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
A Wave-Optics Approach to Paraxial Geometrical Laws Based on Continuity at Boundaries
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…
Geometrical optical illusionists.
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.
Geometrical optics approach in liquid crystal films with three-dimensional director variations.
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.
Vergence, Vision, and Geometric Optics
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…
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.
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
Geometrical optics in the near field: local plane-interface approach with evanescent waves.
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.
Calculation of far-field scattering from nonspherical particles using a geometrical optics approach
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.
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
Simple and practical approach for computing the ray Hessian matrix in geometrical optics.
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.
Geometrical optics in general relativity
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.
Problems in Geometrical Optics
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)
Field guide to geometrical optics
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.
A practical guide to experimental geometrical optics
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.
Geometric Phase Generated Optical Illusion.
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.
Geometrical optics and optimal transport.
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.
Active Learning of Geometrical Optics in High School: The ALOP Approach
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…
Construction of Ray Diagrams in Geometrical Optics: A Media-Focused Approach
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…
Geometrical charged-particle optics
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...
Active learning of geometrical optics in high school: the ALOP approach
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.
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
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)
Thomas Young's contributions to geometrical optics.
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.
A Practical Guide to Experimental Geometrical Optics
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.
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.
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
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)
Advanced Geometric Optics on a Programmable Pocket Calculator.
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)
Coated sphere scattering by geometric optics approximation.
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.
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
Digital polarization holography advancing geometrical phase optics.
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.
Advances on geometric flux optical design method
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.
A geometric morphometric assessment of the optic cup in glaucoma.
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.
Geometrical approach to tumor growth.
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.
Geometrical approach to tumor growth
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...
Geometrical optics model of Mie resonances
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.
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.)
Geometric-optical illusions at isoluminance.
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.
Two solvable problems of planar geometrical optics.
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.
Rayleigh's hypothesis and the geometrical optics limit.
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.
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
Geometrical and wave optics of paraxial beams.
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.
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.)
Geometrical aspects in optical wave-packet dynamics.
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.
A fast method for linear waves based on geometrical optics
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
Active Learning Environment with Lenses in Geometric Optics
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…
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.
Invisibility Cloaking Based on Geometrical Optics for Visible Light
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.
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.
Life Science-Related Physics Laboratory on Geometrical Optics
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)
Resonant inelastic scattering by use of geometrical optics.
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.
Stress measurement in thin films by geometrical optics
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.
Geometrical-optics approximation of forward scattering by coated particles.
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.
Geometrical optics of dense aerosols: forming dense plasma slabs.
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.
Comparisons between geometrical optics and Lorenz-Mie theory
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.
Controlling lightwave in Riemann space by merging geometrical optics with transformation optics.
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.
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.
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
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
The Zoom Lens: A Case Study in Geometrical Optics.
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)
Two-dimensional fast marching for geometrical optics.
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.
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.
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.
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
A Circumzenithal Arc to Study Optics Concepts with Geometrical Optics
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…
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.
Geometrical optics modeling of the grating-slit test.
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.
Homogenous isotropic invisible cloak based on geometrical optics.
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.
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.
Optical rectification using geometrical field enhancement in gold nano-arrays
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.
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)
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.
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.
Geometrical optics, electrostatics, and nanophotonic resonances in absorbing nanowire arrays.
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.
Refraction at a curved dielectric interface - Geometrical optics solution
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.
A Geometrical Approach to Bell's Theorem
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.
International Nuclear Information System (INIS)
Franklin, J.; Duncan, J.; Huete, A.R.; Leeuwen, W.J.D. van; Li, X.; Bégué, A.
1994-01-01
To use optical remote sensing to monitor land surface-climate interactions over large areas, algorithms must be developed to relate multispectral measurements to key variables controlling the exchange of matter (water, carbon dioxide) and energy between the land surface and the atmosphere. The proportion of the ground covered by vegetation and the interception of photosynthetically active radiation (PAR) by vegetation are examples of two variables related to evapotranspiration and primary production, respectively. An areal-proportion model of the multispectral reflectance of shrub savanna, composed of scattered shrubs with a grass, forb or soil understory, predicted the reflectance of two 0.5 km 2 sites as the area-weighted average of the shrub and understory or ‘background’ reflectances. Although the shaded crown and shaded background have darker reflectances, ignoring them in the area-weighted model is not serious when shrub cover is low and solar zenith angle is small. A submodel predicted the reflectance of the shrub crown as a function of the foliage reflectance and amount of plant material within the crown, and the background reflectance scattered or transmitted through canopy gaps (referred to as a soil—plant ‘spectral interaction’ term). One may be able to combine these two models to estimate both the fraction of vegetation cover and interception of PAR by green vegetation in a shrub savanna. (author)
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.
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
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
Analyser-based phase contrast image reconstruction using geometrical optics.
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.
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
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
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
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.
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.)
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.
The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method
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...
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)
General analysis of slab lasers using geometrical optics.
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.
Uncertainty in visual processes predicts geometrical optical illusions.
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.
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.
A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter
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
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
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
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
Symmetry analysis of talus bone: A Geometric morphometric approach.
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.
Different optical properties in different periodic slot cavity geometrical morphologies
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
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.
Expression of the degree of polarization based on the geometrical optics pBRDF model.
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.
Fresnel Lens Solar Concentrator Design Based on Geometric Optics and Blackbody Radiation Equations
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.
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
Geometrical approach to central molecular chirality: a chirality selection rule
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...
Geometrical-optics code for computing the optical properties of large dielectric spheres.
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.
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.
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
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.
Applicability of geometrical optics to in-plane liquid-crystal configurations
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
A New (?) Physiological Effect in a Demonstration Experiment in Geometrical Optics
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.
Geometric optics theory and design of astronomical optical systems using Mathematica
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...
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.
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
Cross-Grade Comparison of Students' Conceptual Understanding with Lenses in Geometric Optics
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…
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)
Geometric Approaches to Quadratic Equations from Other Times and Places.
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)
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
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
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
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.
Shaping up: a geometric morphometric approach to assemblage ecomorphology.
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.
Lorentz Invariance Violation effects on UHECR propagation: A geometrized approach
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.
Applicability of geometrical optics to in-plane liquid-crystal configurations.
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.
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)
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
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.
Geometric and Applied Optics, Science (Experimental): 5318.04.
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…
Complementary Huygens Principle for Geometrical and Nongeometrical Optics
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…
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...
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.)
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.)
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)
A Didactic Sequence of Elementary Geometric Optics Informed by History and Philosophy of Science
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…
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
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)
Designing and Using an Open Graphic Interface for Instruction in Geometrical Optics.
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)
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
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
Using Nonprinciple Rays to Form Images in Geometrical Optics
Marx, Jeff; Mian, Shabbir
2015-01-01
Constructing ray diagrams to locate the image of an object formed by thin lenses and mirrors is a staple of many introductory physics courses at the high school and college levels, and has been the subject of some pedagogy-related articles. Our review of textbooks distributed in the United States suggests that the singular approach involves…
Using Nonprinciple Rays to Form Images in Geometrical Optics
Marx, Jeff; Mian, Shabbir
2015-11-01
Constructing ray diagrams to locate the image of an object formed by thin lenses and mirrors is a staple of many introductory physics courses at the high school and college levels, and has been the subject of some pedagogy-related articles. Our review of textbooks distributed in the United States suggests that the singular approach involves drawing principle rays to locate an object's image. We were pleasantly surprised to read an article in this journal by Suppapittayaporn et al. in which they use an alternative method to construct rays for thin lenses based on a "tilted principle axis" (TPA). In particular, we were struck by the generality of the approach (a single rule for tracing rays as compared to the typical two or three rules), and how it could help students more easily tackle challenging situations, such as multi-lens systems and occluded lenses, where image construction using principle rays may be impractical. In this paper, we provide simple "proofs" for this alternative approach for the case of thin lenses and single refracting surfaces.
Transverse correlations in triphoton entanglement: Geometrical and physical optics
International Nuclear Information System (INIS)
Wen Jianming; Rubin, Morton H.; Shih Yanhua; Xu, P.
2007-01-01
The transverse correlation of triphoton entanglement generated within a single crystal is analyzed. Among many interesting features of the transverse correlation, they arise from the spectral function F of the triphoton state produced in the parametric processes. One consequence of transverse effects of entangled states is quantum imaging, which is theoretically studied in photon counting measurements. Klyshko's two-photon advanced-wave picture is found to be applicable to the multiphoton entanglement with some modifications. We found that in the two-photon coincidence counting measurement by using triphoton entanglement, although the Gaussian thin lens equation (GTLE) holds, the imaging shown in coincidences is obscure and has a poor quality. This is because of tracing the remaining transverse modes in the untouched beam. In the triphoton imaging experiments, two kinds of cases have been examined. For the case that only one object with one thin lens is placed in the system, we found that the GTLE holds as expected in the triphoton coincidences and the effective distance between the lens and imaging plane is the parallel combination of two distances between the lens and two detectors weighted by wavelengths, which behaves as the parallel combination of resistors in the electromagnetism theory. Only in this case, a point-point correspondence for forming an image is well-accomplished. However, when two objects or two lenses are inserted in the system, though the GTLEs are well-satisfied, in general a point-point correspondence for imaging cannot be established. Under certain conditions, two blurred images may be observed in the coincidence counts. We have also studied the ghost interference-diffraction experiments by using double slits as apertures in triphoton entanglement. It was found that when two double slits are used in two optical beams, the interference-diffraction patterns show unusual features compared with the two-photon case. This unusual behavior is a
Geometric and potential dynamics interpretation of the optic ring resonator bistability
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.
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.
An information geometric approach to least squares minimization
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.
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.
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
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.
Establishment of Imaging Spectroscopy of Nuclear Gamma-Rays based on Geometrical Optics.
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.
Material inhomogeneities and their evolution a geometric approach
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.
Geometric and Algebraic Approaches in the Concept of Complex Numbers
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…
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
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.
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
Geometric mechanics of ray optics as particle dynamics: refraction index with cylindrical symmetry
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.
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
Application of semiclassical and geometrical optics theories to resonant modes of a coated sphere.
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.
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.
An algebraic geometric approach to separation of variables
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...
Geometrical-optics solution to light scattering by droxtal ice crystals.
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.
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
Design of an ultra-thin near-eye display with geometrical waveguide and freeform optics.
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.
Urbanisation and 3d Spatial - a Geometric Approach
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.
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.)
A geometrical approach to two-dimensional Conformal Field Theory
Dijkgraaf, Robertus Henricus
1989-09-01
This thesis is organized in the following way. In Chapter 2 we will give a brief introduction to conformal field theory along the lines of standard quantum field theory, without any claims to originality. We introduce the important concepts of the stress-energy tensor, the Virasoro algebra, and primary fields. The general principles are demonstrated by fermionic and bosonic free field theories. This also allows us to discuss some general aspects of moduli spaces of CFT's. In particular, we describe in some detail the space of iiiequivalent toroidal comi)actificalions, giving examples of the quantum equivalences that we already mentioned. In Chapter 3 we will reconsider general quantum field theory from a more geometrical point of view, along the lines of the so-called operator formalism. Crucial to this approach will be the consideration of topology changing amplitudes. After a simple application to 2d topological theories, we proceed to give our second introduction to CFT, stressing the geometry behind it. In Chapter 4 the so-called rational conformal field theories are our object of study. These special CFT's have extended symmetries with only a finite number of representations. If an interpretation as non-linear sigma model exists, this extra symmetry can be seen as a kind of resonance effect due to the commensurability of the size of the string and the target space-time. The structure of rational CFT's is extremely rigid, and one of our results will be that the operator content of these models is—up to some discrete choices—completely determined by the symmetry algebra. The study of rational models is in its rigidity very analogous to finite group theory. In Chapter 5 this analogy is further pursued and substantiated. We will show how one can construct from general grounds rational conformal field theories from finite groups. These models are abstract versions of non-linear o-models describing string propagation on 'orbifoids.' An orbifold is a singular
Type II Superstring Field Theory: Geometric Approach and Operadic Description
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.
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
Modeling thermodynamic distance, curvature and fluctuations a geometric approach
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.
Geometrical Optimization Approach to Isomerization: Models and Limitations.
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.
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
Geometrical-optics approximation of forward scattering by gradient-index spheres.
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.
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
Error performance analysis in K-tier uplink cellular networks using a stochastic geometric approach
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
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
Lie-Hamilton systems on curved spaces: a geometrical approach
Herranz, Francisco J.; de Lucas, Javier; Tobolski, Mariusz
2017-12-01
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra, of Hamiltonian vector fields relative to a Poisson structure. Its general solution can be written as an autonomous function, the superposition rule, of a generic finite family of particular solutions and a set of constants. We pioneer the study of Lie-Hamilton systems on Riemannian spaces (sphere, Euclidean and hyperbolic plane), pseudo-Riemannian spaces (anti-de Sitter, de Sitter, and Minkowski spacetimes) as well as on semi-Riemannian spaces (Newtonian spacetimes). Their corresponding constants of motion and superposition rules are obtained explicitly in a geometric way. This work extends the (graded) contraction of Lie algebras to a contraction procedure for Lie algebras of vector fields, Hamiltonian functions, and related symplectic structures, invariants, and superposition rules.
Tunable orbital angular momentum mode filter based on optical geometric transformation.
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.
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.
Johann Joseph on Geometrical-Optical Illusions: A Translation and Commentary.
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.
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.
A geometric approach to aortic root surgical anatomy.
Contino, Monica; Mangini, Andrea; Lemma, Massimo Giovanni; Romagnoni, Claudia; Zerbi, Pietro; Gelpi, Guido; Antona, Carlo
2016-01-01
The aim of this study was the analysis of the geometrical relationships between the different structures constituting the aortic root, with particular attention to interleaflet triangles, haemodynamic ventriculo-arterial junction and functional aortic annulus in normal subjects. Sixteen formol-fixed human hearts with normal aortic roots were studied. The aortic root was isolated, sectioned at the midpoint of the non-coronary sinus, spread apart and photographed by a high-resolution digital camera. After calibration and picture resizing, the software AutoCAD 2004 was used to identify and measure all the elements of the interleaflets triangles and of the aortic root that were objects of our analysis. Multiple comparisons were performed with one-way analysis of variance for continuous data and with Kruskal-Wallis analysis for non-continuous data. Linear regression and Pearson's product correlation were used to correlate root element dimensions when appropriate. Student's t-test was used to compare means for unpaired data. Heron's formula was applied to estimate the functional aortic annular diameters. The non coronary-left coronary interleaflets triangles were larger, followed by inter-coronary and right-non-coronary ones. The apical angle is <60° and its standard deviation can be considered an asymmetry index. The sinu-tubular junction was shown to be 10% larger than the virtual basal ring (VBR). The mathematical relationship between the haemodynamic ventriculo-arterial junction and the VBR calculated by linear regression and expressed in terms of the diameter was: haemodynamic ventriculo-arterial junction = 2.29 VBR (diameter) + 47. Conservative aortic surgery is based on a better understanding of aortic root anatomy and physiology. The relationships among its elements are of paramount importance during aortic valve repair/sparing procedures and they can be useful also in echocardiographic analysis and in computed tomography reconstruction. © The Author 2015
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.
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.
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.
Symmetries of stochastic differential equations: A geometric approach
Energy Technology Data Exchange (ETDEWEB)
De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)
2016-06-15
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.
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
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)
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)
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)
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.
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
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)
Effects of source shape on the numerical aperture factor with a geometrical-optics model.
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.
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.
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°.
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.
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°.
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
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.
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...
Geometric Form Drawing: A Perceptual-Motor Approach to Preventive Remediation (The Steiner Approach)
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)
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...
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.
Present State of the Art of Composite Fabric Forming: Geometrical and Mechanical Approaches
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.
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.
Inexpensive demonstration set for teaching geometrical optics made by 3D printer
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.
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
A geometric approach to multiperiod mean variance optimization of assets and liabilities
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...
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
Demystifying the memory effect: A geometrical approach to understanding speckle correlations
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.
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.
Nonlinear optics an analytical approach
Mandel, Paul
2010-01-01
Based on the author's extensive teaching experience and lecture notes, this textbook provides a substantially analytical rather than descriptive presentation of nonlinear optics. Divided into five parts, with most chapters corresponding to a two-hour lecture, the book begins with a unique account of the historical development from Kirchhoff's law for the black-body radiation to Planck's quantum hypothesis and Einstein's discovery of spontaneous emission - providing all the explicit proofs. The subsequent sections deal with matter quantization, ultrashort pulse propagation in 2-level media, cavity nonlinear optics, chi(2) and chi(3) media. For graduate and PhD students in nonlinear optics or photonics, while also representing a valuable reference for researchers in these fields.
Geometric Lagrangian approach to the physical degree of freedom count in field theory
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.
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.
Geometric approach to the design of an imaging probe to evaluate the iridocorneal angle structures
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.
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.
Finsler metrics—a global approach with applications to geometric function theory
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.
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.
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.
Quantum criticality of geometric phase in coupled optical cavity arrays under linear quench
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...
The Wigner distribution function and Hamilton's characteristics of a geometric-optical system
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
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.)
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.
Autocorrelated process control: Geometric Brownian Motion approach versus Box-Jenkins approach
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.
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.
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
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.
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
Error performance analysis in K-tier uplink cellular networks using a stochastic geometric approach
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.
Proportional-delayed controllers design for LTI-systems: a geometric approach
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.
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.
A network approach to the geometric structure of shallow cloud fields
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
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.
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.
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.
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.
Directory of Open Access Journals (Sweden)
Masuda Kazuhiko
2016-01-01
Full Text Available Backscattering properties of ice crystal models (Voronoi aggregates (VA, hexagonal columns (COL, and six-branched bullet rosettes (BR6 are calculated by using geometrical-opticsintegral-equation (GOIE method. Characteristics of depolarization ratio (δ and lidar ratio (L of the crystal models are examined. δ (L values are 0.2~0.3 (4~50, 0.3~0.4 (10~25, and 0.5~0.6 (50~100 for COL, BR6, and VA, respectively, at wavelength λ=0.532 μm. It is found that small deformation of COL model could produce significant changes in δ and L.
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)
A differential-geometric approach to generalized linear models with grouped predictors
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
Iron-dextran complex: geometrical structure and magneto-optical features.
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.
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.
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.
Simulation Experiment on Landing Site Selection Using a Simple Geometric Approach
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.
Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations
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.
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.
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.
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…
Methods of Stimulating the Students' Creativity in the Study of Geometrical Optics
Florian, Gabriel; Trocaru, Sorin; Florian, Aurelia-Daniela; Bâna, Alexandru-Dumitru
2015-01-01
The aim of the present article is to focus on the operational aspects referring to the actions--strategies and on the defined modalities of establishing educational objectives/competences. In the achievement of our work a special attention has been paid to the operational aspects of the learning process of the optical phenomena. There were carried…
Maurines, Laurence
2010-01-01
This particular study is part of a research programme on the difficulties encountered by students when learning about wave phenomena in a three-dimensional medium in the absence or presence of obstacles. It focuses on how students reason in situations in which wave optics need to be used: diffraction of light by an aperture, imaging in the…
Sheil, Conor J; Bahrami, Mehdi; Goncharov, Alexander V
2014-05-01
We present an analytical method to describe the accommodative changes in the human crystalline lens. The method is based on the geometry-invariant lens model, in which the gradient-index (GRIN) iso-indicial contours are coupled to the external shape. This feature ensures that any given number of iso-indicial contours does not change with accommodation, which preserves the optical integrity of the GRIN structure. The coupling also enables us to define the GRIN structure if the radii and asphericities of the external lens surfaces are known. As an example, the accommodative changes in lenticular radii and central thickness were taken from the literature, while the asphericities of the external surfaces were derived analytically by adhering to the basic physical conditions of constant lens volume and its axial position. The resulting changes in lens geometry are consistent with experimental data, and the optical properties are in line with expected values for optical power and spherical aberration. The aim of the paper is to provide an anatomically and optically accurate lens model that is valid for 3 mm pupils and can be used as a new tool for better understanding of accommodation.
Transformation of Didactic Intensions by Teachers: The Case of Geometrical Optics in Grade 8.
Hirn, Colette; Viennot, Laurence
2000-01-01
Investigates the idea that teachers are not passive transmitters, and that some general trends can be found in the way they transform proposed strategies. Presents the case of elementary optics in grade 8 in France in which four sets of data--interviews before teaching, logbooks, assessment tasks, and video-recorded class observations--lead to…
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.
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.
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.
Accurate geometrical optics model for single-lens stereovision system using a prism.
Cui, Xiaoyu; Lim, Kah Bin; Guo, Qiyong; Wang, DaoLei
2012-09-01
In this paper, we proposed a new method for analyzing the image formation of a prism. The prism was considered as a single optical system composed of some planes. By analyzing each plane individually and then combining them together, we derived a transformation matrix which can express the relationship between an object point and its image by the refraction of a prism. We also explained how to use this matrix for epipolar geometry and three-dimensional point reconstruction. Our method is based on optical geometry and could be used in a multiocular prism. Experimentation results are presented to prove the accuracy of our method is better than former researchers' and is comparable with that of the multicamera stereovision system.
Automatic low-order aberration correction based on geometrical optics for slab lasers.
Yu, Xin; Dong, Lizhi; Lai, Boheng; Yang, Ping; Liu, Yong; Kong, Qingfeng; Yang, Kangjian; Tang, Guomao; Xu, Bing
2017-02-20
In this paper, we present a method based on geometry optics to simultaneously correct low-order aberrations and reshape the beams of slab lasers. A coaxial optical system with three lenses is adapted. The positions of the three lenses are directly calculated based on the beam parameters detected by wavefront sensors. The initial sizes of the input beams are 1.8 mm×11 mm, and peak-to-valley (PV) values of the wavefront range up to several tens of microns. After automatic correction, the dimensions may reach nearly 22 mm×22 mm as expected, and PV values of the wavefront are less than 2 μm. The effectiveness and precision of this method are verified with experiments.
Lessons from the History of the Concept of the Ray for Teaching Geometrical Optics
Andreou, C.; Raftopoulos, A.
2011-10-01
There are two indisputable findings in science education research. First, students go to school with some intuitive beliefs about the natural world and physical phenomena that pose an obstacle to the learning of formal science. Second, these beliefs result from the confluence of two factors, namely, their everyday experience as they interact with the world around them and a set of operational constraints or principles that channel both perceptually and conceptually the way these experiences are perceived and interpreted. History of science suggests that the theories of early scientists through which they sought to explain physical phenomena relied mostly on ideas that closely fitted their experiences of the relevant phenomena. This characteristic of the early scientific ideas is the root of the epistemological difficulties that early scientists faced in their attempts to explain the phenomena. In this paper, we focus on the early theories in optics (from ancient Greek to the late Islamic scientific traditions) and argue that students face some of the same epistemological problems as early scientists in explaining vision and optical phenomena for the reason that students' intuitive beliefs are also closely tied to particular phenomena and as a result the underlying notions are fragmentary and lack the necessary generality that would allow them to cover many disparate phenomena. Knowledge of these epistemological problems can help the instructor to identify the key elements for a better understanding of the formal theory of optics and, in turn, lead to a more effective instruction.
MODELING AND SIMULATION OF HIGH RESOLUTION OPTICAL REMOTE SENSING SATELLITE GEOMETRIC CHAIN
Directory of Open Access Journals (Sweden)
Z. Xia
2018-04-01
Full Text Available The high resolution satellite with the longer focal length and the larger aperture has been widely used in georeferencing of the observed scene in recent years. The consistent end to end model of high resolution remote sensing satellite geometric chain is presented, which consists of the scene, the three line array camera, the platform including attitude and position information, the time system and the processing algorithm. The integrated design of the camera and the star tracker is considered and the simulation method of the geolocation accuracy is put forward by introduce the new index of the angle between the camera and the star tracker. The model is validated by the geolocation accuracy simulation according to the test method of the ZY-3 satellite imagery rigorously. The simulation results show that the geolocation accuracy is within 25m, which is highly consistent with the test results. The geolocation accuracy can be improved about 7 m by the integrated design. The model combined with the simulation method is applicable to the geolocation accuracy estimate before the satellite launching.
Beam splitter phase shifts: Wave optics approach
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.
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
Energy Technology Data Exchange (ETDEWEB)
Korayem, M. H., E-mail: hkorayem@iust.ac.ir; Hefzabad, R. N.; Homayooni, A.; Aslani, H. [Iran University of Science and Technology, Robotic Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering (Iran, Islamic Republic of)
2017-01-15
Carbon allotropes are used as nanocarriers for drug and cell delivery. To obtain an accurate result in the nanoscale, it is important to use a precise model. In this paper, a multiscale approach is presented to investigate the manipulation process of carbon allotropes based on atomic force microscopy (AFM). For this purpose, the AFM setup is separated into two parts with different sizes as macro field (MF) and nano field (NF). Using Kirchhoff’s plate model, the cantilever (the main part of MF) is modeled. The molecular dynamics method is applied to model the NF part, and then the MF and NF are coupled with the multiscale algorithm. With this model, by considering the effect of size and shape, the manipulation of carbon allotropes is carried out. The manipulations of armchair CNTs and fullerenes are performed to study the diameter changing effects. The result shows that the manipulation and friction force increases by increasing the diameter. The result of the indentation depth for the armchair CNTs indicates that decreasing the diameter causes the indentation depth to reduce. Moreover, the manipulations of four kinds of carbon allotropes with the same number of atoms have been studied to investigate the geometrical effects. The shapes of these nanoparticles change from sphere to cylinder. The results illustrate that the manipulation and the friction force decrease as the nanoparticle shape varies from sphere to cylinder. The Von-Mises results demonstrate that by changing the nanoparticle shape from the spherical to the cylindrical form, the stress increases, although the manipulation force reduces.
Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics
International Nuclear Information System (INIS)
Vollick, Dan N.
2004-01-01
The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric. For sufficiently small curvatures the resulting field equations can be divided into two sets. One set, involving the antisymmetric part of the Ricci tensor R or μν , consists of the field equation for a massive vector field. The other set consists of the Einstein field equations with an energy momentum tensor for the vector field plus additional corrections. In a vacuum with R or μν =0 the field equations are shown to be the usual Einstein vacuum equations. This extends the universality of the vacuum Einstein equations, discussed by Ferraris et al., to the Born-Infeld-Einstein action. In the simplest version of the theory there is a single coupling constant and by requiring that the Einstein field equations hold to a good approximation in neutron stars it is shown that mass of the vector field exceeds the lower bound on the mass of the photon. Thus, in this case the vector field cannot represent the electromagnetic field and would describe a new geometrical field. In a more general version in which the symmetric and antisymmetric parts of the Ricci tensor have different coupling constants it is possible to satisfy all of the observational constraints if the antisymmetric coupling is much larger than the symmetric coupling. In this case the antisymmetric part of the Ricci tensor can describe the electromagnetic field
International Nuclear Information System (INIS)
Korayem, M. H.; Hefzabad, R. N.; Homayooni, A.; Aslani, H.
2017-01-01
Carbon allotropes are used as nanocarriers for drug and cell delivery. To obtain an accurate result in the nanoscale, it is important to use a precise model. In this paper, a multiscale approach is presented to investigate the manipulation process of carbon allotropes based on atomic force microscopy (AFM). For this purpose, the AFM setup is separated into two parts with different sizes as macro field (MF) and nano field (NF). Using Kirchhoff’s plate model, the cantilever (the main part of MF) is modeled. The molecular dynamics method is applied to model the NF part, and then the MF and NF are coupled with the multiscale algorithm. With this model, by considering the effect of size and shape, the manipulation of carbon allotropes is carried out. The manipulations of armchair CNTs and fullerenes are performed to study the diameter changing effects. The result shows that the manipulation and friction force increases by increasing the diameter. The result of the indentation depth for the armchair CNTs indicates that decreasing the diameter causes the indentation depth to reduce. Moreover, the manipulations of four kinds of carbon allotropes with the same number of atoms have been studied to investigate the geometrical effects. The shapes of these nanoparticles change from sphere to cylinder. The results illustrate that the manipulation and the friction force decrease as the nanoparticle shape varies from sphere to cylinder. The Von-Mises results demonstrate that by changing the nanoparticle shape from the spherical to the cylindrical form, the stress increases, although the manipulation force reduces.
Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
International Nuclear Information System (INIS)
Bliokh, Konstantin Yu.
2006-01-01
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed
Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect.
Bliokh, Konstantin Yu
2006-07-28
We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.
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
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)
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.
The mathematics of geometrical and physical optics. The k-funktion and its ramifications
Energy Technology Data Exchange (ETDEWEB)
Stavroudis, O.N. [Centro de Investigaciones en Optica, Leon, Guanajuato (Mexico)
2006-07-01
In this sequel to his book, 'The Optics of Rays, Wavefronts, and Caustics', Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen's principle, and Maxwell's model of Gauss' perfect lens. From the contents: Part I: Preliminaries - Calculus of variations - Calculus of variations: differential geometry of space curves (helix and ellipse) - Fermat's principle and the ray equation for inhomogeneous isotropic media - Hilbert integral, the derivation of the Hamilton-Jacobi theory, and the eikonal equation - First-order partial differential equations. Part II: The k-Function - Calculation of surface differential geometry parameters - Ray tracing - Refraction of wavefronts at surfaces - Solution of the Maxwell equation in the context of the k-function. Part III: Applications - Pseudo Maxwell equations - Derivation and discussion of the Cartesian oval - The modern Schiefspiegler - Huygen's principle - Maxwell's model of Gauss' perfect lens. (orig.)
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.
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.
Right-invertibility for a class of nonlinear control systems: A geometric approach
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
DEFF Research Database (Denmark)
Baldi, P.; Blanke, Mogens; Castaldi, P.
2016-01-01
This paper presents a novel scheme for diagnosis of faults affecting the sensors measuring the satellite attitude, body angular velocity and flywheel spin rates as well as defects related to the control torques provided by satellite reaction wheels. A nonlinear geometric design is used to avoid t...
Jurling, Alden S; Fienup, James R
2014-03-01
Extending previous work by Thurman on wavefront sensing for segmented-aperture systems, we developed an algorithm for estimating segment tips and tilts from multiple point spread functions in different defocused planes. We also developed methods for overcoming two common modes for stagnation in nonlinear optimization-based phase retrieval algorithms for segmented systems. We showed that when used together, these methods largely solve the capture range problem in focus-diverse phase retrieval for segmented systems with large tips and tilts. Monte Carlo simulations produced a rate of success better than 98% for the combined approach.
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.
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.
International Nuclear Information System (INIS)
Anni, R.; Taffara, L.
1976-01-01
A fictitious scattering phenomenon between neutral heavy particles is analysed by using both the square-well and trapezoidal complex potentials. After a preliminary phenomenological discussion based on the behaviour of the exact scattering matrix and the trajectories of Regge poles and zeros as continuous functions of the imaginary part of the potential, the contributions to the scattering amplitude from the external and multiple internal reflections and from the ''surface waves'' are separated by using the Debye expansion of the S(lambda)-matrix. The most important first two terms of this expansion are then compared with the exact behaviour of both the partial-wave scattering amplitude and cross-section, and the results are discussed. In particular, for potentials with large imaginary parts, the first term of the Debye expansion, which is associated with the rays directly reflected by the surface, well approximates the exact scattering matrix for all angular momenta. In these cases, by applying to this first term the Watson transformation, one is able to separate the contributions from the reflected rays (saddle-point contribution in the background integral)from that of the surface waves(surface pole contribution) which are responsible for the diffraction phenomenon. Studies are in progress in order to extend this approach to the Saxon-Wood potential with Coulomb interaction
The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics
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.
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.
Smith, Tony E.; Lee, Ka Lok
2012-01-01
There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce "spurious correlation" that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.
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.
An approach to the optical MSD adder
Takahashi, Hideya; Matsushita, Kenji; Shimizu, Eiji
1990-07-01
The intrinsic parallelism of optical elements for computation is presently taken fuller advantage of than heretofore possible through an optical implementation of the modified signed digit (MSD) number system, which yields carry-free addition and subtraction. In the present optical implementation of the MSD system, optical phase data are used to preclude negative value representation. Attention is given to an MSD adder array for addition operations on two n-digit trinary numbers; the output is composed of n + 1 trinary digits.
A toric varieties approach to geometrical structure of multi partite states
International Nuclear Information System (INIS)
Heydari, Hoshang
2010-01-01
We investigate the geometrical structures of multipartite states based on construction of toric varieties. In particular, we describe pure quantum systems in terms of affine toric varieties and projective embedding of these varieties in complex projective spaces. We show that a quantum system can be corresponds to a toric variety of a fan which is constructed by gluing together affine toric varieties of polytopes. Moreover, we show that the projective toric varieties are the spaces of separable multipartite quantum states. The construction is a generalization of the complex multi-projective Segre variety. Our construction suggests a systematic way of looking at the structures of multipartite quantum systems.
Sadjadi, Seyed Jafar; Hamidi Hesarsorkh, Aghil; Mohammadi, Mehdi; Bonyadi Naeini, Ali
2015-06-01
Coordination and harmony between different departments of a company can be an important factor in achieving competitive advantage if the company corrects alignment between strategies of different departments. This paper presents an integrated decision model based on recent advances of geometric programming technique. The demand of a product considers as a power function of factors such as product's price, marketing expenditures, and consumer service expenditures. Furthermore, production cost considers as a cubic power function of outputs. The model will be solved by recent advances in convex optimization tools. Finally, the solution procedure is illustrated by numerical example.
Clerici, Giancarlo; Burnside, Walter D.
1989-01-01
In recent years, the compact range has become very popular for measuring Radar Cross Section (RCS) and antenna patterns. The compact range, in fact, offers several advantages due to reduced size, a controlled environment, and privacy. On the other hand, it has some problems of its own, which must be solved properly in order to achieve high quality measurement results. For example, diffraction from the edges of the main reflector corrupts the plane wave in the target zone and creates spurious scattering centers in RCS measurements. While diffraction can be minimized by using rolled edges, the field of an offset single reflector compact range is corrupted by three other errors: the taper of the reflected field, the cross polarization introduced by the tilt of the feed and the aperture blockage introduced by the feed itself. These three errors can be eliminated by the use of a subreflector system. A properly designed subreflector system offers very little aperture blockage, no cross-polarization introduced and a minimization of the taper of the reflected field. A Gregorian configuration has been adopted in order to enclose the feed and the ellipsoidal subreflector in a lower chamber, which is isolated by absorbers from the upper chamber, where the main parabolic reflector and the target zone are enclosed. The coupling between the two rooms is performed through a coupling aperture. The first cut design for such a subreflector system is performed through Geometrical Optics ray tracing techniques (GO), and is greatly simplified by the use of the concept of the central ray introduced by Dragone. The purpose of the GO design is to establish the basic dimensions of the main reflector and subreflector, the size of the primary and secondary illuminating surfaces, the tilt angles of the subreflector and feed, and estimate the feed beamwidth. At the same time, the shape of the coupling aperture is initially determined.
Wall-corner classification using sonar: a new approach based on geometric features.
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.
A Geometric Approach to CP Violation: Applications to the MCPMFV SUSY Model
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...
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
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
Geometrical superresolved imaging using nonperiodic spatial masking.
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.
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.
A new geometrical approach to Nash equilibria organization in Eisert's quantum games
International Nuclear Information System (INIS)
Schneider, David
2012-01-01
We extend the periodic point-based method for Eisert's quantum games (Schneider 2011 J. Phys. A: Math. Theor. 44 095301) to games not previously analyzed. From the comparison of different cases, we observe that games sharing the same classical features (as for instance the symmetrized Battle of the Sexes and the Chicken game) can have different characteristics after the quantization, and conversely, games with different classical behaviors (the Chicken game and the Prisoner's dilemma), are completely equivalent within Eisert's protocol. This fact is reflected in the structure of the map that the periodic point-procedure associates to the quantum game (from which the Nash equilibria are deduced). In order to understand how these unexpected outcomes are generated, we give a geometrical description of our observations in terms of bifurcation theory for maps. (paper)
Zhang, Pengcheng; De Crevoisier, Renaud; Simon, Antoine; Haigron, Pascal; Coatrieux, Jean-Louis; Li, Baosheng; Shu, Huazhong
2013-09-01
This work addresses random geometrical uncertainties that are intrinsically observed in radiation therapy by means of a new deconvolution method combining a series expansion and a Butterworth filter. The method efficiently suppresses high-frequency components by discarding the higher order terms of the series expansion and then filtering out deviations on the field edges. An additional approximation is made in order to set the fluence values outside the field to zero in the robust profiles. This method is compared to the deconvolution kernel method for a regular 2D fluence map, a real intensity-modulated radiation therapy field, and a prostate case. The results show that accuracy is improved while fulfilling clinical planning requirements.
International Nuclear Information System (INIS)
Zhang Pengcheng; Coatrieux, Jean-Louis; Shu Huazhong; De Crevoisier, Renaud; Simon, Antoine; Haigron, Pascal; Li Baosheng
2013-01-01
This work addresses random geometrical uncertainties that are intrinsically observed in radiation therapy by means of a new deconvolution method combining a series expansion and a Butterworth filter. The method efficiently suppresses high-frequency components by discarding the higher order terms of the series expansion and then filtering out deviations on the field edges. An additional approximation is made in order to set the fluence values outside the field to zero in the robust profiles. This method is compared to the deconvolution kernel method for a regular 2D fluence map, a real intensity-modulated radiation therapy field, and a prostate case. The results show that accuracy is improved while fulfilling clinical planning requirements. (paper)
On open questions in the geometric approach to structural learning Bayesian nets
Czech Academy of Sciences Publication Activity Database
Studený, Milan; Vomlel, Jiří
2011-01-01
Roč. 52, č. 5 (2011), s. 627-640 ISSN 0888-613X. [Workshop on Uncertainty Processing WUPES'09 /8./. Liblice, 19.09.2009-23.09.2009] R&D Projects: GA MŠk(CZ) 1M0572; GA ČR GA201/08/0539; GA ČR GEICC/08/E010 Grant - others:GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : structural learning Bayesian nets * standard imset * polytope * geometric neighborhood * differential imset Subject RIV: BA - General Mathematics Impact factor: 1.948, year: 2011 http://library.utia.cas.cz/separaty/2011/MTR/studeny-0358907. pdf
Micro-universes and strong black-roles: a purely geometric approach to elementary particles
International Nuclear Information System (INIS)
Recami, E.; Raciti, F.; Rodrigues Junior, W.A.; Zanchin, V.T.
1993-09-01
A panoramic view is presented of a proposed unified, bi-scale theory of gravitational and strong interactions [which is mathematically analogous to the last version of N. Rosen's bi-metric theory; and yields physical results similar to strong gravity's]. This theory, is purely geometrical in nature, adopting the methods of General Relativity for the description of hadron structure and strong interactions. In particular, hadrons are associated with strong black-holes, from the external point of view, and with micro-universes, from the internal point of view. Among the results herein presented, it should be mentioned the derivation: of confinement and asymptotic freedom from the hadron constituents; of the Yukawa behaviour for the potential at the static limit; of the strong coupling constant, and of mesonic mass spectra. (author)
del Castillo, Daniela L; Flores, David A; Cappozzo, Humberto L
2014-12-01
The aim of this work was to study the postnatal ontogenetic development of Pontoporia blainvillei skull, identifying major changes on shape, and relating them to relevant factors in the life history of the species. We analyzed a complete ontogenetic series (73♂, 83♀) with three-dimensional geometric morphometric techniques. Immature dolphins showed a very well-developed braincase and a poorly developed rostrum, and the principal postnatal changes affected the rostrum and the temporal fossa, both structures implied functionally to the feeding apparatus, thus suggesting a specialized mode for catch fast prey in P. blainvillei. Osseous elements associated with sound production were already well developed on immature dolphins, suggesting the importance of this apparatus since the beginning of postnatal life. Sexual dimorphism was detected on both shape and size variables. Females were bigger than males, in accordance with previous studies. Shape differences between sexes were found on the posterior part of premaxillaries and external bony nares (P < 0.01), suggesting that this sexual dimorphism is related to differences on vocalization capabilities. © 2014 Wiley Periodicals, Inc.
Directory of Open Access Journals (Sweden)
Adília Nogueira
2015-11-01
Full Text Available The South American hypopomid electric fish tribe Microsternarchini includes three small species from the Upper Orinoco and Negro rivers. These are placed in monotypic genera: Microsternarchus, Racenisia and Procerusternarchus. Recent collections from tributaries in Negro, Solimões and Amazonas Basins have revealed new specimens of Microsternarchus with significant variations in external morphology and in Electric Organ Discharge parameters (EOD. In order to estimate the diversity within the genus a previous molecular study was done using DNA barcoding, that suggested the presence of multiple Microsternarchus's lineages with high levels of genetic divergence between them. Here we try to determine if the variation in morphology and EOD parameters in the new specimens meet the genetic divergence found. To test the presence of differences in shape among the different lineages we performed a geometric morphometric analysis, which included a relative warp and multivariate analysis on distances between 14 anatomical landmarks defined on the basis of external morphology and homologous among the lineages. The EOD variations were also explored using multivariate analyses of 20 electrophysiological parameters calculated through an algorithm developed in Matlab. The results show that there are significant differences in body shape and EOD in three lineages of Microsternarchus, and the features that contributed most were related to the shape of the head, the coefficient of variation of the signal and the duration and area of the different phases of the pulse. The discrimination of the three lineages confirms the occurrence of new species in the group that are currently being described.
Lockwood, Charles A; Lynch, John M; Kimbel, William H
2002-01-01
The hominid temporal bone offers a complex array of morphology that is linked to several different functional systems. Its frequent preservation in the fossil record gives the temporal bone added significance in the study of human evolution, but its morphology has proven difficult to quantify. In this study we use techniques of 3D geometric morphometrics to quantify differences among humans and great apes and discuss the results in a phylogenetic context. Twenty-three landmarks on the ectocranial surface of the temporal bone provide a high level of anatomical detail. Generalized Procrustes analysis (GPA) is used to register (adjust for position, orientation and scale) landmark data from 405 adults representing Homo, Pan, Gorilla and Pongo. Principal components analysis of residuals from the GPA shows that the major source of variation is between humans and apes. Human characteristics such as a coronally orientated petrous axis, a deep mandibular fossa, a projecting mastoid process, and reduced lateral extension of the tympanic element strongly impact the analysis. In phenetic cluster analyses, gorillas and orangutans group together with respect to chimpanzees, and all apes group together with respect to humans. Thus, the analysis contradicts depictions of African apes as a single morphotype. Gorillas and orangutans lack the extensive preglenoid surface of chimpanzees, and their mastoid processes are less medially inflected. These and other characters shared by gorillas and orangutans are probably primitive for the African hominid clade. PMID:12489757
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.
TU-H-206-01: An Automated Approach for Identifying Geometric Distortions in Gamma Cameras
Energy Technology Data Exchange (ETDEWEB)
Mann, S; Nelson, J [Clinical Imaging Physics Group and Carl E. Ravin Advanced Imaging Laboratories, Department of Radiology, Duke University Medical Center, Durham, North Carolina 27705 and Medical Physics Graduate Program, Duke University, Durham, North Carolina 27705 (United States); Samei, E [Clinical Imaging Physics Group and Carl E. Ravin Advanced Imaging Laboratories, Department of Radiology, Duke University Medical Center, Durham, North Carolina 27705 and Departments of Physics, Electrical and Computer Engineering, and Biomedical Engineering, and Medical Physics Graduate Program, Duke University, Durham, North Carolina 27705 (United States)
2016-06-15
Purpose: To develop a clinically-deployable, automated process for detecting artifacts in routine nuclear medicine (NM) quality assurance (QA) bar phantom images. Methods: An artifact detection algorithm was created to analyze bar phantom images as part of an ongoing QA program. A low noise, high resolution reference image was acquired from an x-ray of the bar phantom with a Philips Digital Diagnost system utilizing image stitching. NM bar images, acquired for 5 million counts over a 512×512 matrix, were registered to the template image by maximizing mutual information (MI). The MI index was used as an initial test for artifacts; low values indicate an overall presence of distortions regardless of their spatial location. Images with low MI scores were further analyzed for bar linearity, periodicity, alignment, and compression to locate differences with respect to the template. Findings from each test were spatially correlated and locations failing multiple tests were flagged as potential artifacts requiring additional visual analysis. The algorithm was initially deployed for GE Discovery 670 and Infinia Hawkeye gamma cameras. Results: The algorithm successfully identified clinically relevant artifacts from both systems previously unnoticed by technologists performing the QA. Average MI indices for artifact-free images are 0.55. Images with MI indices < 0.50 have shown 100% sensitivity and specificity for artifact detection when compared with a thorough visual analysis. Correlation of geometric tests confirms the ability to spatially locate the most likely image regions containing an artifact regardless of initial phantom orientation. Conclusion: The algorithm shows the potential to detect gamma camera artifacts that may be missed by routine technologist inspections. Detection and subsequent correction of artifacts ensures maximum image quality and may help to identify failing hardware before it impacts clinical workflow. Going forward, the algorithm is being
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.
Functional morphology and integration of corvid skulls – a 3D geometric morphometric approach
Directory of Open Access Journals (Sweden)
Gunz Philipp
2009-01-01
Full Text Available Abstract Background Sympatric corvid species have evolved differences in nesting, habitat choice, diet and foraging. Differences in the frequency with which corvid species use their repertoire of feeding techniques is expected to covary with bill-shape and with the frontal binocular field. Species that frequently probe are expected to have a relatively longer bill and more sidewise oriented orbits in contrast to species that frequently peck. We tested this prediction by analyzing computed tomography scans of skulls of six corvid species by means of three-dimensional geometric morphometrics. We (1 explored patterns of major variation using principal component analysis, (2 compared within and between species relationships of size and shape and (3 quantitatively compared patterns of morphological integration between bill and cranium by means of partial least squares (singular warp analysis. Results Major shape variation occurs at the bill, in the orientation of orbits, in the position of the foramen magnum and in the angle between bill and cranium. The first principal component correlated positively with centroid-size, but within-species allometric relationships differed markedly. Major covariation between the bill and cranium lies in the difference in orbit orientation relative to bill-length and in the angle between bill and cranium. Conclusion Corvid species show pronounced differences in skull shape, which covary with foraging mode. Increasing bill-length, bill-curvature and sidewise orientation of the eyes is associated with an increase in the observed frequency in probing (vice versa in pecking. Hence, the frequency of probing, bill-length, bill-curvature and sidewise orientation of the eyes is progressively increased from jackdaw, to Eurasian jay, to black-billed magpie, to hooded crow, to rook and to common raven (when feeding on carcasses is considered as probing. Our results on the morphological integration suggest that most of the
Spectral approach to optical resonator theory
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.
1981-01-01
A new computational method for unloaded optical resonators is developed based on the discrete Fourier analysis of informaton generated by repated iterations of the optical field corresponding to transits between reflectors. The method is a straightforward extension of the propagating beam method developed earlier for optical fibers for extracting modal properties from numerical solutions to the paraxial scalar wave equation. The method requires computation of a field correlation function, whose Fourier transform reveals the eigenmodes as resonant peaks. Analysis of the location and breadth of these peaks determines the resonator eigenvalues When the eigenvalues are known, additional discrete Fourier transforms of the field are used to generate the mode eigenfunctions. This new method makes possible the unambiguous identification and accurate characterization of the entire spectrum of transverse resonator modes
DEFF Research Database (Denmark)
Hansen, Anders L.; Lund, Erik; Pinho, Silvestre T.
2009-01-01
In this paper a hierarchical FE approach is utilized to simulate delamination in a composite plate loaded in uni-axial compression. Progressive delamination is modelled by use of cohesive interface elements that are automatically embedded. The non-linear problem is solved quasi-statically in whic...
A Geometric Dictionary Learning Based Approach for Fluorescence Spectroscopy Image Fusion
Zhiqin Zhu; Guanqiu Qi; Yi Chai; Penghua Li
2017-01-01
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 ...
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.
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.
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.
Optical pulse shaping approaches to coherent control
International Nuclear Information System (INIS)
Goswami, Debabrata
2003-01-01
The last part of the twentieth century has experienced a huge resurge of activity in the field of coherent light-matter interaction, more so in attempting to exert control over such interactions. Birth of coherent control was originally spurred by the theoretical understanding of the quantum interferences that lead to energy randomization and experimental developments in ultrafast laser spectroscopy. The theoretical predictions on control of reaction channels or energy randomization processes are still more dramatic than the experimental demonstrations, though this gap between the two is consistently reducing over the recent years with realistic theoretical models and technological developments. Experimental demonstrations of arbitrary optical pulse shaping have made some of the previously impracticable theoretical predictions possible to implement. Starting with the simple laser modulation schemes to provide proof-of-the-principle demonstrations, feedback loop pulse shaping systems have been developed that can actively manipulate some atomic and molecular processes. This tremendous experimental boost of optical pulse shaping developments has prospects and implications into many more new directions, such as quantum computing and terabit/sec data communications. This review captures certain aspects and impacts of optical pulse shaping into the fast developing areas of coherent control and other related fields. Currently available reviews focus on one or the other detailed aspects of coherent control, and the reader will be referred to such details as and when necessary for issues that are dealt in brief here. We will focus on the current issues including control of intramolecular dynamics and make connections to the future concepts, such as, quantum computation, biomedical applications, etc
Directory of Open Access Journals (Sweden)
Nita H. SHAH
2010-07-01
Full Text Available This paper deals with the rigorous photogrammetric solution to model the uncertainty in the orientation parameters of Indian Remote Sensing Satellite IRS-P5 (Cartosat-1. Cartosat-1 is a three axis stabilized spacecraft launched into polar sun-synchronous circular orbit at an altitude of 618 km. The satellite has two panchromatic (PAN cameras with nominal resolution of ~2.5 m. The camera looking ahead is called FORE mounted with +26 deg angle and the other looking near nadir is called AFT mounted with -5 deg, in along track direction. Data Product Generation Software (DPGS system uses the rigorous photogrammetric Collinearity model in order to utilize the full system information, together with payload geometry & control points, for estimating the uncertainty in attitude parameters. The initial orbit, attitude knowledge is obtained from GPS bound orbit measurement, star tracker and gyros. The variations in satellite attitude with time are modelled using simple linear polynomial model. Also, based on this model, Kalman filter approach is studied and applied to improve the uncertainty in the orientation of spacecraft with high quality ground control points (GCPs. The sequential estimator (Kalman filter is used in an iterative process which corrects the parameters at each time of observation rather than at epoch time. Results are presented for three stereo data sets. The accuracy of model depends on the accuracy of the control points.
International Nuclear Information System (INIS)
Jaffray, D A; Sharpe, M; Rink, A; Letourneau, D
2010-01-01
The development of image-guidance technologies offer increased precision and accuracy in the placement of radiation therapy dose distributions in the human body. Kilovoltage and megavoltage systems now offer sub-mm accuracy and precision in localizing the treatment and planned isocenters. While this represents a significant improvement in our ability to target lesions, the performance of these systems in terms of their precise and accurate placement of field edges, including individual multi-leaves, is not performing at the same level. The development of dosimeters with small, imageable regions of response will allow these new systems to be evaluated with a much higher level of precision and accuracy. Furthermore, the development of completely automated systems that exploit the robotic nature of the imaging and delivery subsystems should permit the true performance of current IG-IMRT systems to be realized, quantified, and monitored. This includes adjustments to the treatment machines operating parameters, as well as, refinements of the planning system's beam model. Specifically, investigations into novel approaches of employing these detectors, automating their use to maximize system performance, and, the development of novel detectors for compatibility in MR-based systems will be discussed.
Espath, L. F R; Braun, Alexandre Luis; Awruch, Armando Miguel; Dalcin, Lisandro
2015-01-01
A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
Espath, L. F R
2015-02-03
A numerical model to deal with nonlinear elastodynamics involving large rotations within the framework of the finite element based on NURBS (Non-Uniform Rational B-Spline) basis is presented. A comprehensive kinematical description using a corotational approach and an orthogonal tensor given by the exact polar decomposition is adopted. The state equation is written in terms of corotational variables according to the hypoelastic theory, relating the Jaumann derivative of the Cauchy stress to the Eulerian strain rate.The generalized-α method (Gα) method and Generalized Energy-Momentum Method with an additional parameter (GEMM+ξ) are employed in order to obtain a stable and controllable dissipative time-stepping scheme with algorithmic conservative properties for nonlinear dynamic analyses.The main contribution is to show that the energy-momentum conservation properties and numerical stability may be improved once a NURBS-based FEM in the spatial discretization is used. Also it is shown that high continuity can postpone the numerical instability when GEMM+ξ with consistent mass is employed; likewise, increasing the continuity class yields a decrease in the numerical dissipation. A parametric study is carried out in order to show the stability and energy budget in terms of several properties such as continuity class, spectral radius and lumped as well as consistent mass matrices.
Geometric Simulation Approach for Grading and Assessing the Thermostability of CALBs
Directory of Open Access Journals (Sweden)
B. Senthilkumar
2016-01-01
Full Text Available Candida antarctica lipase B (CALB is a known stable and highly active enzyme used widely in biodiesel synthesis. In this work, the stability of native (4K6G and mutant (4K5Q CALB was studied through various structural parameters using conformational sampling approach. The contours of polar surface area and surface area of mutant CALB were 11357.67 Å2 and 30007.4 Å2, respectively, showing an enhanced stability compared to native CALB with a statistically significant P value of < 0.0001. Moreover, simulated thermal denaturation of CALB, a process involving dilution of hydrogen bond, significantly shielded against different intervals of energy application in mutant CALB revealing its augmentation of structural rigidity against native CALB. Finally, computational docking analysis showed an increase in the binding affinity of CALB and its substrate (triglyceride in mutant CALB with Atomic Contact Energy (ACE of −91.23 kcal/mol compared to native CALB (ACE of −70.3 kcal/mol. The computational observations proposed that the use of mutant CALB (4K5Q could serve as a best template for production of biodiesel in the future. Additionally, it can also be used as a template to identify efficient thermostable lipases through further mutations.
Yu, Zhaoyuan; Yuan, Linwang; Luo, Wen; Feng, Linyao; Lv, Guonian
2015-12-30
Passive infrared (PIR) motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA)-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks.
Directory of Open Access Journals (Sweden)
Zhaoyuan Yu
2015-12-01
Full Text Available Passive infrared (PIR motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks.
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.
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.
Field approach in the transformation optics concept
DEFF Research Database (Denmark)
Novitsky, Andrey; Zhukovsky, Sergei; Barkovsky, L. M.
2012-01-01
distribution (e.g., Gaussian and sinusoidal) is studied to validate the effectiveness of the field-based formulation. As for the boundary conditions for the cloaked region the absence of the normal component of the Poynting vector is justified. In the frames of the field-based approach the physical reasons...
High-throughput proteomics : optical approaches.
Energy Technology Data Exchange (ETDEWEB)
Davidson, George S.
2008-09-01
Realistic cell models could greatly accelerate our ability to engineer biochemical pathways and the production of valuable organic products, which would be of great use in the development of biofuels, pharmaceuticals, and the crops for the next green revolution. However, this level of engineering will require a great deal more knowledge about the mechanisms of life than is currently available. In particular, we need to understand the interactome (which proteins interact) as it is situated in the three dimensional geometry of the cell (i.e., a situated interactome), and the regulation/dynamics of these interactions. Methods for optical proteomics have become available that allow the monitoring and even disruption/control of interacting proteins in living cells. Here, a range of these methods is reviewed with respect to their role in elucidating the interactome and the relevant spatial localizations. Development of these technologies and their integration into the core competencies of research organizations can position whole institutions and teams of researchers to lead in both the fundamental science and the engineering applications of cellular biology. That leadership could be particularly important with respect to problems of national urgency centered around security, biofuels, and healthcare.
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....
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
Tournaire, O.; Paparoditis, N.
Road detection has been a topic of great interest in the photogrammetric and remote sensing communities since the end of the 70s. Many approaches dealing with various sensor resolutions, the nature of the scene or the wished accuracy of the extracted objects have been presented. This topic remains challenging today as the need for accurate and up-to-date data is becoming more and more important. Based on this context, we will study in this paper the road network from a particular point of view, focusing on road marks, and in particular dashed lines. Indeed, they are very useful clues, for evidence of a road, but also for tasks of a higher level. For instance, they can be used to enhance quality and to improve road databases. It is also possible to delineate the different circulation lanes, their width and functionality (speed limit, special lanes for buses or bicycles...). In this paper, we propose a new robust and accurate top-down approach for dashed line detection based on stochastic geometry. Our approach is automatic in the sense that no intervention from a human operator is necessary to initialise the algorithm or to track errors during the process. The core of our approach relies on defining geometric, radiometric and relational models for dashed lines objects. The model also has to deal with the interactions between the different objects making up a line, meaning that it introduces external knowledge taken from specifications. Our strategy is based on a stochastic method, and in particular marked point processes. Our goal is to find the objects configuration minimising an energy function made-up of a data attachment term measuring the consistency of the image with respect to the objects and a regularising term managing the relationship between neighbouring objects. To sample the energy function, we use Green algorithm's; coupled with a simulated annealing to find its minimum. Results from aerial images at various resolutions are presented showing that our
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...
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
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.
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.
Optical approaches to macroscopic and microscopic engineering
International Nuclear Information System (INIS)
Bartolo, Paulo Jorge da Silva
2001-01-01
This research investigates the theoretical basis of a new photo-fabrication system. By this system, optical and thermal effects are used, together or separately, to locally induce a phase change in a liquid resin. This phase change phenomena is used to 'write' three-dimensional shapes. In addition, a thermal-kinetic model has been developed to correctly simulate the physical and chemical changes that occur in the bulk (and surroundings) of the material directly exposed to radiation and/or heat, and the rates at which these changes occur. Through this model, the law of conservation of energy describing the heat transfer phenomena is coupled with a kinetic model describing in detail the cure kinetics in both chemical and diffusion-controlled regimes. The thermal-kinetic model has been implemented using the finite element method. Linear rectangular elements have been considered and the concept of isoparametric formulation used. The Cranck-Nicolson algorithm has been used to integrate the system of equations, resulting from the finite element discretisation, with respect to time. Three different photo-fabrication processes were investigated. The first process uses ultraviolet radiation to cure a thermosetting polymer containing a certain amount of photo-initiator. The radiation generates free radicals by cleavage the initiator molecules, starting the chemical reaction. The second one uses ultraviolet radiation to start the curing reaction of a liquid thermosetting polymer containing a certain amount of photo-initiator. In this case, a heat source is also used to increase the temperature, and consequently, to increase the rate of gel formation and the fractional conversion, decreasing the necessary exposure time. Finally, the third system uses a thermosetting material containing small amounts of both thermal and photo-initiators. In this case ultraviolet radiation and heat are used to simultaneously start two types of chemical reactions: thermal-initiated and photo
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
Nonlinear Optics Approaches Towards Subdiffraction Resolution in CARS Imaging
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
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.
A new approach for the verification of optical systems
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.
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).
Femtosecond pulse shaping using the geometric phase.
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.
International Nuclear Information System (INIS)
Sutter, J.P.; Amboage, M.; Hayama, S.; Diaz-Moreno, S.
2010-01-01
The X-ray focusing properties of a bent single crystal diffracting in Bragg geometry are discussed. First, it is assumed that a polychromatic point source is focused to a point image. The elliptical arc that the crystal must trace and the aberrations caused by bending the crystal cylindrically are derived from the ray paths. For a source of finite size, the magnification is found to vary over the crystal's length, so that rays of different wavelength produce images of different size. More realistic treatments of penetration and diffraction are performed with spherical monochromatic incident waves, using Takagi-Taupin calculations to create the diffracted wave and the Fresnel integral to trace the diffracted wave's evolution. Such 'wave-optical' calculations on a symmetric Si (1 1 1) crystal with 7 keV X-rays predict beam sizes different from those found in ray traces. Optimal sample and detector placement therefore requires wave effects to be considered.
Salah, Wa'el; Sanchez del Rio, Manuel
2011-05-01
The layout and the optical performance of the SGM branch of the D09 bending-magnet beamline, under construction at SESAME, are presented. The beamline is based on the Dragon-type design and delivers photons over the spectral range 15-250 eV. One fixed entrance slit and a movable exit slit are used. The performance of the beamline has been characterized by calculating the mirror reflectivities and the grating efficiencies. The flux and resolution were calculated by ray-tracing using SHADOW. The grating diffraction efficiencies were calculated using the GRADIF code. The results and the overall shapes of the predicted curves are in reasonable agreement with those obtained using an analytical formula.
Paas, Fred G.W.C.; van Merrienboer, Jeroen J.G.; van Merrienboer, J.J.G.
1994-01-01
Four computer-based training strategies for geometrical problem solving in the domain of computer numerically controlled machinery programming were studied with regard to their effects on training performance, transfer performance, and cognitive load. A low- and a high-variability conventional
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
Polarizing Beam Splitter: A New Approach Based on Transformation Optics
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.
A new approach to stitching optical metrology data
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
Energy Technology Data Exchange (ETDEWEB)
Cooper, W. James [Washington State Univ., Pullman, WA (United States); Albertson, R Craig [Univ. of Massachusetts, Amherst, MA (United States); Jacob, Rick E. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Westneat, Mark W. [Field Museum of Natural History, Chicago, IL (United States)
2014-12-01
Here we present a re-description of Abudefduf luridus and reassign it to the genus Similiparma. We supplement traditional diagnoses and descriptions of this species with quantitative anatomical data collected from a family-wide geometric morphometric analysis of head morphology (44 species representing all 30 damselfish genera) and data from cranial micro-CT scans of fishes in the genus Similiparma. The use of geometric morphometric analyses (and other methods of shape analysis) permits detailed comparisons between the morphology of specific taxa and the anatomical diversity that has arisen in an entire lineage. This provides a particularly useful supplement to traditional description methods and we recommend the use of such techniques by systematists. Similiparma and its close relatives constitute a branch of the damselfish phylogenetic tree that predominantly inhabits rocky reefs in the Atlantic and Eastern Pacific, as opposed to the more commonly studied damselfishes that constitute a large portion of the ichthyofauna on all coral-reef communities.
Directory of Open Access Journals (Sweden)
José Ignacio Rojas-Sola
2016-12-01
Full Text Available The present study shows the process followed in making the three-dimensional model and geometric documentation of a historical invention of the renowned Spanish engineer Agustin de Betancourt y Molina, which forms part of his rich legacy. Specifically, this was a wind machine for draining marshy ground, designed in 1789. The present research relies on the computer-aided design (CAD techniques using Autodesk Inventor Professional software, based on the scant information provided by the only two drawings of the machine, making it necessary to propose a number of dimensional and geometric hypotheses as well as a series of movement restrictions (degrees of freedom, to arrive at a consistent design. The results offer a functional design for this historic invention.
Maillard, Philippe; Gomes, Marília F.
2016-06-01
This article presents an original algorithm created to detect and count trees in orchards using very high resolution images. The algorithm is based on an adaptation of the "template matching" image processing approach, in which the template is based on a "geometricaloptical" model created from a series of parameters, such as illumination angles, maximum and ambient radiance, and tree size specifications. The algorithm is tested on four images from different regions of the world and different crop types. These images all have the GoogleEarth application. Results show that the algorithm is very efficient at detecting and counting trees as long as their spectral and spatial characteristics are relatively constant. For walnut, mango and orange trees, the overall accuracy was clearly above 90%. However, the overall success rate for apple trees fell under 75%. It appears that the openness of the apple tree crown is most probably responsible for this poorer result. The algorithm is fully explained with a step-by-step description. At this stage, the algorithm still requires quite a bit of user interaction. The automatic determination of most of the required parameters is under development.
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
International Nuclear Information System (INIS)
Liu, Chao; Lee Panetta, R.; Yang, Ping
2013-01-01
Effects of surface roughness on the optical scattering properties of ice crystals are investigated using a random wave superposition model of roughness that is a simplification of models used in studies of scattering by surface water waves. Unlike previous work with models of rough surfaces applicable only in limited size ranges, such as surface perturbation methods in the small particle regime or the tilted-facet (TF) method in the large particle regime, ours uses a single roughness model to cover a range in sizes extending from the Rayleigh to the geometric optics regimes. The basic crystal shape we examine is the hexagonal column but our roughening model can be used for a wide variety of particle geometries. To compute scattering properties over the range of sizes we use the pseudo-spectral time domain method (PSTD) for small to moderate sized particles and the improved geometric optics method (IGOM) for large ones. Use of the PSTD with our roughness model is straightforward. By discretizing the roughened surface with triangular sub-elements, we adapt the IGOM to give full consideration of shadow effects, multiple reflections/refractions at the surface, and possible reentrance of the scattered beams. We measure the degree of roughness of a surface by the variance (σ 2 ) of surface slopes occurring on the surfaces. For moderately roughened surfaces (σ 2 ≤0.1) in the large particle regime, the scattering properties given by the TF and IGOM agree well, but differences in results obtained with the two methods become noticeable as the surface becomes increasingly roughened. Having a definite, albeit idealized, roughness model we are able to use the combination of the PSTD and IGOM to examine how a fixed degree of surface roughness affects the scattering properties of a particle as the size parameter of the particle changes. We find that for moderately rough surfaces in our model, as particle size parameter increases beyond about 20 the influence of surface
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Borot, Gaëtan; Orantin, Nicolas
We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions...... as Poisson structures on the moduli space of flat connections. The theory has a wider scope than that and one expects that many functorial objects in low-dimensional geometry and topology should have a GR construction. The geometric recursion has various projections to topological recursion (TR) and we...... in particular show it retrieves all previous variants and applications of TR. We also show that, for any initial data for topological recursion, one can construct initial data for GR with values in Frobenius algebra-valued continuous functions on Teichmueller space, such that the ωg,n of TR are obtained...
Omisore, Olatunji Mumini; Han, Shipeng; Ren, Lingxue; Zhang, Nannan; Ivanov, Kamen; Elazab, Ahmed; Wang, Lei
2017-08-01
Snake-like robot is an emerging form of serial-link manipulator with the morphologic design of biological snakes. The redundant robot can be used to assist medical experts in accessing internal organs with minimal or no invasion. Several snake-like robotic designs have been proposed for minimal invasive surgery, however, the few that were developed are yet to be fully explored for clinical procedures. This is due to lack of capability for full-fledged spatial navigation. In rare cases where such snake-like designs are spatially flexible, there exists no inverse kinematics (IK) solution with both precise control and fast response. In this study, we proposed a non-iterative geometric method for solving IK of lead-module of a snake-like robot designed for therapy or ablation of abdominal tumors. The proposed method is aimed at providing accurate and fast IK solution for given target points in the robot's workspace. n-1 virtual points (VPs) were geometrically computed and set as coordinates of intermediary joints in an n-link module. Suitable joint angles that can place the end-effector at given target points were then computed by vectorizing coordinates of the VPs, in addition to coordinates of the base point, target point, and tip of the first link in its default pose. The proposed method is applied to solve IK of two-link and redundant four-link modules. Both two-link and four-link modules were simulated with Robotics Toolbox in Matlab 8.3 (R2014a). Implementation result shows that the proposed method can solve IK of the spatially flexible robot with minimal error values. Furthermore, analyses of results from both modules show that the geometric method can reach 99.21 and 88.61% of points in their workspaces, respectively, with an error threshold of 1 mm. The proposed method is non-iterative and has a maximum execution time of 0.009 s. This paper focuses on solving IK problem of a spatially flexible robot which is part of a developmental project for abdominal
International Nuclear Information System (INIS)
Bruscaglioni, P.; Ismaelli, A.
1978-01-01
The contribution of doubly scattered radiation to the return of a monostatic Lidar, used for measurement of atmospheric visibility, is evaluated by means of a simple geometrical scheme. A very narrow laser beam is considered, to obtain an expression of the ratio D/S of doubly scattered power to singly scattered power. This assumption allows an easy consideration of any angle of scattering and the introduction of time into the calculations. Numerical computations are performed for several models of fog. Our results are similar, though a little lower, than the results of other theoretical treatments of this problem based on different assumptions. (author)
Stress Measurement by Geometrical Optics
Robinson, R. S.; Rossnagel, S. M.
1986-01-01
Fast, simple technique measures stresses in thin films. Sample disk bowed by stress into approximately spherical shape. Reflected image of disk magnified by amount related to curvature and, therefore, stress. Method requires sample substrate, such as cheap microscope cover slide, two mirrors, laser light beam, and screen.
Bi, Lei; Yang, Ping
2016-07-01
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.
Rodríguez-González, Abril; Míguez-Lozano, Raúl; Llopis-Belenguer, Cristina; Balbuena, Juan Antonio
2015-04-01
Evaluating phenotypic plasticity in attachment organs of parasites can provide information on the capacity to colonise new hosts and illuminate evolutionary processes driving host specificity. We analysed the variability in shape and size of the dorsal and ventral anchors of Ligophorus cephali from Mugil cephalus by means of geometric morphometrics and multivariate statistics. We also assessed the morphological integration between anchors and between the roots and points in order to gain insight into their functional morphology. Dorsal and ventral anchors showed a similar gradient of overall shape variation, but the amount of localised changes was much higher in the former. Statistical models describing variations in shape and size revealed clear differences between anchors. The dorsal anchor/bar complex seems more mobile than the ventral one in Ligophorus, and these differences may reflect different functional roles in attachment to the gills. The lower residual variation associated with the ventral anchor models suggests a tighter control of their shape and size, perhaps because these anchors seem to be responsible for firmer attachment and their size and shape would allow more effective responses to characteristics of the microenvironment within the individual host. Despite these putative functional differences, the high level of morphological integration indicates a concerted action between anchors. In addition, we found a slight, although significant, morphological integration between roots and points in both anchors, which suggests that a large fraction of the observed phenotypic variation does not compromise the functional role of anchors as levers. Given the low level of genetic variation in our sample, it is likely that much of the morphological variation reflects host-driven plastic responses. This supports the hypothesis of monogenean specificity through host-switching and rapid speciation. The present study demonstrates the potential of geometric
Geometrically Consistent Mesh Modification
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.
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.
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.
Tabassum, Hina
2014-07-01
This paper presents a novel framework to derive the statistics of the interference considering dedicated and shared spectrum access for uplink transmission in two-tier small cell networks such as the macrocell-femtocell networks. The framework exploits the distance distributions from geometric probability theory to characterize the uplink interference while considering a traditional grid-model set-up for macrocells along with the randomly deployed femtocells. The derived expressions capture the impact of path-loss, composite shadowing and fading, uniform and non-uniform traffic loads, spatial distribution of femtocells, and partial and full spectral reuse among femtocells. Considering dedicated spectrum access, first, we derive the statistics of co-tier interference incurred at both femtocell and macrocell base stations (BSs) from a single interferer by approximating generalized- K composite fading distribution with the tractable Gamma distribution. We then derive the distribution of the number of interferers considering partial spectral reuse and moment generating function (MGF) of the cumulative interference for both partial and full spectral reuse scenarios. Next, we derive the statistics of the cross-tier interference at both femtocell and macrocell BSs considering shared spectrum access. Finally, we utilize the derived expressions to analyze the capacity in both dedicated and shared spectrum access scenarios. The derived expressions are validated by the Monte Carlo simulations. Numerical results are generated to assess the feasibility of shared and dedicated spectrum access in femtocells under varying traffic load and spectral reuse scenarios. © 2014 IEEE.
International Nuclear Information System (INIS)
Gawand, Hemangi Laxman; Bhattacharjee, A. K.; Roy, Kallol
2017-01-01
In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA) software. A targeted attack (also termed a control aware attack) on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications
Energy Technology Data Exchange (ETDEWEB)
Gawand, Hemangi Laxman [Homi Bhabha National Institute, Computer Section, BARC, Mumbai (India); Bhattacharjee, A. K. [Reactor Control Division, BARC, Mumbai (India); Roy, Kallol [BHAVINI, Kalpakkam (India)
2017-04-15
In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA) software. A targeted attack (also termed a control aware attack) on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications.
Directory of Open Access Journals (Sweden)
Hemangi Laxman Gawand
2017-04-01
Full Text Available In industrial plants such as nuclear power plants, system operations are performed by embedded controllers orchestrated by Supervisory Control and Data Acquisition (SCADA software. A targeted attack (also termed a control aware attack on the controller/SCADA software can lead a control system to operate in an unsafe mode or sometimes to complete shutdown of the plant. Such malware attacks can result in tremendous cost to the organization for recovery, cleanup, and maintenance activity. SCADA systems in operational mode generate huge log files. These files are useful in analysis of the plant behavior and diagnostics during an ongoing attack. However, they are bulky and difficult for manual inspection. Data mining techniques such as least squares approximation and computational methods can be used in the analysis of logs and to take proactive actions when required. This paper explores methodologies and algorithms so as to develop an effective monitoring scheme against control aware cyber attacks. It also explains soft computation techniques such as the computational geometric method and least squares approximation that can be effective in monitor design. This paper provides insights into diagnostic monitoring of its effectiveness by attack simulations on a four-tank model and using computation techniques to diagnose it. Cyber security of instrumentation and control systems used in nuclear power plants is of paramount importance and hence could be a possible target of such applications.
Scattered Data Processing Approach Based on Optical Facial Motion Capture
Directory of Open Access Journals (Sweden)
Qiang Zhang
2013-01-01
Full Text Available In recent years, animation reconstruction of facial expressions has become a popular research field in computer science and motion capture-based facial expression reconstruction is now emerging in this field. Based on the facial motion data obtained using a passive optical motion capture system, we propose a scattered data processing approach, which aims to solve the common problems of missing data and noise. To recover missing data, given the nonlinear relationships among neighbors with the current missing marker, we propose an improved version of a previous method, where we use the motion of three muscles rather than one to recover the missing data. To reduce the noise, we initially apply preprocessing to eliminate impulsive noise, before our proposed three-order quasi-uniform B-spline-based fitting method is used to reduce the remaining noise. Our experiments showed that the principles that underlie this method are simple and straightforward, and it delivered acceptable precision during reconstruction.
Directory of Open Access Journals (Sweden)
Thomas Cucchi
Full Text Available Pigs have played a major role in the economic, social and symbolic systems of China since the Early Neolithic more than 8,000 years ago. However, the interaction between the history of pig domestication and transformations in Chinese society since then, have not been fully explored. In this paper, we investigated the co-evolution from the earliest farming communities through to the new political and economic models of state-like societies, up to the Chinese Empire, using 5,000 years of archaeological records from the Xiawanggang (XWG and Xinzhai (XZ sites (Henan Province. To trace the changes of pig populations against husbandry practices, we combined the geometric morphometric analysis of dental traits with a study of the stable carbon and nitrogen isotope ratios from bone collagen. The domestication process intensified during the Neolithic Yangshao, prompted by greater selective pressure and/or better herd control against wild introgression. After that, pig farming, in XWG, relied on local livestock and a gradual change of husbandry practices overtime. This was characterized by a gentle increase in millet foddering and animal protein intake, until a complete change over to household management during the Han dynasty. The only rupture in this steady trend of husbandry occurred during the Longshan period, with the appearance of small sized and idiosyncratic pigs with specific feeding practices (relying on millet and household scraps. From three exploratory hypothesis, we explored the possibility of anti-elite pig production in XWG during the Longshan period, as a means to resist incorporation into a new economic model promoting intensified domestic production. This exploratory hypothesis is the most suitable to our dataset; however, numerous areas need to be explored further in order to adequately document the role of pigs in the rise of China's complex societies.
Balasse, Marie; Zhao, Chunqing; Gao, Jiangtao; Hu, Yaowu; Yuan, Jing; Vigne, Jean-Denis
2016-01-01
Pigs have played a major role in the economic, social and symbolic systems of China since the Early Neolithic more than 8,000 years ago. However, the interaction between the history of pig domestication and transformations in Chinese society since then, have not been fully explored. In this paper, we investigated the co-evolution from the earliest farming communities through to the new political and economic models of state-like societies, up to the Chinese Empire, using 5,000 years of archaeological records from the Xiawanggang (XWG) and Xinzhai (XZ) sites (Henan Province). To trace the changes of pig populations against husbandry practices, we combined the geometric morphometric analysis of dental traits with a study of the stable carbon and nitrogen isotope ratios from bone collagen. The domestication process intensified during the Neolithic Yangshao, prompted by greater selective pressure and/or better herd control against wild introgression. After that, pig farming, in XWG, relied on local livestock and a gradual change of husbandry practices overtime. This was characterized by a gentle increase in millet foddering and animal protein intake, until a complete change over to household management during the Han dynasty. The only rupture in this steady trend of husbandry occurred during the Longshan period, with the appearance of small sized and idiosyncratic pigs with specific feeding practices (relying on millet and household scraps). From three exploratory hypothesis, we explored the possibility of anti-elite pig production in XWG during the Longshan period, as a means to resist incorporation into a new economic model promoting intensified domestic production. This exploratory hypothesis is the most suitable to our dataset; however, numerous areas need to be explored further in order to adequately document the role of pigs in the rise of China’s complex societies. PMID:27384523
Cucchi, Thomas; Dai, Lingling; Balasse, Marie; Zhao, Chunqing; Gao, Jiangtao; Hu, Yaowu; Yuan, Jing; Vigne, Jean-Denis
2016-01-01
Pigs have played a major role in the economic, social and symbolic systems of China since the Early Neolithic more than 8,000 years ago. However, the interaction between the history of pig domestication and transformations in Chinese society since then, have not been fully explored. In this paper, we investigated the co-evolution from the earliest farming communities through to the new political and economic models of state-like societies, up to the Chinese Empire, using 5,000 years of archaeological records from the Xiawanggang (XWG) and Xinzhai (XZ) sites (Henan Province). To trace the changes of pig populations against husbandry practices, we combined the geometric morphometric analysis of dental traits with a study of the stable carbon and nitrogen isotope ratios from bone collagen. The domestication process intensified during the Neolithic Yangshao, prompted by greater selective pressure and/or better herd control against wild introgression. After that, pig farming, in XWG, relied on local livestock and a gradual change of husbandry practices overtime. This was characterized by a gentle increase in millet foddering and animal protein intake, until a complete change over to household management during the Han dynasty. The only rupture in this steady trend of husbandry occurred during the Longshan period, with the appearance of small sized and idiosyncratic pigs with specific feeding practices (relying on millet and household scraps). From three exploratory hypothesis, we explored the possibility of anti-elite pig production in XWG during the Longshan period, as a means to resist incorporation into a new economic model promoting intensified domestic production. This exploratory hypothesis is the most suitable to our dataset; however, numerous areas need to be explored further in order to adequately document the role of pigs in the rise of China's complex societies.
Werneburg, Ingmar; Wilson, Laura A B; Parr, William C H; Joyce, Walter G
2015-03-01
The unique ability of modern turtles to retract their head and neck into the shell through a side-necked (pleurodiran) or hidden-necked (cryptodiran) motion is thought to have evolved independently in crown turtles. The anatomical changes that led to the vertebral shapes of modern turtles, however, are still poorly understood. Here we present comprehensive geometric morphometric analyses that trace turtle vertebral evolution and reconstruct disparity across phylogeny. Disparity of vertebral shape was high at the dawn of turtle evolution and decreased after the modern groups evolved, reflecting a stabilization of morphotypes that correspond to the two retraction modes. Stem turtles, which had a very simple mode of retraction, the lateral head tuck, show increasing flexibility of the neck through evolution towards a pleurodiran-like morphotype. The latter was the precondition for evolving pleurodiran and cryptodiran vertebrae. There is no correlation between the construction of formed articulations in the cervical centra and neck mobility. An increasing mobility between vertebrae, associated with changes in vertebral shape, resulted in a more advanced ability to retract the neck. In this regard, we hypothesize that the lateral tucking retraction of stem turtles was not only the precondition for pleurodiran but also of cryptodiran retraction. For the former, a kink in the middle third of the neck needed to be acquired, whereas for the latter modification was necessary between the eighth cervical vertebra and first thoracic vertebra. Our paper highlights the utility of 3D shape data, analyzed in a phylogenetic framework, to examine the magnitude and mode of evolutionary modifications to vertebral morphology. By reconstructing and visualizing ancestral anatomical shapes, we provide insight into the anatomical features underlying neck retraction mode, which is a salient component of extant turtle classification. © The Author(s) 2014. Published by Oxford University Press
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.
Khelouat, Samir; Benalia, Atallah; Boukhetala, Djamel; Laleg-Kirati, Taous-Meriem
2012-01-01
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
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.
Geometric inequalities methods of proving
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. .
Devalla, Sripad Krishna; Chin, Khai Sing; Mari, Jean-Martial; Tun, Tin A; Strouthidis, Nicholas G; Aung, Tin; Thiéry, Alexandre H; Girard, Michaël J A
2018-01-01
To develop a deep learning approach to digitally stain optical coherence tomography (OCT) images of the optic nerve head (ONH). A horizontal B-scan was acquired through the center of the ONH using OCT (Spectralis) for one eye of each of 100 subjects (40 healthy and 60 glaucoma). All images were enhanced using adaptive compensation. A custom deep learning network was then designed and trained with the compensated images to digitally stain (i.e., highlight) six tissue layers of the ONH. The accuracy of our algorithm was assessed (against manual segmentations) using the dice coefficient, sensitivity, specificity, intersection over union (IU), and accuracy. We studied the effect of compensation, number of training images, and performance comparison between glaucoma and healthy subjects. For images it had not yet assessed, our algorithm was able to digitally stain the retinal nerve fiber layer + prelamina, the RPE, all other retinal layers, the choroid, and the peripapillary sclera and lamina cribrosa. For all tissues, the dice coefficient, sensitivity, specificity, IU, and accuracy (mean) were 0.84 ± 0.03, 0.92 ± 0.03, 0.99 ± 0.00, 0.89 ± 0.03, and 0.94 ± 0.02, respectively. Our algorithm performed significantly better when compensated images were used for training (P deep learning algorithm can simultaneously stain the neural and connective tissues of the ONH, offering a framework to automatically measure multiple key structural parameters of the ONH that may be critical to improve glaucoma management.
An introduction to geometrical physics
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
Directory of Open Access Journals (Sweden)
Cova Matteo
2014-06-01
Full Text Available Fatigue strength is known to decrease with increasing dimension of the component. This is due to a technological size effect, related to the production process, and to a geometrical size effect, due to a higher probability of finding a large defect. To investigate the latter, an heavy-walled component made of Ductile Cast Iron (DCI has been trepanned and a fatigue test plan has been carried out using 4 different specimen geometries. An attempt has been made to relate the resulting fatigue strength using a weakest-link approach based on the effective volumes and surfaces. This approach seems to work well only in cases of different specimen's lengths. Some of the fracture surfaces were analyzed by means of SEM and the initiating defects were identified and measured. An approach in which the defects population can be randomly distributed in the specimen has been tried. Virtual fatigue tests have been carried out by considering pure propagation of the worst defect. The resulting fatigue curves showed that this approach is promising but needs further description of the initiation phase.
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
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
The value of art-oriented pedagogical approaches to the teaching of optics and photonics
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.
Noise and signal interference in optical fiber transmission systems an optimum design approach
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
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.
Visualizing the Geometric Series.
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)
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…
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)
A variational approach to nonlinear evolution equations in optics
Indian Academy of Sciences (India)
optics. D ANDERSON, M LISAK and A BERNTSON£. Department of Electromagnetics, Chalmers University of Technology, SE-41296 Göteborg, Sweden. £Ericsson Telcom ... Many works in nonlinear optics have made efficient ...... focusing dynamics of a laser beam (or a Bose–Einstein condensate) in a parabolic external.
International Nuclear Information System (INIS)
Mohammad Yaser Heidari Khajepour; Ferrer, Jean-Luc; Lebrette, Hugo; Vernede, Xavier; Rogues, Pierrick
2013-01-01
High-throughput protein crystallography projects pushed forward the development of automated crystallization platforms that are now commonly used. This created an urgent need for adapted and automated equipment for crystal analysis. However, first these crystals have to be harvested, cryo-protected and flash-cooled, operations that can fail or negatively impact on the crystal. In situ X-ray diffraction analysis has become a valid alternative to these operations, and a growing number of users apply it for crystal screening and to solve structures. Nevertheless, even this shortcut may require a significant amount of beam time. In this in situ high-throughput approach, the centering of crystals relative to the beam represents the bottleneck in the analysis process. In this article, a new method to accelerate this process, by recording accurately the local geometry coordinates for each crystal in the crystallization plate, is presented. Subsequently, the crystallization plate can be presented to the X-ray beam by an automated plate-handling device, such as a six-axis robot arm, for an automated crystal centering in the beam, in situ screening or data collection. Here the preliminary results of such a semi-automated pipeline are reported for two distinct test proteins. (authors)
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.
MEMS: A new approach to micro-optics
Energy Technology Data Exchange (ETDEWEB)
Sniegowski, J.J.
1997-12-31
MicroElectroMechanical Systems (MEMS) and their fabrication technologies provide great opportunities for application to micro-optical systems (MOEMS). Implementing MOEMS technology ranges from simple, passive components to complicated, active systems. Here, an overview of polysilicon surface micromachining MEMS combined with optics is presented. Recent advancements to the technology, which may enhance its appeal for micro-optics applications are emphasized. Of all the MEMS fabrication technologies, polysilicon surface micromachining technology has the greatest basis in and leverages the most the infrastructure for silicon integrated circuit fabrication. In that respect, it provides the potential for very large volume, inexpensive production of MOEMS. This paper highlights polysilicon surface micromachining technology in regards to its capability to provide both passive and active mechanical elements with quality optical elements.
Heuristic approach to the passive optical network with fibre duct ...
African Journals Online (AJOL)
Integer programming, network flow optimisation, passive optical network, ... This paper uses concepts from network flow optimisation to incorporate fibre duct shar ... [4] studied the survivable constrained ConFL problem and solved a number of.
A possible approach on optical analogues of gravitational attractors
San-Romá n-Alerigi, Damiá n P.; Ben Slimane, Ahmed; Ng, Tien Khee; Alsunaidi, Mohammad; Ooi, Boon S.
2013-01-01
, for example, providing an on-demand time delay or optical memories. Furthermore, beyond their practical applications to photonics, these mappings set forth an attractive realm to construct a panoply of celestial mechanics analogies and experiments
Analytic approach to dielectric optical bent slab waveguides
Czech Academy of Sciences Publication Activity Database
Hiremath, K. R.; Hammer, M.; Stoffer, R.; Prkna, Ladislav; Čtyroký, Jiří
2005-01-01
Roč. 37, 1/3 (2005), s. 37-61 ISSN 0306-8919 R&D Projects: GA ČR(CZ) GA102/05/0987 Grant - others:European Commission(XE) IST-2000-28018 NAIS Institutional research plan: CEZ:AV0Z20670512 Keywords : integrated optics * optical waveguide theory * modelling Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 0.688, year: 2005
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
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...
Geometrical approach to elementary particles
International Nuclear Information System (INIS)
Elbaz, E.; Meyer, J.
Starting with an isospin doublet R = (T/V) with spin 1/2 and hypercharge 1/3, the rishon considered as a vector in the color-space, we define the dirishon R* rank-one tensor product with spin 0 and hypercharge 2/3. Leptons and quarks of the first generation are then obtained as the scalar and dot product l = R*. R and f vector = R* Λ R'. The internal quantum numbers are then expressed with the rishon number. The lepton and quark generations are then defined and a quark mass formula proposed. Baryon magnetic moments are calculated and compared to experiment [fr
Effective and efficient optics inspection approach using machine learning algorithms
International Nuclear Information System (INIS)
Abdulla, G.; Kegelmeyer, L.; Liao, Z.; Carr, W.
2010-01-01
The Final Optics Damage Inspection (FODI) system automatically acquires and utilizes the Optics Inspection (OI) system to analyze images of the final optics at the National Ignition Facility (NIF). During each inspection cycle up to 1000 images acquired by FODI are examined by OI to identify and track damage sites on the optics. The process of tracking growing damage sites on the surface of an optic can be made more effective by identifying and removing signals associated with debris or reflections. The manual process to filter these false sites is daunting and time consuming. In this paper we discuss the use of machine learning tools and data mining techniques to help with this task. We describe the process to prepare a data set that can be used for training and identifying hardware reflections in the image data. In order to collect training data, the images are first automatically acquired and analyzed with existing software and then relevant features such as spatial, physical and luminosity measures are extracted for each site. A subset of these sites is 'truthed' or manually assigned a class to create training data. A supervised classification algorithm is used to test if the features can predict the class membership of new sites. A suite of self-configuring machine learning tools called 'Avatar Tools' is applied to classify all sites. To verify, we used 10-fold cross correlation and found the accuracy was above 99%. This substantially reduces the number of false alarms that would otherwise be sent for more extensive investigation.
Jumadi, Nur Anida; Beng, Gan Kok; Ali, Mohd Alauddin Mohd; Zahedi, Edmond; Morsin, Marlia
2017-09-01
The implementation of surface-based Monte Carlo simulation technique for oxygen saturation (SaO2) calibration curve estimation is demonstrated in this paper. Generally, the calibration curve is estimated either from the empirical study using animals as the subject of experiment or is derived from mathematical equations. However, the determination of calibration curve using animal is time consuming and requires expertise to conduct the experiment. Alternatively, an optical simulation technique has been used widely in the biomedical optics field due to its capability to exhibit the real tissue behavior. The mathematical relationship between optical density (OD) and optical density ratios (ODR) associated with SaO2 during systole and diastole is used as the basis of obtaining the theoretical calibration curve. The optical properties correspond to systolic and diastolic behaviors were applied to the tissue model to mimic the optical properties of the tissues. Based on the absorbed ray flux at detectors, the OD and ODR were successfully calculated. The simulation results of optical density ratio occurred at every 20 % interval of SaO2 is presented with maximum error of 2.17 % when comparing it with previous numerical simulation technique (MC model). The findings reveal the potential of the proposed method to be used for extended calibration curve study using other wavelength pair.
Genetic algorithm approach to thin film optical parameters determination
International Nuclear Information System (INIS)
Jurecka, S.; Jureckova, M.; Muellerova, J.
2003-01-01
Optical parameters of thin film are important for several optical and optoelectronic applications. In this work the genetic algorithm proposed to solve optical parameters of thin film values. The experimental reflectance is modelled by the Forouhi - Bloomer dispersion relations. The refractive index, the extinction coefficient and the film thickness are the unknown parameters in this model. Genetic algorithm use probabilistic examination of promissing areas of the parameter space. It creates a population of solutions based on the reflectance model and then operates on the population to evolve the best solution by using selection, crossover and mutation operators on the population individuals. The implementation of genetic algorithm method and the experimental results are described too (Authors)
A possible approach on optical analogues of gravitational attractors
San-Román-Alerigi, Damián P.
2013-04-01
In this paper we report on the feasibility of light confinement in orbital geodesics on stationary, planar, and centro-symmetric refractive index mappings. Constrained to fabrication and [meta]material limitations, the refractive index, n, has been bounded to the range: 0.8 ? n(r) ? 3.5. Mappings are obtained through the inverse problem to the light geodesics equations, considering trappings by generalized orbit conditions defined a priori. Our simulation results show that the above mentioned refractive index distributions trap light in an open orbit manifold, both perennial and temporal, in regards to initial conditions. Moreover, due to their characteristics, these mappings could be advantageous to optical computing and telecommunications, for example, providing an on-demand time delay or optical memories. Furthermore, beyond their practical applications to photonics, these mappings set forth an attractive realm to construct a panoply of celestial mechanics analogies and experiments in the laboratory. © 2013 Optical Society of America.
Asymptotic geometric analysis, part I
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
The three-grating Mach-Zehnder optical interferometer: a tutorial approach using particle optics
International Nuclear Information System (INIS)
Miffre, A; Delhuille, R; Viaris Lesegno, B de; Buechner, M; Rizzo, C; Vigue, J
2002-01-01
In this paper, we present a tutorial set-up based on an optical three-grating Mach-Zehnder interferometer. As this apparatus is very similar in its principle to the Mach-Zehnder interferometers used with matter waves (neutrons, atoms and molecules), it can be used to familiarize students with particle optics, and in our explanations, we use the complementary points of view of wave optics and particle optics. Finally, we have used this interferometer to measure the index of refraction of BK7 glass for red light at 633 nm, with a technique equivalent to the one used to measure the index of refraction of solid matter for thermal neutrons. The dimensions of this interferometer and its cost make it very interesting for laboratory courses and the experiment described here can be reproduced by students
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)
A Pragmatic Approach to Impairment Awareness in Optical Networks
Iqbal, F.; Smets, R.; Kuipers, F.A.
2015-01-01
The points-of-presence of optical networks are interconnected by photonic paths capable of carrying Terabits of data. However, signals along those photonic paths accumulate transmission impairments and thus can be unreadable at the receiver if the accumulated impairments are too high. Our
A simulator-based approach to evaluating optical trackers
Smit, F.A.; Liere, van R.
2009-01-01
We describe a software framework to evaluate the performance of model-based optical trackers in virtual environments. The framework can be used to evaluate and compare the performance of different trackers under various conditions, to study the effects of varying intrinsic and extrinsic camera
Remarks on the differential algebraic approach to particle beam optics by M. Berz
International Nuclear Information System (INIS)
Garczynski, V.
1992-01-01
The underlying mathematical structure of the differential algebraic approach of M. Berz to particle beam optics is isomorphic to the familiar truncated polynomial algebra. Concrete examples of derivations in this algebra, consistent with the truncation operation, are given
Geometrization of quantum physics
International Nuclear Information System (INIS)
Ol'khov, O.A.
2009-01-01
It is shown that the Dirac equation for a free particle can be considered as a description of specific distortion of the space Euclidean geometry (space topological defect). This approach is based on the possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such a concept explains all so-called 'strange' properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of the suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There are no any particles a priory, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device
Geometrization of quantum physics
Ol'Khov, O. A.
2009-12-01
It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.
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)
International Nuclear Information System (INIS)
Andersen, T.
1979-01-01
Raytracing methods have been used to show that the geometrical aberrations of a direct-vision prism situated in front of the focal plane in the converging beam of the Danish 1.5 m f/8.76 Ritchey-Chretien telescope and yielding a dispersion of 497 A/mm at Hγ are of the same size as the seeing disc in the wavelength range lambda 3500 - lambda 6000 A over a 40 mm field. Furthermore, raytracing methods have been used to determine the positions of the slot edges for a simultaneous uvby spectrograph-photometer for the Danish 1.5 m telescope. A theoretical sensitivity function for the photometer is presented. (Auth.)
Adaptive Optical System for Retina Imaging Approaches Clinic Applications
Ling, N.; Zhang, Y.; Rao, X.; Wang, C.; Hu, Y.; Jiang, W.; Jiang, C.
We presented "A small adaptive optical system on table for human retinal imaging" at the 3rd Workshop on Adaptive Optics for Industry and Medicine. In this system, a 19 element small deformable mirror was used as wavefront correction element. High resolution images of photo receptors and capillaries of human retina were obtained. In recent two years, at the base of this system a new adaptive optical system for human retina imaging has been developed. The wavefront correction element is a newly developed 37 element deformable mirror. Some modifications have been adopted for easy operation. Experiments for different imaging wavelengths and axial positions were conducted. Mosaic pictures of photoreceptors and capillaries were obtained. 100 normal and abnormal eyes of different ages have been inspected.The first report in the world concerning the most detailed capillary distribution images cover ±3° by ± 3° field around the fovea has been demonstrated. Some preliminary very early diagnosis experiment has been tried in laboratory. This system is being planned to move to the hospital for clinic experiments.
Directory of Open Access Journals (Sweden)
Natália Lima Boroni
2017-10-01
Full Text Available ABSTRACT The taxonomic identification of micromammals might be complicated when the study material is fragmented, as it is the case with pellets and fossil material. On the other hand, tooth morphology generally provides accurate information for species identification. Teeth preserve notably well, retaining their original morphology, unlike skulls and mandibles, which can get crushed or have missing parts. Here, we explored a geometric morphometrics approach (GM to identify fragmented specimens of two sympatric Calomys Waterhouse, 1837 species - Calomys tener (Winge, 1888 and Calomys expulsus (Lund, 1841 - using the morphology of intact molars as the basis for identification. Furthermore, we included some specimens of uncertain taxonomic identification to test their affinities and the utility of the shape of the molar to identify incomplete specimens. We evaluated the variations in the shape of the first upper molar (M1 among 46 owl pellets specimens of Calomys, including C. expulsus (n = 15, C. tener (n = 15, and unidentified specimens treated as Calomys sp. (n = 16 through GM analysis using 17 landmarks. The data was explored using PCA, PERMANOVA, and Discriminant analyses over the Procrustes residuals matrix were applied to evaluate inter- and intraspecific shape differences. Also, we evaluated whether allometric shape differences could impact the data, but found no evidence of a correlation between size and shape. Our results support that shape differences in the M1 are effective for discriminating between C. tener and C. expulsus. Moreover, the unidentified specimens do not represent a third shape but could be identified with confidence either as C. tener or C. expulsus. Our results show that even with fragmentary materials, GM is a feasible and useful tool for exploring inter-specific shape differences and assisting in taxonomic identification as a complement to traditional qualitative description of diagnostic features in poorly preserved
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.
Simplified approach for quantitative calculations of optical pumping
International Nuclear Information System (INIS)
Atoneche, Fred; Kastberg, Anders
2017-01-01
We present a simple and pedagogical method for quickly calculating optical pumping processes based on linearised population rate equations. The method can easily be implemented on mathematical software run on modest personal computers, and can be generalised to any number of concrete situations. We also show that the method is still simple with realistic experimental complications taken into account, such as high level degeneracy, impure light polarisation, and an added external magnetic field. The method and the associated mathematical toolbox should be of value in advanced physics teaching, and can also facilitate the preparation of research tasks. (paper)
Simplified approach for quantitative calculations of optical pumping
Atoneche, Fred; Kastberg, Anders
2017-07-01
We present a simple and pedagogical method for quickly calculating optical pumping processes based on linearised population rate equations. The method can easily be implemented on mathematical software run on modest personal computers, and can be generalised to any number of concrete situations. We also show that the method is still simple with realistic experimental complications taken into account, such as high level degeneracy, impure light polarisation, and an added external magnetic field. The method and the associated mathematical toolbox should be of value in advanced physics teaching, and can also facilitate the preparation of research tasks.
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)
Advanced free space optics (FSO) a systems approach
Majumdar, Arun K
2015-01-01
This book provides a comprehensive, unified tutorial covering the most recent advances in the technology of free-space optics (FSO). It is an all-inclusive source of information on the fundamentals of FSO as well as up-to-date information on the state-of-the-art in technologies available today. This text is intended for graduate students, and will also be useful for research scientists and engineers with an interest in the field. FSO communication is a practical solution for creating a three dimensional global broadband communications grid, offering bandwidths far beyond what is possible in the Radio Frequency (RF) range. However, the attributes of atmospheric turbulence and scattering impose perennial limitations on availability and reliability of FSO links. From a systems point-of-view, this groundbreaking book provides a thorough understanding of channel behavior, which can be used to design and evaluate optimum transmission techniques that operate under realistic atmospheric conditions. Topics addressed...
Kulkarni, Ashutosh; Stork, David G.
2009-02-01
A recent theory claims that some Renaissance artists, as early as 1425, secretly traced optically projected images during the execution of some passages in some of their works, nearly a quarter millennium before historians of art and of optics have secure evidence anyone recorded an image this way. Key evidence adduced by the theory's proponents includes the trelliswork in the right panel of Robert Campin's Merode altarpiece triptych (c. 1425-28). If their claim were verified for this work, such a discovery would be extremely important to the history of art and of image making more generally: the Altarpiece would be the earliest surviving image believed to record the projected image of an illuminated object, the first step towards photography, over 400 years later. The projection theory proponents point to teeny "kinks" in the depicted slats of one orientation in the Altarpiece as evidence that Campin refocussed a projector twice and traced images of physically straight slats in his studio. However, the proponents rotated the digital images of each slat individually, rather than the full trelliswork as a whole, and thereby disrupted the relative alignment between the images of the kinks and thus confounded their analysis. We found that when properly rotated, the kinks line up nearly perfectly and are consistent with Campin using a subtly kinked straightedge repeatedly, once for each of the slats. Moreover, the proponents did not report any analysis of the other set of slats-the ones nearly perpendicular to the first set. These perpendicular slats are straight across the break line of the first set-an unlikely scenario in the optical explanation. Finally, whereas it would have been difficult for Campin to draw the middle portions of the slats perfectly straight by tracing a projected image, it would have been trivially simple had he used a straightedge. Our results and the lack of any contemporaneous documentary evidence for the projection technique imply that
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.
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
Molecular Architectural Approach to Novel Electro-Optical Materials
Energy Technology Data Exchange (ETDEWEB)
Li, D.; Johal, M.S.; Smilowitz, L.B.; Robinson, J.M.
1999-06-29
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). The goal is to construct polar multilayers with nonlinear optical coefficients larger than classical inorganic crystals such as KDP or quartz. The strategy is to use various chemical interactions such as covalent bonds or hydrogen bonding to build polar structures. We have synthesized novel barbituric acid and melamine derivatives that will spontaneously self-assemble into a supramolecular ribbon according to their complementary H-bond motif. This supramolecular ribbon can then stack into a polar multilayer structure as verified by sum frequency generation (w{sub 1}+w{sub 2}) or second harmonic generation (when w{sub 1}=w{sub 2}). Second harmonic generation yields a value of d{sub 33}=3.2 pm/V for the self-assembled films and sum frequency generation shows a net polar orientation of the methyl groups in the multilayer along the surface normal. X-ray diffraction confirms the layered structure and produces the periodicity of {approximately}41 A, which corresponds well to the width of the supramolecular ribbons ({approximately}40 A).
Sharma, Dinesh Kumar; Sharma, Anurag; Tripathi, Saurabh Mani
2018-04-01
Microstructured optical fibers (MOFs) allow a variety of advanced materials to be infiltrated in their air-voids for obtaining the increased fiber functionality, and offering a new versatile platform for developing the compact sensors devices. We aim to investigate the thermal characteristics of high-index core triangular hybrid polymer/silica MOFs with circular air-voids infused with polymer by using the analytical field model [1]. We demonstrate that infiltration of air-voids with polymer, e.g., polydimethylsiloxane (PDMS) can facilitate to tune the fundamental modal properties of MOF such as effective index of the mode, near and the far-field profiles, effective mode area and the numerical aperture over the temperature ranging from 0 °C to 100 °C, for different values of relative air-void ratios. The evolution of the mode shape for a given temperature has been investigated in transition from near-field to far-field regime. We have studied the thermal dependence of splice losses between hybrid MOF and the standard step-index single-mode optical fiber in combination with Fresnel losses. For enhancing the evanescent field interactions, we have evaluated fraction of power associated with fundamental mode of hybrid MOF. We have compared the accuracy of our results with those based on full-vector finite-difference (FD) method, as available in the literature.
Winrow, Edward G.; Chavez, Victor H.
2011-09-01
High-precision opto-mechanical structures have historically been plagued by high costs for both hardware and the associated alignment and assembly process. This problem is especially true for space applications where only a few production units are produced. A methodology for optical alignment and optical structure design is presented which shifts the mechanism of maintaining precision from tightly toleranced, machined flight hardware to reusable, modular tooling. Using the proposed methodology, optical alignment error sources are reduced by the direct alignment of optics through their surface retroreflections (pips) as seen through a theodolite. Optical alignment adjustments are actualized through motorized, sub-micron precision actuators in 5 degrees of freedom. Optical structure hardware costs are reduced through the use of simple shapes (tubes, plates) and repeated components. This approach produces significantly cheaper hardware and more efficient assembly without sacrificing alignment precision or optical structure stability. The design, alignment plan and assembly of a 4" aperture, carbon fiber composite, Schmidt-Cassegrain concept telescope is presented.
Geometric mean for subspace selection.
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.
Kokkalis, P.; Papayannis, A.; Amiridis, V.; Mamouri, R. E.; Veselovskii, I.; Kolgotin, A.; Tsaknakis, G.; Kristiansen, N. I.; Stohl, A.; Mona, L.
2013-09-01
Vertical profiles of the optical (extinction and backscatter coefficients, lidar ratio and Ångström exponent), microphysical (mean effective radius, mean refractive index, mean number concentration) and geometrical properties as well as the mass concentration of volcanic particles from the Eyjafjallajökull eruption were retrieved at selected heights over Athens, Greece, using multi-wavelength Raman lidar measurements performed during the period 21-24 April 2010. Aerosol Robotic Network (AERONET) particulate columnar measurements along with inversion schemes were initialized together with lidar observations to deliver the aforementioned products. The well-known FLEXPART (FLEXible PARTicle dispersion model) model used for volcanic dispersion simulations is initiated as well in order to estimate the horizontal and vertical distribution of volcanic particles. Compared with the lidar measurements within the planetary boundary layer over Athens, FLEXPART proved to be a useful tool for determining the state of mixing of ash with other, locally emitted aerosol types. The major findings presented in our work concern the identification of volcanic particles layers in the form of filaments after 7-day transport from the volcanic source (approximately 4000 km away from our site) from the surface and up to 10 km according to the lidar measurements. Mean hourly averaged lidar signals indicated that the layer thickness of volcanic particles ranged between 1.5 and 2.2 km. The corresponding aerosol optical depth was found to vary from 0.01 to 0.18 at 355 nm and from 0.02 up to 0.17 at 532 nm. Furthermore, the corresponding lidar ratios (S) ranged between 60 and 80 sr at 355 nm and 44 and 88 sr at 532 nm. The mean effective radius of the volcanic particles estimated by applying inversion scheme to the lidar data found to vary within the range 0.13-0.38 μm and the refractive index ranged from 1.39+0.009i to 1.48+0.006i. This high variability is most probably attributed to the
Alternative approach of developing all-optical Fredkin and Toffoli gates
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.
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...
Geometric and engineering drawing
Morling, K
2010-01-01
The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
Differential geometric structures
Poor, Walter A
2007-01-01
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Geometric ghosts and unitarity
International Nuclear Information System (INIS)
Ne'eman, Y.
1980-09-01
A review is given of the geometrical identification of the renormalization ghosts and the resulting derivation of Unitarity equations (BRST) for various gauges: Yang-Mills, Kalb-Ramond, and Soft-Group-Manifold
Güven, Dilek; Balcıoğlu, Nihal; Türker, Cağrı; Baydar, Yasemin; Sendül, Yekta
2013-12-01
Serous macular detachment (SMD) may accompany optic disc pit (ODP) and cause visual loss if untreated. We want to present different therapeutic approaches and interesting optical coherence tomography (OCT) findings in three consecutive cases. In this case series, two patients with SMD and one patient with partial macular detachment and inferior retinal detachment accompanying ODP were evaluated before and after surgical intervention clinically and by spectral-domain OCT. The patients were 44 (case 1), 22 (case 2) and 24 (case 3) years old. Pars plana vitrectomy (PPV) + silicone oil + laser, PPV + sulfur hexafluoride gas (SF6) + laser and pneumatic retinopexy were applied, respectively. The patients were followed for 18, 15 and 14 months. Preoperative best-corrected visual acuities (BCVAs) were 5/100, 7/10 and counting fingers at 1 m. Vision improved in all cases with resolution of subretinal fluid. Final BCVAs were 3/10, 10/10 and 1/10, respectively. OCT images revealed optic disc anomaly details and changes after surgical intervention, photoreceptor outer segment alterations at the detached area and macular surface changes. Surgical intervention should be tailored individually in cases with SMD. OCT is efficient for in vivo evaluation of this pathological condition and anatomical outcomes of surgery.
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
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.)
An empirical InSAR-optical fusion approach to mapping vegetation canopy height
Wayne S. Walker; Josef M. Kellndorfer; Elizabeth LaPoint; Michael Hoppus; James Westfall
2007-01-01
Exploiting synergies afforded by a host of recently available national-scale data sets derived from interferometric synthetic aperture radar (InSAR) and passive optical remote sensing, this paper describes the development of a novel empirical approach for the provision of regional- to continental-scale estimates of vegetation canopy height. Supported by data from the...
Geometrical method of decoupling
Directory of Open Access Journals (Sweden)
C. Baumgarten
2012-12-01
Full Text Available The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E[over →], B[over →], and P[over →], which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of transformations must be symplectic and hence canonical. When
Mathieu, Jean Paul
1975-01-01
Optics, Parts 1 and 2 covers electromagnetic optics and quantum optics. The first part of the book examines the various of the important properties common to all electromagnetic radiation. This part also studies electromagnetic waves; electromagnetic optics of transparent isotropic and anisotropic media; diffraction; and two-wave and multi-wave interference. The polarization states of light, the velocity of light, and the special theory of relativity are also examined in this part. The second part is devoted to quantum optics, specifically discussing the classical molecular theory of optical p
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.
The geometric semantics of algebraic quantum mechanics.
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.
Acton, Charles H., Jr.
1990-01-01
The Navigation Ancillary Information Facility (NAIF), acting under the direction of NASA's Office of Space Science and Applications, and with substantial participation of the planetary science community, is designing and implementing an ancillary data system - called SPICE - to assist scientists in planning and interpreting scientific observations taken from spaceborne instruments. The principal objective of the implemented SPICE system is that it will hold the essential geometric and related ancillary information needed to recover the full value of science instrument data, and that it will facilitate correlations of individual instrument datasets with data obtained from other instruments on the same or other spacecraft.
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.)
A wave optics approach to the theory of the Michelson-Morley experiment
Smid, Thomas
2017-11-01
A consistent classical wave optics approach to the theory of the Michelson-Morley experiment shows that the original theory as applied by Michelson and Morley and others does not calculate the optical paths of the two beams correctly, primarily because of incorrectly assuming a right angle reflection in the instrument’s reference frame for the transverse beam, but also because of the incorrect assumption of aberration for the wave fronts. The theory presented in this work proves the expected variation of the phase difference when rotating the interferometer to be more than twice as large and also strongly asymmetrical around the zero line.
Microscopic optical potential for 208Pb in the nuclear structure approach
International Nuclear Information System (INIS)
Bernard, V.; Nguyen Van Gai.
1979-04-01
The optical potential for nucleon- 208 Pb scattering below 30 MeV is calculated microscopically as the sum of a real Hartree-Fock term and a complex correction term arising from the coupling to excited states of the target. The Skyrme effective interaction is used to generate the Hartree-Fock field, the RPA excited states and the coupling. A complex local equivalent potential is defined and used to calculate scattering and absorption cross-sections. The real part of the optical potential is reasonably well described in this approach while the imaginary part is too weak. Inclusion of rearrangement processes could improve the agreement with experiment
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.
Fincham, W H A
2013-01-01
Optics: Ninth Edition Optics: Ninth Edition covers the work necessary for the specialization in such subjects as ophthalmic optics, optical instruments and lens design. The text includes topics such as the propagation and behavior of light; reflection and refraction - their laws and how different media affect them; lenses - thick and thin, cylindrical and subcylindrical; photometry; dispersion and color; interference; and polarization. Also included are topics such as diffraction and holography; the limitation of beams in optical systems and its effects; and lens systems. The book is recommen
Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics
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.
Geometric approximation algorithms
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.
International Nuclear Information System (INIS)
Pili, Giorgio; Grimaldi, Luca; Fidanza, Christian; Florio, Elena T.; Petruzzelli, Maria F.; D'Errico, Maria P.; De Tommaso, Cristina; Tramacere, Francesco; Musaio, Francesca; Castagna, Roberta; Francavilla, Maria C.; Gianicolo, Emilio A.L.; Portaluri, Maurizio
2011-01-01
Purpose: To evaluate the probability of late cardiac mortality resulting from left breast irradiation planned with tangential fields and to compare this probability between the wedged beam and field-in-field (FIF) techniques and to investigate whether some geometric/dosimetric indicators can be determined to estimate the cardiac mortality probability before treatment begins. Methods and Materials: For 30 patients, differential dose-volume histograms were calculated for the wedged beam and FIF plans, and the corresponding cardiac mortality probabilities were determined using the relative seriality model. As a comparative index of the dose distribution uniformity, the planning target volume (PTV) percentages involved in 97-103% of prescribed dose were determined for the two techniques. Three geometric parameters were measured for each patient: the maximal length, indicates how much the heart contours were displaced toward the PTV, the angle subtended at the center of the computed tomography slice by the PTV contour, and the thorax width/thickness ratio. Results: Evaluating the differential dose-volume histograms showed that the gain in uniformity between the two techniques was about 1.5. With the FIF technique, the mean dose sparing for the heart, the left anterior descending coronary artery, and the lung was 15% (2.5 Gy vs. 2.2 Gy), 21% (11.3 Gy vs. 9.0 Gy), and 42% (8.0 Gy vs. 4.6 Gy) respectively, compared with the wedged beam technique. Also, the cardiac mortality probability decreased by 40% (from 0.9% to 0.5%). Three geometric parameters, the maximal length, angle subtended at the center of the computed tomography slice by the PTV contour, and thorax width/thickness ratio, were the determining factors (p = .06 for FIF, and p = .10 for wedged beam) for evaluating the cardiac mortality probability. Conclusion: The FIF technique seemed to yield a lower cardiac mortality probability than the conventional wedged beam technique. However, although our study
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
A unified approach for radiative losses and backscattering in optical waveguides
International Nuclear Information System (INIS)
Melati, D; Morichetti, F; Melloni, A
2014-01-01
Sidewall roughness in optical waveguides represents a severe impairment for the proper functionality of photonic integrated circuits. The interaction between the propagating mode and the roughness is responsible for both radiative losses and distributed backscattering. In this paper, a unified vision on these extrinsic loss phenomena is discussed, highlighting the fundamental role played by the sensitivity of the effective index n eff of the optical mode to waveguide width variations. The n w model presented applies to both 2D slab waveguides and 3D laterally confined waveguides and is in very good agreement with existing models that individually describe radiative loss or backscattering only. Experimental results are presented, demonstrating the validity of the n w model for arbitrary waveguide geometries and technologies. This approach enables an accurate description of realistic optical waveguides and provides simple design rules for optimization of the waveguide geometry in order to reduce the propagation losses generated by sidewall roughness. (paper)
International Nuclear Information System (INIS)
Loock, Peter van; Nemoto, Kae; Munro, William J.; Raynal, Philippe; Luetkenhaus, Norbert
2006-01-01
We discuss the problem of implementing generalized measurements [positive operator-valued measures (POVMs)] with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions for the linear-optics implementation of the POVM that realizes the quantum mechanically optimal unambiguous discrimination of two pure nonorthogonal states. This extends our previous results on projection measurements and the exact discrimination of orthogonal states
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.
Naik, Naren; Vasu, R M; Ananthasayanam, M R
2010-02-20
The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances.
An Inertial and Optical Sensor Fusion Approach for Six Degree-of-Freedom Pose Estimation
He, Changyu; Kazanzides, Peter; Sen, Hasan Tutkun; Kim, Sungmin; Liu, Yue
2015-01-01
Optical tracking provides relatively high accuracy over a large workspace but requires line-of-sight between the camera and the markers, which may be difficult to maintain in actual applications. In contrast, inertial sensing does not require line-of-sight but is subject to drift, which may cause large cumulative errors, especially during the measurement of position. To handle cases where some or all of the markers are occluded, this paper proposes an inertial and optical sensor fusion approach in which the bias of the inertial sensors is estimated when the optical tracker provides full six degree-of-freedom (6-DOF) pose information. As long as the position of at least one marker can be tracked by the optical system, the 3-DOF position can be combined with the orientation estimated from the inertial measurements to recover the full 6-DOF pose information. When all the markers are occluded, the position tracking relies on the inertial sensors that are bias-corrected by the optical tracking system. Experiments are performed with an augmented reality head-mounted display (ARHMD) that integrates an optical tracking system (OTS) and inertial measurement unit (IMU). Experimental results show that under partial occlusion conditions, the root mean square errors (RMSE) of orientation and position are 0.04° and 0.134 mm, and under total occlusion conditions for 1 s, the orientation and position RMSE are 0.022° and 0.22 mm, respectively. Thus, the proposed sensor fusion approach can provide reliable 6-DOF pose under long-term partial occlusion and short-term total occlusion conditions. PMID:26184191
International Nuclear Information System (INIS)
La, H.
1992-01-01
A new geometric formulation of Liouville gravity based on the area preserving diffeo-morphism is given and a possible alternative to reinterpret Liouville gravity is suggested, namely, a scalar field coupled to two-dimensional gravity with a curvature constraint
A Geometric Dissection Problem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 7. A Geometric Dissection Problem. M N Deshpande. Think It Over Volume 7 Issue 7 July 2002 pp 91-91. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/07/0091-0091. Author Affiliations.
Geometric statistical inference
International Nuclear Information System (INIS)
Periwal, Vipul
1999-01-01
A reparametrization-covariant formulation of the inverse problem of probability is explicitly solved for finite sample sizes. The inferred distribution is explicitly continuous for finite sample size. A geometric solution of the statistical inference problem in higher dimensions is outlined
Geometric Series via Probability
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
Pragmatic geometric model evaluation
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
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.
Fincham, W H A
2013-01-01
Optics: Eighth Edition covers the work necessary for the specialization in such subjects as ophthalmic optics, optical instruments and lens design. The text includes topics such as the propagation and behavior of light; reflection and refraction - their laws and how different media affect them; lenses - thick and thin, cylindrical and subcylindrical; photometry; dispersion and color; interference; and polarization. Also included are topics such as diffraction and holography; the limitation of beams in optical systems and its effects; and lens systems. The book is recommended for engineering st
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...
RAYS: a geometrical optics code for EBT
International Nuclear Information System (INIS)
Batchelor, D.B.; Goldfinger, R.C.
1982-04-01
The theory, structure, and operation of the code are described. Mathematical details of equilibrium subroutiones for slab, bumpy torus, and tokamak plasma geometry are presented. Wave dispersion and absorption subroutines are presented for frequencies ranging from ion cyclotron frequency to electron cyclotron frequency. Graphics postprocessors for RAYS output data are also described
Novel Combinatory Approaches to Repair Visual System after Optic Nerve Damage
2014-09-01
Novel Combinatory Approaches to Repair Visual System After Optic Nerve Damage 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6...biological functions such as metabolism, growth, cell cycle, and survival ( Cardone et al., 1998; Diehl, Cheng, Roussel, & Sherr, 1998; Hers, Vincent...of injured adult sensory neurons. The Journal of Neuroscience, 21, 7161–7170. Cardone , M. H., Roy, N., Stennicke, H. R., Salvesen, G. S., Franke, T. F
Technical Approaches For Implementation Of CSMA/CD On A Fiber Optic Medium
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.
Garcia-Diaz, Antón; Leborán, Víctor; Fdez-Vidal, Xosé R; Pardo, Xosé M
2012-06-12
A hierarchical definition of optical variability is proposed that links physical magnitudes to visual saliency and yields a more reductionist interpretation than previous approaches. This definition is shown to be grounded on the classical efficient coding hypothesis. Moreover, we propose that a major goal of contextual adaptation mechanisms is to ensure the invariance of the behavior that the contribution of an image point to optical variability elicits in the visual system. This hypothesis and the necessary assumptions are tested through the comparison with human fixations and state-of-the-art approaches to saliency in three open access eye-tracking datasets, including one devoted to images with faces, as well as in a novel experiment using hyperspectral representations of surface reflectance. The results on faces yield a significant reduction of the potential strength of semantic influences compared to previous works. The results on hyperspectral images support the assumptions to estimate optical variability. As well, the proposed approach explains quantitative results related to a visual illusion observed for images of corners, which does not involve eye movements.
Bio-optical data integration based on a 4 D database system approach
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.
Dynamics in geometrical confinement
Kremer, Friedrich
2014-01-01
This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
Lectures in geometric combinatorics
Thomas, Rekha R
2006-01-01
This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Gr�bner bases of toric ideals and other methods from commutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational as...
Geometric information provider platform
Directory of Open Access Journals (Sweden)
Meisam Yousefzadeh
2015-07-01
Full Text Available Renovation of existing buildings is known as an essential stage in reduction of the energy loss. Considerable part of renovation process depends on geometric reconstruction of building based on semantic parameters. Following many research projects which were focused on parameterizing the energy usage, various energy modelling methods were developed during the last decade. On the other hand, by developing accurate measuring tools such as laser scanners, the interests of having accurate 3D building models are rapidly growing. But the automation of 3D building generation from laser point cloud or detection of specific objects in that is still a challenge. The goal is designing a platform through which required geometric information can be efficiently produced to support energy simulation software. Developing a reliable procedure which extracts required information from measured data and delivers them to a standard energy modelling system is the main purpose of the project.
Frè, Pietro Giuseppe
2013-01-01
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differe...
Ruffino, Fabio Ferrari
2013-01-01
Given a cohomology theory, there is a well-known abstract way to define the dual homology theory using the theory of spectra. In [4] the author provides a more geometric construction of the homology theory, using a generalization of the bordism groups. Such a generalization involves in its definition the vector bundle modification, which is a particular case of the Gysin map. In this paper we provide a more natural variant of that construction, which replaces the vector bundle modification wi...
Waerden, B
1996-01-01
From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society.
Developing geometrical reasoning
Brown, Margaret; Jones, Keith; Taylor, Ron; Hirst, Ann
2004-01-01
This paper summarises a report (Brown, Jones & Taylor, 2003) to the UK Qualifications and Curriculum Authority of the work of one geometry group. The group was charged with developing and reporting on teaching ideas that focus on the development of geometrical reasoning at the secondary school level. The group was encouraged to explore what is possible both within and beyond the current requirements of the UK National Curriculum and the Key Stage 3 strategy, and to consider the whole atta...
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Su, Huaizhi; Li, Hao; Kang, Yeyuan; Wen, Zhiping
2018-02-01
Seepage is one of key factors which affect the levee engineering safety. The seepage danger without timely detection and rapid response may likely lead to severe accidents such as seepage failure, slope instability, and even levee break. More than 90 percent of levee break events are caused by the seepage. It is very important for seepage behavior identification to determine accurately saturation line in levee engineering. Furthermore, the location of saturation line has a major impact on slope stability in levee engineering. Considering the structure characteristics and service condition of levee engineering, the distributed optical fiber sensing technology is introduced to implement the real-time observation of saturation line in levee engineering. The distributed optical fiber temperature sensor system (DTS)-based monitoring principle of saturation line in levee engineering is investigated. An experimental platform, which consists of DTS, heating system, water-supply system, auxiliary analysis system and levee model, is designed and constructed. The monitoring experiment of saturation line in levee model is implemented on this platform. According to the experimental results, the numerical relationship between moisture content and thermal conductivity in porous medium is identified. A line heat source-based distributed optical fiber method obtaining the thermal conductivity in porous medium is developed. A DTS-based approach is proposed to monitor the saturation line in levee engineering. The embedment pattern of optical fiber for monitoring saturation line is presented.
A new approach to correlate transport processes and optical efficiency in GaN-based LEDs
International Nuclear Information System (INIS)
Pavesi, M; Manfredi, M; Rossi, F; Salviati, G; Meneghini, M; Zanoni, E
2009-01-01
Carrier injection and non-radiative processes are determinants of the optical efficiency of InGaN/GaN LEDs. Among transport mechanisms, tunnelling is crucial for device functioning, but other contributions can be decisive on a varying bias. It is not easy to identify the weights and roles of these terms by a simple current-voltage characterization, so it needs a careful investigation by means of complementary experimental techniques. The correlation between luminescence and microscopic transport processes in InGaN/GaN LEDs has been investigated by means of a set of techniques: electroluminescence, cathodoluminescence, current-voltage dc measurements and thermal admittance spectroscopy. Green and blue LEDs, designed with a multi-quantum-well injector layer and an optically active single-quantum-well, have been tested. They showed distinctive current and temperature dependences of the optical efficiency, with a better performance at room temperature observed for green devices. This was discussed in terms of the carrier injection efficiency controlled by electrically active traps. The comparative analysis of the optical and electrical experimental data comes in handy as a methodological approach to correlate the emission properties with the carrier injection mechanisms and to improve the functionality in a large number of quantum well heterostructures for lighting applications.
Single-molecule approach to bacterial genomic comparisons via optical mapping.
Energy Technology Data Exchange (ETDEWEB)
Zhou, Shiguo [Univ. Wisc.-Madison; Kile, A. [Univ. Wisc.-Madison; Bechner, M. [Univ. Wisc.-Madison; Kvikstad, E. [Univ. Wisc.-Madison; Deng, W. [Univ. Wisc.-Madison; Wei, J. [Univ. Wisc.-Madison; Severin, J. [Univ. Wisc.-Madison; Runnheim, R. [Univ. Wisc.-Madison; Churas, C. [Univ. Wisc.-Madison; Forrest, D. [Univ. Wisc.-Madison; Dimalanta, E. [Univ. Wisc.-Madison; Lamers, C. [Univ. Wisc.-Madison; Burland, V. [Univ. Wisc.-Madison; Blattner, F. R. [Univ. Wisc.-Madison; Schwartz, David C. [Univ. Wisc.-Madison
2004-01-01
Modern comparative genomics has been established, in part, by the sequencing and annotation of a broad range of microbial species. To gain further insights, new sequencing efforts are now dealing with the variety of strains or isolates that gives a species definition and range; however, this number vastly outstrips our ability to sequence them. Given the availability of a large number of microbial species, new whole genome approaches must be developed to fully leverage this information at the level of strain diversity that maximize discovery. Here, we describe how optical mapping, a single-molecule system, was used to identify and annotate chromosomal alterations between bacterial strains represented by several species. Since whole-genome optical maps are ordered restriction maps, sequenced strains of Shigella flexneri serotype 2a (2457T and 301), Yersinia pestis (CO 92 and KIM), and Escherichia coli were aligned as maps to identify regions of homology and to further characterize them as possible insertions, deletions, inversions, or translocations. Importantly, an unsequenced Shigella flexneri strain (serotype Y strain AMC[328Y]) was optically mapped and aligned with two sequenced ones to reveal one novel locus implicated in serotype conversion and several other loci containing insertion sequence elements or phage-related gene insertions. Our results suggest that genomic rearrangements and chromosomal breakpoints are readily identified and annotated against a prototypic sequenced strain by using the tools of optical mapping.
Studies in geometric quantization
International Nuclear Information System (INIS)
Tuynman, G.M.
1988-01-01
This thesis contains five chapters, of which the first, entitled 'What is prequantization, and what is geometric quantization?', is meant as an introduction to geometric quantization for the non-specialist. The second chapter, entitled 'Central extensions and physics' deals with the notion of central extensions of manifolds and elaborates and proves the statements made in the first chapter. Central extensions of manifolds occur in physics as the freedom of a phase factor in the quantum mechanical state vector, as the phase factor in the prequantization process of classical mechanics and it appears in mathematics when studying central extension of Lie groups. In this chapter the connection between these central extensions is investigated and a remarkable similarity between classical and quantum mechanics is shown. In chapter three a classical model is given for the hydrogen atom including spin-orbit and spin-spin interaction. The method of geometric quantization is applied to this model and the results are discussed. In the final chapters (4 and 5) an explicit method to calculate the operators corresponding to classical observables is given when the phase space is a Kaehler manifold. The obtained formula are then used to quantise symplectic manifolds which are irreducible hermitian symmetric spaces and the results are compared with other quantization procedures applied to these manifolds (in particular to Berezin's quantization). 91 refs.; 3 tabs
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.
Directory of Open Access Journals (Sweden)
Monika Soja-Woźniak
2017-04-01
Full Text Available Eutrophication is an increasing problem in coastal waters of the Baltic Sea. Moreover, algal blooms, which occur every summer in the Gulf of Gdansk can deleteriously impact human health, the aquatic environment, and economically important fisheries, tourism, and recreation industries. Traditional laboratory-based techniques for water monitoring are expensive and time consuming, which usually results in limited numbers of observations and discontinuity in space and time. The use of hyperspectral radiometers for coastal water observation provides the potential for more detailed remote optical monitoring. A statistical approach to develop local models for the estimation of optically significant components from in situ measured hyperspectral remote sensing reflectance in case 2 waters is presented in this study. The models, which are based on empirical orthogonal function (EOF analysis and stepwise multilinear regression, allow for the estimation of parameters strongly correlated with phytoplankton (pigment concentration, absorption coefficient and coloured detrital matter abundance (absorption coefficient directly from reflectance spectra measured in situ. Chlorophyll a concentration, which is commonly used as a proxy for phytoplankton biomass, was retrieved with low error (median percent difference, MPD = 17%, root mean square error RMSE = 0.14 in log10 space and showed a high correlation with chlorophyll a measured in situ (R = 0.84. Furthermore, phycocyanin and phycoerythrin, both characteristic pigments for cyanobacteria species, were also retrieved reliably from reflectance with MPD = 23%, RMSE = 0.23, R2 = 0.77 and MPD = 24%, RMSE = 0.15, R2 = 0.74, respectively. The EOF technique proved to be accurate in the derivation of the absorption spectra of phytoplankton and coloured detrital matter (CDM, with R2 (λ above 0.83 and RMSE around 0.10. The approach was also applied to satellite multispectral remote sensing reflectance data, thus allowing
Institute of Scientific and Technical Information of China (English)
高文; 陈熙霖
1997-01-01
The blur in target images caused by camera vibration due to robot motion or hand shaking and by object(s) moving in the background scene is different to deal with in the computer vision system.In this paper,the authors study the relation model between motion and blur in the case of object motion existing in video image sequence,and work on a practical computation algorithm for both motion analysis and blut image restoration.Combining the general optical flow and stochastic process,the paper presents and approach by which the motion velocity can be calculated from blurred images.On the other hand,the blurred image can also be restored using the obtained motion information.For solving a problem with small motion limitation on the general optical flow computation,a multiresolution optical flow algoritm based on MAP estimation is proposed. For restoring the blurred image ,an iteration algorithm and the obtained motion velocity are used.The experiment shows that the proposed approach for both motion velocity computation and blurred image restoration works well.
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
Geometrical model of multiple production
International Nuclear Information System (INIS)
Chikovani, Z.E.; Jenkovszky, L.L.; Kvaratshelia, T.M.; Struminskij, B.V.
1988-01-01
The relation between geometrical and KNO-scaling and their violation is studied in a geometrical model of multiple production of hadrons. Predictions concerning the behaviour of correlation coefficients at future accelerators are given
Geometric Computing for Freeform Architecture
Wallner, J.; Pottmann, Helmut
2011-01-01
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area
Quantum teleportation and entanglement. A hybrid approach to optical quantum information procesing
Energy Technology Data Exchange (ETDEWEB)
Furusawa, Akira [Tokyo Univ. (Japan). Dept. of Applied Physics; Loock, Peter van [Erlangen-Nuernberg Univ. (Germany). Lehrstuhl fuer Optik
2011-07-01
Unique in that it is jointly written by an experimentalist and a theorist, this monograph presents universal quantum computation based on quantum teleportation as an elementary subroutine and multi-party entanglement as a universal resource. Optical approaches to measurement-based quantum computation are also described, including schemes for quantum error correction, with most of the experiments carried out by the authors themselves. Ranging from the theoretical background to the details of the experimental realization, the book describes results and advances in the field, backed by numerous illustrations of the authors' experimental setups. Aimed at researchers, physicists, and graduate and PhD students in physics, theoretical quantum optics, quantum mechanics, and quantum information. (orig.)
Bone Marrow-Derived Cells as a Therapeutic Approach to Optic Nerve Diseases
Directory of Open Access Journals (Sweden)
Louise A. Mesentier-Louro
2016-01-01
Full Text Available Following optic nerve injury associated with acute or progressive diseases, retinal ganglion cells (RGCs of adult mammals degenerate and undergo apoptosis. These diseases have limited therapeutic options, due to the low inherent capacity of RGCs to regenerate and due to the inhibitory milieu of the central nervous system. Among the numerous treatment approaches investigated to stimulate neuronal survival and axonal extension, cell transplantation emerges as a promising option. This review focuses on cell therapies with bone marrow mononuclear cells and bone marrow-derived mesenchymal stem cells, which have shown positive therapeutic effects in animal models of optic neuropathies. Different aspects of available preclinical studies are analyzed, including cell distribution, potential doses, routes of administration, and mechanisms of action. Finally, published and ongoing clinical trials are summarized.
Mei, Shuang; Wang, Yudan; Wen, Guojun; Hu, Yang
2018-05-03
Increasing deployment of optical fiber networks and the need for reliable high bandwidth make the task of inspecting optical fiber connector end faces a crucial process that must not be neglected. Traditional end face inspections are usually performed by manual visual methods, which are low in efficiency and poor in precision for long-term industrial applications. More seriously, the inspection results cannot be quantified for subsequent analysis. Aiming at the characteristics of typical defects in the inspection process for optical fiber end faces, we propose a novel method, “difference of min-max ranking filtering” (DO2MR), for detection of region-based defects, e.g., dirt, oil, contamination, pits, and chips, and a special model, a “linear enhancement inspector” (LEI), for the detection of scratches. The DO2MR is a morphology method that intends to determine whether a pixel belongs to a defective region by comparing the difference of gray values of pixels in the neighborhood around the pixel. The LEI is also a morphology method that is designed to search for scratches at different orientations with a special linear detector. These two approaches can be easily integrated into optical inspection equipment for automatic quality verification. As far as we know, this is the first time that complete defect detection methods for optical fiber end faces are available in the literature. Experimental results demonstrate that the proposed DO2MR and LEI models yield good comprehensive performance with high precision and accepted recall rates, and the image-level detection accuracies reach 96.0 and 89.3%, respectively.
Directory of Open Access Journals (Sweden)
Shuang Mei
2018-05-01
Full Text Available Increasing deployment of optical fiber networks and the need for reliable high bandwidth make the task of inspecting optical fiber connector end faces a crucial process that must not be neglected. Traditional end face inspections are usually performed by manual visual methods, which are low in efficiency and poor in precision for long-term industrial applications. More seriously, the inspection results cannot be quantified for subsequent analysis. Aiming at the characteristics of typical defects in the inspection process for optical fiber end faces, we propose a novel method, “difference of min-max ranking filtering” (DO2MR, for detection of region-based defects, e.g., dirt, oil, contamination, pits, and chips, and a special model, a “linear enhancement inspector” (LEI, for the detection of scratches. The DO2MR is a morphology method that intends to determine whether a pixel belongs to a defective region by comparing the difference of gray values of pixels in the neighborhood around the pixel. The LEI is also a morphology method that is designed to search for scratches at different orientations with a special linear detector. These two approaches can be easily integrated into optical inspection equipment for automatic quality verification. As far as we know, this is the first time that complete defect detection methods for optical fiber end faces are available in the literature. Experimental results demonstrate that the proposed DO2MR and LEI models yield good comprehensive performance with high precision and accepted recall rates, and the image-level detection accuracies reach 96.0 and 89.3%, respectively.
Autonomous optical navigation using nanosatellite-class instruments: a Mars approach case study
Enright, John; Jovanovic, Ilija; Kazemi, Laila; Zhang, Harry; Dzamba, Tom
2018-02-01
This paper examines the effectiveness of small star trackers for orbital estimation. Autonomous optical navigation has been used for some time to provide local estimates of orbital parameters during close approach to celestial bodies. These techniques have been used extensively on spacecraft dating back to the Voyager missions, but often rely on long exposures and large instrument apertures. Using a hyperbolic Mars approach as a reference mission, we present an EKF-based navigation filter suitable for nanosatellite missions. Observations of Mars and its moons allow the estimator to correct initial errors in both position and velocity. Our results show that nanosatellite-class star trackers can produce good quality navigation solutions with low position (<300 {m}) and velocity (<0.15 {m/s}) errors as the spacecraft approaches periapse.
Image understanding using geometric context
Zhang, Xiaochun; Liu, Chuancai
2017-07-01
A Gibbs Sampler based topic model for image annotation, which takes into account the interaction between visual geometric context and related topic, is presented. Most of the existing topic models for scene annotation use segmentation-based algorithm. However, topic models using segmentation algorithm alone sometimes can produce erroneous results when used to annotate real-life scene pictures. Therefore, our algorithm makes use of peaks of image surface instead of segmentation regions. Existing approaches use SIFT algorithm and treat the peaks as round blob features. In this paper, the peaks are treated as anisotropic blob features, which models low level visual elements more precisely. In order to better utilize visual features, our model not only takes into consideration visual codeword, but also considers influence of visual properties to topic formation, such as orientation, width, length and color. The basic idea is based on the assumption that different topics will produce distinct visual appearance, and different visual appearance is helpful to distinguish topics. During the learning stage, each topic will be associated with a set of distributions of visual properties, which depicts appearance of the topic. This paper considers more geometric properties, which will reduce topic uncertainty and learn the images better. Tested with Corel5K, SAIAPR-TC12 and Espgame100k Datasets, our method performs moderately better than some state of the arts methods.
Geometric Constructions with the Computer.
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…
The Spacetime Memory of Geometric Phases and Quantum Computing
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.
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.
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.
Rejuvenating Allen's Arc with the Geometric Mean.
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)
Geometric Models for Collaborative Search and Filtering
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…
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)
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....
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
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Geometric multipartite entanglement measures
International Nuclear Information System (INIS)
Paz-Silva, Gerardo A.; Reina, John H.
2007-01-01
Within the framework of constructions for quantifying entanglement, we build a natural scenario for the assembly of multipartite entanglement measures based on Hopf bundle-like mappings obtained through Clifford algebra representations. Then, given the non-factorizability of an arbitrary two-qubit density matrix, we give an alternate quantity that allows the construction of two types of entanglement measures based on their arithmetical and geometrical averages over all pairs of qubits in a register of size N, and thus fully characterize its degree and type of entanglement. We find that such an arithmetical average is both additive and strongly super additive
Geometric correlations and multifractals
International Nuclear Information System (INIS)
Amritkar, R.E.
1991-07-01
There are many situations where the usual statistical methods are not adequate to characterize correlations in the system. To characterize such situations we introduce mutual correlation dimensions which describe geometric correlations in the system. These dimensions allow us to distinguish between variables which are perfectly correlated with or without a phase lag, variables which are uncorrelated and variables which are partially correlated. We demonstrate the utility of our formalism by considering two examples from dynamical systems. The first example is about the loss of memory in chaotic signals and describes auto-correlations while the second example is about synchronization of chaotic signals and describes cross-correlations. (author). 19 refs, 6 figs
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.
Energy Technology Data Exchange (ETDEWEB)
De Pretto, Lucas R., E-mail: lucas.de.pretto@usp.br; Nogueira, Gesse E. C.; Freitas, Anderson Z. [Instituto de Pesquisas Energéticas e Nucleares, IPEN–CNEN/SP, Avenida Lineu Prestes, 2242, 05508-000 São Paulo (Brazil)
2016-04-28
Functional modalities of Optical Coherence Tomography (OCT) based on speckle analysis are emerging in the literature. We propose a simple approach to the autocorrelation of OCT signal to enable volumetric flow rate differentiation, based on decorrelation time. Our results show that this technique could distinguish flows separated by 3 μl/min, limited by the acquisition speed of the system. We further perform a B-scan of gradient flow inside a microchannel, enabling the visualization of the drag effect on the walls.
AN AERIAL-IMAGE DENSE MATCHING APPROACH BASED ON OPTICAL FLOW FIELD
Directory of Open Access Journals (Sweden)
W. Yuan
2016-06-01
Full Text Available Dense matching plays an important role in many fields, such as DEM (digital evaluation model producing, robot navigation and 3D environment reconstruction. Traditional approaches may meet the demand of accuracy. But the calculation time and out puts density is hardly be accepted. Focus on the matching efficiency and complex terrain surface matching feasibility an aerial image dense matching method based on optical flow field is proposed in this paper. First, some high accurate and uniformed control points are extracted by using the feature based matching method. Then the optical flow is calculated by using these control points, so as to determine the similar region between two images. Second, the optical flow field is interpolated by using the multi-level B-spline interpolation in the similar region and accomplished the pixel by pixel coarse matching. Final, the results related to the coarse matching refinement based on the combined constraint, which recognizes the same points between images. The experimental results have shown that our method can achieve per-pixel dense matching points, the matching accuracy achieves sub-pixel level, and fully meet the three-dimensional reconstruction and automatic generation of DSM-intensive matching’s requirements. The comparison experiments demonstrated that our approach’s matching efficiency is higher than semi-global matching (SGM and Patch-based multi-view stereo matching (PMVS which verifies the feasibility and effectiveness of the algorithm.
Understanding geometric algebra for electromagnetic theory
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.
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....
A Real Time AI Approach to Discrimination Boost Phase Optical Sensor Systems in SDI Architectures
Sloggett, David R.
1990-04-01
are resolved by sensor systems feature data can be extracted on individual objects that can be used by the defence system to attempt to discriminate between warheads, decoys and other penetration aids. This paper reviews work that has arisen from joint US SDIO and UK MOD research programmes into the feasibility of Theatre Missile Defence (TMD) systems that would be suitable for deploy ment and operation in a European theatre. The paper focuses on the problems of threat classification and discrimination in TtD systems and highlights the role of optical sensors. The paper discusses the integration of data derived from optical and radar sensors 6 and expands upon work previously reported into the use of an Artificial Intelligence (AI) approach to object classification and discrimination.