus system. This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.

  7. Finsler metrics—a global approach with applications to geometric function theory

    CERN Document Server

    Abate, Marco

    1994-01-01

    Complex Finsler metrics appear naturally in complex analysis. To develop new tools in this area, the book provides a graduate-level introduction to differential geometry of complex Finsler metrics. After reviewing real Finsler geometry stressing global results, complex Finsler geometry is presented introducing connections, Kählerianity, geodesics, curvature. Finally global geometry and complex Monge-Ampère equations are discussed for Finsler manifolds with constant holomorphic curvature, which are important in geometric function theory. Following E. Cartan, S.S. Chern and S. Kobayashi, the global approach carries the full strength of hermitian geometry of vector bundles avoiding cumbersome computations, and thus fosters applications in other fields.

  8. Three-dimensional inverse problem of geometrical optics: a mathematical comparison between Fermat's principle and the eikonal equation.

    Science.gov (United States)

    Borghero, Francesco; Demontis, Francesco

    2016-09-01

    In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c1,g(x,y,z)=c2), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.

  9. Laboratory testing & measurement on optical imaging systems

    CSIR Research Space (South Africa)

    Theron, B

    2013-04-01

    Full Text Available on Optical Imaging Systems Bertus Theron 27 April 2013 presented at SIECPC 2013, Riyadh, Saudi Arabia Overview of Workshop Part 1. Introduction & Context  Some history of Arabic Optics  Context: Global vs Local optical testing... of Arabic Optics 1 See [4]  Arabic records of study of geometrical optics  Traced to Hellenistic (Greek) optics  Translated to Arabic  9th century  Arabic contribution to geometric optics  Not just translation to Arabic  Innovative research...

  10. Shaping up: a geometric morphometric approach to assemblage ecomorphology.

    Science.gov (United States)

    Bower, L M; Piller, K R

    2015-09-01

    This study adopts an ecomorphological approach to test the utility of body shape as a predictor of niche relationships among a stream fish assemblage of the Tickfaw River (Lake Pontchartrain Basin) in southeastern Louisiana, U.S.A. To examine the potential influence of evolutionary constraints, analyses were performed with and without the influence of phylogeny. Fish assemblages were sampled throughout the year, and ecological data (habitat and tropic guild) and body shape (geometric morphometric) data were collected for each fish specimen. Multivariate analyses were performed to examine relationships and differences between body shape and ecological data. Results indicate that a relationship exists between body shape and trophic guild as well as flow regime, but no significant correlation between body shape and substratum was found. Body shape was a reliable indicator of position within assemblage niche space. © 2015 The Fisheries Society of the British Isles.

  11. Ventricular dyssynchrony assessed by gated myocardial perfusion SPECT using a geometrical approach: a feasibility study

    International Nuclear Information System (INIS)

    Veen, Berlinda J. van der; Younis, Imad Al; Ajmone-Marsan, Nina; Bax, Jeroen J.; Westenberg, Jos J.M.; Roos, Albert de; Stokkel, Marcel P.M.

    2012-01-01

    Left ventricular dyssynchrony may predict response to cardiac resynchronization therapy and may well predict adverse cardiac events. Recently, a geometrical approach for dyssynchrony analysis of myocardial perfusion scintigraphy (MPS) was introduced. In this study the feasibility of this geometrical method to detect dyssynchrony was assessed in a population with a normal MPS and in patients with documented ventricular dyssynchrony. For the normal population 80 patients (40 men and 40 women) with normal perfusion (summed stress score ≤2 and summed rest score ≤2) and function (left ventricular ejection fraction 55-80%) on MPS were selected; 24 heart failure patients with proven dyssynchrony on MRI were selected for comparison. All patients underwent a 2-day stress/rest MPS protocol. Perfusion, function and dyssynchrony parameters were obtained by the Corridor4DM software package (Version 6.1). For the normal population time to peak motion was 42.8 ± 5.1% RR cycle, SD of time to peak motion was 3.5 ± 1.4% RR cycle and bandwidth was 18.2 ± 6.0% RR cycle. No significant gender-related differences or differences between rest and post-stress acquisition were found for the dyssynchrony parameters. Discrepancies between the normal and abnormal populations were most profound for the mean wall motion (p value <0.001), SD of time to peak motion (p value <0.001) and bandwidth (p value <0.001). It is feasible to quantify ventricular dyssynchrony in MPS using the geometrical approach as implemented by Corridor4DM. (orig.)

  12. Proportional-delayed controllers design for LTI-systems: a geometric approach

    Science.gov (United States)

    Hernández-Díez, J.-E.; Méndez-Barrios, C.-F.; Mondié, S.; Niculescu, S.-I.; González-Galván, E. J.

    2018-04-01

    This paper focuses on the design of P-δ controllers for single-input-single-output linear time-invariant systems. The basis of this work is a geometric approach allowing to partitioning the parameter space in regions with constant number of unstable roots. This methodology defines the hyper-planes separating the aforementioned regions and characterises the way in which the number of unstable roots changes when crossing such a hyper-plane. The main contribution of the paper is that it provides an explicit tool to find P-δ gains ensuring the stability of the closed-loop system. In addition, the proposed methodology allows to design a non-fragile controller with a desired exponential decay rate σ. Several numerical examples illustrate the results and a haptic experimental set-up shows the effectiveness of P-δ controllers.

  13. Micro-taper as focusing or scattering optical element

    Energy Technology Data Exchange (ETDEWEB)

    Degtyarev, S. A., E-mail: sealek@gmail.com; Ustinov, A. V., E-mail: andr@smr.ru; Khonina, S. N., E-mail: khonina@smr.ru [Samara State Aerospace University, Moskovskoye Shosse 34, Samara, Russia, 443086 (Russian Federation); Imaging Processing Systems Institute of the Russian Academy of Science, Molodogvardeyskaya street, 151, Samara, Russia, 443001 (Russian Federation)

    2016-04-13

    We consider micro-taper (narrow refractive axicon) as optical element which is focusing or scattering in dependence on axicon’s cone angle. The diffraction of laser beam by micro-taper is simulated by two methods: multiply internal ray reflections using geometrical approach and Helmholtz equation solving using finite elements method. Based on ray optics we derive analytic formulas for conical angles values which provide focusing or scattering features of micro-taper. Numerical simulation by finite elements method verifies theoretical results.

  14. A Geometric Fuzzy-Based Approach for Airport Clustering

    Directory of Open Access Journals (Sweden)

    Maria Nadia Postorino

    2014-01-01

    Full Text Available Airport classification is a common need in the air transport field due to several purposes—such as resource allocation, identification of crucial nodes, and real-time identification of substitute nodes—which also depend on the involved actors’ expectations. In this paper a fuzzy-based procedure has been proposed to cluster airports by using a fuzzy geometric point of view according to the concept of unit-hypercube. By representing each airport as a point in the given reference metric space, the geometric distance among airports—which corresponds to a measure of similarity—has in fact an intrinsic fuzzy nature due to the airport specific characteristics. The proposed procedure has been applied to a test case concerning the Italian airport network and the obtained results are in line with expectations.

  15. Geometric inequalities methods of proving

    CERN Document Server

    Sedrakyan, Hayk

    2017-01-01

    This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities. .

  16. A differential-geometric approach to generalized linear models with grouped predictors

    NARCIS (Netherlands)

    Augugliaro, Luigi; Mineo, Angelo M.; Wit, Ernst C.

    We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important

  17. Flow line asymmetric nonimaging concentrating optics

    Science.gov (United States)

    Jiang, Lun; Winston, Roland

    2016-09-01

    Nonimaging Optics has shown that it achieves the theoretical limits by utilizing thermodynamic principles rather than conventional optics. Hence in this paper the condition of the "best" design are both defined and fulfilled in the framework of thermodynamic arguments, which we believe has profound consequences for the designs of thermal and even photovoltaic systems, even illumination and optical communication tasks. This new way of looking at the problem of efficient concentration depends on probabilities, geometric flux field and radiative heat transfer while "optics" in the conventional sense recedes into the background. Some of the new development of flow line designs will be introduced and the connection between the thermodynamics and flow line design will be officially formulated in the framework of geometric flux field. A new way of using geometric flux to design nonimaging optics will be introduced. And finally, we discuss the possibility of 3D ideal nonimaing optics.

  18. Geometrical Approach to the Grid System in the KOPEC Pilot Code

    International Nuclear Information System (INIS)

    Lee, E. J.; Park, C. E.; Lee, S. Y.

    2008-01-01

    KOPEC has been developing a pilot code to analyze two phase flow. The earlier version of the pilot code adopts the geometry with one-dimensional structured mesh system. As the pilot code is required to handle more complex geometries, a systematic geometrical approach to grid system has been introduced. Grid system can be classified as two types; structured grid system and unstructured grid system. The structured grid system is simple to apply but is less flexible than the other. The unstructured grid system is more complicated than the structured grid system. But it is more flexible to model the geometry. Therefore, two types of grid systems are utilized to allow code users simplicity as well as the flexibility

  19. Geometric Programming Approach to an Interactive Fuzzy Inventory Problem

    Directory of Open Access Journals (Sweden)

    Nirmal Kumar Mandal

    2011-01-01

    Full Text Available An interactive multiobjective fuzzy inventory problem with two resource constraints is presented in this paper. The cost parameters and index parameters, the storage space, the budgetary cost, and the objective and constraint goals are imprecise in nature. These parameters and objective goals are quantified by linear/nonlinear membership functions. A compromise solution is obtained by geometric programming method. If the decision maker is not satisfied with this result, he/she may try to update the current solution to his/her satisfactory solution. In this way we implement man-machine interactive procedure to solve the problem through geometric programming method.

  20. Investigation of the Geometrical Distortions in the Nuclear Emulsion

    International Nuclear Information System (INIS)

    Batusov, Yu.A.; Rumyantseva, V.P.; Soroko, L.M.; Tereshchenko, V.V.

    1994-01-01

    The geometrical distortions in the nuclear emulsion were investigated by means of two devices: 1) stereoscopic meso-optical Fourier transform microscope (MFTM) and 2) traditional optical microscope (KSM-1) designed for precise measurements. The particle tracks were produced by primary Oxygen-nuclei with impulse 65.6 GeV/c and by secondary α-particles in various regions of the nuclear emulsion. The measurement errors were: 1.8' (angular minute) for orientation angle θ xy ; 2.7' (angular minute) for dip angle θ z ; 0.3 μm for transverse coordinate x; 0.1 μm for longitudinal coordinate y and 0.3 μm for depth coordinate z. The effect of the global forced bending of the nuclear emulsion glass support was detected and estimated as dθ z /dy=2' (angular minute) per mm. To suppress the local geometrical distortions, a difference plot was calculated for two secondary α-particles going very close within ≤ 10 μm over the distance 6 mm. It was shown that this mode of the local geometrical distortions is kept constant over the mutual transverse distances up to 0.6 mm. By observing the zy-plots of four secondary α-particles we have isolated the rotating mode of the local geometrical distortions in the nuclear emulsion. 5 refs., 11 figs

  1. Operational geometric phase for mixed quantum states

    International Nuclear Information System (INIS)

    Andersson, O; Heydari, H

    2013-01-01

    The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics. (paper)

  2. Teaching Mathematical Functions Using Geometric Functions Approach and Its Effect on Ninth Grade Students' Motivation

    Science.gov (United States)

    Akçakin, Veysel

    2018-01-01

    The purpose of this study is to investigate the effects of using geometric functions approach on 9th grade students' motivation levels toward mathematics in functions unit. Participants of this study were 87 students who were ongoing in the first year of high school in Turkey. In this research, pretest and posttest control group quasiexperimental…

  3. From the geometric quantization to conformal field theory

    International Nuclear Information System (INIS)

    Alekseev, A.; Shatashvili, S.

    1990-01-01

    Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant) r-matrices and this geometrical approach. (orig.)

  4. Lorentz Invariance Violation effects on UHECR propagation: A geometrized approach

    Science.gov (United States)

    Torri, Marco Danilo Claudio; Bertini, Stefano; Giammarchi, Marco; Miramonti, Lino

    2018-06-01

    We explore the possibility to geometrize the interaction of massive fermions with the quantum structure of space-time, trying to create a theoretical background, in order to explain what some recent experimental results seem to implicate on the propagation of Ultra High Energy Cosmic Rays (UHECR). We will investigate part of the phenomenological implications of this approach on the predicted effect of the UHECR suppression, in fact recent evidences seem to involve the modification of the GZK cut-off phenomenon. The search for an effective theory, which can explain this physical effect, is based on Lorentz Invariance Violation (LIV), which is introduced via Modified Dispersion Relations (MDRs). Furthermore we illustrate that this perspective implies a more general geometry of space-time than the usual Riemannian one, indicating, for example, the opportunity to resort to Finsler theory.

  5. Laser-induced stimulated Raman scattering in the forward direction of a droplet - Comparison of Mie theory with geometrical optics

    Science.gov (United States)

    Srivastava, Vandana; Jarzembski, Maurice A.

    1991-01-01

    This paper uses Mie theory to treat electromagnetic scattering and to evaluate field enhancement in the forward direction of a small droplet irradiated by a high-energy beam and compares the results of calculations with the field-enhancement evaluation obtained via geometrical optics treatment. Results of this comparison suggest that the field enhancement located at the critical ring region encircling the axis in the forward direction of the droplet can support laser-induced Raman scattering. The results are supported by experimental observations of the interaction of a 120-micron-diam water droplet with a high-energy Nd:YAG laser beam.

  6. Urbanisation and 3d Spatial - a Geometric Approach

    Science.gov (United States)

    Duncan, E. E.; Rahman, A. Abdul

    2013-09-01

    Urbanisation creates immense competition for space, this may be attributed to an increase in population owing to domestic and external tourism. Most cities are constantly exploring all avenues in maximising its limited space. Hence, urban or city authorities need to plan, expand and use such three dimensional (3D) space above, on and below the city space. Thus, difficulties in property ownership and the geometric representation of the 3D city space is a major challenge. This research, investigates the concept of representing a geometric topological 3D spatial model capable of representing 3D volume parcels for man-made constructions above and below the 3D surface volume parcel. A review of spatial data models suggests that the 3D TIN (TEN) model is significant and can be used as a unified model. The concepts, logical and physical models of 3D TIN for 3D volumes using tetrahedrons as the base geometry is presented and implemented to show man-made constructions above and below the surface parcel within a user friendly graphical interface. Concepts for 3D topology and 3D analysis are discussed. Simulations of this model for 3D cadastre are implemented. This model can be adopted by most countries to enhance and streamline geometric 3D property ownership for urban centres. 3D TIN concept for spatial modelling can be adopted for the LA_Spatial part of the Land Administration Domain Model (LADM) (ISO/TC211, 2012), this satisfies the concept of 3D volumes.

  7. The undergraduate optics course at Millersville University

    Science.gov (United States)

    Gilani, Tariq H.; Dushkina, Natalia M.

    2009-06-01

    For many years, there was no stand alone course in optics at Millersville University (MU). In the fall of 2007, the Physics Department offered for the first time PHYS 331: Fundamentals in Optics, a discovery based lab course in geometrical, physical and modern optics. This 300-level, 2 credits course consists of four contact hours per week including one-hour lecture and three hours laboratory. This course is required for BS in physics majors, but is open also to other science majors, who have the appropriate background and have met the prerequisites. This course deals with fundamental optics and optical techniques in greater depth so that the student is abreast of the activities in the forefront of the field. The goal of the course is to provide hands-on experience and in-depth preparation of our students for graduate programs in optics or as a workforce for new emerging high-tech local industries. Students learn applied optics through sequence of discovery based laboratory experiments chosen from a broad range of topics in optics and lasers, as the emphasis is on geometrical optics, geometrical aberrations in optical systems, wave optics, microscopy, spectroscopy, polarization, birefringence, laser generation, laser properties and applications, and optical standards. The peer-guided but open-ended approach provides excellent practice for the academic model of science research. Solving problems is embedded in the laboratory part as an introduction to or a conclusion of the experiment performed during the lab period. The homework problems are carefully chosen to reflect the most important relations from the covered material. Important part of the student learning strategy is the individual work on a final mini project which is presented in the class and is included in the final grading. This new course also impacted the department's undergraduate research and training programs. Some of the individual projects were extended to senior research projects in optics as

  8. Optical properties of polarization-dependent geometrical phase elements with partially polarized light

    International Nuclear Information System (INIS)

    Gorodetski, Y.; Biener, G.; Niv, A.; Kleiner, V.; Hasman, E.

    2005-01-01

    Full Text:The behavior of geometrical phase elements illuminated with partially polarized monochromatic beams is being theoretically as well as experimentally investigated. The element discussed in this paper is composed of wave plates with retardation and space-variant orientation angle. We found that a beam emerging from such an element comprises two polarization orders of right and left-handed circularly polarized states with conjugate geometrical phase modification. This phase equals twice the orientation angle of the space-variant wave plate comprising the element. Apart from the two polarization orders, the emerging beam coherence polarization matrix comprises a matrix termed as the vectorial interference matrix. This matrix contains the information concerning the correlation between the two orthogonal circularly polarized portions of the incident beam. In this paper we measure this correlation by a simple interference experiment. Furthermore, we found that the equivalent mutual intensity of the emerging beam is being modulated according to the geometrical phase induced by the element. Other interesting phenomena along propagation will be discussed theoretically and experimentally demonstrated. We demonstrate experimentally our analysis by using a spherical geometrical phase element, which is realized by use of space-variant sub wavelength grating and illuminated with a CO 2 laser radiation of 10.6μm wavelength

  9. Material inhomogeneities and their evolution a geometric approach

    CERN Document Server

    Epstein, Marcelo

    2007-01-01

    Presents a unified treatment of the inhomogeneity theory using some of the tools of modern differential geometry. This book deals with the geometrical description of uniform bodies and their homogeneity conditions. It also develops a theory of material evolution and discusses its relevance in various applied contexts.

  10. An algebraic geometric approach to separation of variables

    CERN Document Server

    Schöbel, Konrad

    2015-01-01

    Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.”   (Jim Stasheff)   Contents The Foundation: The Algebraic Integrability Conditions The Proof of Concept: A Complete Solution for the 3-Sphere The Generalisation: A Solution for Spheres of Arbitrary Dimension The Perspectives: Applications and Generalisations   Target Groups Scientists in the fie...

  11. Modifying Geometric-Optical Bidirectional Reflectance Model for Direct Inversion of Forest Canopy Leaf Area Index

    Directory of Open Access Journals (Sweden)

    Congrong Li

    2015-08-01

    Full Text Available Forest canopy leaf area index (LAI inversion based on remote sensing data is an important method to obtain LAI. Currently, the most widely-used model to achieve forest canopy structure parameters is the Li-Strahler geometric-optical bidirectional reflectance model, by considering the effect of crown shape and mutual shadowing, which is referred to as the GOMS model. However, it is difficult to retrieve LAI through the GOMS model directly because LAI is not a fundamental parameter of the model. In this study, a gap probability model was used to obtain the relationship between the canopy structure parameter nR2 and LAI. Thus, LAI was introduced into the GOMS model as an independent variable by replacing nR2 The modified GOMS (MGOMS model was validated by application to Dayekou in the Heihe River Basin of China. The LAI retrieved using the MGOMS model with optical multi-angle remote sensing data, high spatial resolution images and field-measured data was in good agreement with the field-measured LAI, with an R-square (R2 of 0.64, and an RMSE of 0.67. The results demonstrate that the MGOMS model obtained by replacing the canopy structure parameter nR2 of the GOMS model with LAI can be used to invert LAI directly and precisely.

  12. Capacity-Approaching Superposition Coding for Optical Fiber Links

    DEFF Research Database (Denmark)

    Estaran Tolosa, Jose Manuel; Zibar, Darko; Tafur Monroy, Idelfonso

    2014-01-01

    We report on the first experimental demonstration of superposition coded modulation (SCM) for polarization-multiplexed coherent-detection optical fiber links. The proposed coded modulation scheme is combined with phase-shifted bit-to-symbol mapping (PSM) in order to achieve geometric and passive......-SCM) is employed in the framework of bit-interleaved coded modulation with iterative decoding (BICM-ID) for forward error correction. The fiber transmission system is characterized in terms of signal-to-noise ratio for back-to-back case and correlated with simulated results for ideal transmission over additive...... white Gaussian noise channel. Thereafter, successful demodulation and decoding after dispersion-unmanaged transmission over 240-km standard single mode fiber of dual-polarization 6-Gbaud 16-, 32- and 64-ary SCM-PSM is experimentally demonstrated....

  13. Geometric control theory and sub-Riemannian geometry

    CERN Document Server

    Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

    2014-01-01

    This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.

  14. Geometric Form Drawing: A Perceptual-Motor Approach to Preventive Remediation (The Steiner Approach)

    Science.gov (United States)

    Ogletree, Earl J.

    1975-01-01

    Provided is a rationale for geometric form drawing developed by Rudolf Steiner as a tool to develop motor coordination, perceptual skills, and cognition for mentally retarded and perceptually handicapped children. (Author/CL)

  15. Noncritical String Liouville Theory and Geometric Bootstrap Hypothesis

    Science.gov (United States)

    Hadasz, Leszek; Jaskólski, Zbigniew

    The applications of the existing Liouville theories for the description of the longitudinal dynamics of noncritical Nambu-Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition — the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularities.

  16. A new approach toward geometrical concept of black hole thermodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Hendi, Seyed Hossein [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Panahiyan, Shahram; Panah, Behzad Eslam; Momennia, Mehrab [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)

    2015-10-15

    Motivated by the energy representation of Riemannian metric, in this paper we study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solve these problems. We show that the denominator of the Ricci scalar of the new metric contains terms which coincide with different types of phase transitions. We elaborate the effectiveness of the new metric and shortcomings of the previous metrics with some examples. Furthermore, we find a characteristic behavior of the new thermodynamical Ricci scalar which enables one to distinguish two types of phase transitions. In addition, we generalize the new metric for the cases of more than two extensive parameters and show that in these cases the divergencies of thermodynamical Ricci scalar coincide with phase transition points of the heat capacity. (orig.)

  17. A new approach toward geometrical concept of black hole thermodynamics

    International Nuclear Information System (INIS)

    Hendi, Seyed Hossein; Panahiyan, Shahram; Panah, Behzad Eslam; Momennia, Mehrab

    2015-01-01

    Motivated by the energy representation of Riemannian metric, in this paper we study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solve these problems. We show that the denominator of the Ricci scalar of the new metric contains terms which coincide with different types of phase transitions. We elaborate the effectiveness of the new metric and shortcomings of the previous metrics with some examples. Furthermore, we find a characteristic behavior of the new thermodynamical Ricci scalar which enables one to distinguish two types of phase transitions. In addition, we generalize the new metric for the cases of more than two extensive parameters and show that in these cases the divergencies of thermodynamical Ricci scalar coincide with phase transition points of the heat capacity. (orig.)

  18. Asymptotic geometric analysis, part I

    CERN Document Server

    Artstein-Avidan, Shiri

    2015-01-01

    The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen

  19. Estimation of Dynamic Errors in Laser Optoelectronic Dimension Gauges for Geometric Measurement of Details

    Directory of Open Access Journals (Sweden)

    Khasanov Zimfir

    2018-01-01

    Full Text Available The article reviews the capabilities and particularities of the approach to the improvement of metrological characteristics of fiber-optic pressure sensors (FOPS based on estimation estimation of dynamic errors in laser optoelectronic dimension gauges for geometric measurement of details. It is shown that the proposed criteria render new methods for conjugation of optoelectronic converters in the dimension gauge for geometric measurements in order to reduce the speed and volume requirements for the Random Access Memory (RAM of the video controller which process the signal. It is found that the lower relative error, the higher the interrogetion speed of the CCD array. It is shown that thus, the maximum achievable dynamic accuracy characteristics of the optoelectronic gauge are determined by the following conditions: the parameter stability of the electronic circuits in the CCD array and the microprocessor calculator; linearity of characteristics; error dynamics and noise in all electronic circuits of the CCD array and microprocessor calculator.

  20. Nonimaging optics

    Science.gov (United States)

    Winston, Roland

    1991-03-01

    Various uses of nonimaging concentrators and advances in the field of nonimaging optics are discussed. A nonimaging concentrator acts as a type of funnel for light by collecting and intensifying radiation far better than a lens or mirror would. It thus has found useful applications in fields ranging from high-energy physics to solar energy. The history of the field of nonimaging optics is traced, beginning with the design of the first compound parabolic concentrators in the mid-1960s. It is noted that at present there are two known ways to design nonimaging concentrators: the edge-ray method and the geometric vector flux approach. The use of nonimaging optical devices in the design of nontracking solar concentrators is traced. It is noted that the upper limit of concentration turns out to be about 46,000 times the intensity of sunlight at the surface of the earth. Methods used to maximize this concentration are discussed. The development and use of a solar-pumped laser which would have applications in satellite communications are discussed.

  1. Geometrical analysis of the interacting boson model

    International Nuclear Information System (INIS)

    Dieperink, A.E.L.

    1983-01-01

    The Interacting Boson Model is considered, in relation with geometrical models and the application of mean field techniques to algebraic models, in three lectures. In the first, several methods are reviewed to establish a connection between the algebraic formulation of collective nuclear properties in terms of the group SU(6) and the geometric approach. In the second lecture the geometric interpretation of new degrees of freedom that arise in the neutron-proton IBA is discussed, and in the third one some further applications of algebraic techniques to the calculation of static and dynamic collective properties are presented. (U.K.)

  2. Energy-efficient virtual optical network mapping approaches over converged flexible bandwidth optical networks and data centers.

    Science.gov (United States)

    Chen, Bowen; Zhao, Yongli; Zhang, Jie

    2015-09-21

    In this paper, we develop a virtual link priority mapping (LPM) approach and a virtual node priority mapping (NPM) approach to improve the energy efficiency and to reduce the spectrum usage over the converged flexible bandwidth optical networks and data centers. For comparison, the lower bound of the virtual optical network mapping is used for the benchmark solutions. Simulation results show that the LPM approach achieves the better performance in terms of power consumption, energy efficiency, spectrum usage, and the number of regenerators compared to the NPM approach.

  3. PROCEDURE ENABLING SIMULATION AND IN-DEPTH ANALYSIS OF OPTICAL EFFECTS IN CAMERA-BASED TIME-OF-FLIGHT SENSORS

    Directory of Open Access Journals (Sweden)

    M. Baumgart

    2018-05-01

    Full Text Available This paper presents a simulation approach for Time-of-Flight cameras to estimate sensor performance and accuracy, as well as to help understanding experimentally discovered effects. The main scope is the detailed simulation of the optical signals. We use a raytracing-based approach and use the optical path length as the master parameter for depth calculations. The procedure is described in detail with references to our implementation in Zemax OpticStudio and Python. Our simulation approach supports multiple and extended light sources and allows accounting for all effects within the geometrical optics model. Especially multi-object reflection/scattering ray-paths, translucent objects, and aberration effects (e.g. distortion caused by the ToF lens are supported. The optical path length approach also enables the implementation of different ToF senor types and transient imaging evaluations. The main features are demonstrated on a simple 3D test scene.

  4. The geometric semantics of algebraic quantum mechanics.

    Science.gov (United States)

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-06

    In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

  5. Transformation optics with artificial Riemann sheets

    Science.gov (United States)

    Xu, Lin; Chen, Huanyang

    2013-11-01

    The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777-80 and Pendry et al 2006 Science 312 1780-2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110-12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results.

  6. A Geometrical Approach to Bell's Theorem

    Science.gov (United States)

    Rubincam, David Parry

    2000-01-01

    Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

  7. The effects of a geometrical size, external electric fields and impurity on the optical gain of a quantum dot laser with a semi-parabolic spherical well potential

    Science.gov (United States)

    Owji, Erfan; Keshavarz, Alireza; Mokhtari, Hosein

    2017-03-01

    In this paper, a GaAs / Alx Ga1-x As quantum dot laser with a semi-parabolic spherical well potential is assumed. By using Runge-Kutta method the eigenenergies and the eigenstates of valence and conduct bands are obtained. The effects of geometrical sizes, external electric fields and hydrogen impurity on the different electronic transitions of the optical gain are studied. The results show that the optical gain peak increases and red-shifts, by increasing the width of well or barrier, while more increasing of the width causes blue-shift and decreases it. The hydrogen impurity decreases the optical gain peak and blue-shifts it. Also, the increasing of the external electric fields cause to increase the peak of the optical gain, and (blue) red shift it. Finally, the optical gain for 1s-1s and 2s-1s transitions is prominent, while it is so weak for other transitions.

  8. The Spacetime Memory of Geometric Phases and Quantum Computing

    CERN Document Server

    Binder, B

    2002-01-01

    Spacetime memory is defined with a holonomic approach to information processing, where multi-state stability is introduced by a non-linear phase-locked loop. Geometric phases serve as the carrier of physical information and geometric memory (of orientation) given by a path integral measure of curvature that is periodically refreshed. Regarding the resulting spin-orbit coupling and gauge field, the geometric nature of spacetime memory suggests to assign intrinsic computational properties to the electromagnetic field.

  9. Geometric phase from dielectric matrix

    International Nuclear Information System (INIS)

    Banerjee, D.

    2005-10-01

    The dielectric property of the anisotropic optical medium is found by considering the polarized photon as two component spinor of spherical harmonics. The Geometric Phase of a polarized photon has been evaluated in two ways: the phase two-form of the dielectric matrix through a twist and the Pancharatnam phase (GP) by changing the angular momentum of the incident polarized photon over a closed triangular path on the extended Poincare sphere. The helicity in connection with the spin angular momentum of the chiral photon plays the key role in developing these phase holonomies. (author)

  10. Image Mosaicking Approach for a Double-Camera System in the GaoFen2 Optical Remote Sensing Satellite Based on the Big Virtual Camera.

    Science.gov (United States)

    Cheng, Yufeng; Jin, Shuying; Wang, Mi; Zhu, Ying; Dong, Zhipeng

    2017-06-20

    The linear array push broom imaging mode is widely used for high resolution optical satellites (HROS). Using double-cameras attached by a high-rigidity support along with push broom imaging is one method to enlarge the field of view while ensuring high resolution. High accuracy image mosaicking is the key factor of the geometrical quality of complete stitched satellite imagery. This paper proposes a high accuracy image mosaicking approach based on the big virtual camera (BVC) in the double-camera system on the GaoFen2 optical remote sensing satellite (GF2). A big virtual camera can be built according to the rigorous imaging model of a single camera; then, each single image strip obtained by each TDI-CCD detector can be re-projected to the virtual detector of the big virtual camera coordinate system using forward-projection and backward-projection to obtain the corresponding single virtual image. After an on-orbit calibration and relative orientation, the complete final virtual image can be obtained by stitching the single virtual images together based on their coordinate information on the big virtual detector image plane. The paper subtly uses the concept of the big virtual camera to obtain a stitched image and the corresponding high accuracy rational function model (RFM) for concurrent post processing. Experiments verified that the proposed method can achieve seamless mosaicking while maintaining the geometric accuracy.

  11. Geometric modeling in the problem of ball bearing accuracy

    Science.gov (United States)

    Glukhov, V. I.; Pushkarev, V. V.; Khomchenko, V. G.

    2017-06-01

    The manufacturing quality of ball bearings is an urgent problem for machine-building industry. The aim of the research is to improve the geometric specifications accuracy of bearings based on evidence-based systematic approach and the method of adequate size, location and form deviations modeling of the rings and assembled ball bearings. The present work addressed the problem of bearing geometric specifications identification and the study of these specifications. The deviation from symmetric planar of rings and bearings assembly and mounting width are among these specifications. A systematic approach to geometric specifications values and ball bearings tolerances normalization in coordinate systems will improve the quality of bearings by optimizing and minimizing the number of specifications. The introduction of systematic approach to the international standards on rolling bearings is a guarantee of a significant increase in accuracy of bearings and the quality of products where they are applied.

  12. A simple geometrical approach to particle production in collisions with nuclei

    International Nuclear Information System (INIS)

    Dias de Deus, J.

    1975-11-01

    It is argued that hadron collisions with nuclei are similar to hadron-hadron collisions, having similar properties for the impact parameter distributions and the leading particle spectra. The relevant existing high energy data, including the universality of multiplicity distributions and the possibility of geometrical scaling in reactions with nuclei, are easily understood in the framework of geometrical models by extending to p-nucleus collisions what was learnt about impact parameter and leading particles in p-p collisions. The question of forward-backward correlations and photo and electroproduction are briefly discussed. (author)

  13. Vehicle ego-motion estimation with geometric algebra

    NARCIS (Netherlands)

    Mark, W. van der; Fontijne, D.; Dorst, L.; Groen, F.C.A.

    2003-01-01

    A method for estimating ego-motion with vehicle mounted stereo cameras is presented. This approach is based on finding corresponding features in stereo images and tracking them between succeeding stereo frames. Our approach estimates stereo ego-motion with geometric algebra techniques. Starting with

  14. Quantum criticality of geometric phase in coupled optical cavity arrays under linear quench

    OpenAIRE

    Sarkar, Sujit

    2013-01-01

    The atoms trapped in microcavities and interacting through the exchange of virtual photons can be modeled as an anisotropic Heisenberg spin-1/2 lattice. We study the dynamics of the geometric phase of this system under the linear quenching process of laser field detuning which shows the XX criticality of the geometric phase in presence of single Rabi frequency oscillation. We also study the quantum criticality for different quenching rate in the presence of single or two Rabi frequencies osci...

  15. Application of Riesz transforms to the isotropic AM-PM decomposition of geometrical-optical illusion images.

    Science.gov (United States)

    Sierra-Vázquez, Vicente; Serrano-Pedraza, Ignacio

    2010-04-01

    The existence of a special second-order mechanism in the human visual system, able to demodulate the envelope of visual stimuli, suggests that spatial information contained in the image envelope may be perceptually relevant. The Riesz transform, a natural isotropic extension of the Hilbert transform to multidimensional signals, was used here to demodulate band-pass filtered images of well-known visual illusions of length, size, direction, and shape. We show that the local amplitude of the monogenic signal or envelope of each illusion image conveys second-order information related to image holistic spatial structure, whereas the local phase component conveys information about the spatial features. Further low-pass filtering of the illusion image envelopes creates physical distortions that correspond to the subjective distortions perceived in the illusory images. Therefore the envelope seems to be the image component that physically carries the spatial information about these illusions. This result contradicts the popular belief that the relevant spatial information to perceive geometrical-optical illusions is conveyed only by the lower spatial frequencies present in their Fourier spectrum.

  16. The Study of Birefringent Homogenous Medium with Geometric Phase

    International Nuclear Information System (INIS)

    Banerjee, Dipti

    2010-12-01

    The property of linear and circular birefringence at each point of the optical medium has been evaluated here from differential matrix N using the Jones calculus. This matrix lies on the OAM sphere for l = 1 orbital angular momentum. The geometric phase is developed by twisting the medium uniformly about the direction of propagation of the light ray. The circular birefringence of the medium, is visualized through the solid angle and the angular twist per unit thickness of the medium, k, that is equivalent to the topological charge of the optical element. (author)

  17. Modified polarized geometrical attenuation model for bidirectional reflection distribution function based on random surface microfacet theory.

    Science.gov (United States)

    Liu, Hong; Zhu, Jingping; Wang, Kai

    2015-08-24

    The geometrical attenuation model given by Blinn was widely used in the geometrical optics bidirectional reflectance distribution function (BRDF) models. Blinn's geometrical attenuation model based on symmetrical V-groove assumption and ray scalar theory causes obvious inaccuracies in BRDF curves and negatives the effects of polarization. Aiming at these questions, a modified polarized geometrical attenuation model based on random surface microfacet theory is presented by combining of masking and shadowing effects and polarized effect. The p-polarized, s-polarized and unpolarized geometrical attenuation functions are given in their separate expressions and are validated with experimental data of two samples. It shows that the modified polarized geometrical attenuation function reaches better physical rationality, improves the precision of BRDF model, and widens the applications for different polarization.

  18. Iron-dextran complex: geometrical structure and magneto-optical features.

    Science.gov (United States)

    Graczykowski, Bartłomiej; Dobek, Andrzej

    2011-11-15

    Molecular mass of the iron-dextran complex (M(w)=1133 kDa), diameter of its particles (∼8.3 nm) and the content of iron ions in the complex core (N(Fe)=6360) were determined by static light scattering, measurements of refractive index increment and the Cotton-Mouton effect in solution. The known number of iron ions permitted the calculation of the permanent magnetic dipole moment value to be μ(Fe)=3.17×10(-18) erg Oe(-1) and the determination of anisotropy of linear magneto-optical polarizabilities components as Δχ=9.2×10(-21) cm(3). Knowing both values and the value of the mean linear optical polarizability α=7.3×10(-20) cm(3), it was possible to show that the total measured CM effect was due to the reorientation of the permanent and the induced magnetic dipole moments of the complex. Analysis of the measured magneto-optical birefringence indicated very small optical anisotropy of linear optical polarizability components, κ(α), which suggested a homogeneous structure of particles of spherical symmetry. Copyright © 2011 Elsevier Inc. All rights reserved.

  19. Analytical calculation of geometric and chromatic aberrations in a bi-potential electrostatic and bell-shaped magnetic combined lens

    International Nuclear Information System (INIS)

    Ximen Jiye; Liu Zhixiong

    2000-01-01

    In the present paper, Gaussian optical property in the bi-potential electrostatic and the bell-shaped magnetic combined lens - a new theoretical model first proposed in electron optics - has been thoroughly studied. Meanwhile, based on electron optical canonical aberration theory, analytical formulas of third-order geometrical and first-order chromatic aberration coefficients and their computational results have first been derived for this bi-potential electrostatic and bell-shaped magnetic combined lens. It is to emphasized that this theoretical study can be used to estimate third-order geometric and first-order chromatic aberrations and to provide a theoretical criterion for numerical computation in a rotationally symmetric electromagnetic lens

  20. Optical computing - an alternate approach to trigger processing

    International Nuclear Information System (INIS)

    Cleland, W.E.

    1981-01-01

    The enormous rate reduction factors required by most ISABELLE experiments suggest that we should examine every conceivable approach to trigger processing. One approach that has not received much attention by high energy physicists is optical data processing. The past few years have seen rapid advances in optoelectronic technology, stimulated mainly by the military and the communications industry. An intriguing question is whether one can utilize this technology together with the optical computing techniques that have been developed over the past two decades to develop a rapid trigger processor for high energy physics experiments. Optical data processing is a method for performing a few very specialized operations on data which is inherently two dimensional. Typical operations are the formation of convolution or correlation integrals between the input data and information stored in the processor in the form of an optical filter. Optical processors are classed as coherent or incoherent, according to the spatial coherence of the input wavefront. Typically, in a coherent processor a laser beam is modulated with a photographic transparency which represents the input data. In an incoherent processor, the input may be an incoherently illuminated transparency, but self-luminous objects, such as an oscilloscope trace, have also been used. We consider here an incoherent processor in which the input data is converted into an optical wavefront through the excitation of an array of point sources - either light emitting diodes or injection lasers

  1. Transformation optics with artificial Riemann sheets

    International Nuclear Information System (INIS)

    Xu, Lin; Chen, Huanyang

    2013-01-01

    The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777–80 and Pendry et al 2006 Science 312 1780–2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110–12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results. (paper)

  2. Synchronization of integral and fractional order chaotic systems a differential algebraic and differential geometric approach with selected applications in real-time

    CERN Document Server

    Martínez-Guerra, Rafael; Gómez-Cortés, Gian Carlo

    2015-01-01

    This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only...

  3. Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit.

    Science.gov (United States)

    Song, Chao; Zheng, Shi-Biao; Zhang, Pengfei; Xu, Kai; Zhang, Libo; Guo, Qiujiang; Liu, Wuxin; Xu, Da; Deng, Hui; Huang, Keqiang; Zheng, Dongning; Zhu, Xiaobo; Wang, H

    2017-10-20

    Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a paradigm, where quantum logic operations are realized through geometric phase manipulation that has some intrinsic noise-resilient advantages and may enable simplified implementation of multi-qubit gates compared to the dynamical approach. Here we report observation of a continuous-variable geometric phase and demonstrate a quantum gate protocol based on this phase in a superconducting circuit, where five qubits are controllably coupled to a resonator. Our geometric approach allows for one-step implementation of n-qubit controlled-phase gates, which represents a remarkable advantage compared to gate decomposition methods, where the number of required steps dramatically increases with n. Following this approach, we realize these gates with n up to 4, verifying the high efficiency of this geometric manipulation for quantum computation.

  4. Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

    Science.gov (United States)

    Ray, S. Saha

    2018-04-01

    In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

  5. Engineering Optics

    CERN Document Server

    Iizuka, Keigo

    2008-01-01

    Engineering Optics is a book for students who want to apply their knowledge of optics to engineering problems, as well as for engineering students who want to acquire the basic principles of optics. It covers such important topics as optical signal processing, holography, tomography, holographic radars, fiber optical communication, electro- and acousto-optic devices, and integrated optics (including optical bistability). As a basis for understanding these topics, the first few chapters give easy-to-follow explanations of diffraction theory, Fourier transforms, and geometrical optics. Practical examples, such as the video disk, the Fresnel zone plate, and many more, appear throughout the text, together with numerous solved exercises. There is an entirely new section in this updated edition on 3-D imaging.

  6. Geometric mean for subspace selection.

    Science.gov (United States)

    Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

    2009-02-01

    Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.

  7. Optical, geometric and thermal study for solar parabolic concentrator efficiency improvement under Tunisia environment: A case study

    International Nuclear Information System (INIS)

    Skouri, Safa; Ben Salah, Mohieddine; Bouadila, Salwa; Balghouthi, Moncef; Ben Nasrallah, Sassi

    2013-01-01

    Highlights: • Design and construction of solar parabolic concentrator. • Photogrammetry study of SPC. • Slope error and optical efficiency of SPC. • Reflector materials of SPC. • Programmed tracking solar system. - Abstract: Renewable energy generation is becoming more prevalent today. It is relevant to consider that solar concentration technologies contribute to provide a real alternative to the consumption of fossil fuels. The purpose of this work is the characterization of a solar parabolic solar concentrator (SPC) designed, constructed and tested in the Research and Technologies Centre of Energy in Tunisia (CRTEn) in order to improve the performance of the system. Photogrammetry measurement used to analyze the slope errors and to determine hence determining the geometric deformation of the SPC system, which presents an average slope error around 0.0002 and 0.0073 mrad respectively in the center and in the extremities. An optimization of the most performed reflector material has been done by an experimental study of three types of reflectors. A two axes programmed tracking system realized, used and tested in this study. An experimental study is carried out to evaluate the solar parabolic concentrator thermal efficiency after the mechanical and the optical SPC optimization. The thermal energy efficiency varies from 40% to 77%, the concentrating system reaches an average concentration factor around 178

  8. Experimental realization of universal geometric quantum gates with solid-state spins.

    Science.gov (United States)

    Zu, C; Wang, W-B; He, L; Zhang, W-G; Dai, C-Y; Wang, F; Duan, L-M

    2014-10-02

    Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. In an 'all-geometric' approach to quantum computation, the quantum gates are implemented using Berry phases and their non-Abelian extensions, holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilience features. On the experimental side, geometric phases and holonomies have been observed in thermal ensembles of liquid molecules using nuclear magnetic resonance; however, such systems are known to be non-scalable for the purposes of quantum computing. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions, superconducting quantum bits and quantum dots, and a recent experiment has realized geometric single-bit gates in a superconducting system. Here we report the experimental realization of a universal set of geometric quantum gates using the solid-state spins of diamond nitrogen-vacancy centres. These diamond defects provide a scalable experimental platform with the potential for room-temperature quantum computing, which has attracted strong interest in recent years. Our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system.

  9. Interference electron microscopy of one-dimensional electron-optical phase objects

    International Nuclear Information System (INIS)

    Fazzini, P.F.; Ortolani, L.; Pozzi, G.; Ubaldi, F.

    2006-01-01

    The application of interference electron microscopy to the investigation of electron optical one-dimensional phase objects like reverse biased p-n junctions and ferromagnetic domain walls is considered. In particular the influence of diffraction from the biprism edges on the interference images is analyzed and the range of applicability of the geometric optical equation for the interpretation of the interference fringe shifts assessed by comparing geometric optical images with full wave-optical simulations. Finally, the inclusion of partial spatial coherence effects are discussed

  10. Optical imaging and spectroscopy

    CERN Document Server

    Brady, David J

    2009-01-01

    An essential reference for optical sensor system design This is the first text to present an integrated view of the optical and mathematical analysis tools necessary to understand computational optical system design. It presents the foundations of computational optical sensor design with a focus entirely on digital imaging and spectroscopy. It systematically covers: Coded aperture and tomographic imaging Sampling and transformations in optical systems, including wavelets and generalized sampling techniques essential to digital system analysis Geometric, wave, and statis

  11. Optical properties of non-spherical desert dust particles in the terrestrial infrared – An asymptotic approximation approach

    International Nuclear Information System (INIS)

    Klüser, Lars; Di Biagio, Claudia; Kleiber, Paul D.; Formenti, Paola; Grassian, Vicki H.

    2016-01-01

    Optical properties (extinction efficiency, single scattering albedo, asymmetry parameter and scattering phase function) of five different desert dust minerals have been calculated with an asymptotic approximation approach (AAA) for non-spherical particles. The AAA method combines Rayleigh-limit approximations with an asymptotic geometric optics solution in a simple and straightforward formulation. The simulated extinction spectra have been compared with classical Lorenz–Mie calculations as well as with laboratory measurements of dust extinction. This comparison has been done for single minerals and with bulk dust samples collected from desert environments. It is shown that the non-spherical asymptotic approximation improves the spectral extinction pattern, including position of the extinction peaks, compared to the Lorenz–Mie calculations for spherical particles. Squared correlation coefficients from the asymptotic approach range from 0.84 to 0.96 for the mineral components whereas the corresponding numbers for Lorenz–Mie simulations range from 0.54 to 0.85. Moreover the blue shift typically found in Lorenz–Mie results is not present in the AAA simulations. The comparison of spectra simulated with the AAA for different shape assumptions suggests that the differences mainly stem from the assumption of the particle shape and not from the formulation of the method itself. It has been shown that the choice of particle shape strongly impacts the quality of the simulations. Additionally, the comparison of simulated extinction spectra with bulk dust measurements indicates that within airborne dust the composition may be inhomogeneous over the range of dust particle sizes, making the calculation of reliable radiative properties of desert dust even more complex. - Highlights: • A fast and simple method for estimating optical properties of dust. • Can be used with non-spherical particles of arbitrary size distributions. • Comparison with Mie simulations and

  12. Progress in linear optics, non-linear optics and surface alignment of liquid crystals

    Science.gov (United States)

    Ong, H. L.; Meyer, R. B.; Hurd, A. J.; Karn, A. J.; Arakelian, S. M.; Shen, Y. R.; Sanda, P. N.; Dove, D. B.; Jansen, S. A.; Hoffmann, R.

    We first discuss the progress in linear optics, in particular, the formulation and application of geometrical-optics approximation and its generalization. We then discuss the progress in non-linear optics, in particular, the enhancement of a first-order Freedericksz transition and intrinsic optical bistability in homeotropic and parallel oriented nematic liquid crystal cells. Finally, we discuss the liquid crystal alignment and surface effects on field-induced Freedericksz transition.

  13. Understanding geometric algebra for electromagnetic theory

    CERN Document Server

    Arthur, John W

    2011-01-01

    "This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison"--Provided by publisher.

  14. Optical Microbubble Resonators with High Refractive Index Inner Coating for Bio-Sensing Applications: An Analytical Approach

    Directory of Open Access Journals (Sweden)

    Andrea Barucci

    2016-11-01

    Full Text Available The design of Whispering Gallery Mode Resonators (WGMRs used as an optical transducer for biosensing represents the first and crucial step towards the optimization of the final device performance in terms of sensitivity and Limit of Detection (LoD. Here, we propose an analytical method for the design of an optical microbubble resonator (OMBR-based biosensor. In order to enhance the OMBR sensing performance, we consider a polymeric layer of high refractive index as an inner coating for the OMBR. The effect of this layer and other optical/geometrical parameters on the mode field distribution, sensitivity and LoD of the OMBR is assessed and discussed, both for transverse electric (TE and transverse magnetic (TM polarization. The obtained results do provide physical insights for the development of OMBR-based biosensor.

  15. Geometrical themes inspired by the n-body problem

    CERN Document Server

    Herrera, Haydeé; Herrera, Rafael

    2018-01-01

    Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions.   R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order t...

  16. Extraordinary optical transmission through nonlocal holey metal films

    DEFF Research Database (Denmark)

    David, Christin; Christensen, Johan

    2017-01-01

    We investigate nonlocal electrodynamics based on the generalized hydrodynamic approach including electron diffusion in holey gold films, showing extraordinary optical transmission (EOT). Dramatic changes with respect to the local approximation for rather large film thicknesses t less than...... or similar to 100 nm impact both reflectance and absorbance at normal incidence. Beyond the familiar resonance blueshift with the decreasing film thickness, the interference of longitudinal pressure waves in the holey structure generates an unexpected oscillatory response with geometrical parameters...

  17. GEOMETRIZATION OF NONHOLONOMIC MECHANICAL SYSTEMS AND THEIR SOLVABILITY

    Institute of Scientific and Technical Information of China (English)

    慕小武; 郭仲衡

    1990-01-01

    A new geometrization approach to nonholonomic mechanical systems is proposed and a series of solvability conditions under the proposed geometric frame are given. The proposed frame differs essentially from Hermann’s. The limitations of Hermann’s frame are also discussed. It is shown that a system under Hermann’s frame is solvable only if its constraints are given by natural conservation laws of the corresponding constraint-free system.

  18. The value of art-oriented pedagogical approaches to the teaching of optics and photonics

    Science.gov (United States)

    Pompea, Stephen M.; Regens, Nancy L.

    2017-08-01

    Art-oriented pedagogical approaches have been successfully applied to optics and photonics education. We will describe how art-based programs that incorporate a Visual Thinking Strategies (VTS) approach can be used by optics and photonics educators. VTS encourages both a deep appreciation of the content of optics images and phenomena and a highly participatory approach to understanding them. This type of approach has been used by the authors in a variety of educational settings including teacher professional development workshops, museum and science center-based programs, after school programs and in two-week intensive summer academies for students. These approaches work well with multiple age groups including primary and secondary grade students, university students, and adults who may have little apparent connection to optics and photonics. This art-science hybrid approach can be used by university professors, optics/photonics professionals who do public programs, museum educators, and classroom science teachers.

  19. Extending the possibilities in phase space analysis of synchrotron radiation x-ray optics.

    Science.gov (United States)

    Ferrero, Claudio; Smilgies, Detlef-Matthias; Riekel, Christian; Gatta, Gilles; Daly, Peter

    2008-08-01

    A simple analytical approach to phase space analysis of the performance of x-ray optical setups (beamlines) combining several elements in position-angle-wavelength space is presented. The mathematical description of a large class of optical elements commonly used on synchrotron beamlines has been reviewed and extended with respect to the existing literature and is reported in a revised form. Novel features are introduced, in particular, the possibility to account for imperfections on mirror surfaces and to incorporate nanofocusing devices like refractive lenses in advanced beamline setups using the same analytical framework. Phase space analysis results of the simulation of an undulator beamline with focusing optics at the European Synchrotron Radiation Facility compare favorably with results obtained by geometric ray-tracing methods and, more importantly, with experimental measurements. This approach has been implemented into a simple and easy-to-use program toolkit for optical calculations based on the Mathematica software package.

  20. Comparison of matrix method and ray tracing in the study of complex optical systems

    Science.gov (United States)

    Anterrieu, Eric; Perez, Jose-Philippe

    2000-06-01

    In the context of the classical study of optical systems within the geometrical Gauss approximation, the cardinal elements are efficiently obtained with the aid of the transfer matrix between the input and output planes of the system. In order to take into account the geometrical aberrations, a ray tracing approach, using the Snell- Descartes laws, has been implemented in an interactive software. Both methods are applied for measuring the correction to be done to a human eye suffering from ametropia. This software may be used by optometrists and ophthalmologists for solving the problems encountered when considering this pathology. The ray tracing approach gives a significant improvement and could be very helpful for a better understanding of an eventual surgical act.

  1. Geometric approach to a massive p form duality

    International Nuclear Information System (INIS)

    Arias, Pio J.; Leal, Lorenzo; Perez-Mosquera, J. C.

    2003-01-01

    Massive theories of Abelian p forms are quantized in a generalized path representation that leads to a description of the phase space in terms of a pair of dual nonlocal operators analogous to the Wilson loop and the 't Hooft disorder operators. Special attention is devoted to the study of the duality between the topologically massive and self-dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one nonlocal operator suffices to describe the observables

  2. Transformation optics, isotropic chiral media and non-Riemannian geometry

    International Nuclear Information System (INIS)

    Horsley, S A R

    2011-01-01

    The geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include chiral media that are isotropic but inhomogeneous. It was found that such media may be described through introducing the non-Riemannian geometrical property of torsion into the Maxwell equations, and it is shown how such an interpretation may be applied to the design of optical devices.

  3. Design of fiber optic probes for laser light scattering

    Science.gov (United States)

    Dhadwal, Harbans S.; Chu, Benjamin

    1989-01-01

    A quantitative analysis is presented of the role of optical fibers in laser light scattering. Design of a general fiber optic/microlens probe by means of ray tracing is described. Several different geometries employing an optical fiber of the type used in lightwave communications and a graded index microlens are considered. Experimental results using a nonimaging fiber optic detector probe show that due to geometrical limitations of single mode fibers, a probe using a multimode optical fiber has better performance, for both static and dynamic measurements of the scattered light intensity, compared with a probe using a single mode fiber. Fiber optic detector probes are shown to be more efficient at data collection when compared with conventional approaches to measurements of the scattered laser light. Integration of fiber optic detector probes into a fiber optic spectrometer offers considerable miniaturization of conventional light scattering spectrometers, which can be made arbitrarily small. In addition static and dynamic measurements of scattered light can be made within the scattering cell and consequently very close to the scattering center.

  4. Optical holography

    CERN Document Server

    Collier, Robert J; Lin, Lawrence H

    1971-01-01

    Optical Holography deals with the use of optical holography to solve technical problems, with emphasis on the properties of holograms formed with visible light. Topics covered include the Fourier transform, propagation and diffraction, pulsed-laser holography, and optical systems with spherical lenses. A geometric analysis of point-source holograms is also presented, and holograms and hologram spatial filters formed with spatially modulated reference waves are described. This book is comprised of 20 chapters and begins with an introduction to concepts that are basic to understanding hologr

  5. Direction-dependent waist-shift-difference of Gaussian beam in a multiple-pass zigzag slab amplifier and geometrical optics compensation method.

    Science.gov (United States)

    Li, Zhaoyang; Kurita, Takashi; Miyanaga, Noriaki

    2017-10-20

    Zigzag and non-zigzag beam waist shifts in a multiple-pass zigzag slab amplifier are investigated based on the propagation of a Gaussian beam. Different incident angles in the zigzag and non-zigzag planes would introduce a direction-dependent waist-shift-difference, which distorts the beam quality in both the near- and far-fields. The theoretical model and analytical expressions of this phenomenon are presented, and intensity distributions in the two orthogonal planes are simulated and compared. A geometrical optics compensation method by a beam with 90° rotation is proposed, which not only could correct the direction-dependent waist-shift-difference but also possibly average the traditional thermally induced wavefront-distortion-difference between the horizontal and vertical beam directions.

  6. Automatic design of optical systems by digital computer

    Science.gov (United States)

    Casad, T. A.; Schmidt, L. F.

    1967-01-01

    Computer program uses geometrical optical techniques and a least squares optimization method employing computing equipment for the automatic design of optical systems. It evaluates changes in various optical parameters, provides comprehensive ray-tracing, and generally determines the acceptability of the optical system characteristics.

  7. Simulation Experiment on Landing Site Selection Using a Simple Geometric Approach

    Science.gov (United States)

    Zhao, W.; Tong, X.; Xie, H.; Jin, Y.; Liu, S.; Wu, D.; Liu, X.; Guo, L.; Zhou, Q.

    2017-07-01

    Safe landing is an important part of the planetary exploration mission. Even fine scale terrain hazards (such as rocks, small craters, steep slopes, which would not be accurately detected from orbital reconnaissance) could also pose a serious risk on planetary lander or rover and scientific instruments on-board it. In this paper, a simple geometric approach on planetary landing hazard detection and safe landing site selection is proposed. In order to achieve full implementation of this algorithm, two easy-to-compute metrics are presented for extracting the terrain slope and roughness information. Unlike conventional methods which must do the robust plane fitting and elevation interpolation for DEM generation, in this work, hazards is identified through the processing directly on LiDAR point cloud. For safe landing site selection, a Generalized Voronoi Diagram is constructed. Based on the idea of maximum empty circle, the safest landing site can be determined. In this algorithm, hazards are treated as general polygons, without special simplification (e.g. regarding hazards as discrete circles or ellipses). So using the aforementioned method to process hazards is more conforming to the real planetary exploration scenario. For validating the approach mentioned above, a simulated planetary terrain model was constructed using volcanic ash with rocks in indoor environment. A commercial laser scanner mounted on a rail was used to scan the terrain surface at different hanging positions. The results demonstrate that fairly hazard detection capability and reasonable site selection was obtained compared with conventional method, yet less computational time and less memory usage was consumed. Hence, it is a feasible candidate approach for future precision landing selection on planetary surface.

  8. SIMULATION EXPERIMENT ON LANDING SITE SELECTION USING A SIMPLE GEOMETRIC APPROACH

    Directory of Open Access Journals (Sweden)

    W. Zhao

    2017-07-01

    Full Text Available Safe landing is an important part of the planetary exploration mission. Even fine scale terrain hazards (such as rocks, small craters, steep slopes, which would not be accurately detected from orbital reconnaissance could also pose a serious risk on planetary lander or rover and scientific instruments on-board it. In this paper, a simple geometric approach on planetary landing hazard detection and safe landing site selection is proposed. In order to achieve full implementation of this algorithm, two easy-to-compute metrics are presented for extracting the terrain slope and roughness information. Unlike conventional methods which must do the robust plane fitting and elevation interpolation for DEM generation, in this work, hazards is identified through the processing directly on LiDAR point cloud. For safe landing site selection, a Generalized Voronoi Diagram is constructed. Based on the idea of maximum empty circle, the safest landing site can be determined. In this algorithm, hazards are treated as general polygons, without special simplification (e.g. regarding hazards as discrete circles or ellipses. So using the aforementioned method to process hazards is more conforming to the real planetary exploration scenario. For validating the approach mentioned above, a simulated planetary terrain model was constructed using volcanic ash with rocks in indoor environment. A commercial laser scanner mounted on a rail was used to scan the terrain surface at different hanging positions. The results demonstrate that fairly hazard detection capability and reasonable site selection was obtained compared with conventional method, yet less computational time and less memory usage was consumed. Hence, it is a feasible candidate approach for future precision landing selection on planetary surface.

  9. Geometrical Optimization Approach to Isomerization: Models and Limitations.

    Science.gov (United States)

    Chang, Bo Y; Shin, Seokmin; Engel, Volker; Sola, Ignacio R

    2017-11-02

    We study laser-driven isomerization reactions through an excited electronic state using the recently developed Geometrical Optimization procedure. Our goal is to analyze whether an initial wave packet in the ground state, with optimized amplitudes and phases, can be used to enhance the yield of the reaction at faster rates, driven by a single picosecond pulse or a pair of femtosecond pulses resonant with the electronic transition. We show that the symmetry of the system imposes limitations in the optimization procedure, such that the method rediscovers the pump-dump mechanism.

  10. Manual of the Option.com program (ion optics)

    International Nuclear Information System (INIS)

    Fernandez B, M.

    1991-02-01

    The laws that govern the trajectory that follow the charged particles in the hole, inside magnetic fields (to first approach) are similar to those of the geometric classic optics by it to observe a graph of the trajectories gives an excellent understanding of that is happening to the beam. The object of this program is that besides providing the numeric data of the solution of the problem of the transverse section of the beam, be also shown a graph of the trajectories but external regarding the optic axis in the treated region and aid the user asking in the case of a system of two quadrupoles, where it is wanted to focus the beam. (Author)

  11. Traceability of Height Measurements on Green Sand Molds using Optical 3D Scanning

    DEFF Research Database (Denmark)

    Mohaghegh, Kamran; Yazdanbakhsh, S.A.; Tiedje, N. S.

    2016-01-01

    Establishing a reliable measurement procedure for dimensional measurements on green sand molds is a prerequisite for analysis of geometric deviations in mass production of quality castings. Surface of the green sand mold is not suitable for measurements using a tactile coordinate measuring machine....... This paper presents a metrological approach for height measurement on green sand molds using an optical 3D scanner with fringe projection. A new sand sample was developed with a hard binder to withstand the contact force of a touch probe, while keeping optical cooperativeness similar to green sand...

  12. Multiscale geometric modeling of macromolecules I: Cartesian representation

    Science.gov (United States)

    Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei

    2014-01-01

    This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the

  13. Multiscale geometric modeling of macromolecules I: Cartesian representation

    Energy Technology Data Exchange (ETDEWEB)

    Xia, Kelin [Department of Mathematics, Michigan State University, MI 48824 (United States); Feng, Xin [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Chen, Zhan [Department of Mathematics, Michigan State University, MI 48824 (United States); Tong, Yiying [Department of Computer Science and Engineering, Michigan State University, MI 48824 (United States); Wei, Guo-Wei, E-mail: wei@math.msu.edu [Department of Mathematics, Michigan State University, MI 48824 (United States); Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824 (United States)

    2014-01-15

    This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the

  14. Nonlocal transformation optics.

    Science.gov (United States)

    Castaldi, Giuseppe; Galdi, Vincenzo; Alù, Andrea; Engheta, Nader

    2012-02-10

    We show that the powerful framework of transformation optics may be exploited for engineering the nonlocal response of artificial electromagnetic materials. Relying on the form-invariant properties of coordinate-transformed Maxwell's equations in the spectral domain, we derive the general constitutive "blueprints" of transformation media yielding prescribed nonlocal field-manipulation effects and provide a physically incisive and powerful geometrical interpretation in terms of deformation of the equifrequency contours. In order to illustrate the potentials of our approach, we present an example of application to a wave-splitting refraction scenario, which may be implemented via a simple class of artificial materials. Our results provide a systematic and versatile framework which may open intriguing venues in dispersion engineering of artificial materials.

  15. Using computer-assisted demonstrations of optical phenomena in an undergraduate optics course

    Science.gov (United States)

    Tarvin, John T.; Cobb, Stephen H.; Beyer, Louis M.

    1995-10-01

    A set of computer programs has been developed for the visual presentation of introductory optical phenomena. These computer simulations were created to serve a dual purpose: as demonstration aids in an NSF-sponsored Optics Demonstration Laboratory, and as teaching aids in undergraduate geometrical and physical optics courses. In the field of diffractive optics, simulations include the calculation of intensity patterns for unobscured and obscured apertures in both rectangular and circular geometries. These patterns can be compared to those measured in the laboratory with a CCD camera. A program for calculating the diffraction pattern for a two-dimensional aperture of arbitrary shape has also been developed. These programs, when coordinated with homework assignments, allow students to compare their theoretical derivations with a correct numerical solution for the same problem. In the field of geometrical optics, a ray-trace program appropriate for gradient-index fibers with cylindrical symmetry has been developed. This program enables the student to study the focusing properties of such fibers, and to predict how such properties depend on the index profile and on the length of the optical fiber. Examples of these programs will be presented, along with a report on the success of these programs as a vehicle for imparting a conceptual understanding of the physical principles involved.

  16. Lattice of optical islets: a novel treatment modality in photomedicine

    International Nuclear Information System (INIS)

    Altshuler, Gregory; Smirnov, Mikhail; Yaroslavsky, Ilya

    2005-01-01

    A majority of photothermal applications of laser and non-laser light sources in medicine (in particular, in dermatology) are based on the paradigm of (extended) selective photothermolysis. However, realization of this principle in its strict form may not always be possible and/or practical. Spatial (or geometric) selectivity (as opposed to wavelength and temporal selectivity) can provide an alternative approach delivering effective and safe treatment techniques. A method of creating a lattice of localized areas of light-tissue interaction (optical islets) is an example of this 'spatially confined' approach. The lattice of optical islets can be formed using a variety of energy sources and delivery optics, including application of lenslet arrays, phase masks and matrices of exogenous chromophores. Using a state-of-the-art theory of optical and thermal light-tissue interactions and a comprehensive computer model of skin, we have conducted a theoretical and numerical analysis of the process of formation of such a lattice in human tissue. Effects of the wavelength, beam geometry, pulsewidth and physical properties of tissues have been considered. Conditions for obtaining optical, thermal and damage islet lattices in the human skin without inducing adverse side effects (e.g. bulk damage) have been established

  17. Geometric leaf placement strategies

    International Nuclear Information System (INIS)

    Fenwick, J D; Temple, S W P; Clements, R W; Lawrence, G P; Mayles, H M O; Mayles, W P M

    2004-01-01

    Geometric leaf placement strategies for multileaf collimators (MLCs) typically involve the expansion of the beam's-eye-view contour of a target by a uniform MLC margin, followed by movement of the leaves until some point on each leaf end touches the expanded contour. Film-based dose-distribution measurements have been made to determine appropriate MLC margins-characterized through an index d 90 -for multileaves set using one particular strategy to straight lines lying at various angles to the direction of leaf travel. Simple trigonometric relationships exist between different geometric leaf placement strategies and are used to generalize the results of the film work into d 90 values for several different strategies. Measured d 90 values vary both with angle and leaf placement strategy. A model has been derived that explains and describes quite well the observed variations of d 90 with angle. The d 90 angular variations of the strategies studied differ substantially, and geometric and dosimetric reasoning suggests that the best strategy is the one with the least angular variation. Using this criterion, the best straightforwardly implementable strategy studied is a 'touch circle' approach for which semicircles are imagined to be inscribed within leaf ends, the leaves being moved until the semicircles just touch the expanded target outline

  18. Frequency-Domain Robust Performance Condition for Controller Uncertainty in SISO LTI Systems: A Geometric Approach

    Directory of Open Access Journals (Sweden)

    Vahid Raissi Dehkordi

    2009-01-01

    Full Text Available This paper deals with the robust performance problem of a linear time-invariant control system in the presence of robust controller uncertainty. Assuming that plant uncertainty is modeled as an additive perturbation, a geometrical approach is followed in order to find a necessary and sufficient condition for robust performance in the form of a bound on the magnitude of controller uncertainty. This frequency domain bound is derived by converting the problem into an optimization problem, whose solution is shown to be more time-efficient than a conventional structured singular value calculation. The bound on controller uncertainty can be used in controller order reduction and implementation problems.

  19. Accounting for optical errors in microtensiometry.

    Science.gov (United States)

    Hinton, Zachary R; Alvarez, Nicolas J

    2018-09-15

    Drop shape analysis (DSA) techniques measure interfacial tension subject to error in image analysis and the optical system. While considerable efforts have been made to minimize image analysis errors, very little work has treated optical errors. There are two main sources of error when considering the optical system: the angle of misalignment and the choice of focal plane. Due to the convoluted nature of these sources, small angles of misalignment can lead to large errors in measured curvature. We demonstrate using microtensiometry the contributions of these sources to measured errors in radius, and, more importantly, deconvolute the effects of misalignment and focal plane. Our findings are expected to have broad implications on all optical techniques measuring interfacial curvature. A geometric model is developed to analytically determine the contributions of misalignment angle and choice of focal plane on measurement error for spherical cap interfaces. This work utilizes a microtensiometer to validate the geometric model and to quantify the effect of both sources of error. For the case of a microtensiometer, an empirical calibration is demonstrated that corrects for optical errors and drastically simplifies implementation. The combination of geometric modeling and experimental results reveal a convoluted relationship between the true and measured interfacial radius as a function of the misalignment angle and choice of focal plane. The validated geometric model produces a full operating window that is strongly dependent on the capillary radius and spherical cap height. In all cases, the contribution of optical errors is minimized when the height of the spherical cap is equivalent to the capillary radius, i.e. a hemispherical interface. The understanding of these errors allow for correct measure of interfacial curvature and interfacial tension regardless of experimental setup. For the case of microtensiometry, this greatly decreases the time for experimental setup

  20. Tunneling effects in electromagnetic wave scattering by nonspherical particles: A comparison of the Debye series and physical-geometric optics approximations

    International Nuclear Information System (INIS)

    Bi, Lei; Yang, Ping

    2016-01-01

    The accuracy of the physical-geometric optics (PG-O) approximation is examined for the simulation of electromagnetic scattering by nonspherical dielectric particles. This study seeks a better understanding of the tunneling effect on the phase matrix by employing the invariant imbedding method to rigorously compute the zeroth-order Debye series, from which the tunneling efficiency and the phase matrix corresponding to the diffraction and external reflection are obtained. The tunneling efficiency is shown to be a factor quantifying the relative importance of the tunneling effect over the Fraunhofer diffraction near the forward scattering direction. Due to the tunneling effect, different geometries with the same projected cross section might have different diffraction patterns, which are traditionally assumed to be identical according to the Babinet principle. For particles with a fixed orientation, the PG-O approximation yields the external reflection pattern with reasonable accuracy, but ordinarily fails to predict the locations of peaks and minima in the diffraction pattern. The larger the tunneling efficiency, the worse the PG-O accuracy is at scattering angles less than 90°. If the particles are assumed to be randomly oriented, the PG-O approximation yields the phase matrix close to the rigorous counterpart, primarily due to error cancellations in the orientation-average process. Furthermore, the PG-O approximation based on an electric field volume-integral equation is shown to usually be much more accurate than the Kirchhoff surface integral equation at side-scattering angles, particularly when the modulus of the complex refractive index is close to unity. Finally, tunneling efficiencies are tabulated for representative faceted particles. - Highlights: • Concepts of diffraction, reflection and tunneling are refined. • The diffraction together with reflection is rigorously treated. • An improved invariant imbedding method is employed to compute the Debye

  1. Geometric and Algebraic Approaches in the Concept of Complex Numbers

    Science.gov (United States)

    Panaoura, A.; Elia, I.; Gagatsis, A.; Giatilis, G.-P.

    2006-01-01

    This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

  2. 3D-printed optical active components

    Science.gov (United States)

    Suresh Nair, S.; Nuding, J.; Heinrich, A.

    2018-02-01

    Additive Manufacturing (AM) has the potential to become a powerful tool in the realization of complex optical components. The primary advantage that meets the eye, is that fabrication of geometrically complicated optical structures is made easier in AM as compared to the conventional fabrication methods (using molds for instance). But this is not the only degree of freedom that AM has to offer. With the multitude of materials suitable for AM in the market, it is possible to introduce functionality into the components one step before fabrication: by altering the raw material. A passive example would be to use materials with varying properties together, in a single manufacturing step, constructing samples with localized refractive indices for instance. An active approach is to blend in materials with distinct properties into the photopolymer resin and manufacturing with this composite material. Our research is currently focused in this direction, with the desired optical property to be introduced being Photoluminescence. Formation of nanocomposite mixtures to produce samples is the current approach. With this endeavor, new sensor systems can be realized, which may be used to measure the absorption spectra of biological samples. Thereby the sample compartment, the optics and the spectral light source (different quantum dots) are 3D-printed in one run. This component can be individually adapted to the biological sample with respect to wavelength, optical and mechanical properties. Here we would like to present our work on the additive manufacturing of an active optical component. Based on the stereolithography method, a monolithic optical component was 3D-printed, showing light emission at different defined wavelengths due to UV excited quantum dots inside the 3D-printed optics.

  3. Non-contact measurement machine for freeform optics

    NARCIS (Netherlands)

    Henselmans, R.

    2009-01-01

    The performance of high-precision optical systems using spherical optics is limited by aberrations. By applying aspherical and freeform optics, the geometrical aberrations can be reduced or eliminated while at the same time also reducing the required number of components, the size and the weight of

  4. A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics

    Science.gov (United States)

    Pujol, O.; Perez, J. P.

    2007-01-01

    The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…

  5. Innovative approach towards understanding optics

    International Nuclear Information System (INIS)

    Garg, Amit; Bharadwaj, Sadashiv Raj; Kumar, Raj; Shudhanshu, Avinash Kumar; Verma, Deepak Kumar

    2016-01-01

    Over the last few years, there has been a decline in the students’ interest towards Science and Optics. Use of technology in the form of various types of sensors and data acquisition systems has come as a saviour. Till date, manual routine tools and techniques are used to perform various experimental procedures in most of the science/optics laboratories in our country. The manual tools are cumbersome whereas the automated ones are costly. It does not enthuse young researchers towards the science laboratories. There is a need to develop applications which can be easily integrated, tailored at school and undergraduate level laboratories and are economical at the same time. Equipments with advanced technologies are available but they are uneconomical and have complicated working principle with a black box approach. The present work describes development of portable tools and applications which are user-friendly. This is being implemented using open-source physical computing platform based on a simple low cost microcontroller board and a development environment for writing software. The present paper reports the development of an automated spectrometer, an instrument used in almost all optics experiments at undergraduate level, and students’ response to this innovation. These tools will inspire young researchers towards science and facilitate development of advance low cost equipments making life easier for Indian as well as developing nations. (paper)

  6. Floating-point geometry: toward guaranteed geometric computations with approximate arithmetics

    Science.gov (United States)

    Bajard, Jean-Claude; Langlois, Philippe; Michelucci, Dominique; Morin, Géraldine; Revol, Nathalie

    2008-08-01

    Geometric computations can fail because of inconsistencies due to floating-point inaccuracy. For instance, the computed intersection point between two curves does not lie on the curves: it is unavoidable when the intersection point coordinates are non rational, and thus not representable using floating-point arithmetic. A popular heuristic approach tests equalities and nullities up to a tolerance ɛ. But transitivity of equality is lost: we can have A approx B and B approx C, but A not approx C (where A approx B means ||A - B|| < ɛ for A,B two floating-point values). Interval arithmetic is another, self-validated, alternative; the difficulty is to limit the swell of the width of intervals with computations. Unfortunately interval arithmetic cannot decide equality nor nullity, even in cases where it is decidable by other means. A new approach, developed in this paper, consists in modifying the geometric problems and algorithms, to account for the undecidability of the equality test and unavoidable inaccuracy. In particular, all curves come with a non-zero thickness, so two curves (generically) cut in a region with non-zero area, an inner and outer representation of which is computable. This last approach no more assumes that an equality or nullity test is available. The question which arises is: which geometric problems can still be solved with this last approach, and which cannot? This paper begins with the description of some cases where every known arithmetic fails in practice. Then, for each arithmetic, some properties of the problems they can solve are given. We end this work by proposing the bases of a new approach which aims to fulfill the geometric computations requirements.

  7. The strong coupling constant: its theoretical derivation from a geometric approach to hadron structure

    International Nuclear Information System (INIS)

    Recami, E.; Tonin-Zanchin, V.

    1991-01-01

    Since more than a decade, a bi-scale, unified approach to strong and gravitational interactions has been proposed, that uses the geometrical methods of general relativity, and yielded results similar to strong gravity theory's. We fix our attention, in this note, on hadron structure, and show that also the strong interaction strength α s, ordinarily called the (perturbative) coupling-constant square, can be evaluated within our theory, and found to decrease (increase) as the distance r decreases (increases). This yields both the confinement of the hadron constituents for large values of r, and their asymptotic freedom [for small values of r inside the hadron]: in qualitative agreement with the experimental evidence. In other words, our approach leads us, on a purely theoretical ground, to a dependence of α s on r which had been previously found only on phenomenological and heuristical grounds. We expect the above agreement to be also quantitative, on the basis of a few checks performed in this paper, and of further work of ours about calculating meson mass-spectra. (author)

  8. Geometrically Consistent Mesh Modification

    KAUST Repository

    Bonito, A.

    2010-01-01

    A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.

  9. GEOMETRIC MODELLING OF TREE ROOTS WITH DIFFERENT LEVELS OF DETAIL

    Directory of Open Access Journals (Sweden)

    J. I. Guerrero Iñiguez

    2017-09-01

    Full Text Available This paper presents a geometric approach for modelling tree roots with different Levels of Detail, suitable for analysis of the tree anchoring, potentially occupied underground space, interaction with urban elements and damage produced and taken in the built-in environment. Three types of tree roots are considered to cover several species: tap root, heart shaped root and lateral roots. Shrubs and smaller plants are not considered, however, a similar approach can be considered if the information is available for individual species. The geometrical approach considers the difficulties of modelling the actual roots, which are dynamic and almost opaque to direct observation, proposing generalized versions. For each type of root, different geometric models are considered to capture the overall shape of the root, a simplified block model, and a planar or surface projected version. Lower detail versions are considered as compatibility version for 2D systems while higher detail models are suitable for 3D analysis and visualization. The proposed levels of detail are matched with CityGML Levels of Detail, enabling both analysis and aesthetic views for urban modelling.

  10. Geometric Modelling of Tree Roots with Different Levels of Detail

    Science.gov (United States)

    Guerrero Iñiguez, J. I.

    2017-09-01

    This paper presents a geometric approach for modelling tree roots with different Levels of Detail, suitable for analysis of the tree anchoring, potentially occupied underground space, interaction with urban elements and damage produced and taken in the built-in environment. Three types of tree roots are considered to cover several species: tap root, heart shaped root and lateral roots. Shrubs and smaller plants are not considered, however, a similar approach can be considered if the information is available for individual species. The geometrical approach considers the difficulties of modelling the actual roots, which are dynamic and almost opaque to direct observation, proposing generalized versions. For each type of root, different geometric models are considered to capture the overall shape of the root, a simplified block model, and a planar or surface projected version. Lower detail versions are considered as compatibility version for 2D systems while higher detail models are suitable for 3D analysis and visualization. The proposed levels of detail are matched with CityGML Levels of Detail, enabling both analysis and aesthetic views for urban modelling.

  11. Optical coatings material aspects in theory and practice

    CERN Document Server

    Stenzel, Olaf

    2014-01-01

    Optical coatings, i.e. multilayer stacks composed from a certain number of thin individual layers, are an essential part of any optical system necessary to tailor the properties of the optical surfaces. Hereby, the performance of any optical coating is defined by a well-balanced interplay between the properties of the individual coating materials and the geometrical parameters (such as film thickness) which define their arrangement. In all scientific books dealing with the performance of optical coatings, the main focus is on optimizing the geometrical coating parameters, particularly the number of individual layers and their thickness. At the same time, much less attention is paid to another degree of freedom in coating design, namely the possibility to tailor optical material properties to an optimum relevant for the required specification. This book, on the contrary, concentrates on the material aside of the problem. After a comprehensive review of the basics of thin film theory, traditional optical coatin...

  12. Computer programs simplify optical system analysis

    Science.gov (United States)

    1965-01-01

    The optical ray-trace computer program performs geometrical ray tracing. The energy-trace program calculates the relative monochromatic flux density on a specific target area. This program uses the ray-trace program as a subroutine to generate a representation of the optical system.

  13. The Wigner distribution function and Hamilton's characteristics of a geometric-optical system

    NARCIS (Netherlands)

    Bastiaans, M.J.

    1979-01-01

    Four system functions have been defined for an optical system; each of these functions describes the system completely in terms of Fourier optics. From the system functions the Wigner distribution function of an optical system has been defined; although derived from Fourier optics, this Wigner

  14. A Geometric Dictionary Learning Based Approach for Fluorescence Spectroscopy Image Fusion

    Directory of Open Access Journals (Sweden)

    Zhiqin Zhu

    2017-02-01

    Full Text Available In recent years, sparse representation approaches have been integrated into multi-focus image fusion methods. The fused images of sparse-representation-based image fusion methods show great performance. Constructing an informative dictionary is a key step for sparsity-based image fusion method. In order to ensure sufficient number of useful bases for sparse representation in the process of informative dictionary construction, image patches from all source images are classified into different groups based on geometric similarities. The key information of each image-patch group is extracted by principle component analysis (PCA to build dictionary. According to the constructed dictionary, image patches are converted to sparse coefficients by simultaneous orthogonal matching pursuit (SOMP algorithm for representing the source multi-focus images. At last the sparse coefficients are fused by Max-L1 fusion rule and inverted to fused image. Due to the limitation of microscope, the fluorescence image cannot be fully focused. The proposed multi-focus image fusion solution is applied to fluorescence imaging area for generating all-in-focus images. The comparison experimentation results confirm the feasibility and effectiveness of the proposed multi-focus image fusion solution.

  15. Rejuvenating Allen's Arc with the Geometric Mean.

    Science.gov (United States)

    Phillips, William A.

    1994-01-01

    Contends that, despite ongoing criticism, Allen's arc elasticity formula remains entrenched in the microeconomics principles curriculum. Reviews the evolution and continuing scrutiny of the formula. Argues that the use of the geometric mean offers pedagogical advantages over the traditional arithmetic mean approach. (CFR)

  16. On Kaehler's geometric description of dirac fields

    International Nuclear Information System (INIS)

    Goeckeler, M.; Joos, H.

    1983-12-01

    A differential geometric generalization of the Dirac equation due to E. Kaehler seems to be an appropriate starting point for the lattice approximation of matter fields. It is the purpose of this lecture to illustrate several aspects of this approach. (orig./HSI)

  17. Two strategies of lowering surface deformations of internally cooled X-ray optics

    International Nuclear Information System (INIS)

    Oberta, P.; Áč, V.; Hrdý, J.

    2013-01-01

    Internally cooled X-ray optics, like X-ray monochromators and reflecting X-ray mirrors, play a crucial role in defining a beamlines resolution, degree of coherence and flux. A great effort is invested in the development of these optical components. An important aspect of the functionality of high heat load optics is its cooling and its influence on surface deformation. The authors present a study of two different geometrical cooling approaches. Its influence on beam inhomogeneity due to the strain from the manufacturing process is presented. X-ray topographic images and FWHM measurements are presented. FEA simulations of cooling efficiency and surface deformations were performed. The best achieved results are under an enlargement of 0.4μrad of the measured rocking curve

  18. Self-interference digital holography with a geometric-phase hologram lens.

    Science.gov (United States)

    Choi, KiHong; Yim, Junkyu; Yoo, Seunghwi; Min, Sung-Wook

    2017-10-01

    Self-interference digital holography (SIDH) is actively studied because the hologram acquisition under the incoherent illumination condition is available. The key component in this system is wavefront modulating optics, which modulates an incoming object wave into two different wavefront curvatures. In this Letter, the geometric-phase hologram lens is introduced in the SIDH system to perform as a polarization-sensitive wavefront modulator and a single-path beam splitter. This special optics has several features, such as high transparency, a modulation efficiency up to 99%, a thinness of a few millimeters, and a flat structure. The demonstration system is devised, and the numerical reconstruction results from an acquired complex hologram are presented.

  19. Asymptotic approach to the pricing of geometric asian options under the CEV model

    International Nuclear Information System (INIS)

    Lee, Min-Ku

    2016-01-01

    This paper studies the pricing of Asian options whose payoffs depend on the average value of an underlying asset during the period to a maturity. Since the Asian option is not so sensitive to the value of underlying asset, the possibility of manipulation is relatively small than the other options such as European vanilla and barrier options. We derive the pricing formula of geometric Asian options under the constant elasticity of variance (CEV) model that is one of local volatility models, and investigate the implication of the CEV model for geometric Asian options.

  20. Bat Species Comparisons Based on External Morphology: A Test of Traditional versus Geometric Morphometric Approaches.

    Science.gov (United States)

    Schmieder, Daniela A; Benítez, Hugo A; Borissov, Ivailo M; Fruciano, Carmelo

    2015-01-01

    External morphology is commonly used to identify bats as well as to investigate flight and foraging behavior, typically relying on simple length and area measures or ratios. However, geometric morphometrics is increasingly used in the biological sciences to analyse variation in shape and discriminate among species and populations. Here we compare the ability of traditional versus geometric morphometric methods in discriminating between closely related bat species--in this case European horseshoe bats (Rhinolophidae, Chiroptera)--based on morphology of the wing, body and tail. In addition to comparing morphometric methods, we used geometric morphometrics to detect interspecies differences as shape changes. Geometric morphometrics yielded improved species discrimination relative to traditional methods. The predicted shape for the variation along the between group principal components revealed that the largest differences between species lay in the extent to which the wing reaches in the direction of the head. This strong trend in interspecific shape variation is associated with size, which we interpret as an evolutionary allometry pattern.

  1. Bat Species Comparisons Based on External Morphology: A Test of Traditional versus Geometric Morphometric Approaches.

    Directory of Open Access Journals (Sweden)

    Daniela A Schmieder

    Full Text Available External morphology is commonly used to identify bats as well as to investigate flight and foraging behavior, typically relying on simple length and area measures or ratios. However, geometric morphometrics is increasingly used in the biological sciences to analyse variation in shape and discriminate among species and populations. Here we compare the ability of traditional versus geometric morphometric methods in discriminating between closely related bat species--in this case European horseshoe bats (Rhinolophidae, Chiroptera--based on morphology of the wing, body and tail. In addition to comparing morphometric methods, we used geometric morphometrics to detect interspecies differences as shape changes. Geometric morphometrics yielded improved species discrimination relative to traditional methods. The predicted shape for the variation along the between group principal components revealed that the largest differences between species lay in the extent to which the wing reaches in the direction of the head. This strong trend in interspecific shape variation is associated with size, which we interpret as an evolutionary allometry pattern.

  2. Nonimaging optical concentrators using graded-index dielectric.

    Science.gov (United States)

    Zitelli, M

    2014-04-01

    A new generation of inhomogeneous nonimaging optical concentrators is proposed, able to achieve simultaneously high optical efficiency and acceptance solid angle at a given geometrical concentration factor. General design methods are given, and concentrators are numerically investigated and optimized.

  3. High-performance geometric phase elements in silica glass

    Directory of Open Access Journals (Sweden)

    Rokas Drevinskas

    2017-06-01

    Full Text Available High-precision three-dimensional ultrafast laser direct nanostructuring of silica glass resulting in multi-layered space-variant dielectric metasurfaces embedded in volume is demonstrated. Continuous phase profiles of nearly any optical component are achieved solely by the means of geometric phase. Complex designs of half-wave retarders with 90% transmission at 532 nm and >95% transmission at >1 μm, including polarization gratings with efficiency nearing 90% and computer generated holograms with a phase gradient of ∼0.8π rad/μm, were fabricated. A vortex half-wave retarder generating a single beam optical vortex with a tunable orbital angular momentum of up to ±100ℏ is shown. The high damage threshold of silica elements enables the simultaneous optical manipulation of a large number of micro-objects using high-power laser beams. Thus, the continuous control of torque without altering the intensity distribution was implemented in optical trapping demonstration with a total of 5 W average power, which is otherwise impossible with alternate beam shaping devices. In principle, the direct-write technique can be extended to any transparent material that supports laser assisted nanostructuring and can be effectively exploited for the integration of printed optics into multi-functional optoelectronic systems.

  4. Visualizing the Geometric Series.

    Science.gov (United States)

    Bennett, Albert B., Jr.

    1989-01-01

    Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

  5. Lyapunov vs. geometrical stability analysis of the Kepler and the restricted three body problems

    International Nuclear Information System (INIS)

    Yahalom, A.; Levitan, J.; Lewkowicz, M.; Horwitz, L.

    2011-01-01

    In this Letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al. predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well. - Highlights: → Lyapunov analysis predicts Kepler motion to be unstable. → Geometrical analysis predicts the observed stability. → Lyapunov analysis predicts chaotic behavior in restricted three body problem. → The geometric approach predicts the correct stable motion in restricted three body problem.

  6. Geometric analysis

    CERN Document Server

    Bray, Hubert L; Mazzeo, Rafe; Sesum, Natasa

    2015-01-01

    This volume includes expanded versions of the lectures delivered in the Graduate Minicourse portion of the 2013 Park City Mathematics Institute session on Geometric Analysis. The papers give excellent high-level introductions, suitable for graduate students wishing to enter the field and experienced researchers alike, to a range of the most important areas of geometric analysis. These include: the general issue of geometric evolution, with more detailed lectures on Ricci flow and Kähler-Ricci flow, new progress on the analytic aspects of the Willmore equation as well as an introduction to the recent proof of the Willmore conjecture and new directions in min-max theory for geometric variational problems, the current state of the art regarding minimal surfaces in R^3, the role of critical metrics in Riemannian geometry, and the modern perspective on the study of eigenfunctions and eigenvalues for Laplace-Beltrami operators.

  7. Complementary Huygens Principle for Geometrical and Nongeometrical Optics

    Science.gov (United States)

    Luis, Alfredo

    2007-01-01

    We develop a fundamental principle depicting the generalized ray formulation of optics provided by the Wigner function. This principle is formally identical to the Huygens-Fresnel principle but in terms of opposite concepts, rays instead of waves, and incoherent superpositions instead of coherent ones. This ray picture naturally includes…

  8. On bivariate geometric distribution

    Directory of Open Access Journals (Sweden)

    K. Jayakumar

    2013-05-01

    Full Text Available Characterizations of bivariate geometric distribution using univariate and bivariate geometric compounding are obtained. Autoregressive models with marginals as bivariate geometric distribution are developed. Various bivariate geometric distributions analogous to important bivariate exponential distributions like, Marshall-Olkin’s bivariate exponential, Downton’s bivariate exponential and Hawkes’ bivariate exponential are presented.

  9. On the geometric nature of high energy nucleus-nucleus reaction cross sections

    International Nuclear Information System (INIS)

    Townsend, L.W.; Wilson, J.W.; Bidasaria, H.B.

    1982-01-01

    Within the context of a high energy double-folding optical potential approximation to the exact nucleus-nucleus multiple-scattering series, eikonal scattering theory is used to investigate the validity of geometric reaction cross sections in relativistic heavy ion collisions. The potential used includes a finite range interaction and nuclear single-particle densities extracted from nuclear charge distributions by unfolding the proton charge distribution. Pauli correlation effects are also included in an approximate way. The sensitivity of the predictions to be assumed interaction, Pauli correlation approximation, and nuclear density distributions is investigated. These results are in agreement with early predictions concerning the geometric nature of relativistic heavy ion collisions and in disagreement with a recent analysis, utilizing the zero range approximation, which suggested otherwise. Reasons for the lack of agreement between the analyses are also presented. Finally, approximate applicability for geometric reaction cross sections are determined

  10. Autocorrelated process control: Geometric Brownian Motion approach versus Box-Jenkins approach

    Science.gov (United States)

    Salleh, R. M.; Zawawi, N. I.; Gan, Z. F.; Nor, M. E.

    2018-04-01

    Existing of autocorrelation will bring a significant effect on the performance and accuracy of process control if the problem does not handle carefully. When dealing with autocorrelated process, Box-Jenkins method will be preferred because of the popularity. However, the computation of Box-Jenkins method is too complicated and challenging which cause of time-consuming. Therefore, an alternative method which known as Geometric Brownian Motion (GBM) is introduced to monitor the autocorrelated process. One real case of furnace temperature data is conducted to compare the performance of Box-Jenkins and GBM methods in monitoring autocorrelation process. Both methods give the same results in terms of model accuracy and monitoring process control. Yet, GBM is superior compared to Box-Jenkins method due to its simplicity and practically with shorter computational time.

  11. Concepts of classical optics

    CERN Document Server

    Strong, John

    1958-01-01

    An intermediate course in optics, this volume explores both experimental and theoretical concepts, offering practical knowledge of geometrical optics that will enhance students' comprehension of any relevant applied science. Its exposition of the concepts of classical optics is presented with a minimum of mathematical detail but presumes some knowledge of calculus, vectors, and complex numbers.Subjects include light as wave motion; superposition of wave motions; electromagnetic waves; interaction of light and matter; velocities and scattering of light; polarized light and dielectric boundarie

  12. Geometrical phases from global gauge invariance of nonlinear classical field theories

    International Nuclear Information System (INIS)

    Garrison, J.C.; Chiao, R.Y.

    1988-01-01

    We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics

  13. Spherical projections and liftings in geometric tomography

    DEFF Research Database (Denmark)

    Goodey, Paul; Kiderlen, Markus; Weil, Wolfgang

    2011-01-01

    We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies and to rad......We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies...... and to radial functions of star bodies. We then investigate averages of lifted projections and show that they correspond to self-adjoint intertwining operators. We obtain formulas for the eigenvalues of these operators and use them to ascertain circumstances under which tomographic measurements determine...... the original bodies. This approach via mean lifted projections leads us to some unexpected relationships between seemingly disparate geometric constructions....

  14. Beam splitter phase shifts: Wave optics approach

    Science.gov (United States)

    Agnesi, Antonio; Degiorgio, Vittorio

    2017-10-01

    We investigate the phase relationships between transmitted and reflected waves in a lossless beam splitter having a multilayer structure, using the matrix approach as outlined in classical optics books. Contrarily to the case of the quantum optics formalism generally employed to describe beam splitters, these matrices are not unitary. In this note we point out the existence of general relations among the elements of the transfer matrix that describes the multilayer beam splitter. Such relations, which are independent of the detailed structure of the beam splitter, fix the phase shifts between reflected and transmitted waves. It is instructive to see how the results obtained by Zeilinger by using spinor algebra and Pauli matrices can be easily derived from our general relations.

  15. Geometric and Applied Optics, Science (Experimental): 5318.04.

    Science.gov (United States)

    Sanderson, Robert C.

    This unit of instruction presents a laboratory-oriented course which relates the sources and behaviors of light to man's control and uses of light. Successful completion of Algebra I and Plane Geometry is strongly recommended as indicators of success. The course is recommended if the student plans further studies in science, optical technology, or…

  16. The differential-geometric aspects of integrable dynamical systems

    International Nuclear Information System (INIS)

    Prykarpatsky, Y.A.; Samoilenko, A.M.; Prykarpatsky, A.K.; Bogolubov, N.N. Jr.; Blackmore, D.L.

    2007-05-01

    The canonical reduction method on canonically symplectic manifolds is analyzed in detail, and the relationships with the geometric properties of associated principal fiber bundles endowed with connection structures are described. Some results devoted to studying geometrical properties of nonabelian Yang-Mills type gauge field equations are presented. A symplectic theory approach is developed for partially solving the problem of algebraic-analytical construction of integral submanifold embeddings for integrable (via the abelian and nonabelian Liouville-Arnold theorems) Hamiltonian systems on canonically symplectic phase spaces. The fundamental role of the so-called Picard-Fuchs type equations is revealed, and their differential-geometric and algebraic properties are studied in detail. Some interesting examples of integrable Hamiltonian systems are are studied in detail in order to demonstrate the ease of implementation and effectiveness of the procedure for investigating the integral submanifold embedding mapping. (author)

  17. Three-dimensional crossbar interconnection using planar-integrated free-space optics and digital mirror-device

    Science.gov (United States)

    Lohmann, U.; Jahns, J.; Limmer, S.; Fey, D.

    2011-01-01

    We consider the implementation of a dynamic crossbar interconnect using planar-integrated free-space optics (PIFSO) and a digital mirror-device™ (DMD). Because of the 3D nature of free-space optics, this approach is able to solve geometrical problems with crossings of the signal paths that occur in waveguide optical and electrical interconnection, especially for large number of connections. The DMD device allows one to route the signals dynamically. Due to the large number of individual mirror elements in the DMD, different optical path configurations are possible, thus offering the chance for optimizing the network configuration. The optimization is achieved by using an evolutionary algorithm for finding best values for a skewless parallel interconnection. Here, we present results and experimental examples for the use of the PIFSO/DMD-setup.

  18. Error performance analysis in K-tier uplink cellular networks using a stochastic geometric approach

    KAUST Repository

    Afify, Laila H.

    2015-09-14

    In this work, we develop an analytical paradigm to analyze the average symbol error probability (ASEP) performance of uplink traffic in a multi-tier cellular network. The analysis is based on the recently developed Equivalent-in-Distribution approach that utilizes stochastic geometric tools to account for the network geometry in the performance characterization. Different from the other stochastic geometry models adopted in the literature, the developed analysis accounts for important communication system parameters and goes beyond signal-to-interference-plus-noise ratio characterization. That is, the presented model accounts for the modulation scheme, constellation type, and signal recovery techniques to model the ASEP. To this end, we derive single integral expressions for the ASEP for different modulation schemes due to aggregate network interference. Finally, all theoretical findings of the paper are verified via Monte Carlo simulations.

  19. Geometrical parton

    Energy Technology Data Exchange (ETDEWEB)

    Ebata, T [Tohoku Univ., Sendai (Japan). Coll. of General Education

    1976-06-01

    The geometrical distribution inferred from the inelastic cross section is assumed to be proportional to the partial waves. The precocious scaling and the Q/sup 2/-dependence of various quantities are treated from the geometrical point of view. It is shown that the approximate conservation of the orbital angular momentum may be a very practical rule to understand the helicity structure of various hadronic and electromagnetic reactions. The rule can be applied to inclusive reactions as well. The model is also applied to large angle processes. Through the discussion, it is suggested that many peculiar properties of the quark-parton can be ascribed to the geometrical effects.

  20. Improved Object Proposals with Geometrical Features for Autonomous Driving

    Directory of Open Access Journals (Sweden)

    Yiliu Feng

    2017-01-01

    Full Text Available This paper aims at generating high-quality object proposals for object detection in autonomous driving. Most existing proposal generation methods are designed for the general object detection, which may not perform well in a particular scene. We propose several geometrical features suited for autonomous driving and integrate them into state-of-the-art general proposal generation methods. In particular, we formulate the integration as a feature fusion problem by fusing the geometrical features with existing proposal generation methods in a Bayesian framework. Experiments on the challenging KITTI benchmark demonstrate that our approach improves the existing methods significantly. Combined with a convolutional neural net detector, our approach achieves state-of-the-art performance on all three KITTI object classes.

  1. Analysis of aggregate optical spectra using moments. Application to the purple membrane of halobacterium halobium

    International Nuclear Information System (INIS)

    Hemenger, R.P.

    1978-01-01

    The problem of extracting structural information from the optical spectra of aggregates of molecules interacting through their electronic transitions is studied. One serious difficulty common to all approaches to this problem is that of properly taking into account the effects of molecular vibrations. A series of exact relations derived previously which are correct with regard to molecular vibrations provide a number of independent, explicit connections between aggregate geometrical parameters and moments of experimental spectra. It is shown that, by applying these moment relations to the optical absorption and circular dichroism spectra of simple aggregates, a complete set of equations can be found, i.e., enough equations can be found to solve for all of the geometrical parameters which enter into the expressions for absorption and circular dichroism spectra. This procedure is applied in some detail to the purple membrane of Halobacterium halobium. The results are completely consistent with what is known about its structure

  2. Analysis of Geometric Thinking Students’ and Process-Guided Inquiry Learning Model

    Science.gov (United States)

    Hardianti, D.; Priatna, N.; Priatna, B. A.

    2017-09-01

    This research aims to analysis students’ geometric thinking ability and theoretically examine the process-oriented guided iquiry (POGIL) model. This study uses qualitative approach with descriptive method because this research was done without any treatment on subjects. Data were collected naturally. This study was conducted in one of the State Junior High School in Bandung. The population was second grade students and the sample was 32 students. Data of students’ geometric thinking ability were collected through geometric thinking test. These questions are made based on the characteristics of geometry thinking based on van hiele’s theory. Based on the results of the analysis and discussion, students’ geometric thinking ability is still low so it needs to be improved. Therefore, an effort is needed to overcome the problems related to students’ geometric thinking ability. One of the efforts that can be done by doing the learning that can facilitate the students to construct their own geometry concept, especially quadrilateral’s concepts so that students’ geometric thinking ability can enhance maximally. Based on study of the theory, one of the learning models that can enhance the students’ geometric thinking ability is POGIL model.

  3. A new approach to stitching optical metrology data

    Science.gov (United States)

    King, Christopher W.

    The next generation of optical instruments, including telescopes and imaging apparatus, will generate an increased requirement for larger and more complex optical forms. A major limiting factor for the production of such optical components is the metrology: how do we measure such parts and with respect to what reference datum This metrology can be thought of as part of a complete cycle in the production of optical components and it is currently the most challenging aspect of production. This thesis investigates a new and complete approach to stitching optical metrology data to extend the effective aperture or, in future, the dynamic range of optical metrology instruments. A practical approach is used to build up a complete process for stitching on piano and spherical parts. The work forms a basis upon which a stitching system for aspheres might be developed in the future, which is inherently more complicated. Beginning with a historical perspective and a review of optical polishing and metrology, the work presented relates the commercially available metrology instruments to the stitching process developed. The stitching is then performed by a numerical optimization routine that seeks to join together overlapping sub-aperture measurements by consideration of the aberrations introduced by the measurement scenario, and by the overlap areas between measurements. The stitching is part of a larger project, the PPARC Optical Manipulation and Metrology project, and was to benefit from new wavefront sensing technology developed by a project partner, and to be used for the sub-aperture measurement. Difficult mathematical problems meant that such a wavefront sensor was not avail able for this work and a work-around was therefore developed using commercial instruments. The techniques developed can be adapted to work on commercial ma chine platforms, and in partuicular, the OMAM NPL/UCL swing-arm profilometer described in chapter 5, or the computer controlled polishing machines

  4. Handbook of optical design

    CERN Document Server

    Malacara-Hernández, Daniel

    2013-01-01

    Handbook of Optical Design, Third Edition covers the fundamental principles of geometric optics and their application to lens design in one volume. It incorporates classic aspects of lens design along with important modern methods, tools, and instruments, including contemporary astronomical telescopes, Gaussian beams, and computer lens design. Written by respected researchers, the book has been extensively classroom-tested and developed in their lens design courses. This well-illustrated handbook clearly and concisely explains the intricacies of optical system design and evaluation. It also di

  5. THE METHOD OF GEOMETRIC CALIBRATION OF OPTOELECTRONIC SYSTEMS BASED ON ELECTRONIC TEST OBJECT

    Directory of Open Access Journals (Sweden)

    D. A. Kozhevnikov

    2017-01-01

    Full Text Available Designing remote sensing of the Earth devices is requires a lot of attention to evaluation lens distortion level and providing the required accuracy values of geometric calibration of optoelectronic systems at all. Test- objects known as most common tools for optical systems geometric calibration. The purpose of the research was creating an automatically method of distortion correction coefficients calculating with a 3 μm precision in the measurement process. The method of geometric calibration of the internal orientation elements of the optical system based on the electronic test object is proposed. The calculation of the test string brightness image from its multispectral image and filtered signal extrema position determination are presented. Ratio of magnitude of the distortion and interval center is given. Three variants of electronic test-objects with different step and element size are considered. Оptimal size of calibration element was defined as 3×3 pixels due to shape of the subpixels with the aspect ratio of the radiating areas about 1 : 3. It is advisable to use IPS as an electronic test object template. An experimental test and measurement stand functional diagram based on the collimator and optical bench «OSK-2CL» is showed. It was determined that test objects with a grid spacing of 4 and 8 pixels can’t provide tolerable image because of non-collimated emission of active sites and scattering on optical surfaces – the shape of the elements is substantially disrupted. Test-object with a 12 pixels grid spacing was used to distortion level analyzing as most suitable.Ratio of coordinate increment and element number graphs for two photographic lenses (Canon EF-S 17-85 f/4-5.6 IS USM and EF-S 18-55 f/3.5-5.6 IS II are presented. A calculation of the distortion values in edge zones was held, which were respectively 43 μm and 51.6 μm. The technique and algorithm of software implementation is described. Possible directions of the

  6. Strong dependence of rain-induced lidar depolarization on the illumination angle: experimental evidence and geometrical-optics interpretation.

    Science.gov (United States)

    Roy, G; Bissonnette, L R

    2001-09-20

    Backscatter and depolarization lidar measurements from clouds and precipitation are reported as functions of the elevation angle of the pointing lidar direction. We recorded the data by scanning the lidar beam (Nd:YAG) at a constant angular speed of ~3.5 degrees /s while operating at a repetition rate of 10 Hz. We show that in rain there is an evident and at times spectacular dependence on the elevation angle. That dependence appears to be sensitive to raindrop size. We have developed a three-dimensional polarization-dependent ray-tracing algorithm to calculate the backscatter and the depolarization ratio by large nonspherical droplets. We have applied it to raindrop shapes derived from existing static and dynamic (oscillating) models. We show that many of the observed complex backscatter and depolarization features can be interpreted to a good extent by geometrical optics. These results suggest that there is a definite need for more extensive calculations of the scattering phase matrix elements for large deformed raindrops as functions of the direction of illumination. Obvious applications are retrieval of information on the liquid-solid phase of precipitation and on the size and the vibration state of raindrops.

  7. Practice-oriented optical thin film growth simulation via multiple scale approach

    Energy Technology Data Exchange (ETDEWEB)

    Turowski, Marcus, E-mail: m.turowski@lzh.de [Laser Zentrum Hannover e.V., Hollerithallee 8, Hannover 30419 (Germany); Jupé, Marco [Laser Zentrum Hannover e.V., Hollerithallee 8, Hannover 30419 (Germany); QUEST: Centre of Quantum Engineering and Space-Time Research, Leibniz Universität Hannover (Germany); Melzig, Thomas [Fraunhofer Institute for Surface Engineering and Thin Films IST, Bienroder Weg 54e, Braunschweig 30108 (Germany); Moskovkin, Pavel [Research Centre for Physics of Matter and Radiation (PMR-LARN), University of Namur (FUNDP), 61 rue de Bruxelles, Namur 5000 (Belgium); Daniel, Alain [Centre for Research in Metallurgy, CRM, 21 Avenue du bois Saint Jean, Liège 4000 (Belgium); Pflug, Andreas [Fraunhofer Institute for Surface Engineering and Thin Films IST, Bienroder Weg 54e, Braunschweig 30108 (Germany); Lucas, Stéphane [Research Centre for Physics of Matter and Radiation (PMR-LARN), University of Namur (FUNDP), 61 rue de Bruxelles, Namur 5000 (Belgium); Ristau, Detlev [Laser Zentrum Hannover e.V., Hollerithallee 8, Hannover 30419 (Germany); QUEST: Centre of Quantum Engineering and Space-Time Research, Leibniz Universität Hannover (Germany)

    2015-10-01

    Simulation of the coating process is a very promising approach for the understanding of thin film formation. Nevertheless, this complex matter cannot be covered by a single simulation technique. To consider all mechanisms and processes influencing the optical properties of the growing thin films, various common theoretical methods have been combined to a multi-scale model approach. The simulation techniques have been selected in order to describe all processes in the coating chamber, especially the various mechanisms of thin film growth, and to enable the analysis of the resulting structural as well as optical and electronic layer properties. All methods are merged with adapted communication interfaces to achieve optimum compatibility of the different approaches and to generate physically meaningful results. The present contribution offers an approach for the full simulation of an Ion Beam Sputtering (IBS) coating process combining direct simulation Monte Carlo, classical molecular dynamics, kinetic Monte Carlo, and density functional theory. The simulation is performed exemplary for an existing IBS-coating plant to achieve a validation of the developed multi-scale approach. Finally, the modeled results are compared to experimental data. - Highlights: • A model approach for simulating an Ion Beam Sputtering (IBS) process is presented. • In order to combine the different techniques, optimized interfaces are developed. • The transport of atomic species in the coating chamber is calculated. • We modeled structural and optical film properties based on simulated IBS parameter. • The modeled and the experimental refractive index data fit very well.

  8. Further results on geometric operators in quantum gravity

    NARCIS (Netherlands)

    Loll, R.

    1996-01-01

    We investigate some properties of geometric operators in canonical quantum gravity in the connection approach `a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous discretized lattice quantities, compute various quantum

  9. Comparing Different Approaches to Visualizing Light Waves: An Experimental Study on Teaching Wave Optics

    Science.gov (United States)

    Mešic, Vanes; Hajder, Erna; Neumann, Knut; Erceg, Nataša

    2016-01-01

    Research has shown that students have tremendous difficulties developing a qualitative understanding of wave optics, at all educational levels. In this study, we investigate how three different approaches to visualizing light waves affect students' understanding of wave optics. In the first, the conventional, approach light waves are represented…

  10. Nonlinear Optics Approaches Towards Subdiffraction Resolution in CARS Imaging

    NARCIS (Netherlands)

    Boller, Klaus J.; Beeker, W.P.; Cleff, C.; Kruse, K.; Lee, Christopher James; Gross, P.; Offerhaus, Herman L.; Fallnich, Carsten; Herek, Jennifer Lynn; Fornasiero, E.F.; Rizzoli, S.O.

    2014-01-01

    In theoretical investigations, we review several nonlinear optical approaches towards subdiffraction-limited resolution in label-free imaging via coherent anti-Stokes Raman scattering (CARS). Using a density matrix model and numerical integration, we investigate various level schemes and

  11. Geometrical methods in learning theory

    International Nuclear Information System (INIS)

    Burdet, G.; Combe, Ph.; Nencka, H.

    2001-01-01

    The methods of information theory provide natural approaches to learning algorithms in the case of stochastic formal neural networks. Most of the classical techniques are based on some extremization principle. A geometrical interpretation of the associated algorithms provides a powerful tool for understanding the learning process and its stability and offers a framework for discussing possible new learning rules. An illustration is given using sequential and parallel learning in the Boltzmann machine

  12. Geometric Design Laboratory

    Data.gov (United States)

    Federal Laboratory Consortium — Purpose: The mission of the Geometric Design Laboratory (GDL) is to support the Office of Safety Research and Development in research related to the geometric design...

  13. Reflective optics

    CERN Document Server

    Korsch, Dietrich

    1991-01-01

    This is the first book dedicated exclusively to all-reflective imaging systems. It is a teaching tool as well as a practical design tool for anyone who specializes in optics, particularly for those interested in telescopes, infrared, and grazing-incidence systems. The first part of the book describes a unified geometric optical theory of all-reflective imaging systems (from near-normal to grazing incidence) developed from basic principles. The second part discusses correction methods and a multitude of closed-form solutions of well-corrected systems, supplemented with many conventional and unc

  14. Polarization Control with Plasmonic Antenna Tips: A Universal Approach to Optical Nanocrystallography and Vector-Field Imaging

    Science.gov (United States)

    Park, Kyoung-Duck; Raschke, Markus B.

    2018-05-01

    Controlling the propagation and polarization vectors in linear and nonlinear optical spectroscopy enables to probe the anisotropy of optical responses providing structural symmetry selective contrast in optical imaging. Here we present a novel tilted antenna-tip approach to control the optical vector-field by breaking the axial symmetry of the nano-probe in tip-enhanced near-field microscopy. This gives rise to a localized plasmonic antenna effect with significantly enhanced optical field vectors with control of both \\textit{in-plane} and \\textit{out-of-plane} components. We use the resulting vector-field specificity in the symmetry selective nonlinear optical response of second-harmonic generation (SHG) for a generalized approach to optical nano-crystallography and -imaging. In tip-enhanced SHG imaging of monolayer MoS$_2$ films and single-crystalline ferroelectric YMnO$_3$, we reveal nano-crystallographic details of domain boundaries and domain topology with enhanced sensitivity and nanoscale spatial resolution. The approach is applicable to any anisotropic linear and nonlinear optical response, and provides for optical nano-crystallographic imaging of molecular or quantum materials.

  15. The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

    Science.gov (United States)

    Estabrook, F. B.; Wahlquist, H. D.

    1975-01-01

    The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

  16. Tangram solved? Prefrontal cortex activation analysis during geometric problem solving.

    Science.gov (United States)

    Ayaz, Hasan; Shewokis, Patricia A; Izzetoğlu, Meltem; Çakır, Murat P; Onaral, Banu

    2012-01-01

    Recent neuroimaging studies have implicated prefrontal and parietal cortices for mathematical problem solving. Mental arithmetic tasks have been used extensively to study neural correlates of mathematical reasoning. In the present study we used geometric problem sets (tangram tasks) that require executive planning and visuospatial reasoning without any linguistic representation interference. We used portable optical brain imaging (functional near infrared spectroscopy--fNIR) to monitor hemodynamic changes within anterior prefrontal cortex during tangram tasks. Twelve healthy subjects were asked to solve a series of computerized tangram puzzles and control tasks that required same geometric shape manipulation without problem solving. Total hemoglobin (HbT) concentration changes indicated a significant increase during tangram problem solving in the right hemisphere. Moreover, HbT changes during failed trials (when no solution found) were significantly higher compared to successful trials. These preliminary results suggest that fNIR can be used to assess cortical activation changes induced by geometric problem solving. Since fNIR is safe, wearable and can be used in ecologically valid environments such as classrooms, this neuroimaging tool may help to improve and optimize learning in educational settings.

  17. Engineering modes in optical fibers with metamaterial

    DEFF Research Database (Denmark)

    Yan, Min; Mortensen, Asger; Qiu, Min

    2009-01-01

    In this paper, we report a preliminary theoretical study on optical fibers with fine material inclusions whose geometrical inhomogeneity is almost indistinguishable by the operating wavelength.We refer to such fibers as metamaterial optical fibers, which can conceptually be considered...... as an extension from the previously much publicized microstructured optical fibers. Metamaterials can have optical properties not obtainable in naturally existing materials, including artificial anisotropy as well as graded material properties. Therefore, incorporation of metamaterial in optical fiber designs can...

  18. Cluster Validity Classification Approaches Based on Geometric Probability and Application in the Classification of Remotely Sensed Images

    Directory of Open Access Journals (Sweden)

    LI Jian-Wei

    2014-08-01

    Full Text Available On the basis of the cluster validity function based on geometric probability in literature [1, 2], propose a cluster analysis method based on geometric probability to process large amount of data in rectangular area. The basic idea is top-down stepwise refinement, firstly categories then subcategories. On all clustering levels, use the cluster validity function based on geometric probability firstly, determine clusters and the gathering direction, then determine the center of clustering and the border of clusters. Through TM remote sensing image classification examples, compare with the supervision and unsupervised classification in ERDAS and the cluster analysis method based on geometric probability in two-dimensional square which is proposed in literature 2. Results show that the proposed method can significantly improve the classification accuracy.

  19. Optical and geometrical properties of cirrus clouds in Amazonia derived from 1 year of ground-based lidar measurements

    Science.gov (United States)

    Gouveia, Diego A.; Barja, Boris; Barbosa, Henrique M. J.; Seifert, Patric; Baars, Holger; Pauliquevis, Theotonio; Artaxo, Paulo

    2017-03-01

    Cirrus clouds cover a large fraction of tropical latitudes and play an important role in Earth's radiation budget. Their optical properties, altitude, vertical and horizontal coverage control their radiative forcing, and hence detailed cirrus measurements at different geographical locations are of utmost importance. Studies reporting cirrus properties over tropical rain forests like the Amazon, however, are scarce. Studies with satellite profilers do not give information on the diurnal cycle, and the satellite imagers do not report on the cloud vertical structure. At the same time, ground-based lidar studies are restricted to a few case studies. In this paper, we derive the first comprehensive statistics of optical and geometrical properties of upper-tropospheric cirrus clouds in Amazonia. We used 1 year (July 2011 to June 2012) of ground-based lidar atmospheric observations north of Manaus, Brazil. This dataset was processed by an automatic cloud detection and optical properties retrieval algorithm. Upper-tropospheric cirrus clouds were observed more frequently than reported previously for tropical regions. The frequency of occurrence was found to be as high as 88 % during the wet season and not lower than 50 % during the dry season. The diurnal cycle shows a minimum around local noon and maximum during late afternoon, associated with the diurnal cycle of precipitation. The mean values of cirrus cloud top and base heights, cloud thickness, and cloud optical depth were 14.3 ± 1.9 (SD) km, 12.9 ± 2.2 km, 1.4 ± 1.1 km, and 0.25 ± 0.46, respectively. Cirrus clouds were found at temperatures down to -90 °C. Frequently cirrus were observed within the tropical tropopause layer (TTL), which are likely associated to slow mesoscale uplifting or to the remnants of overshooting convection. The vertical distribution was not uniform, and thin and subvisible cirrus occurred more frequently closer to the tropopause. The mean lidar ratio was 23.3 ± 8.0 sr. However, for

  20. The Wigner distribution function applied to optical signals and systems

    NARCIS (Netherlands)

    Bastiaans, M.J.

    1978-01-01

    In this paper the Wigner distribution function has been introduced for optical signals and systems. The Wigner distribution function of an optical signal appears to be in close resemblance to the ray concept in geometrical optics. This resemblance reaches even farther: although derived from Fourier

  1. Alternative approach of developing all-optical Fredkin and Toffoli gates

    Science.gov (United States)

    Mandal, Dhoumendra; Mandal, Sumana; Garai, Sisir Kumar

    2015-09-01

    Reversible logic gates show potential roles in communication technology, and it has a wide area of applicability such as in sequential and combinational circuit of optical computing, optical signal processing, multi-valued logic operations, etc. because of its advantageous aspects of data-recovering capabilities, low power consumption, least power dissipation, faster speed of processing, less hardware complexity, etc. In a reversible logic gate not only the outputs can be determined from the inputs, but also the inputs can be uniquely recovered from the outputs. In this article an alternative approach has been made to develop three-input-output Fredkin and Toffoli gates using the frequency conversion property of semiconductor optical amplifier (SOA) and frequency-based beam routing by optical multiplexers and demultiplexers. Simulation results show the feasibility of our proposed scheme.

  2. Geometric Models for Collaborative Search and Filtering

    Science.gov (United States)

    Bitton, Ephrat

    2011-01-01

    This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…

  3. Fiber-Optic Chemical Sensors and Fiber-Optic Bio-Sensors

    Science.gov (United States)

    Pospíšilová, Marie; Kuncová, Gabriela; Trögl, Josef

    2015-01-01

    This review summarizes principles and current stage of development of fiber-optic chemical sensors (FOCS) and biosensors (FOBS). Fiber optic sensor (FOS) systems use the ability of optical fibers (OF) to guide the light in the spectral range from ultraviolet (UV) (180 nm) up to middle infrared (IR) (10 µm) and modulation of guided light by the parameters of the surrounding environment of the OF core. The introduction of OF in the sensor systems has brought advantages such as measurement in flammable and explosive environments, immunity to electrical noises, miniaturization, geometrical flexibility, measurement of small sample volumes, remote sensing in inaccessible sites or harsh environments and multi-sensing. The review comprises briefly the theory of OF elaborated for sensors, techniques of fabrications and analytical results reached with fiber-optic chemical and biological sensors. PMID:26437407

  4. Fiber-Optic Chemical Sensors and Fiber-Optic Bio-Sensors.

    Science.gov (United States)

    Pospíšilová, Marie; Kuncová, Gabriela; Trögl, Josef

    2015-09-30

    This review summarizes principles and current stage of development of fiber-optic chemical sensors (FOCS) and biosensors (FOBS). Fiber optic sensor (FOS) systems use the ability of optical fibers (OF) to guide the light in the spectral range from ultraviolet (UV) (180 nm) up to middle infrared (IR) (10 μm) and modulation of guided light by the parameters of the surrounding environment of the OF core. The introduction of OF in the sensor systems has brought advantages such as measurement in flammable and explosive environments, immunity to electrical noises, miniaturization, geometrical flexibility, measurement of small sample volumes, remote sensing in inaccessible sites or harsh environments and multi-sensing. The review comprises briefly the theory of OF elaborated for sensors, techniques of fabrications and analytical results reached with fiber-optic chemical and biological sensors.

  5. Technical Approaches For Implementation Of CSMA/CD On A Fiber Optic Medium

    Science.gov (United States)

    Cronin, William J.

    1990-01-01

    The IEEE 802.3 10BASE-F Task Force is currently working on two approaches for 10 Megabit per second CSMA/CD networks using fiber optic media. The two approaches have distinct application spaces. One approach is based on Passive Fiber Optic Star technology, the other on Active Star technology. One standard, covering both application spaces, is expected sometime in 1991. This paper will summarize the proposals presented to the committee, and its predecessors, over the last two years. Three types of proposals were considered for the Active Star application space. These included CSMA/CD on a ring topology, an Active Star based on the Fiber Optic Inter Repeater Link, and an Active Star based on a synchronous signaling scheme. Three proposals were considered for the Passive Star application space. These included techniques for detecting collisions via special pulses, code rule violations, and amplitude sensing techniques. The paper concludes with a summary of the proposals being standardized by the 10BASE-F Task Force.

  6. Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space

    Science.gov (United States)

    Wang, Yong-Long; Jiang, Hua; Zong, Hong-Shi

    2017-08-01

    In the spirit of the thin-layer quantization approach, we give the formula of the geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space. The geometric contributions can result from the reduced commutation relation between the acted function depending on normal variable and the normal derivative. According to the formula, we obtain the geometric potential, geometric momentum, geometric orbital angular momentum, geometric linear Rashba, and cubic Dresselhaus spin-orbit couplings. As an example, a truncated cone surface is considered. We find that the geometric orbital angular momentum can provide an azimuthal polarization for spin, and the sign of the geometric Dresselhaus spin-orbit coupling can be flipped through the inclination angle of generatrix.

  7. Geometric scaling behavior of the scattering amplitude for DIS with nuclei

    Science.gov (United States)

    Kormilitzin, Andrey; Levin, Eugene; Tapia, Sebastian

    2011-12-01

    The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky-Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran-Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at x=1/mR given by the solution to Balitsky-Kovchegov equation, leads to the geometric scaling behavior. The McLerran-Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory.

  8. Geometric scaling behavior of the scattering amplitude for DIS with nuclei

    International Nuclear Information System (INIS)

    Kormilitzin, Andrey; Levin, Eugene; Tapia, Sebastian

    2011-01-01

    The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky–Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran–Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at x A =1/mR A given by the solution to Balitsky–Kovchegov equation, leads to the geometric scaling behavior. The McLerran–Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory.

  9. Image Retrieval based on Integration between Color and Geometric Moment Features

    International Nuclear Information System (INIS)

    Saad, M.H.; Saleh, H.I.; Konbor, H.; Ashour, M.

    2012-01-01

    Content based image retrieval is the retrieval of images based on visual features such as colour, texture and shape. .the Current approaches to CBIR differ in terms of which image features are extracted; recent work deals with combination of distances or scores from different and usually independent representations in an attempt to induce high level semantics from the low level descriptors of the images. content-based image retrieval has many application areas such as, education, commerce, military, searching, commerce, and biomedicine and Web image classification. This paper proposes a new image retrieval system, which uses color and geometric moment feature to form the feature vectors. Bhattacharyya distance and histogram intersection are used to perform feature matching. This framework integrates the color histogram which represents the global feature and geometric moment as local descriptor to enhance the retrieval results. The proposed technique is proper for precisely retrieving images even in deformation cases such as geometric deformations and noise. It is tested on a standard the results shows that a combination of our approach as a local image descriptor with other global descriptors outperforms other approaches.

  10. ''Atomic Optics'': Nonimaging Optics on the Nanoscale

    Energy Technology Data Exchange (ETDEWEB)

    Roland Winston Joseph O' Gallagher

    2005-01-15

    This is the final report for a one year close out extension of our basic research program that was established at the University of Chicago more than sixteen years ago to explore and develop the optical sub-discipline that has come to be known as ''nonimaging optics''. This program has been extremely fruitful, having both broadened the range of formalism available for workers in this field and led to the discovery of many new families of optical devices. These devices and techniques have applications wherever the efficient transport and transformation of light distributions are important, in particular in illumination, fiber optics, collection and concentration of sunlight, and the detection of faint light signals in physics and astrophysics. Over the past thirty years, Nonimaging Optics (Welford and Winston, 1989) has brought a fresh approach to the analysis of many problems in classical macro-scale optics. Through the application of phase-space concepts, statistical methods, thermodynamic arguments, etc., many previously established performance limits were able to be broken and many technical surprises with exciting practical applications were discovered. The most recent three-year phase of our long-term continuing program ended in late 2002 and emphasized extending our work in geometrical optics and expanding it to include some interesting questions in physical optics as well as in the new field of statistical optics. This report presents a survey of the basic history and concepts of nonimaging optics and reviews highlights and significant accomplishments over the past fifteen years. This is followed by a more detailed summary of recent research directions and accomplishments during the last three years. This most recent phase was marked by the broadening in scope to include a separate project involving a collaboration with an industrial partner, Science Applications International Corporation (SAIC). This effort was proposed and approved in

  11. LUCID - an optical design and raytrace code

    International Nuclear Information System (INIS)

    Nicholas, D.J.; Duffey, K.P.

    1980-11-01

    A 2D optical design and ray trace code is described. The code can operate either as a geometric optics propagation code or provide a scalar diffraction treatment. There are numerous non-standard options within the code including design and systems optimisation procedures. A number of illustrative problems relating to the design of optical components in the field of high power lasers is included. (author)

  12. Polarizing Beam Splitter: A New Approach Based on Transformation Optics

    Science.gov (United States)

    Mueller, Jonhatan; Wegener, Martin

    Standard optical elements (e.g. lenses, prisms) are mostly designed of piecewise homogeneous and isotropic dielectrics. However, in theory one has far more possibilities to influence electromagnetic waves, namely all the components of the permittivity and permeability tensors. In the past few years, on the one hand, new micro fabrication methods allowed for new freedom in controlling of the optical parameters using so called artificial metamaterials. On the other hand, the theory of transformation optics has given a somewhat intuitive approach for the design of such structures. The most popular feature of this kind is certainly optical cloaking (i.e. [1,2]). However, the full capabilities of other transformation optical devices are far from being fully explored. In my work, I focused on pure dielectric structures in a non-resonant and therefore non-lossy regime. Although the relative permittivity one can achieve this way is limited by the available natural dielectrics, a broad spectrum of features can be realized.

  13. Geometrical metrology on vacuum cast silicone rubber form using computed tomography

    DEFF Research Database (Denmark)

    Pacurar, Ramona; Müller, Pavel; De Chiffre, Leonardo

    An investigation on geometrical measurements of silicone rubber cake form and polyamide molds using three measuring techniques - CMM, optical scanner and CT scanner - was carried out. The only measurand was diameter of a cone measured at specified levels. An uncertainty budget for all three...... techniques. It was found that when the silicon rubber form was measured on the supported bottom mold or the bottom mold was measured itself, the diameter measurements performed on optical scanner and CT scanner were bigger compared to CMM measurements. On the other hand, the diameter resulted in smaller...... values when the silicon rubber form was measured on the supported top mold or the top mold was measured itself. A procedure for measurement of highly deformable part, such as silicone rubber form, was developed. Uncertainties from measurement on the optical scanner were big. This was mainly connected...

  14. Modeling thermodynamic distance, curvature and fluctuations a geometric approach

    CERN Document Server

    Badescu, Viorel

    2016-01-01

    This textbook aims to briefly outline the main directions in which the geometrization of thermodynamics has been developed in the last decades. The textbook is accessible to people trained in thermal sciences but not necessarily with solid formation in mathematics. For this, in the first chapters a summary of the main mathematical concepts is made. In some sense, this makes the textbook self-consistent. The rest of the textbook consists of a collection of results previously obtained in this young branch of thermodynamics. The manner of presentation used throughout the textbook is adapted for ease of access of readers with education in natural and technical sciences.

  15. Electronic and optical properties of finite carbon nanotubes in an electric field

    International Nuclear Information System (INIS)

    Chen, R B; Lee, C H; Chang, C P; Lin, M F

    2007-01-01

    The effects, caused by the geometric structure and an electric field (E), on the electronic and optical properties of quasi-zero-dimensional finite carbon nanotubes are explored by employing the tight-binding model coupled with curvature effects. Electronic properties (state energies, symmetry of electronic states, energy spacing and state degeneracy) are significantly affected by the magnitude and the direction of the electric field and the geometric structure (radius, length and chirality). The electric field, by lowering the symmetry of finite carbon nanotubes, modifies the electronic properties. Thus, the optical excitation spectra, excited by electric polarization parallel to the nanotube axis, exhibit rich delta-function-like peaks, which reveal the characteristics of the electronic properties. Therefore it follows that geometric structure and E influence the low-energy absorption spectra, i.e. the change of frequency of the first peak, the alternation of the peak height and the production of the new peaks. There are more absorption peaks when E is oriented closer to the cross-section plane. Moreover, the very complicated optical absorption spectra are characteristic for the individual chiral carbon nanotube due to its specific geometric structure. Above all, the predicted absorption spectra and the associated electronic properties could be verified by optical measurements

  16. Tailoring optical complex field with spiral blade plasmonic vortex lens

    Science.gov (United States)

    Rui, Guanghao; Zhan, Qiwen; Cui, Yiping

    2015-01-01

    Optical complex fields have attracted increasing interests because of the novel effects and phenomena arising from the spatially inhomogeneous state of polarizations and optical singularities of the light beam. In this work, we propose a spiral blade plasmonic vortex lens (SBPVL) that offers unique opportunities to manipulate these novel fields. The strong interaction between the SBPVL and the optical complex fields enable the synthesis of highly tunable plasmonic vortex. Through theoretical derivations and numerical simulations we demonstrated that the characteristics of the plasmonic vortex are determined by the angular momentum (AM) of the light, and the geometrical topological charge of the SBPVL, which is govern by the nonlinear superposition of the pitch and the number of blade element. In addition, it is also shown that by adjusting the geometric parameters, SBPVL can be utilized to focus and manipulate optical complex field with fractional AM. This miniature plasmonic device may find potential applications in optical trapping, optical data storage and many other related fields. PMID:26335894

  17. Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations

    KAUST Repository

    Carles, Ré mi; Dumas, Eric; Sparber, Christof

    2010-01-01

    We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrödinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation of the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrödinger equation on the torus in negative order Sobolev spaces. © 2010 Society for Industrial and Applied Mathematics.

  18. Light distribution in diffractive multifocal optics and its optimization.

    Science.gov (United States)

    Portney, Valdemar

    2011-11-01

    To expand a geometrical model of diffraction efficiency and its interpretation to the multifocal optic and to introduce formulas for analysis of far and near light distribution and their application to multifocal intraocular lenses (IOLs) and to diffraction efficiency optimization. Medical device consulting firm, Newport Coast, California, USA. Experimental study. Application of a geometrical model to the kinoform (single focus diffractive optical element) was expanded to a multifocal optic to produce analytical definitions of light split between far and near images and light loss to other diffraction orders. The geometrical model gave a simple interpretation of light split in a diffractive multifocal IOL. An analytical definition of light split between far, near, and light loss was introduced as curve fitting formulas. Several examples of application to common multifocal diffractive IOLs were developed; for example, to light-split change with wavelength. The analytical definition of diffraction efficiency may assist in optimization of multifocal diffractive optics that minimize light loss. Formulas for analysis of light split between different foci of multifocal diffractive IOLs are useful in interpreting diffraction efficiency dependence on physical characteristics, such as blaze heights of the diffractive grooves and wavelength of light, as well as for optimizing multifocal diffractive optics. Disclosure is found in the footnotes. Copyright © 2011 ASCRS and ESCRS. Published by Elsevier Inc. All rights reserved.

  19. Optical appearance of white holes

    International Nuclear Information System (INIS)

    Lake, K.; Roeder, R.C.

    1978-01-01

    The detailed optical properties of white holes are examined within the framework of geometrical optics. It is shown that the appearance of the objects most likely to be observed at late times is in fact determined by their early histories. These ccalculations indicate that one cannot invoke the simple concept of a stable white hole as a ''natural'' explanation of highly energetic astrophysical phenomena

  20. Geometric algebra with applications in science and engineering

    CERN Document Server

    Sobczyk, Garret

    2001-01-01

    The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer­ ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar­ ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math­ ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling ...

  1. Control of the spin geometric phase in semiconductor quantum rings.

    Science.gov (United States)

    Nagasawa, Fumiya; Frustaglia, Diego; Saarikoski, Henri; Richter, Klaus; Nitta, Junsaku

    2013-01-01

    Since the formulation of the geometric phase by Berry, its relevance has been demonstrated in a large variety of physical systems. However, a geometric phase of the most fundamental spin-1/2 system, the electron spin, has not been observed directly and controlled independently from dynamical phases. Here we report experimental evidence on the manipulation of an electron spin through a purely geometric effect in an InGaAs-based quantum ring with Rashba spin-orbit coupling. By applying an in-plane magnetic field, a phase shift of the Aharonov-Casher interference pattern towards the small spin-orbit-coupling regions is observed. A perturbation theory for a one-dimensional Rashba ring under small in-plane fields reveals that the phase shift originates exclusively from the modulation of a pure geometric-phase component of the electron spin beyond the adiabatic limit, independently from dynamical phases. The phase shift is well reproduced by implementing two independent approaches, that is, perturbation theory and non-perturbative transport simulations.

  2. The effect of photometric and geometric context on photometric and geometric lightness effects.

    Science.gov (United States)

    Lee, Thomas Y; Brainard, David H

    2014-01-24

    We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects.

  3. Frame-Based Facial Expression Recognition Using Geometrical Features

    Directory of Open Access Journals (Sweden)

    Anwar Saeed

    2014-01-01

    Full Text Available To improve the human-computer interaction (HCI to be as good as human-human interaction, building an efficient approach for human emotion recognition is required. These emotions could be fused from several modalities such as facial expression, hand gesture, acoustic data, and biophysiological data. In this paper, we address the frame-based perception of the universal human facial expressions (happiness, surprise, anger, disgust, fear, and sadness, with the help of several geometrical features. Unlike many other geometry-based approaches, the frame-based method does not rely on prior knowledge of a person-specific neutral expression; this knowledge is gained through human intervention and not available in real scenarios. Additionally, we provide a method to investigate the performance of the geometry-based approaches under various facial point localization errors. From an evaluation on two public benchmark datasets, we have found that using eight facial points, we can achieve the state-of-the-art recognition rate. However, this state-of-the-art geometry-based approach exploits features derived from 68 facial points and requires prior knowledge of the person-specific neutral expression. The expression recognition rate using geometrical features is adversely affected by the errors in the facial point localization, especially for the expressions with subtle facial deformations.

  4. Optimal Route Searching with Multiple Dynamical Constraints—A Geometric Algebra Approach

    Directory of Open Access Journals (Sweden)

    Dongshuang Li

    2018-05-01

    Full Text Available The process of searching for a dynamic constrained optimal path has received increasing attention in traffic planning, evacuation, and personalized or collaborative traffic service. As most existing multiple constrained optimal path (MCOP methods cannot search for a path given various types of constraints that dynamically change during the search, few approaches for dynamic multiple constrained optimal path (DMCOP with type II dynamics are available for practical use. In this study, we develop a method to solve the DMCOP problem with type II dynamics based on the unification of various types of constraints under a geometric algebra (GA framework. In our method, the network topology and three different types of constraints are represented by using algebraic base coding. With a parameterized optimization of the MCOP algorithm based on a greedy search strategy under the generation-refinement paradigm, this algorithm is found to accurately support the discovery of optimal paths as the constraints of numerical values, nodes, and route structure types are dynamically added to the network. The algorithm was tested with simulated cases of optimal tourism route searches in China’s road networks with various combinations of constraints. The case study indicates that our algorithm can not only solve the DMCOP with different types of constraints but also use constraints to speed up the route filtering.

  5. Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review.

    Science.gov (United States)

    Savio, Gianpaolo; Rosso, Stefano; Meneghello, Roberto; Concheri, Gianmaria

    2018-01-01

    Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed.

  6. 3D geometrically isotropic metamaterial for telecom wavelengths

    DEFF Research Database (Denmark)

    Malureanu, Radu; Andryieuski, Andrei; Lavrinenko, Andrei

    2009-01-01

    of the unit cell is not infinitely small, certain geometrical constraints have to be fulfilled to obtain an isotropic response of the material [3]. These conditions and the metal behaviour close to the plasma frequency increase the design complexity. Our unit cell is composed of two main parts. The first part...... is obtained in a certain bandwidth. The proposed unit cell has the cubic point group of symmetry and being repeatedly placed in space can effectively reveal isotropic optical properties. We use the CST commercial software to characterise the “cube-in-cage” structure. Reflection and transmission spectra...

  7. Robust Geometric Control of a Distillation Column

    DEFF Research Database (Denmark)

    Kymmel, Mogens; Andersen, Henrik Weisberg

    1987-01-01

    A frequency domain method, which makes it possible to adjust multivariable controllers with respect to both nominal performance and robustness, is presented. The basic idea in the approach is that the designer assigns objectives such as steady-state tracking, maximum resonance peaks, bandwidth, m...... is used to examine and improve geometric control of a binary distillation column....

  8. A new approach for the verification of optical systems

    Science.gov (United States)

    Siddique, Umair; Aravantinos, Vincent; Tahar, Sofiène

    2013-09-01

    Optical systems are increasingly used in microsystems, telecommunication, aerospace and laser industry. Due to the complexity and sensitivity of optical systems, their verification poses many challenges to engineers. Tra­ditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide perfectly accurate results due to the risk of human error and inherent approximations of numerical algorithms. In order to overcome these limitations, we propose to use theorem proving (i.e., a computer-based technique that allows to express mathematical expressions and reason about them by taking into account all the details of mathematical reasoning) as an alternative to computational and numerical approaches to improve optical system analysis in a comprehensive framework. In particular, this paper provides a higher-order logic (a language used to express mathematical theories) formalization of ray optics in the HOL Light theorem prover. Based on the multivariate analysis library of HOL Light, we formalize the notion of light ray and optical system (by defining medium interfaces, mirrors, lenses, etc.), i.e., we express these notions mathematically in the software. This allows us to derive general theorems about the behavior of light in such optical systems. In order to demonstrate the practical effectiveness, we present the stability analysis of a Fabry-Perot resonator.

  9. Functional geometric method for solving free boundary problems for harmonic functions

    Energy Technology Data Exchange (ETDEWEB)

    Demidov, Aleksander S [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

    2010-01-01

    A survey is given of results and approaches for a broad spectrum of free boundary problems for harmonic functions of two variables. The main results are obtained by the functional geometric method. The core of these methods is an interrelated analysis of the functional and geometric characteristics of the problems under consideration and of the corresponding non-linear Riemann-Hilbert problems. An extensive list of open questions is presented. Bibliography: 124 titles.

  10. Optical design of transmitter lens for asymmetric distributed free space optical networks

    Science.gov (United States)

    Wojtanowski, Jacek; Traczyk, Maciej

    2018-05-01

    We present a method of transmitter lens design dedicated for light distribution shaping on a curved and asymmetric target. In this context, target is understood as a surface determined by hypothetical optical detectors locations. In the proposed method, ribbon-like surfaces of arbitrary shape are considered. The designed lens has the task to transform collimated and generally non-uniform input beam into desired irradiance distribution on such irregular targets. Desired irradiance is associated with space-dependant efficiency of power flow between the source and receivers distributed on the target surface. This unconventional nonimaging task is different from most illumination or beam shaping objectives, where constant or prescribed irradiance has to be produced on a flat target screen. The discussed optical challenge comes from the applications where single transmitter cooperates with multitude of receivers located in various positions in space and oriented in various directions. The proposed approach is not limited to optical networks, but can be applied in a variety of other applications where nonconventional irradiance distribution has to be engineered. The described method of lens design is based on geometrical optics, radiometry and ray mapping philosophy. Rays are processed as a vector field, each of them carrying a certain amount of power. Having the target surface shape and orientation of receivers distribution, the rays-surface crossings map is calculated. It corresponds to the output rays vector field, which is referred to the calculated input rays spatial distribution on the designed optical surface. The application of Snell's law in a vector form allows one to obtain surface local normal vector and calculate lens profile. In the paper, we also present the case study dealing with exemplary optical network. The designed freeform lens is implemented in commercially available optical design software and irradiance three-dimensional spatial distribution is

  11. Right-invertibility for a class of nonlinear control systems: A geometric approach

    NARCIS (Netherlands)

    Nijmeijer, Henk

    1986-01-01

    In recent years it has become evident that various synthesis problems known from linear system theory can also be solved for nonlinear control systems by using differential geometric methods. The purpose of this paper is to use this mathematical framework for giving a preliminary account on the

  12. Optimization of the geometrical stability in square ring laser gyroscopes

    International Nuclear Information System (INIS)

    Santagata, R; Beghi, A; Cuccato, D; Belfi, J; Beverini, N; Virgilio, A Di; Ortolan, A; Porzio, A; Solimeno, S

    2015-01-01

    Ultra-sensitive ring laser gyroscopes are regarded as potential detectors of the general relativistic frame-dragging effect due to the rotation of the Earth. Our project for this goal is called GINGER (gyroscopes in general relativity), and consists of a ground-based triaxial array of ring lasers aimed at measuring the rotation rate of the Earth with an accuracy of 10 −14 rad s −1 . Such an ambitious goal is now within reach, as large-area ring lasers are very close to the required sensitivity and stability. However, demanding constraints on the geometrical stability of the optical path of the laser inside the ring cavity are required. Thus, we have begun a detailed study of the geometry of an optical cavity in order to find a control strategy for its geometry that could meet the specifications of the GINGER project. As the cavity perimeter has a stationary point for the square configuration, we identify a set of transformations on the mirror positions that allows us to adjust the laser beam steering to the shape of a square. We show that the geometrical stability of a square cavity strongly increases by implementing a suitable system to measure the mirror distances, and that the geometry stabilization can be achieved by measuring the absolute lengths of the two diagonals and the perimeter of the ring. (paper)

  13. Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics

    Science.gov (United States)

    McClelland, Ryan S.

    2016-01-01

    Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low thermal distortion. Recent results are discussed including Structural Thermal Optical Performance (STOP) analysis as well as vibration and shock testing of prototype meta-shells.

  14. Geometrical relaxation of excitations in one-dimensional conjugated polymers; Giichijigen kyoeki kobunshi reiki jotai no shusa kozo kanwa

    Energy Technology Data Exchange (ETDEWEB)

    Yoshizawa, M. [Tohoku University, Sendai (Japan). Faculty of Engineering

    1995-12-15

    Large ultrafast optical nonlinearities in conjugated polymers have attracted much attention because of possible applications to nonlinear optical devices. One-dimensional systems such as conjugated polymers have localized excited states with geometrical relaxation. In this study, photoexcited states in polydiacetylene has been investigated by femtosecond Raman gain spectroscopy with 300-fs resolution. A new photoinduced Raman peak with lifetime of 1.5 ps has been observed at 1200cm{sup -1} for the first time. This peak indicates acetylene-like structure of the main chain relaxes to butatriene-like structure due to the formation of self-trapped exciting with the geometrical relaxation. The formation and decay kinetics of the Raman signals is consistent with the relaxation processes of exciting observed by femtosecond absorption spectroscopy. 8 refs., 5 figs.

  15. A Geometric Approach to CP Violation: Applications to the MCPMFV SUSY Model

    CERN Document Server

    Ellis, John; Pilaftsis, Apostolos

    2010-01-01

    We analyze the constraints imposed by experimental upper limits on electric dipole moments (EDMs) within the Maximally CP- and Minimally Flavour-Violating (MCPMFV) version of the MSSM. Since the MCPMFV scenario has 6 non-standard CP-violating phases, in addition to the CP-odd QCD vacuum phase \\theta_QCD, cancellations may occur among the CP-violating contributions to the three measured EDMs, those of the Thallium, neutron and Mercury, leaving open the possibility of relatively large values of the other CP-violating observables. We develop a novel geometric method that uses the small-phase approximation as a starting point, takes the existing EDM constraints into account, and enables us to find maximal values of other CP-violating observables, such as the EDMs of the Deuteron and muon, the CP-violating asymmetry in b --> s \\gamma decay, and the B_s mixing phase. We apply this geometric method to provide upper limits on these observables within specific benchmark supersymmetric scenarios, including extensions t...

  16. Geometric group theory

    CERN Document Server

    Druţu, Cornelia

    2018-01-01

    The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the f...

  17. Lagrangian optics

    CERN Document Server

    Lakshminarayanan, Vasudevan; Thyagarajan, K

    2002-01-01

    Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the ...

  18. A high precision recipe for correcting images distorted by a tapered fiber optic

    International Nuclear Information System (INIS)

    Islam, M Sirajul; Kitchen, M J; Lewis, R A; Uesugi, K

    2010-01-01

    Images captured with a tapered fiber optic camera show significant spatial distortion mainly because the spatial orientation of the fiber bundles is not identical at each end of the taper. We present three different techniques for the automatic distortion correction of images acquired with a charge-coupled device (CCD) camera bonded to a tapered optical fiber. In this paper we report - (i) comparison of various methods for distortion correction (ii) extensive quantitative analysis of the techniques and (iii) experiments carried out using a high resolution fiber optic camera. A pinhole array was used to find control points in the distorted image space. These control points were then associated with their known true coordinates. To apply geometric correction, three different approaches were investigated - global polynomial fitting, local polynomial fitting and triangulated interpolation. Sub-pixel accuracy was achieved in all approaches, but the experimental results reveal that the triangulated interpolation gave the most satisfactory result for the distortion correction. The effect of proper alignment of the mask with the fiber optic taper (FOT) camera was also investigated. It was found that the overall dewarping error is minimal when the mask is almost parallel to the CCD.

  19. Fiber-Optic Chemical Sensors and Fiber-Optic Bio-Sensors

    Directory of Open Access Journals (Sweden)

    Marie Pospíšilová

    2015-09-01

    Full Text Available This review summarizes principles and current stage of development of fiber-optic chemical sensors (FOCS and biosensors (FOBS. Fiber optic sensor (FOS systems use the ability of optical fibers (OF to guide the light in the spectral range from ultraviolet (UV (180 nm up to middle infrared (IR (10 μm and modulation of guided light by the parameters of the surrounding environment of the OF core. The introduction of OF in the sensor systems has brought advantages such as measurement in flammable and explosive environments, immunity to electrical noises, miniaturization, geometrical flexibility, measurement of small sample volumes, remote sensing in inaccessible sites or harsh environments and multi-sensing. The review comprises briefly the theory of OF elaborated for sensors, techniques of fabrications and analytical results reached with fiber-optic chemical and biological sensors.

  20. Reconstruction of the spatial dependence of dielectric and geometrical properties of adhesively bonded structures

    International Nuclear Information System (INIS)

    Mackay, C; Hayward, D; Mulholland, A J; McKee, S; Pethrick, R A

    2005-01-01

    An inverse problem motivated by the nondestructive testing of adhesively bonded structures used in the aircraft industry is studied. Using transmission line theory, a model is developed which, when supplied with electrical and geometrical parameters, accurately predicts the reflection coefficient associated with such structures. Particular attention is paid to modelling the connection between the structures and the equipment used to measure the reflection coefficient. The inverse problem is then studied and an optimization approach employed to recover these electrical and geometrical parameters from experimentally obtained data. In particular the approach focuses on the recovery of spatially varying geometrical parameters as this is paramount to the successful reconstruction of electrical parameters. Reconstructions of structure geometry using this method are found to be in close agreement with experimental observations

  1. Imaginary geometric phases of quantum trajectories in high-order terahertz sideband generation

    Science.gov (United States)

    Yang, Fan; Liu, Ren-Bao

    2014-03-01

    Quantum evolution of particles under strong fields can be described by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integral. The quantum trajectories are the key concept to understand the high-order terahertz siedeband generation (HSG) in semiconductors. Due to the nontrivial ``vacuum'' states of band materials, the quantum trajectories of optically excited electron-hole pairs in semiconductors can accumulate geometric phases under the driving of an elliptically polarized THz field. We find that the geometric phase of the stationary trajectory is generally complex with both real and imaginary parts. In monolayer MoS2, the imaginary parts of the geometric phase leads to a changing of the polarization ellipticity of the sideband. We further show that the imaginary part originates from the quantum interference of many trajectories with different phases. Thus the observation of the polarization ellipticity of the sideband shall be a good indication of the quantum nature of the stationary trajectory. This work is supported by Hong Kong RGC/GRF 401512 and the CUHK Focused Investments Scheme.

  2. The Master level optics laboratory at the Institute of Optics

    Science.gov (United States)

    Adamson, Per

    2017-08-01

    The master level optics laboratory is a biannual, intensive laboratory course in the fields of geometrical, physical and modern optics. This course is intended for the master level student though Ph.D. advisors which often recommend it to their advisees. The students are required to complete five standard laboratory experiments and an independent project during a semester. The goals of the laboratory experiments are for the students to get hands-on experience setting up optical laboratory equipment, collecting and analyzing data, as well as to communicate key results. The experimental methods, analysis, and results of the standard experiments are submitted in a journal style report, while an oral presentation is given for the independent project.

  3. Manual of the Option.com program (ion optics); Manual del programa Option.com

    Energy Technology Data Exchange (ETDEWEB)

    Fernandez B, M

    1991-02-15

    The laws that govern the trajectory that follow the charged particles in the hole, inside magnetic fields (to first approach) are similar to those of the geometric classic optics by it to observe a graph of the trajectories gives an excellent understanding of that is happening to the beam. The object of this program is that besides providing the numeric data of the solution of the problem of the transverse section of the beam, be also shown a graph of the trajectories but external regarding the optic axis in the treated region and aid the user asking in the case of a system of two quadrupoles, where it is wanted to focus the beam. (Author)

  4. Noise and signal interference in optical fiber transmission systems an optimum design approach

    CERN Document Server

    Bottacchi, Stefano

    2008-01-01

    A comprehensive reference to noise and signal interference in optical fiber communications Noise and Signal Interference in Optical Fiber Transmission Systems is a compendium on specific topics within optical fiber transmission and the optimization process of the system design. It offers comprehensive treatment of noise and intersymbol interference (ISI) components affecting optical fiber communications systems, containing coverage on noise from the light source, the fiber and the receiver. The ISI is modeled with a statistical approach, leading to new useful computational m

  5. Light and optics conceptual evaluation findings from first year optometry students

    Science.gov (United States)

    Thapa, Damber; Lakshminarayanan, Vasudevan

    2014-07-01

    The Light and Optics Conceptual Evaluation (LOCE) was developed to examine conceptual understanding of basic geometric and physical optics for the Active Learning in Optics and Photonics program administered by UNESCO. This 50 item test (46 multiple choice, 4 ray-tracing short answer) was administered to entering students in the Optometry professional degree (OD) program. We wanted to determine how much of the physics/optics concepts from undergraduate physics courses (a pre-requisite for entry to the OD program) were retained. In addition, the test was administered after the first year students had taken a required course in geometric and visual optics as part of their first semester courses. The LOCE was completed by two consecutive classes to the program in 2010 (n=89) and 2011 (n=84). The tests were administered the first week of the term and the test was given without any prior notice. In addition, the test was administered to the class of 2010 students after they had completed the course in geometric and visual optics. The means of the test were 22.1 (SD=4.5; range: 12-35) and 21.3(SD=5.1; range: 11-35) for the two entering classes. There was no statistical significance between the two classes (t-test, poptometry (and other allied health programs such as opticianry or ophthalmology).

  6. Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review

    Directory of Open Access Journals (Sweden)

    Gianpaolo Savio

    2018-01-01

    Full Text Available Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed.

  7. Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review

    Science.gov (United States)

    Rosso, Stefano; Meneghello, Roberto; Concheri, Gianmaria

    2018-01-01

    Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed. PMID:29487626

  8. On geometrized gravitation theories

    International Nuclear Information System (INIS)

    Logunov, A.A.; Folomeshkin, V.N.

    1977-01-01

    General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe

  9. Type II Superstring Field Theory: Geometric Approach and Operadic Description

    CERN Document Server

    Jurco, Branislav

    2013-01-01

    We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a $\\mathcal{N}=1$ generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.

  10. A multiple kernel classification approach based on a Quadratic Successive Geometric Segmentation methodology with a fault diagnosis case.

    Science.gov (United States)

    Honório, Leonardo M; Barbosa, Daniele A; Oliveira, Edimar J; Garcia, Paulo A Nepomuceno; Santos, Murillo F

    2018-03-01

    This work presents a new approach for solving classification and learning problems. The Successive Geometric Segmentation technique is applied to encapsulate large datasets by using a series of Oriented Bounding Hyper Box (OBHBs). Each OBHB is obtained through linear separation analysis and each one represents a specific region in a pattern's solution space. Also, each OBHB can be seen as a data abstraction layer and be considered as an individual Kernel. Thus, it is possible by applying a quadratic discriminant function, to assemble a set of nonlinear surfaces separating each desirable pattern. This approach allows working with large datasets using high speed linear analysis tools and yet providing a very accurate non-linear classifier as final result. The methodology was tested using the UCI Machine Learning repository and a Power Transformer Fault Diagnosis real scenario problem. The results were compared with different approaches provided by literature and, finally, the potential and further applications of the methodology were also discussed. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  11. Exotic Optical Beam Classes for Free-Space Communication

    Science.gov (United States)

    2016-03-24

    wandering of an optical vortex is one of the significant problems with the application of vortex beams to FSO applications. From a geometrical optics ...AFRL-AFOSR-VA-TR-2016-0131 Exotic optical beam classes for free-space communication Greg Gbur UNIVERSITY OF NOTH CAROLINA AT CHARLOTTE Final Report...12-2015 4. TITLE AND SUBTITLE Exotic optical beam classes for free-space communication 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-13-1-0009 5c

  12. The physical-optics approximation and its application to light backscattering by hexagonal ice crystals

    International Nuclear Information System (INIS)

    Borovoi, A.; Konoshonkin, A.; Kustova, N.

    2014-01-01

    The physical-optics approximation in the problem of light scattering by large particles is so defined that it includes the classical physical optics concerning the problem of light penetration through a large aperture in an opaque screen. In the second part of the paper, the problem of light backscattering by quasi-horizontally oriented atmospheric ice crystals is considered where conformity between the physical-optics and geometric-optics approximations is discussed. The differential scattering cross section as well as the polarization elements of the Mueller matrix for quasi-horizontally oriented hexagonal ice plates has been calculated in the physical-optics approximation for the case of vertically pointing lidars. - Highlights: • The physical-optics Mueller matrix is a smoothed geometric-optics counterpart. • Backscatter by partially oriented hexagonal ice plates has been calculated. • Depolarization ratio for partially oriented hexagonal ice plates is negligible

  13. Physical optics-based diffraction coefficient for a wedge with different face impedances.

    Science.gov (United States)

    Umul, Yusuf Ziya

    2018-03-20

    A new diffraction field expression is introduced with the aid of the modified theory of physical optics for a wedge with different face impedances. First, the scattered geometrical optics fields are determined when both faces of the wedge are illuminated by the incident wave. The geometrical optics waves are then expressed in terms of the sum of two different fields that occur for different impedance wedges. The diffracted fields are determined for the two cases separately, and the total diffracted field is obtained as a sum of these waves. Lastly, the uniform field expressions are obtained, and the resultant fields are numerically compared with the solution of Maliuzhinets.

  14. Geometric Scaling in New Combined Hadron-Electron Ring Accelerator Data

    International Nuclear Information System (INIS)

    Zhou Xiao-Jiao; Qi Lian; Kang Lin; Xiang Wen-Chang; Zhou Dai-Cui

    2014-01-01

    We study the geometric scaling in the new combined data of the hadron-electron ring accelerator by using the Golec-Biernat—Wüsthoff model. It is found that the description of the data is improved once the high accurate data are used to determine the model parameters. The value of x 0 extracted from the fit is larger than the one from the previous study, which indicates a larger saturation scale in the new combined data. This makes more data located in the saturation region, and our approach is more reliable. This study lets the saturation model confront such high precision new combined data, and tests geometric scaling with those data. We demonstrate that the data lie on the same curve, which shows the geometric scaling in the new combined data. This outcome seems to support that the gluon saturation would be a relevant mechanism to dominate the parton evolution process in deep inelastic scattering, due to the fact that the geometric scaling results from the gluon saturation mechanism

  15. Application of the geometrical theory of diffraction to Cassegrain subreflectors with laterally defocused feeds

    DEFF Research Database (Denmark)

    Sørensen, O.; Rusch, W.

    1975-01-01

    The geometrical theory of diffraction (GTD) as formulated by R. G. Kouyoumjian has been applied to predict the radiation characteristics of hyperboloidal subreflectors with laterally defocused feeds. In caustic or multicaustic directions the scattered fields are determined using an equivalent ring...... current placed along the edge of the subreflector. The theoretical results are compared to measured amplitude and phase data. In order to improve the agreement, the blocking effects of the feed horn have been accounted for using the geometrical theory of diffraction. The calculated subreflector fields...... have been used to illuminate a paraboloid from which the scattered field is determined by physical optics. The results are compared to those obtained using a laterally defocused equivalent paraboloid....

  16. Measurement system and model for simultaneously measuring 6DOF geometric errors.

    Science.gov (United States)

    Zhao, Yuqiong; Zhang, Bin; Feng, Qibo

    2017-09-04

    A measurement system to simultaneously measure six degree-of-freedom (6DOF) geometric errors is proposed. The measurement method is based on a combination of mono-frequency laser interferometry and laser fiber collimation. A simpler and more integrated optical configuration is designed. To compensate for the measurement errors introduced by error crosstalk, element fabrication error, laser beam drift, and nonparallelism of two measurement beam, a unified measurement model, which can improve the measurement accuracy, is deduced and established using the ray-tracing method. A numerical simulation using the optical design software Zemax is conducted, and the results verify the correctness of the model. Several experiments are performed to demonstrate the feasibility and effectiveness of the proposed system and measurement model.

  17. Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics

    Science.gov (United States)

    Parker, Jeffrey B.

    2018-05-01

    Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. We find that CE2-GO retains some similarities to QL. The partitioning of energy that resides in the zonal flow is in good quantitative agreement between CE2-GO and QL. On the other hand, the length scale of the zonal flow does not follow the same qualitative trend in the two models. Overall, these simulations indicate that CE2-GO provides a simpler and more tractable statistical paradigm than CE2, but CE2-GO is missing important physics.

  18. PLEIADES HR IN FLIGHT GEOMETRICAL CALIBRATION : LOCATION AND MAPPING OF THE FOCAL PLANE

    Directory of Open Access Journals (Sweden)

    F. de Lussy

    2012-07-01

    Full Text Available The Pleiades system, ORFEO system optical component (Optical and Radar Federated Earth Observation consists of a constellation of two satellites for very High Resolution panchromatic and multispectral optical observation of the Earth. Its mission is to cover all European civilian needs (mapping, tracking floods and fires and defence in the category of metric resolution: 0.7m Nadir. The first Pleiades satellite was launched at the end of last year. One of the key objectives of the Pleiades HR (PHR project is to achieve a location accuracy that will allow the use of images in GIS (Geographical Information System without geometrical model improvement by refining on ground control points. The image location without refined model was specified with the precision of the most commonly used tool ie the civil GPS. So the location accuracy has been specified at less than 12m for 90% of the images on a nominal satellite configuration. Very special care has been taken all along the PHR project realization to achieve this very good location accuracy. The final touch is given during the in-orbit commissioning phase which lasts until June 2012. The geometric quality implies to tune the parameters involved in the geolocation model (geometric calibration: besides attitude and orbit restitution tuning (not considered here, it consists in estimating the biases between the instrument orientation and the AOCS reference frame, and also the sight line of each detector in the focal plane. This is called static geometrical model. The analysis of dynamic perturbations outside of the model are the second most important image quality objective of in-flight commissioning, not described in this paper. Finally “image quality assessment” consists in evaluating the image quality obtained in the final products. For geolocation model, it is quantified by the absolute geolocation and the pointing accuracies, and it is a main contributor in length alteration and planimetric and

  19. Geometric approximation algorithms

    CERN Document Server

    Har-Peled, Sariel

    2011-01-01

    Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

  20. Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues

    KAUST Repository

    Shakir, Muhammad

    2011-12-01

    In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. The largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results. © 2011 IEEE.

  1. Geometric Modeling and Reasoning of Human-Centered Freeform Products

    CERN Document Server

    Wang, Charlie C L

    2013-01-01

    The recent trend in user-customized product design requires the shape of products to be automatically adjusted according to the human body’s shape, so that people will feel more comfortable when wearing these products.  Geometric approaches can be used to design the freeform shape of products worn by people, which can greatly improve the efficiency of design processes in various industries involving customized products (e.g., garment design, toy design, jewel design, shoe design, and design of medical devices, etc.). These products are usually composed of very complex geometric shapes (represented by free-form surfaces), and are not driven by a parameter table but a digital human model with free-form shapes or part of human bodies (e.g., wrist, foot, and head models).   Geometric Modeling and Reasoning of Human-Centered Freeform Products introduces the algorithms of human body reconstruction, freeform product modeling, constraining and reconstructing freeform products, and shape optimization for improving...

  2. Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

    Science.gov (United States)

    Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan

    2015-01-01

    Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

  3. Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

    Directory of Open Access Journals (Sweden)

    Jorge Arrieta

    Full Text Available Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

  4. Generation of optical vortices in an integrated optical circuit

    Science.gov (United States)

    Tudor, Rebeca; Kusko, Mihai; Kusko, Cristian

    2017-09-01

    In this work, the generation of optical vortices in an optical integrated circuit is numerically demonstrated. The optical vortices with topological charge m = ±1 are obtained by the coherent superposition of the first order modes present in a waveguide with a rectangular cross section, where the phase delay between these two propagating modes is Δφ = ±π/2. The optical integrated circuit consists of an input waveguide continued with a y-splitter. The left and the right arms of the splitter form two coupling regions K1 and K2 with a multimode output waveguide. In each coupling region, the fundamental modes present in the arms of the splitter are selectively coupled into the output waveguide horizontal and vertical first order modes, respectively. We showed by employing the beam propagation method simulations that the fine tuning of the geometrical parameters of the optical circuit makes possible the generation of optical vortices in both transverse electric (TE) and transverse magnetic (TM) modes. Also, we demonstrated that by placing a thermo-optical element on one of the y-splitter arms, it is possible to switch the topological charge of the generated vortex from m = 1 to m = -1.

  5. Modeling of Geometric Error in Linear Guide Way to Improved the vertical three-axis CNC Milling machine’s accuracy

    Science.gov (United States)

    Kwintarini, Widiyanti; Wibowo, Agung; Arthaya, Bagus M.; Yuwana Martawirya, Yatna

    2018-03-01

    The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

  6. Huygens-Feynman-Fresnel principle as the basis of applied optics.

    Science.gov (United States)

    Gitin, Andrey V

    2013-11-01

    The main relationships of wave optics are derived from a combination of the Huygens-Fresnel principle and the Feynman integral over all paths. The stationary-phase approximation of the wave relations gives the correspondent relations from the point of view of geometrical optics.

  7. The problem of assessing landmark error in geometric morphometrics: theory, methods, and modifications.

    Science.gov (United States)

    von Cramon-Taubadel, Noreen; Frazier, Brenda C; Lahr, Marta Mirazón

    2007-09-01

    Geometric morphometric methods rely on the accurate identification and quantification of landmarks on biological specimens. As in any empirical analysis, the assessment of inter- and intra-observer error is desirable. A review of methods currently being employed to assess measurement error in geometric morphometrics was conducted and three general approaches to the problem were identified. One such approach employs Generalized Procrustes Analysis to superimpose repeatedly digitized landmark configurations, thereby establishing whether repeat measures fall within an acceptable range of variation. The potential problem of this error assessment method (the "Pinocchio effect") is demonstrated and its effect on error studies discussed. An alternative approach involves employing Euclidean distances between the configuration centroid and repeat measures of a landmark to assess the relative repeatability of individual landmarks. This method is also potentially problematic as the inherent geometric properties of the specimen can result in misleading estimates of measurement error. A third approach involved the repeated digitization of landmarks with the specimen held in a constant orientation to assess individual landmark precision. This latter approach is an ideal method for assessing individual landmark precision, but is restrictive in that it does not allow for the incorporation of instrumentally defined or Type III landmarks. Hence, a revised method for assessing landmark error is proposed and described with the aid of worked empirical examples. (c) 2007 Wiley-Liss, Inc.

  8. Invisibility cloaking via non-smooth transformation optics and ray tracing

    International Nuclear Information System (INIS)

    Crosskey, Miles M.; Nixon, Andrew T.; Schick, Leland M.; Kovacic, Gregor

    2011-01-01

    We present examples of theoretically-predicted invisibility cloaks with shapes other than spheres and cylinders, including cones and ellipsoids, as well as shapes spliced from parts of these simpler shapes. In addition, we present an example explicitly displaying the non-uniqueness of invisibility cloaks of the same shape. We depict rays propagating through these example cloaks using ray tracing for geometric optics. - Highlights: → Theoretically-predicted conical and ellipsoidal invisibility cloaks. → Non-smooth cloaks spliced from parts of simpler shapes. → Example displaying non-uniqueness of invisibility cloaks of the same shape. → Rays propagating through example cloaks depicted using geometric optics.

  9. Optics. Observation of optical polarization Möbius strips.

    Science.gov (United States)

    Bauer, Thomas; Banzer, Peter; Karimi, Ebrahim; Orlov, Sergej; Rubano, Andrea; Marrucci, Lorenzo; Santamato, Enrico; Boyd, Robert W; Leuchs, Gerd

    2015-02-27

    Möbius strips are three-dimensional geometrical structures, fascinating for their peculiar property of being surfaces with only one "side"—or, more technically, being "nonorientable" surfaces. Despite being easily realized artificially, the spontaneous emergence of these structures in nature is exceedingly rare. Here, we generate Möbius strips of optical polarization by tightly focusing the light beam emerging from a q-plate, a liquid crystal device that modifies the polarization of light in a space-variant manner. Using a recently developed method for the three-dimensional nanotomography of optical vector fields, we fully reconstruct the light polarization structure in the focal region, confirming the appearance of Möbius polarization structures. The preparation of such structured light modes may be important for complex light beam engineering and optical micro- and nanofabrication. Copyright © 2015, American Association for the Advancement of Science.

  10. Geometric decomposition of the conformation tensor in viscoelastic turbulence

    Science.gov (United States)

    Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

    2018-05-01

    This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

  11. Ray tracing the Wigner distribution function for optical simulations

    NARCIS (Netherlands)

    Mout, B.M.; Wick, Michael; Bociort, F.; Petschulat, Joerg; Urbach, Paul

    2018-01-01

    We study a simulation method that uses the Wigner distribution function to incorporate wave optical effects in an established framework based on geometrical optics, i.e., a ray tracing engine. We use the method to calculate point spread functions and show that it is accurate for paraxial systems

  12. Transformation optics beyond the manipulation of light trajectories.

    Science.gov (United States)

    Ginis, Vincent; Tassin, Philippe

    2015-08-28

    Since its inception in 2006, transformation optics has become an established tool to understand and design electromagnetic systems. It provides a geometrical perspective into the properties of light waves without the need for a ray approximation. Most studies have focused on modifying the trajectories of light rays, e.g. beam benders, lenses, invisibility cloaks, etc. In this contribution, we explore transformation optics beyond the manipulation of light trajectories. With a few well-chosen examples, we demonstrate that transformation optics can be used to manipulate electromagnetic fields up to an unprecedented level. In the first example, we introduce an electromagnetic cavity that allows for deep subwavelength confinement of light. The cavity is designed with transformation optics even though the concept of trajectory ceases to have any meaning in a structure as small as this cavity. In the second example, we show that the properties of Cherenkov light emitted in a transformation-optical material can be understood and modified from simple geometric considerations. Finally, we show that optical forces--a quadratic function of the fields--follow the rules of transformation optics too. By applying a folded coordinate transformation to a pair of waveguides, optical forces can be enhanced just as if the waveguides were closer together. With these examples, we open up an entirely new spectrum of devices that can be conceived using transformation optics. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

  13. Bridging the Gap between RF and Optical Patch Antenna Analysis via the Cavity Model.

    Science.gov (United States)

    Unal, G S; Aksun, M I

    2015-11-02

    Although optical antennas with a variety of shapes and for a variety of applications have been proposed and studied, they are still in their infancy compared to their radio frequency (rf) counterparts. Optical antennas have mainly utilized the geometrical attributes of rf antennas rather than the analysis tools that have been the source of intuition for antenna engineers in rf. This study intends to narrow the gap of experience and intuition in the design of optical patch antennas by introducing an easy-to-understand and easy-to-implement analysis tool in rf, namely, the cavity model, into the optical regime. The importance of this approach is not only its simplicity in understanding and implementation but also its applicability to a broad class of patch antennas and, more importantly, its ability to provide the intuition needed to predict the outcome without going through the trial-and-error simulations with no or little intuitive guidance by the user.

  14. Phase-space networks of geometrically frustrated systems.

    Science.gov (United States)

    Han, Yilong

    2009-11-01

    We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.

  15. Optic Disc and Optic Cup Segmentation Methodologies for Glaucoma Image Detection: A Survey

    Directory of Open Access Journals (Sweden)

    Ahmed Almazroa

    2015-01-01

    Full Text Available Glaucoma is the second leading cause of loss of vision in the world. Examining the head of optic nerve (cup-to-disc ratio is very important for diagnosing glaucoma and for patient monitoring after diagnosis. Images of optic disc and optic cup are acquired by fundus camera as well as Optical Coherence Tomography. The optic disc and optic cup segmentation techniques are used to isolate the relevant parts of the retinal image and to calculate the cup-to-disc ratio. The main objective of this paper is to review segmentation methodologies and techniques for the disc and cup boundaries which are utilized to calculate the disc and cup geometrical parameters automatically and accurately to help the professionals in the glaucoma to have a wide view and more details about the optic nerve head structure using retinal fundus images. We provide a brief description of each technique, highlighting its classification and performance metrics. The current and future research directions are summarized and discussed.

  16. Optic Disc and Optic Cup Segmentation Methodologies for Glaucoma Image Detection: A Survey

    Science.gov (United States)

    Almazroa, Ahmed; Burman, Ritambhar; Raahemifar, Kaamran; Lakshminarayanan, Vasudevan

    2015-01-01

    Glaucoma is the second leading cause of loss of vision in the world. Examining the head of optic nerve (cup-to-disc ratio) is very important for diagnosing glaucoma and for patient monitoring after diagnosis. Images of optic disc and optic cup are acquired by fundus camera as well as Optical Coherence Tomography. The optic disc and optic cup segmentation techniques are used to isolate the relevant parts of the retinal image and to calculate the cup-to-disc ratio. The main objective of this paper is to review segmentation methodologies and techniques for the disc and cup boundaries which are utilized to calculate the disc and cup geometrical parameters automatically and accurately to help the professionals in the glaucoma to have a wide view and more details about the optic nerve head structure using retinal fundus images. We provide a brief description of each technique, highlighting its classification and performance metrics. The current and future research directions are summarized and discussed. PMID:26688751

  17. Modelling and experimental investigation of geometrically graded NiTi shape memory alloys

    International Nuclear Information System (INIS)

    Shariat, Bashir S; Liu, Yinong; Rio, Gerard

    2013-01-01

    To improve actuation controllability of a NiTi shape memory alloy component in applications, it is desirable to create a wide stress window for the stress-induced martensitic transformation in the alloy. One approach is to create functionally graded NiTi with a geometric gradient in the actuation direction. This geometric gradient leads to transformation load and displacement gradients in the structure. This paper reports a study of the pseudoelastic behaviour of geometrically graded NiTi by means of mechanical model analysis and experimentation using three types of sample geometry. Closed-form solutions are obtained for nominal stress–strain variation of such components under cyclic tensile loading and the predictions are validated with experimental data. The geometrically graded NiTi samples exhibit a distinctive positive stress gradient for the stress-induced martensitic transformation and the slope of the stress gradient can be adjusted by sample geometry design. (paper)

  18. Geometric calibration of a stationary digital breast tomosynthesis system based on distributed carbon nanotube X-ray source arrays.

    Directory of Open Access Journals (Sweden)

    Changhui Jiang

    Full Text Available Stationary digital breast tomosynthesis (sDBT with distributed X-ray sources based on carbon nanotube (CNT field emission cathodes has been recently proposed as an approach that can prevent motion blur produced by traditional DBT systems. In this paper, we simulate a geometric calibration method based on a proposed multi-source CNT X-ray sDBT system. This method is a projection matrix-based approach with seven geometric parameters, all of which can be obtained from only one projection datum of the phantom. To our knowledge, this study reports the first application of this approach in a CNT-based multi-beam X-ray sDBT system. The simulation results showed that the extracted geometric parameters from the calculated projection matrix are extremely close to the input values and that the proposed method is effective and reliable for a square sDBT system. In addition, a traditional cone-beam computed tomography (CT system was also simulated, and the uncalibrated and calibrated geometric parameters were used in image reconstruction based on the filtered back-projection (FBP method. The results indicated that the images reconstructed with calibrated geometric parameters have fewer artifacts and are closer to the reference image. All the simulation tests showed that this geometric calibration method is optimized for sDBT systems but can also be applied to other application-specific CT imaging systems.

  19. Geometric calibration of a stationary digital breast tomosynthesis system based on distributed carbon nanotube X-ray source arrays.

    Science.gov (United States)

    Jiang, Changhui; Zhang, Na; Gao, Juan; Hu, Zhanli

    2017-01-01

    Stationary digital breast tomosynthesis (sDBT) with distributed X-ray sources based on carbon nanotube (CNT) field emission cathodes has been recently proposed as an approach that can prevent motion blur produced by traditional DBT systems. In this paper, we simulate a geometric calibration method based on a proposed multi-source CNT X-ray sDBT system. This method is a projection matrix-based approach with seven geometric parameters, all of which can be obtained from only one projection datum of the phantom. To our knowledge, this study reports the first application of this approach in a CNT-based multi-beam X-ray sDBT system. The simulation results showed that the extracted geometric parameters from the calculated projection matrix are extremely close to the input values and that the proposed method is effective and reliable for a square sDBT system. In addition, a traditional cone-beam computed tomography (CT) system was also simulated, and the uncalibrated and calibrated geometric parameters were used in image reconstruction based on the filtered back-projection (FBP) method. The results indicated that the images reconstructed with calibrated geometric parameters have fewer artifacts and are closer to the reference image. All the simulation tests showed that this geometric calibration method is optimized for sDBT systems but can also be applied to other application-specific CT imaging systems.

  20. Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

    Science.gov (United States)

    Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio

    2007-10-01

    We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1×M bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a , uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.

  1. Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

    International Nuclear Information System (INIS)

    Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio

    2007-01-01

    We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1xM bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a, uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes

  2. A new approach for handling longitudinal count data with zero-inflation and overdispersion: poisson geometric process model.

    Science.gov (United States)

    Wan, Wai-Yin; Chan, Jennifer S K

    2009-08-01

    For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

  3. Geometric Constructions with the Computer.

    Science.gov (United States)

    Chuan, Jen-chung

    The computer can be used as a tool to represent and communicate geometric knowledge. With the appropriate software, a geometric diagram can be manipulated through a series of animation that offers more than one particular snapshot as shown in a traditional mathematical text. Geometric constructions with the computer enable the learner to see and…

  4. Measurements of Atomic Rayleigh Scattering Cross-Sections: A New Approach Based on Solid Angle Approximation and Geometrical Efficiency

    Science.gov (United States)

    Rao, D. V.; Takeda, T.; Itai, Y.; Akatsuka, T.; Seltzer, S. M.; Hubbell, J. H.; Cesareo, R.; Brunetti, A.; Gigante, G. E.

    Atomic Rayleigh scattering cross-sections for low, medium and high Z atoms are measured in vacuum using X-ray tube with a secondary target as an excitation source instead of radioisotopes. Monoenergetic Kα radiation emitted from the secondary target and monoenergetic radiation produced using two secondary targets with filters coupled to an X-ray tube are compared. The Kα radiation from the second target of the system is used to excite the sample. The background has been reduced considerably and the monochromacy is improved. Elastic scattering of Kα X-ray line energies of the secondary target by the sample is recorded with Hp Ge and Si (Li) detectors. A new approach is developed to estimate the solid angle approximation and geometrical efficiency for a system with experimental arrangement using X-ray tube and secondary target. The variation of the solid angle is studied by changing the radius and length of the collimators towards and away from the source and sample. From these values the variation of the total solid angle and geometrical efficiency is deduced and the optimum value is used for the experimental work. The efficiency is larger because the X-ray fluorescent source acts as a converter. Experimental results based on this system are compared with theoretical estimates and good agreement is observed in between them.

  5. Cepheids Geometrical Distances Using Space Interferometry

    Science.gov (United States)

    Marengo, M.; Karovska, M.; Sasselov, D. D.; Sanchez, M.

    2004-05-01

    A space based interferometer with a sub-milliarcsecond resolution in the UV-optical will provide a new avenue for the calibration of primary distance indicators with unprecedented accuracy, by allowing very accurate and stable measurements of Cepheids pulsation amplitudes at wavelengths not accessible from the ground. Sasselov & Karovska (1994) have shown that interferometers allow very accurate measurements of Cepheids distances by using a ``geometric'' variant of the Baade-Wesselink method. This method has been succesfully applied to derive distances and radii of nearby Cepheids using ground-based near-IR and optical interferometers, within a 15% accuracy level. Our study shows that the main source of error in these measurements is due to the perturbing effects of the Earth atmosphere, which is the limiting factor in the interferometer stability. A space interferometer will not suffer from this intrinsic limitations, and can potentially lead to improve astronomical distance measurements by an order of magnitude in precision. We discuss here the technical requirements that a space based facility will need to carry out this project, allowing distance measurements within a few percent accuracy level. We will finally discuss how a sub-milliarcsecond resolution will allow the direct distance determination for hundreds of galactic sources, and provide a substantial improvement in the zero-point of the Cepheid distance scale.

  6. A scheme of measurement of quantum-vacuum geometric phases in a noncoplanar fibre system

    International Nuclear Information System (INIS)

    Shen Jianqi

    2004-01-01

    We study the quantum-vacuum geometric phases resulting from the vacuum fluctuation of photon fields in a Tomita-Chiao-Wu noncoplanar curved fibre system, and suggest a scheme to test for the potential existence of such a vacuum effect. Since the signs of the quantum-vacuum geometric phases of left- and right-handed (LRH) circularly polarized light are opposite, the sum of the geometric phases at the vacuum level is necessarily zero in the fibre experiments performed previously by other authors. By using the present approach where a fibre made of gyroelectric media is employed, the quantum-vacuum geometric phases of LRH light cannot be exactly cancelled, and it may therefore be possible to test this experimentally. (letter to the editor)

  7. Geometric algebra description of polarization mode dispersion, polarization-dependent loss, and Stokes tensor transformations.

    Science.gov (United States)

    Soliman, George; Yevick, David; Jessop, Paul

    2014-09-01

    This paper demonstrates that numerous calculations involving polarization transformations can be condensed by employing suitable geometric algebra formalism. For example, to describe polarization mode dispersion and polarization-dependent loss, both the material birefringence and differential loss enter as bivectors and can be combined into a single symmetric quantity. Their frequency and distance evolution, as well as that of the Stokes vector through an optical system, can then each be expressed as a single compact expression, in contrast to the corresponding Mueller matrix formulations. The intrinsic advantage of the geometric algebra framework is further demonstrated by presenting a simplified derivation of generalized Stokes parameters that include the electric field phase. This procedure simultaneously establishes the tensor transformation properties of these parameters.

  8. Volume-based geometric modeling for radiation transport calculations

    International Nuclear Information System (INIS)

    Li, Z.; Williamson, J.F.

    1992-01-01

    Accurate theoretical characterization of radiation fields is a valuable tool in the design of complex systems, such as linac heads and intracavitary applicators, and for generation of basic dose calculation data that is inaccessible to experimental measurement. Both Monte Carlo and deterministic solutions to such problems require a system for accurately modeling complex 3-D geometries that supports ray tracing, point and segment classification, and 2-D graphical representation. Previous combinatorial approaches to solid modeling, which involve describing complex structures as set-theoretic combinations of simple objects, are limited in their ease of use and place unrealistic constraints on the geometric relations between objects such as excluding common boundaries. A new approach to volume-based solid modeling has been developed which is based upon topologically consistent definitions of boundary, interior, and exterior of a region. From these definitions, FORTRAN union, intersection, and difference routines have been developed that allow involuted and deeply nested structures to be described as set-theoretic combinations of ellipsoids, elliptic cylinders, prisms, cones, and planes that accommodate shared boundaries. Line segments between adjacent intersections on a trajectory are assigned to the appropriate region by a novel sorting algorithm that generalizes upon Siddon's approach. Two 2-D graphic display tools are developed to help the debugging of a given geometric model. In this paper, the mathematical basis of our system is described, it is contrasted to other approaches, and examples are discussed

  9. On a multiorbit geometrical action for the integrable systems

    International Nuclear Information System (INIS)

    Gorsky, A.S.; Olshanetsky, M.A.; Selivanov, K.G.

    1990-10-01

    The Lagrangian approach to the two dimensional integrable systems (IS) is discussed. The Lagrangians proposed have the form of the interacting geometrical actions for the Kac-Moody and Virasoro groups. In one approach when the first principle is the gauge invariance of the action the scale symmetry is broken by introducing the nontrivial representatives (monodromies) for each orbit. We also have discussed the Lagrangians with the broken gauge symmetry but without the bare massive parameters. (author). 22 refs

  10. Optics learning by computing, with examples using Maple, MathCad, Mathematica, and MATLAB

    CERN Document Server

    Moeller, Karl Dieter

    2007-01-01

    This new edition is intended for a one semester course in optics for juniors and seniors in science and engineering; it uses scripts from Maple, MathCad, Mathematica, and MATLAB provide a simulated laboratory where students can learn by exploration and discovery instead of passive absorption. The text covers all the standard topics of a traditional optics course, including: geometrical optics and aberration, interference and diffraction, coherence, Maxwell's equations, wave guides and propagating modes, blackbody radiation, atomic emission and lasers, optical properties of materials, Fourier transforms and FT spectroscopy, image formation, and holography. It contains step by step derivations of all basic formulas in geometrical, wave and Fourier optics. The basic text is supplemented by over 170 files in Maple, MathCad, Mathematica, and MATLAB (many of which are in the text, each suggesting programs to solve a particular problem, and each linked to a topic in or application of optics. The computer files are d...

  11. Bio-optical data integration based on a 4 D database system approach

    Science.gov (United States)

    Imai, N. N.; Shimabukuro, M. H.; Carmo, A. F. C.; Alcantara, E. H.; Rodrigues, T. W. P.; Watanabe, F. S. Y.

    2015-04-01

    Bio-optical characterization of water bodies requires spatio-temporal data about Inherent Optical Properties and Apparent Optical Properties which allow the comprehension of underwater light field aiming at the development of models for monitoring water quality. Measurements are taken to represent optical properties along a column of water, and then the spectral data must be related to depth. However, the spatial positions of measurement may differ since collecting instruments vary. In addition, the records should not refer to the same wavelengths. Additional difficulty is that distinct instruments store data in different formats. A data integration approach is needed to make these large and multi source data sets suitable for analysis. Thus, it becomes possible, even automatically, semi-empirical models evaluation, preceded by preliminary tasks of quality control. In this work it is presented a solution, in the stated scenario, based on spatial - geographic - database approach with the adoption of an object relational Database Management System - DBMS - due to the possibilities to represent all data collected in the field, in conjunction with data obtained by laboratory analysis and Remote Sensing images that have been taken at the time of field data collection. This data integration approach leads to a 4D representation since that its coordinate system includes 3D spatial coordinates - planimetric and depth - and the time when each data was taken. It was adopted PostgreSQL DBMS extended by PostGIS module to provide abilities to manage spatial/geospatial data. It was developed a prototype which has the mainly tools an analyst needs to prepare the data sets for analysis.

  12. Multiscale unfolding of real networks by geometric renormalization

    Science.gov (United States)

    García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles

    2018-06-01

    Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.

  13. Electrical and Optical Enhancement in Internally Nanopatterned Organic Light-Emitting Diodes

    Science.gov (United States)

    Fina, Michael Dane

    Organic light-emitting diodes (OLEDs) have made tremendous technological progress in the past two decades and have emerged as a top competitor for next generation light-emitting displays and lighting. State-of-the-art OLEDs have been reported in literature to approach, and even surpass, white fluorescent tube efficiency. However, despite rapid technological progress, efficiency metrics must be improved to compete with traditional inorganic light-emitting diode (LED) technology. Organic materials possess specialized traits that permit manipulations to the light-emitting cavity. Overall, as demonstrated within, these modifications can be used to improve electrical and optical device efficiencies. This work is focused at analyzing the effects that nanopatterned geometric modifications to the organic active layers play on device efficiency. In general, OLED efficiency is complicated by the complex, coupled processes which contribute to spontaneous dipole emission. A composite of three sub-systems (electrical, exciton and optical) ultimately dictate the OLED device efficiency. OLED electrical operation is believed to take place via a low-mobility-modified Schottky injection process. In the injection-limited regime, geometric effects are expected to modify the local electric field leading to device current enhancement. It is shown that the patterning effect can be used to enhance charge carrier parity, thereby enhancing overall recombination. Current density and luminance characteristics are shown to be improved by OLED nanopatterning from both the model developed within and experimental techniques. Next, the optical enhancement effects produced by the nanopatterned array are considered. Finite-difference time-domain (FDTD) simulations are used to determine positional, spectral optical enhancement for the nanopatterned device. The results show beneficial effects to the device performance. The optical enhancements are related to the reduction in internal radiative

  14. Vector optical fields with bipolar symmetry of linear polarization.

    Science.gov (United States)

    Pan, Yue; Li, Yongnan; Li, Si-Min; Ren, Zhi-Cheng; Si, Yu; Tu, Chenghou; Wang, Hui-Tian

    2013-09-15

    We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.

  15. Robust adiabatic approach to optical spin entangling in coupled quantum dots

    International Nuclear Information System (INIS)

    Gauger, Erik M; Benjamin, Simon C; Lovett, Brendon W; Nazir, Ahsan; Stace, Thomas M

    2008-01-01

    Excitonic transitions offer a possible route to ultrafast optical spin manipulation in coupled nanostructures. We perform here a detailed study of the three principal exciton-mediated decoherence channels for optically controlled electron spin qubits in coupled quantum dots: radiative decay of the excitonic state, exciton-phonon interactions, and Landau-Zener transitions between laser-dressed states. We consider a scheme for producing an entangling controlled-phase gate on a pair of coupled spins which, in its simplest dynamic form, renders the system subject to fast decoherence rates associated with exciton creation during the gating operation. In contrast, we show that an adiabatic approach employing off-resonant laser excitation allows us to suppress all sources of decoherence simultaneously, significantly increasing the fidelity of operations at only a relatively small gating time cost. We find that controlled-phase gates accurate to one part in 10 2 can realistically be achieved with the adiabatic approach, whereas the conventional dynamic approach does not appear to support a fidelity suitable for scalable quantum computation. Our predictions could be demonstrated experimentally in the near future

  16. Computational Approach for Studying Optical Properties of DNA Systems in Solution

    DEFF Research Database (Denmark)

    Nørby, Morten Steen; Svendsen, Casper Steinmann; Olsen, Jógvan Magnus Haugaard

    2016-01-01

    In this paper we present a study of the methodological aspects regarding calculations of optical properties for DNA systems in solution. Our computational approach will be built upon a fully polarizable QM/MM/Continuum model within a damped linear response theory framework. In this approach...... the environment is given a highly advanced description in terms of the electrostatic potential through the polarizable embedding model. Furthermore, bulk solvent effects are included in an efficient manner through a conductor-like screening model. With the aim of reducing the computational cost we develop a set...... of averaged partial charges and distributed isotropic dipole-dipole polarizabilities for DNA suitable for describing the classical region in ground-state and excited-state calculations. Calculations of the UV-spectrum of the 2-aminopurine optical probe embedded in a DNA double helical structure are presented...

  17. Transmuted Complementary Weibull Geometric Distribution

    Directory of Open Access Journals (Sweden)

    Ahmed Z. A…fify

    2014-12-01

    Full Text Available This paper provides a new generalization of the complementary Weibull geometric distribution that introduced by Tojeiro et al. (2014, using the quadratic rank transmutation map studied by Shaw and Buckley (2007. The new distribution is referred to as transmuted complementary Weibull geometric distribution (TCWGD. The TCWG distribution includes as special cases the complementary Weibull geometric distribution (CWGD, complementary exponential geometric distribution(CEGD,Weibull distribution (WD and exponential distribution (ED. Various structural properties of the new distribution including moments, quantiles, moment generating function and RØnyi entropy of the subject distribution are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the ‡exibility of the transmuted version versus the complementary Weibull geometric distribution.

  18. Iterative feedback bio-printing-derived cell-laden hydrogel scaffolds with optimal geometrical fidelity and cellular controllability.

    Science.gov (United States)

    Wang, Ling; Xu, Ming-En; Luo, Li; Zhou, Yongyong; Si, Peijian

    2018-02-12

    For three-dimensional bio-printed cell-laden hydrogel tissue constructs, the well-designed internal porous geometry is tailored to obtain the desired structural and cellular properties. However, significant differences often exist between the designed and as-printed scaffolds because of the inherent characteristics of hydrogels and cells. In this study, an iterative feedback bio-printing (IFBP) approach based on optical coherence tomography (OCT) for the fabrication of cell-laden hydrogel scaffolds with optimal geometrical fidelity and cellular controllability was proposed. A custom-made swept-source OCT (SS-OCT) system was applied to characterize the printed scaffolds quantitatively. Based on the obtained empirical linear formula from the first experimental feedback loop, we defined the most appropriate design constraints and optimized the printing process to improve the geometrical fidelity. The effectiveness of IFBP was verified from the second run using gelatin/alginate hydrogel scaffolds laden with C3A cells. The mismatch of the morphological parameters greatly decreased from 40% to within 7%, which significantly optimized the cell viability, proliferation, and morphology, as well as the representative expression of hepatocyte markers, including CYP3A4 and albumin, of the printed cell-laden hydrogel scaffolds. The demonstrated protocol paves the way for the mass fabrication of cell-laden hydrogel scaffolds, engineered tissues, and scaled-up applications of the 3D bio-printing technique.

  19. Geometric phases in discrete dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)

    2016-10-14

    In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.

  20. Treatment simulation approaches for the estimation of the distributions of treatment quality parameters generated by geometrical uncertainties

    International Nuclear Information System (INIS)

    Baum, C; Alber, M; Birkner, M; Nuesslin, F

    2004-01-01

    Geometric uncertainties arise during treatment planning and treatment and mean that dose-dependent parameters such as EUD are random variables with a patient specific probability distribution. Treatment planning with highly conformal treatment techniques such as intensity modulated radiation therapy requires new evaluation tools which allow us to estimate this influence of geometrical uncertainties on the probable treatment dose for a planned dose distribution. Monte Carlo simulations of treatment courses with recalculation of the dose according to the daily geometric errors are a gold standard for such an evaluation. Distribution histograms which show the relative frequency of a treatment quality parameter in the treatment simulations can be used to evaluate the potential risks and chances of a planned dose distribution. As treatment simulations with dose recalculation are very time consuming for sufficient statistical accuracy, it is proposed to do treatment simulations in the dose parameter space where the result is mainly determined by the systematic and random component of the geometrical uncertainties. Comparison of the parameter space simulation method with the gold standard for prostate cases and a head and neck case shows good agreement as long as the number of fractions is high enough and the influence of tissue inhomogeneities and surface curvature on the dose is small

  1. Wall-corner classification using sonar: a new approach based on geometric features.

    Science.gov (United States)

    Martínez, Milagros; Benet, Ginés

    2010-01-01

    Ultrasonic signals coming from rotary sonar sensors in a robot gives us several features about the environment. This enables us to locate and classify the objects in the scenario of the robot. Each object and reflector produces a series of peaks in the amplitude of the signal. The radial and angular position of the sonar sensor gives information about location and their amplitudes offer information about the nature of the surface. Early works showed that the amplitude can be modeled and used to classify objects with very good results at short distances-80% average success in classifying both walls and corners at distances less than 1.5 m. In this paper, a new set of geometric features derived from the amplitude analysis of the echo is presented. These features constitute a set of characteristics that can be used to improve the results of classification at distances from 1.5 m to 4 m. Also, a comparative study on classification algorithms widely used in pattern recognition techniques has been carried out for sensor distances ranging between 0.5 to 4 m, and with incidence angles ranging between 20° to 70°. Experimental results show an enhancement on the success in classification rates when these geometric features are considered.

  2. Lepton and quark generations in the geometrical Rishon model

    International Nuclear Information System (INIS)

    Elbaz, E.; Uschersohn, J.; Meyer, J.

    1981-12-01

    We propose a concrete representation of leptons and quarks in different generations in the geometrical approach to the rishon model where rishons behave as the fundamental representations of the SU(3)sub(C) x SU(3)sub(H) group. The model allows a unified description of both hadronic and leptonic decays of elementary particles

  3. Molecular Approaches to Optical Biosensors

    National Research Council Canada - National Science Library

    Fierke, Carol

    1998-01-01

    The goal of this proposal was to develop methodologies for the optimization of field-deployable optical biosensors, in general, and, in particular, to optimize a carbonic anhydrase-based fiber optic zinc biosensor...

  4. Biobeam—Multiplexed wave-optical simulations of light-sheet microscopy

    Science.gov (United States)

    Weigert, Martin; Bundschuh, Sebastian T.

    2018-01-01

    Sample-induced image-degradation remains an intricate wave-optical problem in light-sheet microscopy. Here we present biobeam, an open-source software package that enables simulation of operational light-sheet microscopes by combining data from 105–106 multiplexed and GPU-accelerated point-spread-function calculations. The wave-optical nature of these simulations leads to the faithful reproduction of spatially varying aberrations, diffraction artifacts, geometric image distortions, adaptive optics, and emergent wave-optical phenomena, and renders image-formation in light-sheet microscopy computationally tractable. PMID:29652879

  5. Characterization of radiation within the optical region

    Energy Technology Data Exchange (ETDEWEB)

    Albrecht, H [Stuttgart Univ. (TH) (Germany, F.R.). Inst. fuer Physikalische Elektronik

    1977-04-01

    The notions which are used for the characterization of radiation within the optical region of the spectrum (quantities, units) and their temporal and geometric relations have been arranged synoptically. Quantities of the international system (SI-System) are emphasized.

  6. Geometrical Description of fractional quantum Hall quasiparticles

    Science.gov (United States)

    Park, Yeje; Yang, Bo; Haldane, F. D. M.

    2012-02-01

    We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.

  7. Image-Based Geometric Modeling and Mesh Generation

    CERN Document Server

    2013-01-01

    As a new interdisciplinary research area, “image-based geometric modeling and mesh generation” integrates image processing, geometric modeling and mesh generation with finite element method (FEM) to solve problems in computational biomedicine, materials sciences and engineering. It is well known that FEM is currently well-developed and efficient, but mesh generation for complex geometries (e.g., the human body) still takes about 80% of the total analysis time and is the major obstacle to reduce the total computation time. It is mainly because none of the traditional approaches is sufficient to effectively construct finite element meshes for arbitrarily complicated domains, and generally a great deal of manual interaction is involved in mesh generation. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion,...

  8. The geometric Hopf invariant and surgery theory

    CERN Document Server

    Crabb, Michael

    2017-01-01

    Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .

  9. Improved optical design of nontracking concentrators

    Science.gov (United States)

    Kwan, B. M.; Bannerot, R. B.

    1984-08-01

    Optical designs based on a two reflections or less criterion have been developed for one and two-facet trapezoidal concentrators. Collector designs resulting from this criterion have been evaluated with the aid of a ray-trace computer simulation which includes the effects of nonideal reflectors. Results indicate a marked increase in performance, particularly for the one-facet designs, as compared to the collectors previously designed with the one reflection or less criterion. A significant result is that when a proper accounting is made for the actual acceptance angle for the concentrators, the performances of the optimal one and two-facet designs become nearly identical, indicating that the previously held contention that improved performance could be achieved with multifaceted reflectors (geometrically approaching the compound parabolic shape) may be incorrect.

  10. Probability density cloud as a geometrical tool to describe statistics of scattered light.

    Science.gov (United States)

    Yaitskova, Natalia

    2017-04-01

    First-order statistics of scattered light is described using the representation of the probability density cloud, which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail and are connected to the statistical properties of phase. The moment-generating function for intensity is obtained in a closed form through these parameters. An example of exponentially modified normal distribution is provided to illustrate the functioning of this geometrical approach.

  11. The Relationships between Weight Functions, Geometric Functions,and Compliance Functions in Linear Elastic Fracture Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Yuan, Rong [Univ. of California, Berkeley, CA (United States)

    2007-01-01

    Linear elastic fracture mechanics is widely used in industry because it established simple and explicit relationships between the permissible loading conditions and the critical crack size that is allowed in a structure. Stress intensity factors are the above-mentioned functional expressions that relate load with crack size through geometric functions or weight functions. Compliance functions are to determine the crack/flaw size in a structure when optical inspection is inconvenient. As a result, geometric functions, weight functions and compliance functions have been intensively studied to determine the stress intensity factor expressions for different geometries. However, the relations between these functions have received less attention. This work is therefore to investigate the intrinsic relationships between these functions. Theoretical derivation was carried out and the results were verified on single-edge cracked plate under tension and bending. It is found out that the geometric function is essentially the non-dimensional weight function at the loading point. The compliance function is composed of two parts: a varying part due to crack extension and a constant part from the intact structure if no crack exists. The derivative of the compliance function at any location is the product of the geometric function and the weight function at the evaluation point. Inversely, the compliance function can be acquired by the integration of the product of the geometric function and the weight function with respect to the crack size. The integral constant is just the unchanging compliance from the intact structure. Consequently, a special application of the relations is to obtain the compliance functions along a crack once the geometric function and weight functions are known. Any of the three special functions can be derived once the other two functions are known. These relations may greatly simplify the numerical process in obtaining either geometric functions, weight

  12. Relationship of college student characteristics and inquiry-based geometrical optics instruction to knowledge of image formation with light-ray tracing

    Science.gov (United States)

    Isik, Hakan

    This study is premised on the fact that student conceptions of optics appear to be unrelated to student characteristics of gender, age, years since high school graduation, or previous academic experiences. This study investigated the relationships between student characteristics and student performance on image formation test items and the changes in student conceptions of optics after an introductory inquiry-based physics course. Data was collected from 39 college students who were involved in an inquiry-based physics course teaching topics of geometrical optics. Student data concerning characteristics and previous experiences with optics and mathematics were collected. Assessment of student understanding of optics knowledge for pinholes, plane mirrors, refraction, and convex lenses was collected with, the Test of Image Formation with Light-Ray Tracing instrument. Total scale and subscale scores representing the optics instrument content were derived from student pretest and posttest responses. The types of knowledge, needed to answer each optics item correctly, were categorized as situational, conceptual, procedural, and strategic knowledge. These types of knowledge were associated with student correct and incorrect responses to each item to explain the existences and changes in student scientific and naive conceptions. Correlation and stepwise multiple regression analyses were conducted to identify the student characteristics and academic experiences that significantly predicted scores on the subscales of the test. The results showed that student experience with calculus was a significant predictor of student performance on the total scale as well as on the refraction subscale of the Test of Image Formation with Light-Ray Tracing. A combination of student age and previous academic experience with precalculus was a significant predictor of student performance on the pretest pinhole subscale. Student characteristic of years since high school graduation

  13. Outline of an ultracorrector compensating for all primary chromatic and geometrical aberrations of charged-particle lenses

    International Nuclear Information System (INIS)

    Rose, Harald

    2004-01-01

    A novel ultracorrector is outlined which compensates for the primary and secondary first-order chromatic aberrations and all third-order geometrical aberrations of electron optical systems with a straight axis. Owing to the imposed symmetry conditions on the fields and the paraxial fundamental rays, the corrector does not introduce aberrations with 2-fold symmetry. The chromatic aberrations are corrected by means of crossed electric magnetic quadrupoles while the third-order geometrical aberrations are eliminated by octopoles. By placing these elements at distinct positions within the corrector, it is possible to successively eliminate the third-order aberrations in such a way that each subsequent correction does not affect the aberrations corrected in the preceding correction steps

  14. Long-lived monolithic micro-optics for multispectral GRIN applications.

    Science.gov (United States)

    Lepicard, Antoine; Bondu, Flavie; Kang, Myungkoo; Sisken, Laura; Yadav, Anupama; Adamietz, Frederic; Rodriguez, Vincent; Richardson, Kathleen; Dussauze, Marc

    2018-05-09

    The potential for realizing robust, monolithic, near-surface refractive micro-optic elements with long-lived stability is demonstrated in visible and infrared transmitting glasses capable of use in dual band applications. Employing an enhanced understanding of glass chemistry and geometric control of mobile ion migration made possible with electrode patterning, flat, permanent, thermally-poled micro-optic structures have been produced and characterized. Sub-surface (t~5-10 µm) compositional and structural modification during the poling process results in formation of spatially-varying refractive index profiles, exhibiting induced Δn changes up to 5 × 10 -2 which remain stable for >15 months. The universality of this approach applied to monolithic vis-near infrared [NIR] oxide and NIR-midwave infrared [MIR] chalcogenide glass materials is demonstrated for the first time. Element size, shape and gradient profile variation possible through pattern design and fabrication is shown to enable a variety of design options not possible using other GRIN process methodologies.

  15. Matching Real and Synthetic Panoramic Images Using a Variant of Geometric Hashing

    Science.gov (United States)

    Li-Chee-Ming, J.; Armenakis, C.

    2017-05-01

    This work demonstrates an approach to automatically initialize a visual model-based tracker, and recover from lost tracking, without prior camera pose information. These approaches are commonly referred to as tracking-by-detection. Previous tracking-by-detection techniques used either fiducials (i.e. landmarks or markers) or the object's texture. The main contribution of this work is the development of a tracking-by-detection algorithm that is based solely on natural geometric features. A variant of geometric hashing, a model-to-image registration algorithm, is proposed that searches for a matching panoramic image from a database of synthetic panoramic images captured in a 3D virtual environment. The approach identifies corresponding features between the matched panoramic images. The corresponding features are to be used in a photogrammetric space resection to estimate the camera pose. The experiments apply this algorithm to initialize a model-based tracker in an indoor environment using the 3D CAD model of the building.

  16. GEOMETRIC AND MATERIAL NONLINEAR ANALYSIS OF REINFORCED CONCRETE SLABS AT FIRE ENVIRONMENT

    Directory of Open Access Journals (Sweden)

    Ayad A. Abdul -Razzak

    2013-05-01

    Full Text Available In the present study a nonlinear finite element analysis is presented  to predict the fire resistance of reinforced concrete slabs at fire environment. An eight node layered degenerated shell element utilizing Mindlin/Reissner thick plate theory is employed. The proposed model considered cracking, crushing and yielding of concrete and steel at elevated temperatures. The layered approach is used to represent the steel reinforcement and discretize the concrete slab through the thickness. The reinforcement steel is represented as a smeared layer of equivalent thickness with uniaxial strength and rigidity properties.Geometric nonlinear analysis may play an important role in the behavior of reinforced concrete slabs at high temperature. Geometrical nonlinearity in the layered approach is considered in the mathematical model, which is based on the total Lagrangian approach taking into account Von Karman assumptions.Finally two examples for which experimental results are available are analyzed, using the proposed model .The comparison showed good agreement with experimental results. 

  17. Generalized approach to modifying optical vortices with suppressed sidelobes using Bessel-like functions.

    Science.gov (United States)

    Chen, J; Yuan, X-C; Zhao, X; Fang, Z L; Zhu, S W

    2009-11-01

    We propose a generalized approach to producing optical vortices with suppressed sidelobes using a variable Bessel-like function added to the conventional spiral phase plate. Experimental verifications are implemented by a phase-only spatial light modulator. It is demonstrated that the method is valid for optical vortex beams with arbitrary topological charges and without changing the primary ring size as a unique property among the existing techniques.

  18. Linear ray and wave optics in phase space bridging ray and wave optics via the Wigner phase-space picture

    CERN Document Server

    Torre, Amalia

    2005-01-01

    Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner f

  19. Geometric Algebra Techniques in Flux Compactifications

    International Nuclear Information System (INIS)

    Coman, Ioana Alexandra; Lazaroiu, Calin Iuliu; Babalic, Elena Mirela

    2016-01-01

    We study “constrained generalized Killing (s)pinors,” which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As an application, we show how our approach can be used to efficiently treat N=1 compactification of M-theory on eight manifolds and prove that we recover results previously obtained in the literature.

  20. Five reasons to doubt the existence of a geometric module.

    Science.gov (United States)

    Twyman, Alexandra D; Newcombe, Nora S

    2010-09-01

    It is frequently claimed that the human mind is organized in a modular fashion, a hypothesis linked historically, though not inevitably, to the claim that many aspects of the human mind are innately specified. A specific instance of this line of thought is the proposal of an innately specified geometric module for human reorientation. From a massive modularity position, the reorientation module would be one of a large number that organized the mind. From the core knowledge position, the reorientation module is one of five innate and encapsulated modules that can later be supplemented by use of human language. In this paper, we marshall five lines of evidence that cast doubt on the geometric module hypothesis, unfolded in a series of reasons: (1) Language does not play a necessary role in the integration of feature and geometric cues, although it can be helpful. (2) A model of reorientation requires flexibility to explain variable phenomena. (3) Experience matters over short and long periods. (4) Features are used for true reorientation. (5) The nature of geometric information is not as yet clearly specified. In the final section, we review recent theoretical approaches to the known reorientation phenomena. Copyright © 2009 Cognitive Science Society, Inc.