Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
The Formalization of Discrete Fourier Transform in HOL
Directory of Open Access Journals (Sweden)
Zhiping Shi
2015-01-01
Full Text Available Traditionally, Discrete Fourier Transform (DFT is performed with numerical or symbolic computation, which cannot guarantee 100% accurate analysis which may be necessary for safety-critical applications. Machine theorem proving is one of the formal methods that perform accurate analysis with completeness to some extent. This paper proposes the formalization of DFT in a higher-order logic theorem prover named HOL. We propose the formal definition of DFT and verify the fundamental properties of DFT. Two case studies are presented to illustrate usefulness and correctness of the formalized DFT, including formal verifications of Fast Fourier Transform (FFT and cosine frequency shift.
Introduction to Fourier Optics
Huggins, Elisha
2007-01-01
Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…
Introduction to Fourier Optics
Huggins, Elisha
2007-01-01
Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…
A general formalism for Fourier based Wave Front Sensing
Fauvarque, Olivier; Fusco, Thierry; Sauvage, Jean-François; Girault, Orion
2016-01-01
We introduce in this article a general formalism for Fourier based wave front sensing. To do so, we consider the filtering mask as a free parameter. Such an approach allows to unify sensors like the Pyramid Wave Front Sensor (PWFS) and the Zernike Wave Front Sensor (ZWFS). In particular, we take the opportunity to generalize this two sensors in terms of sensors' class where optical quantities as, for instance, the apex angle for the PWFS or the depth of the Zernike mask for the ZWFS become free parameters. In order to compare all the generated sensors of this two classes thanks to common performance criteria, we firstly define a general phase-linear quantity that we call meta-intensity. Analytical developments allow then to split the perfectly phase-linear behavior of a WFS from the non-linear contributions making robust and analytic definitions of the sensitivity and the linearity range possible. Moreover, we define a new quantity called the SD factor which characterizes the trade-off between these two antag...
Efficient formalism for treating tapered structures using the Fourier modal method
DEFF Research Database (Denmark)
Østerkryger, Andreas Dyhl; Gregersen, Niels
2016-01-01
We investigate the development of the mode occupations in tapered structures using the Fourier modal method. In order to use the Fourier modal method, tapered structures are divided into layers of uniform refractive index in the propagation direction and the optical modes are found within each...... layer. This is not very efficient and in this proceeding we take the first steps towards a more efficient formalism for treating tapered structures using the Fourier modal method. We show that the coupling coefficients through the structure are slowly varying and that only the first few modes...
Fourier-transform optical microsystems
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
Formal analysis of electromagnetic optics
Khan-Afshar, Sanaz; Hasan, Osman; Tahar, Sofiène
2014-09-01
Optical systems are increasingly being used in safety-critical applications. Due to the complexity and sensitivity of optical systems, their verification raises many challenges for 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 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 their correctness by taking into account all the details of mathematical reasoning) as a complementary approach to improve optical system analysis. This paper provides a higher-order logic (a language used to express mathematical theories) formalization of electromagnetic optics in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our approach, we present the analysis of resonant cavity enhanced photonic devices.
Fourier optics of image formation in LEEM
Energy Technology Data Exchange (ETDEWEB)
Pang, A B; Altman, M S [Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Mueller, Th; Bauer, Ernst [Physikalisches Institute, Technische Universitaet Clausthal, Leibnizstrasse 4, D-38678 Clausthal-Zellerfeld (Germany)
2009-08-05
A Fourier optics calculation of image formation in low energy electron microscopy (LEEM) is presented. The adaptation of the existing theory for transmission electron microscopy to the treatment of LEEM and other forms of cathode lens electron microscopy is explained. The calculation incorporates imaging errors that are caused by the objective lens (aberrations), contrast aperture (diffraction), imperfect source characteristics, and voltage and current instabilities. It is used to evaluate the appearance of image features that arise from phase objects such as surface steps and amplitude objects that produce what is alternatively called amplitude, reflectivity or diffraction contrast in LEEM. This formalism can be used after appropriate modification to treat image formation in other emission microscopies. Implications for image formation in the latest aberration-corrected instruments are also discussed.
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
Entangled-photon Fourier optics
Abouraddy, A F; Sergienko, A V; Teich, M C; Abouraddy, Ayman F.; Saleh, Bahaa E. A.; Sergienko, Alexander V.; Teich, Malvin C.
2002-01-01
Entangled photons, generated by spontaneous parametric down-conversion from a second-order nonlinear crystal, present a rich potential for imaging and image-processing applications. Since this source is an example of a three-wave mixing process, there is more flexibility in the choices of illumination and detection wavelengths and in the placement of object(s) to be imaged. Moreover, this source is entangled, a fact that allows for imaging configurations and capabilities that cannot be achieved using classical sources of light. In this paper we examine a number of imaging and image-processing configurations that can be realized using this source. The formalism that we utilize facilitates the determination of the dependence of imaging resolution on the physical parameters of the optical arrangement.
Adaptive optics implementation with a Fourier reconstructor.
Glazer, Oded; Ribak, Erez N; Mirkin, Leonid
2007-02-01
Adaptive optics takes its servo feedback error cue from a wavefront sensor. The common Hartmann-Shack spot grid that represents the wavefront slopes is usually analyzed by finding the spot centroids. In a novel application, we used the Fourier decomposition of a spot pattern to find deviations from grid regularity. This decomposition was performed either in the Fourier domain or in the image domain, as a demodulation of the grid of spots. We analyzed the system, built a control loop for it, and tested it thoroughly. This allowed us to close the loop on wavefront errors caused by turbulence in the optical system.
Illustrative EDOF topics in Fourier optics
George, Nicholas; Chen, Xi; Chi, Wanli
2011-10-01
In this talk we present a series of illustrative topics in Fourier Optics that are proving valuable in the design of EDOF camera systems. They are at the level of final examination problems that have been made solvable by a student or professoi having studied from one of Joseph W. Goodman's books---our tribute for his 75fr year. As time permits, four illustrative topics are l) Electromagnetic waves and Fourier optics;2) The perfect lens; 3) Connection between phase delay and radially varying focal length in an asphere and 4) tailored EDOF designs.
Optical Planar Discrete Fourier and Wavelet Transforms
Cincotti, Gabriella; Moreolo, Michela Svaluto; Neri, Alessandro
2007-10-01
We present all-optical architectures to perform discrete wavelet transform (DWT), wavelet packet (WP) decomposition and discrete Fourier transform (DFT) using planar lightwave circuits (PLC) technology. Any compact-support wavelet filter can be implemented as an optical planar two-port lattice-form device, and different subband filtering schemes are possible to denoise, or multiplex optical signals. We consider both parallel and serial input cases. We design a multiport decoder/decoder that is able to generate/process optical codes simultaneously and a flexible logarithmic wavelength multiplexer, with flat top profile and reduced crosstalk.
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Fauvarque, Olivier; Fusco, Thierry; Sauvage, Jean-François; Giraut, Orion
2016-01-01
In this article, we compare a set of Wave Front Sensors (WFS) based on Fourier filtering technique. In particular, this study explores the "class of pyramidal WFS" defined as the 4 faces pyramid WFS, all its recent variations (6, 8 faces, the flattened PWFS, etc.) and also some new WFSs as the flattened cone WFS or the 3 faces pyramid WFS. In the first part, we describe such a sensors class thanks to the optical parameters of the Fourier filtering mask and the modulation parameters. In the second part, we use the unified formalism to create a set of performance criteria: size of the signal on the detector, efficiency of incoming flux, sensitivity, linear range and chromaticity. In the third part, we show the influence of the previous optical and modulation parameters on these performance criteria. This exhaustive study allows to know how to optimize the sensor regarding to performance specifications. We show in particular that the number of faces has influence on the number of pixels required to do the wave f...
Model of computation for Fourier optical processors
Naughton, Thomas J.
2000-05-01
We present a novel and simple theoretical model of computation that captures what we believe are the most important characteristics of an optical Fourier transform processor. We use this abstract model to reason about the computational properties of the physical systems it describes. We define a grammar for our model's instruction language, and use it to write algorithms for well-known filtering and correlation techniques. We also suggest suitable computational complexity measures that could be used to analyze any coherent optical information processing technique, described with the language, for efficiency. Our choice of instruction language allows us to argue that algorithms describable with this model should have optical implementations that do not require a digital electronic computer to act as a master unit. Through simulation of a well known model of computation from computer theory we investigate the general-purpose capabilities of analog optical processors.
Raman Tensor Formalism for Optically Anisotropic Crystals.
Kranert, Christian; Sturm, Chris; Schmidt-Grund, Rüdiger; Grundmann, Marius
2016-03-25
We present a formalism for calculating the Raman scattering intensity dependent on the polarization configuration for optically anisotropic crystals. It can be applied to crystals of arbitrary orientation and crystal symmetry measured in normal incidence backscattering geometry. The classical Raman tensor formalism cannot be used for optically anisotropic materials due to birefringence causing the polarization within the crystal to be depth dependent. We show that in the limit of averaging over a sufficiently large scattering depth, the observed Raman intensities converge and can be described by an effective Raman tensor given here. Full agreement with experimental results for uniaxial and biaxial crystals is demonstrated.
Maxwell Optics II. An Exact Formalism
Khan, S A
2002-01-01
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \\times 8$ matrix representation is used to construct the optical Hamiltonian. This has a close analogy with the algebraic structure of the Dirac equation, enabling the use of the rich machinery of the Dirac electron theory. We get interesting wavelength-dependent contributions which can not be obtained in any of the traditional approaches.
Canonical formalism for coupled beam optics
Energy Technology Data Exchange (ETDEWEB)
Kheifets, S.A.
1989-09-01
Beam optics of a lattice with an inter-plane coupling is treated using canonical Hamiltonian formalism. The method developed is equally applicable both to a circular (periodic) machine and to an open transport line. A solution of the equation of a particle motion (and correspondingly transfer matrix between two arbitrary points of the lattice) are described in terms of two amplitude functions (and their derivatives and corresponding phases of oscillations) and four coupling functions, defined by a solution of the system of the first-order nonlinear differential equations derived in the paper. Thus total number of independent parameters is equal to ten. 8 refs.
α-bandlimited diffuser in fractional Fourier optics
Patiño-Vanegas, Alberto; Durand, Pierre-Emmanuel; Torres, Rafael; Pellat-Finet, Pierre
2016-04-01
We propose a method for calculating appropriate α-band limited diffusers using the fractional Fourier transform. In order to do this, we implement a method for performing a numerical interpolation in the fractional Fourier domain. Such diffusers with compact support in the Fresnel regime may be used in fractional Fourier optical systems where the use of diffusers produce speckles, e.g. digital holography or optical encryption. Numerical simulations are presented.
Fiber Optic Fourier Transform White-Light Interferometry
Institute of Scientific and Technical Information of China (English)
Yi Jiang; Cai-Jie Tang
2008-01-01
Fiber optic Fourier transform white-light inter-fereometry is presented to interrogate the absolute optical path difference of an Mach-Zehnder inter-ferometer. The phase change of the interferometer caused by scanning wavelength can be calculated by a Fourier transform-based phase demodulation technique. A linear output is achieved.
Fourier transform optical profilometry using fiber optic Lloyd's mirrors.
Kart, Türkay; Kösoğlu, Gülşen; Yüksel, Heba; İnci, Mehmet Naci
2014-12-10
A fiber optic Lloyd's mirror assembly is used to obtain various optical interference patterns for the detection of 3D rigid body shapes. Two types of fiber optic Lloyd's systems are used in this work. The first consists of a single-mode optical fiber and a highly reflecting flat mirror to produce bright and dark strips. The second is constructed by locating a single-mode optical fiber in a v-groove, which is formed by two orthogonal flat mirrors to allow the generation of square-type interference patterns for the desired applications. The structured light patterns formed by these two fiber Lloyd's techniques are projected onto 3D objects. Fringe patterns are deformed due to the object's surface topography, which are captured by a digital CCD camera and processed with a Fourier transform technique to accomplish 3D surface topography of the object. It is demonstrated that the fiber-optic Lloyd's technique proposed in this work is more compact, more stable, and easier to configure than other existing surface profilometry systems, since it does not include any high-cost optical tools such as aligners, couplers, or 3D stages. The fringe patterns are observed to be more robust against environmental disturbances such as ambient temperature and vibrations.
Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie
2015-10-20
In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.
Electro-Optic Imaging Fourier Transform Spectral Polarimeter Project
National Aeronautics and Space Administration — Boulder Nonlinear Systems, Inc. (BNS) proposes to develop an Electro-Optic Imaging Fourier Transform Spectral Polarimeter (E-O IFTSP). The polarimetric system is...
Double random fractional Fourier domain encoding for optical security
Unnikrishnan, G.; Singh, Kehar
2000-11-01
We propose a new optical encryption technique using the fractional Fourier transform. In this method, the data are encrypted to a stationary white noise by two statistically independent random phase masks in fractional Fourier domains. To decrypt the data correctly, one needs to specify the fractional domains in which the input plane, encryption plane, and output planes exist, in addition to the key used for encryption. The use of an anamorphic fractional Fourier transform for the encryption of 2D data is also discussed. We suggest an optical implementation of the proposed idea. Results of a numerical simulation to analyze the performance of the proposed method are presented.
Fourier optics through the looking glass of digital computers
Yaroslavsky, Leonid P.
2011-10-01
Optical transforms are represented in computers by their discrete versions. In particular, Fourier optics is represented through Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT). Being discrete representation of the optical Fourier transform, these transforms feature a number of peculiarities that cast a new light on such fundamental properties of the Fourier Transform as sampling theorem and the uncertainty principle. In this paper, we formulate the Discrete Sampling Theorem and the discrete uncertainty principle, demonstrate that discrete signals can be both bandlimited in DFT or DCT domains and have strictly limited support in signal domain and present examples of such "bandlimited/ space-limited" signals that remain to be so for whatever large of their samples.
Optical correlation based on the fractional Fourier transform.
Granieri, S; Arizaga, R; Sicre, E E
1997-09-10
Some properties of optical correlation based on the fractional Fourier transform are analyzed. For a particular set of fractional orders, a filter is obtained that becomes insensitive to scale variations of the object. An optical configuration is also proposed to carry out the fractional correlation in a flexible way, and some experimental results are shown.
Extending single-molecule microscopy using optical Fourier processing.
Backer, Adam S; Moerner, W E
2014-07-17
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules.
A Fourier Optical Model for the Laser Doppler Velocimeter
DEFF Research Database (Denmark)
Lading, Lars
1972-01-01
The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. ldquodifferential moderdquo and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions. The particles are represented...... filtering ability vanishes as the aperture size converges towards zero. The results based on fourier optics are compared with the rough estimates obtainable by using the "antenna formular" for heterodyning (ArΩr≈λ2)....
Synchronization of Fourier-Synthesized Optical Pulses to a Mode-Locked Optical Clock
Institute of Scientific and Technical Information of China (English)
Masaharu; Hyodo; Kazi; Sarwal; Abedin; Noriaki; Onodera; Masayoshi; Watanabe
2003-01-01
A Fourier-synthesized 40-GHz optical pulse train was successfully synchronized to an 8-GHz optical clock generated from a mode-locked fiber ring laser. The measured timing jitter of the synchronization was 0.43 ps.
Fourier holographic display for augmented reality using holographic optical element
Li, Gang; Lee, Dukho; Jeong, Youngmo; Lee, Byoungho
2016-03-01
A method for realizing a three-dimensional see-through augmented reality in Fourier holographic display is proposed. A holographic optical element (HOE) with the function of Fourier lens is adopted in the system. The Fourier hologram configuration causes the real scene located behind the lens to be distorted. In the proposed method, since the HOE is transparent and it functions as the lens just for Bragg matched condition, there is not any distortion when people observe the real scene through the lens HOE (LHOE). Furthermore, two optical characteristics of the recording material are measured for confirming the feasibility of using LHOE in the proposed see-through augmented reality holographic display. The results are verified experimentally.
Imaginary angle fractional Fourier transform and its optical implementation
Institute of Scientific and Technical Information of China (English)
华建文; 刘立人; 李国强
1997-01-01
The concept of imaginary angle fractional Fourier transform is proposed. Its existence and additive operation are proved. With this concept, FRT is expanded to the optical transform of convex lens outside the range of double focal length and that of concave lens.
Electro-Optical Imaging Fourier-Transform Spectrometer
Chao, Tien-Hsin; Zhou, Hanying
2006-01-01
An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.
Spatial Fourier-decomposition optical fluorescen tomography-theoretical investigation
Institute of Scientific and Technical Information of China (English)
Cheng Liu; Dug Young Kim; Jianqiang Zhu
2008-01-01
A new three-dimensional (3D) optical fluorescent tomographic imaging scheme is proposed with structured illumination and spatial Fourierdomain decomposition methods for the first time. In this spatial Fourier-decomposition optical fluorescence tomography (SF-OFT), the intensity of focused excitation light from an objective lens is modulated to be a cosine function along the optical axis of the system. For a given position in a two-dimensional (2D) raster scanning process, the spatial frequency of the cosine function along the optical axis sweeps in a proper range while a series of fluorescence intensity are detected accordingly. By making an inverse discrete cosine transformation of these recorded intensity profiles, the distribution of fluorescent markers along the optical axis of a focused laser beam is obtained. A 3D optical fluorescent tomography can be achieved with this proposed SF-OFT technique with a simple 2D raster scanning process.
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian;
2015-01-01
We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time.......We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time....
Fourier optics for polymeric substrates and coating textures analysis
Sparavigna, Amelia
2008-01-01
Several devices for substrate texture detection based on diffractive optics, for paper, textiles and non-wovens have been proposed in the past for direct inspection during the production processes. In spite of the presence of devices totally based on image processing, the use of diffractive optics cannot be considered surpassed for many reasons. Compared with image processing procedures, it is less sensitive to vibrations and does not suffer from the presence of ambient light. Based on transmitted light, it can give information on changes in refractive indexes, thickness variation and surface conditions. We study the use of optical Fourier spectrum to identify textures of polymer films. As the power spectrum reveals, the texture is seldom homogeneous. Here we report investigation on several substrates and on thin ink coatings on substrate. Role of bulk and surface conditions is analysed.
Deep subwavelength nanometric image reconstruction using Fourier domain optical normalization
Institute of Scientific and Technical Information of China (English)
Jing Qin; Richard M Silver; Bryan M Barnes; Hui Zhou; Ronald G Dixson; Mark-Alexander Henn
2016-01-01
Quantitative optical measurements of deep subwavelength,three-dimensional (3D),nanometric structures with sensitivity to sub-nanometer details address a ubiquitous measurement challenge.A Fourier domain normalization approach is used in the Fourier optical imaging code to simulate the full 3D scattered light field of nominally 15 nm-sized structures,accurately replicating the light field as a function of the focus position.Using the full 3D light field,nanometer scale details such as a 2 nm thin conformal oxide and nanometer topography are rigorously fitted for features less than one-thirtiethof the wavelength in size.The densely packed structures are positioned nearly an order of magnitude closer than the conventional Rayleigh resolution limit and can be measured with sub-nanometer parametric uncertainties.This approach enables a practical measurement sensitivity to size variations of only a few atoms in size using a high-throughput optical configuration with broad application in measuring nanometric structures and nanoelectronic devices.
Universal discrete Fourier optics RF photonic integrated circuit architecture.
Hall, Trevor J; Hasan, Mehedi
2016-04-04
This paper describes a coherent electro-optic circuit architecture that generates a frequency comb consisting of N spatially separated orders using a generalised Mach-Zenhder interferometer (MZI) with its N × 1 combiner replaced by an optical N × N Discrete Fourier Transform (DFT). Advantage may be taken of the tight optical path-length control, component and circuit symmetries and emerging trimming algorithms offered by photonic integration in any platform that offers linear electro-optic phase modulation such as LiNbO3, silicon, III-V or hybrid technology. The circuit architecture subsumes all MZI-based RF photonic circuit architectures in the prior art given an appropriate choice of output port(s) and dimension N although the principal application envisaged is phase correlated subcarrier generation for all optical orthogonal frequency division multiplexing. A transfer matrix approach is used to model the operation of the architecture. The predictions of the model are validated by simulations performed using an industry standard software tool. Implementation is found to be practical.
DEFF Research Database (Denmark)
Clausen, Anders; Guan, Pengyu; Mulvad, Hans Christian Hansen
2014-01-01
All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented.......All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented....
Integrated optics in an electrically scanned imaging Fourier transform spectrometer
Breckinridge, James B. (Inventor); Ocallaghan, Fred G. (Inventor)
1982-01-01
An efficient, lightweight and stable, Fourier transform spectrometer was developed. The mechanical slide mechanism needed to create a path difference was eliminated by the use of retro-reflecting mirrors in a monolithic interferometer assembly in which the mirrors are not at 90 degrees to the propagation vector of the radiation, but rather at a small angle. The resulting plane wave fronts create a double-sided inteferogram of the source irradiance distribution which is detected by a charge-coupled device image sensor array. The position of each CCD pixel in the array is an indication of the path difference between the two retro-reflecting mirrors in the monolithic optical structure. The Fourier transform of the signals generated by the image sensor provide the spectral irradiance distribution of the source. For imaging, the interferometer assembly scans the source of irradiation by moving the entire instrument, such as would occur if it was fixedly mounted to a moving platform, i.e., a spacecraft. During scanning, the entrace slot to the monolithic optical structure sends different pixels to corresponding interferograms detected by adjacent columns of pixels of the image sensor.
Fourier optics analysis of grating sensors with tilt errors.
Ferhanoglu, Onur; Toy, M Fatih; Urey, Hakan
2011-06-15
Dynamic diffraction gratings can be microfabricated with precision and offer extremely sensitive displacement measurements and light intensity modulation. The effect of pure translation of the moving part of the grating on diffracted order intensities is well known. This study focuses on the parameters that limit the intensity and the contrast of the interference. The effects of grating duty cycle, mirror reflectivities, sensor tilt and detector size are investigated using Fourier optics theory and Gaussian beam optics. Analytical findings reveal that fringe visibility becomes <0.3 when the optical path variation exceeds half the wavelength within the grating interferometer. The fringe visibility can be compensated by monitoring the interfering portion of the diffracted order light only through detector size reduction in the expense of optical power. Experiments were conducted with a grating interferometer that resulted in an eightfold increase in fringe visibility with reduced detector size, which is in agreement with theory. Findings show that diffraction grating readout principle is not limited to translating sensors but also can be used for sensors with tilt or other deflection modes.
Energy Technology Data Exchange (ETDEWEB)
Rodriguez Z, G.; Rodriguez V, R.; Luna C, A. [Centro de Investigaciones en Optica, Apartado Postal 948, 37000 Leon, Guanajuato (Mexico)
1999-05-01
The introduction of tomography as an advanced topic to be included in a Fourier optics course at graduated level is proposed. It is shown a possible presentation sequence which features the use of typical Fourier optics techniques, as well as some well known opto-mechanical devices as examples. Finally, a simplified apparatus which illustrates the central Fourier theorem as an experimental project on Fourier optics is described. Corresponding experimental results are also shown. (Author)
Continuously tunable optical multidimensional Fourier-transform spectrometer.
Dey, P; Paul, J; Bylsma, J; Deminico, S; Karaiskaj, D
2013-02-01
A multidimensional optical nonlinear spectrometer (MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. The MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delays between them while maintaining phase stability. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy. The present work reports on overcoming some important limitations on the original design of the MONSTR apparatus. One important advantage of the MONSTR is the fact that it is a closed platform, which provides the high stability. Once the optical alignment is performed, it is desirable to maintain the alignment over long periods of time. The previous design of the MONSTR was limited to a narrow spectral range defined by the optical coating of the beam splitters. In order to achieve tunability over a broad spectral range the internal optics needed to be changed. By using broadband coated and wedged beam splitters and compensator plates, combined with modifications of the beam paths, continuous tunability can be achieved from 520 nm to 1100 nm without changing any optics or performing alignment of the internal components of the MONSTR. Furthermore, in order to achieve continuous tunability in the spectral region between 520 nm and 720 nm, crucially important for studies on numerous biological molecules, a single longitudinal mode laser at 488.5 nm was identified and used as a metrology laser. The shorter wavelength of the metrology laser as compared to the usual HeNe laser has also increased the phase stability of the system. Finally, in order to perform experiments in the reflection geometry, a simple method to achieve active phase stabilization
Resonant Doppler imaging with Fourier domain optical coherence tomography
Leitgeb, Rainer A.; Szklumowska, Anna; Pircher, Michael; Gotzinger, Erich; Fercher, Adolf F.
2005-04-01
Fourier Domain Optical Coherene Tomography (FD OCT) is a high speed imaging modality with increased sensitivity as compared to standard time domain (TD) OCT. The higher sensitivity is especially important, if strongly scattering tissue such as blood is investigated. Recently it could be shown that retinal blood flow can be assessed in-vivo by high speed FD OCT. However the detection bandwidth of color Doppler (CD) FDOCT is strongly limited due to blurring of the detected interference fringes during exposure. This leads to a loss of sensitivity for detection of fast changes in tissue. Using a moving mirror as a reference one can effectively increase the detection bandwidth for CD FDOCT and perform perfusion sectioning. The modality is called resonant CD FDOCT imaging. The principle of the method is presented and experimentally verified.
Optical design of the ATMOS Fourier transform spectrometer
Abel, I. R.; Reynolds, B. R.; Breckinridge, J. B.; Pritchard, J.
1979-01-01
The optical system design of the ATMOS Fourier transform spectrometer to be operated from Spacelab for the measurement of stratospheric trace molecules is described. The design contains features which can achieve the required fringe contrast of 80% and spectral resolution of 0.02/cm over a spectral range of 2-16 microns. In particular, the design is based on the following features which alleviate the usual requirements for alignment precision: (1) 'cat's eye' mirror configuration in the two arms of the interferometer for retroreflection stability, (2) tilt-compensated system of beamsplitter, compensator, and fold mirrors for wavefront directional stability, (3) paraboloidal 'cat's eye' primary mirror for wavefront stability against shear, (4) rotatable compensator for matching chromatic dispersion, and (5) wedged refractive components to avoid channel spectra due to the Fabry-Perot effect.
Selection of unstable patterns and control of optical turbulence by Fourier plane filtering
DEFF Research Database (Denmark)
Mamaev, A.V.; Saffman, M.
1998-01-01
We report on selection and stabilization of transverse optical patterns in a feedback mirror experiment. Amplitude filtering in the Fourier plane is used to select otherwise unstable spatial patterns. Optical turbulence observed for nonlinearities far above the pattern formation threshold...
Time-Domain Optical Fourier Transformation for OTDM-DWDM and DWDM-OTDM Conversion
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael
2011-01-01
Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats.......Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats....
Olivier, Scot S.; Werner, John S.; Zawadzki, Robert J.; Laut, Sophie P.; Jones, Steven M.
2010-09-07
This invention permits retinal images to be acquired at high speed and with unprecedented resolution in three dimensions (4.times.4.times.6 .mu.m). The instrument achieves high lateral resolution by using adaptive optics to correct optical aberrations of the human eye in real time. High axial resolution and high speed are made possible by the use of Fourier-domain optical coherence tomography. Using this system, we have demonstrated the ability to image microscopic blood vessels and the cone photoreceptor mosaic.
Simple optical setup implementation for digital Fourier transform holography
Energy Technology Data Exchange (ETDEWEB)
De Oliveira, G N [Pos-graduacao em Engenharia Mecanica, TEM/PGMEC, Universidade Federal Fluminense, Rua Passo da Patria, 156, Niteroi, R.J., Cep.: 24.210-240 (Brazil); Rodrigues, D M C; Dos Santos, P A M, E-mail: pams@if.uff.br [Instituto de Fisica, Laboratorio de Optica Nao-linear e Aplicada, Universidade Federal Fluminense, Av. Gal. Nilton Tavares de Souza, s/n, Gragoata, Niteroi, R.J., Cep.:24.210-346 (Brazil)
2011-01-01
In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.
OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation
DEFF Research Database (Denmark)
Palushani, Evarist; Richter, T.; Ludwig, R.
2012-01-01
We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information.......We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information....
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Guan, P.; Kasai, K.
2010-01-01
We demonstrate pre-scaled 40 GHz clock recovery from 640 Gbit/s optical time-division-multiplexed data using LiNbO$_3$ modulators, based on time-domain optical Fourier transformation and optical filtering. The clock recovery is used in a 640 Gbit/s error-free transmission over 300 km....
Optical alignment of high resolution Fourier transform spectrometers
Breckinridge, J. B.; Ocallaghan, F. G.; Cassie, A. G.
1980-01-01
Remote sensing, high resolution FTS instruments often contain three primary optical subsystems: Fore-Optics, Interferometer Optics, and Post, or Detector Optics. We discuss the alignment of a double-pass FTS containing a cat's-eye retro-reflector. Also, the alignment of fore-optics containing confocal paraboloids with a reflecting field stop which relays a field image onto a camera is discussed.
Fourier optics analysis of phase-mask-based path-length-multiplexed optical coherence tomography.
Yin, Biwei; Dwelle, Jordan; Wang, Bingqing; Wang, Tianyi; Feldman, Marc D; Rylander, Henry G; Milner, Thomas E
2015-11-01
Optical coherence tomography (OCT) is an imaging technique that constructs a depth-resolved image by measuring the optical path-length difference between broadband light backscattered from a sample and a reference surface. For many OCT sample arm optical configurations, sample illumination and backscattered light detection share a common path. When a phase mask is placed in the sample path, features in the detected signal are observed, which suggests that an analysis of a generic common path OCT imaging system is warranted. In this study, we present a Fourier optics analysis using a Fresnel diffraction approximation of an OCT system with a path-length-multiplexing element (PME) inserted in the sample arm optics. The analysis may be generalized for most phase-mask-based OCT systems. A radial-angle-diverse PME is analyzed in detail, and the point spread function, coherent transfer function, sensitivity of backscattering angular diversity detection, and signal formation in terms of sample spatial frequency are simulated and discussed. The analysis reveals important imaging features and application limitations of OCT imaging systems with a phase mask in the sample path optics.
Microcomputer Simulation of a Fourier Approach to Optical Wave Propagation
1992-06-01
efficient method to model such ultrasonic propagation has been developed by Guyomar and Powers [Refs. 2,3]. Relying upon linear systems theory and...the application of linear systems theory , and the mathematical derivation of the field solution utilizing the Fourier approach. Chapter III commences...the spatial impulse response. Guyomar and Powers’ view differs from Stepanishen’s work in that linear systems theory is used to point out the
Hamiltonian optics formalism for microring resonator structures with varying ring resonances.
Sun, Xiaolan; Yang, Zhenshan; Liu, Xiaohong; Li, Chao; Dong, Yanhua; Xie, Libin; Sipe, J E
2011-04-11
We develop a Hamiltonian optics formalism to quantitatively analyze a recently proposed scheme for increasing the delay-time-bandwidth product for microring resonator structures with varying ring resonances [Yang and Sipe, Opt. Lett. 32, 918 (2007)]. This theory is formally compact, simple and physically intuitive. We compare this formalism with the more rigorous transfer matrix method, and conclude that the Hamiltonian optics formalism correctly gives the average dispersion, which essentially determines the group delay as well as the dispersive distortion for pulses in the ps regime or longer.
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Morioka, Toshio
2016-01-01
We review recent progress in the use of time lens based optical Fourier transformation for advanced optical signal processing, with focus on all-optical generation, detection and format conversion of spectrally-efficient OFDM and N-WDM signals.......We review recent progress in the use of time lens based optical Fourier transformation for advanced optical signal processing, with focus on all-optical generation, detection and format conversion of spectrally-efficient OFDM and N-WDM signals....
Institute of Scientific and Technical Information of China (English)
CHEN Lin-Fei; ZHAO Dao-Mu
2006-01-01
@@ We propose a new method to add different images together by optical implementation that is realized by the multi-exposure based on fractional Fourier transform hologram. Partial image fusion is proposed and realized by this method. Multiple images encryption can also be implemented by the multi-exposure of the hologram based on fractional Fourier transform. Computer simulations prove that this method is valid.
Fractional Fourier transform-based optical encryption with treble random phase-encoding
Xin, Yi; Tao, Ran; Wang, Yue
2008-03-01
We propose a new architecture of optical encryption technique using the fractional Fourier transform with three statistically independent random phase masks. Compared with the existing double-phase encoding method in the fractional Fourier-domain, the proposed extra phase mask in the last fractional Fourier domain makes the architecture symmetrical, and additive processing to the encrypted image can be turned into complex stationary white noise after decryption, and enlarge the key space without any degradation of its robustness to blind decryption. This property can be utilized to improve the quality of the recover image. Simulation results have verified the validity.
Motion analysis of optically trapped particles and cells using 2D Fourier analysis
DEFF Research Database (Denmark)
Kristensen, Martin Verner; Ahrendt, Peter; Lindballe, Thue Bjerring;
2012-01-01
Motion analysis of optically trapped objects is demonstrated using a simple 2D Fourier transform technique. The displacements of trapped objects are determined directly from the phase shift between the Fourier transform of subsequent images. Using end-and side-view imaging, the stiffness...... of the trap is determined in three dimensions. The Fourier transform method is simple to implement and applicable in cases where the trapped object changes shape or where the lighting conditions change. This is illustrated by tracking a fluorescent particle and a myoblast cell, with subsequent determination...
Fourier optics for polymeric substrates and coating textures analysis
Sparavigna, Amelia; Wolf, Rory A.
2008-01-01
Several devices for substrate texture detection based on diffractive optics, for paper, textiles and non-wovens have been proposed in the past for direct inspection during the production processes. In spite of the presence of devices totally based on image processing, the use of diffractive optics cannot be considered surpassed for many reasons. Compared with image processing procedures, it is less sensitive to vibrations and does not suffer from the presence of ambient light. Based on transm...
Chan, Kenny K H; Tang, Shuo
2011-12-19
Gridding based non-uniform fast Fourier transform (NUFFT) has recently been shown as an efficient method of processing non-linearly sampled data from Fourier-domain optical coherence tomography (FD-OCT). This method requires selecting design parameters, such as kernel function type, oversampling ratio and kernel width, to balance between computational complexity and accuracy. The Kaiser-Bessel (KB) and Gaussian kernels have been used independently on the NUFFT algorithm for FD-OCT. This paper compares the reconstruction error and speed for the optimization of these design parameters and justifies particular kernel choice for FD-OCT applications. It is found that for on-the-fly computation of the kernel function, the simpler Gaussian function offers a better accuracy-speed tradeoff. The KB kernel, however, is a better choice in the pre-computed kernel mode of NUFFT, in which the processing speed is no longer dependent on the kernel function type. Finally, the algorithm is used to reconstruct in-vivo images of a human finger at a camera limited 50k A-line/s.
Optical Fourier techniques for medical image processing and phase contrast imaging.
Yelleswarapu, Chandra S; Kothapalli, Sri-Rajasekhar; Rao, D V G L N
2008-04-01
This paper briefly reviews the basics of optical Fourier techniques (OFT) and applications for medical image processing as well as phase contrast imaging of live biological specimens. Enhancement of microcalcifications in a mammogram for early diagnosis of breast cancer is the main focus. Various spatial filtering techniques such as conventional 4f filtering using a spatial mask, photoinduced polarization rotation in photosensitive materials, Fourier holography, and nonlinear transmission characteristics of optical materials are discussed for processing mammograms. We also reviewed how the intensity dependent refractive index can be exploited as a phase filter for phase contrast imaging with a coherent source. This novel approach represents a significant advance in phase contrast microscopy.
DWDM-TO-OTDM Conversion by Time-Domain Optical Fourier Transformation
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Hu, Hao; Galili, Michael
2011-01-01
We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated.......We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated....
DEFF Research Database (Denmark)
Hu, Hao; Kong, Deming; Palushani, Evarist
2013-01-01
We demonstrate transmission of a 1.28-Tbaud Nyquist-OTDM signal over a record distance of 100 km with detection by time-domain optical Fourier transformation followed by FEC decoding, resulting in error-free performance for all tributaries.......We demonstrate transmission of a 1.28-Tbaud Nyquist-OTDM signal over a record distance of 100 km with detection by time-domain optical Fourier transformation followed by FEC decoding, resulting in error-free performance for all tributaries....
DEFF Research Database (Denmark)
Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads
2016-01-01
We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude......We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...
Formalism of optical coherence and polarization based on material media states
Kuntman, Ertan; Kuntman, M. Ali; Sancho-Parramon, Jordi; Arteaga, Oriol
2017-06-01
The fluctuations or disordered motion of the electromagnetic fields are described by statistical properties rather than instantaneous values. This statistical description of the optical fields is underlying in the Stokes-Mueller formalism that applies to measurable intensities. However, the fundamental concept of optical coherence, which is assessed by the ability of waves to interfere, is not treatable by this formalism because it omits the global phase. In this work we show that using an analogy between deterministic matrix states associated with optical media and quantum mechanical wave functions, it is possible to construct a general formalism that accounts for the additional terms resulting from the coherency effects that average out for incoherent treatments. This method generalizes further the concept of coherent superposition to describe how deterministic states of optical media can superpose to generate another deterministic media state. Our formalism is used to study the combined polarimetric response of interfering plasmonic nanoantennas.
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Lillieholm, Mads;
2016-01-01
four-wave mixing (FWM), separated by a dispersive medium, which enables time-to-frequency and frequency-to-time conversions simultaneously, thus performing an exchange between the temporal and spectral profiles of the input signal. Using the proposed complete OFT, several advanced all-optical signal......We review recent progress in the use of time lens based optical Fourier transformation for advanced all-optical signal processing. A novel time lens based complete optical Fourier transformation (OFT) technique is introduced. This complete OFT is based on two quadratic phase-modulation stages using...... processing schemes for spectrally-efficient systems and networks have been achieved, including all-optical generation, detection and format conversion of spectrally-efficient signals. The spectrally-efficient signals in this paper mainly refer to efficiently multiplexed signals with a high symbol rate per Hz...
Tajahuerce, E; Saavedra, G; Furlan, W D; Sicre, E E; Andrés, P
2000-01-10
An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.
DEFF Research Database (Denmark)
Guan, Pengyu; Da Ros, Francesco; Lillieholm, Mads
2016-01-01
We demonstrate simultaneous phase regeneration of 16-WDM DPSK channels using optical Fourier transformation and a single phase-sensitive amplifier. The BERs of 16-WDM×10-Gbit/s phase noise degraded DPSK signals are improved by 0.4-1.3 orders of magnitude...
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Mulvad, Hans Christian Hansen
2016-01-01
We propose a novel all-optical ultra-high-speed orthogonal frequency-division multiplexing (OFDM) to Nyquist wavelength-division multiplexing (Nyquist-WDM) conversion scheme, achieved by exchanging the temporal and spectral profiles using a complete optical Fourier transformation (OFT). This scheme...... enables high-speed OFDM to Nyquist-WDM conversion without complex optical/electrical/optical conversion. The all-optical OFDM transmitter is based on the generation of OFDM symbols with a low duty cycle by rectangular temporal gating, which in combination with optical time-division multiplexing yields...... a higher symbol-rate OFDM signal. In the receiver, the converted Nyquist-WDM super-channel is WDM demultiplexed into individual Nyquist-WDM channels using a rectangular optical bandpass filter, followed by optical sampling at the intersymbol-interference free point. In the experimental demonstration...
Sun, Zhiwei; Zhi, Ya'nan; Liu, Liren; Sun, Jianfeng; Zhou, Yu; Hou, Peipei
2013-09-01
The synthetic aperture imaging ladar (SAIL) systems typically generate large amounts of data difficult to compress with digital method. This paper presents an optical SAIL processor based on compensation of quadratic phase of echo in azimuth direction and two dimensional Fourier transform. The optical processor mainly consists of one phase-only liquid crystal spatial modulator(LCSLM) to load the phase data of target echo and one cylindrical lens to compensate the quadratic phase and one spherical lens to fulfill the task of two dimensional Fourier transform. We show the imaging processing result of practical target echo obtained by a synthetic aperture imaging ladar demonstrator. The optical processor is compact and lightweight and could provide inherent parallel and the speed-of-light computing capability, it has a promising application future especially in onboard and satellite borne SAIL systems.
General insight into the complementary medium-based camouflage devices from Fourier optics.
Wu, Kedi; Wang, Guo Ping
2010-07-01
We present a general insight into complementary medium-based camouflage devices from Fourier optics. The cloaks are simply spatial filters with different transfer functions and play the role of passively remedying or actively modulating the propagation optical field to make an object invisible or changeable. We further analytically show and numerically demonstrate two filters for realizing another invisibility method: optically camouflaging an object at one place to appear at another place with parallel displacement or orientation changeable displacement, respectively. Our analysis is from a completely different point of view and should clarify understanding of the mechanism of invisibility phenomena.
Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fiber
Wahls, Sander
2015-01-01
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\\mathcal{O}(D\\log^{2}D)$ floating point operations to compute $D$ samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with $\\log^{2}$-linear complexity. The paper also includes a many samples analysis of the generated nonlinear Fourier spectra.
Energy Technology Data Exchange (ETDEWEB)
Lü, X.; Schrottke, L.; Grahn, H. T. [Paul-Drude-Institut für Festkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin e. V., Hausvogteiplatz 5–7, 10117 Berlin (Germany)
2016-06-07
We present scattering rates for electrons at longitudinal optical phonons within a model completely formulated in the Fourier domain. The total intersubband scattering rates are obtained by averaging over the intrasubband electron distributions. The rates consist of the Fourier components of the electron wave functions and a contribution depending only on the intersubband energies and the intrasubband carrier distributions. The energy-dependent part can be reproduced by a rational function, which allows for the separation of the scattering rates into a dipole-like contribution, an overlap-like contribution, and a contribution which can be neglected for low and intermediate carrier densities of the initial subband. For a balance between accuracy and computation time, the number of Fourier components can be adjusted. This approach facilitates an efficient design of complex heterostructures with realistic, temperature- and carrier density-dependent rates.
Measurement of absolute optical thickness of mask glass by wavelength-tuning Fourier analysis.
Kim, Yangjin; Hbino, Kenichi; Sugita, Naohiko; Mitsuishi, Mamoru
2015-07-01
Optical thickness is a fundamental characteristic of an optical component. A measurement method combining discrete Fourier-transform (DFT) analysis and a phase-shifting technique gives an appropriate value for the absolute optical thickness of a transparent plate. However, there is a systematic error caused by the nonlinearity of the phase-shifting technique. In this research the absolute optical-thickness distribution of mask blank glass was measured using DFT and wavelength-tuning Fizeau interferometry without using sensitive phase-shifting techniques. The error occurring during the DFT analysis was compensated for by using the unwrapping correlation. The experimental results indicated that the absolute optical thickness of mask glass was measured with an accuracy of 5 nm.
Detection of mitochondrial fission with orientation-dependent optical Fourier filters.
Pasternack, Robert M; Zheng, Jing-Yi; Boustany, Nada N
2011-02-01
We utilize a recently developed optical imaging method based on Fourier processing with Gabor-like filters to detect changes in light scattering resulting from alterations in mitochondrial structure in endothelial cells undergoing apoptosis. Imaging based on Gabor filters shows a significant decrease in the orientation of subcellular organelles at 60 to 100 minutes following apoptosis induction and concomitant with mitochondrial fragmentation observed by fluorescence. The optical scatter changes can be detected at low resolution at the whole cell level. At high resolution, we combine fluorescence imaging of the mitochondria with optical Fourier-based imaging to demonstrate that the dynamic decrease in organelle orientation measured by optical Gabor filtering is spatially associated with fluorescent mitochondria and remains largely absent from nonfluorescent subcellular regions. These results provide strong evidence that the optical Gabor responses track mitochondrial fission during apoptosis and can be used to provide label-free, rapid monitoring of this morphological process within single cells. Copyright © 2011 International Society for Advancement of Cytometry.
Capacity estimates for optical transmission based on the nonlinear Fourier transform
Derevyanko, Stanislav A.; Prilepsky, Jaroslaw E.; Turitsyn, Sergei K.
2016-09-01
What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km.
Propagation of a general-type beam through a truncated fractional Fourier transform optical system.
Zhao, Chengliang; Cai, Yangjian
2010-03-01
Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.
National Research Council Canada - National Science Library
Robert M. Pasternack; Zhen Qian; Jing-Yi Zheng; Dimitris N. Metaxas; Nada N. Boustany
2009-01-01
.... The method consists of applying an optical Fourier filter bank consisting of Gabor-like filters of varying periods and extracting the optimum filter period that maximizes the filtered object signal...
Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.
Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José
2015-12-14
We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.
Institute of Scientific and Technical Information of China (English)
FENG; Shaotong; HAN; Dianrong; DING; Heping
2004-01-01
By means of experimental technique of optical fractional Fourier transform,we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.
Liao, Chia-Chi; Lo, Yu-Lung
2015-04-20
A method is proposed for extracting the linear birefringence (LB) and linear dichroism (LD) properties of an anisotropic optical sample using reflection-mode optical coherence tomography (OCT) and a hybrid Mueller matrix formalism. To ensure the accuracy of the extracted parameter values, a method is proposed for calibrating and compensating the polarization distortion effect induced by the beam splitters in the OCT system using a composite quarter-waveplate / half-waveplate / quarter-waveplate structure. The validity of the proposed method is confirmed by extracting the LB and LD properties of a quarter-wave plate and a defective polarizer. To the best of the authors' knowledge, the method proposed in this study represents the first reported attempt to utilize an inverse Mueller matrix formalism and a reflection-mode OCT structure to extract the LB and LD parameters of optically anisotropic samples.
Energy Technology Data Exchange (ETDEWEB)
Narayanamurthy, C S [Department of Physics, Indian Institute of Space Science and Technology (IIST), Department of Space (Govt of India), ATF Campus, VSSC, ISRO - PO, Thiruvananthapuram 695 022 (India)], E-mail: naamu.s@gmail.com
2009-01-15
Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in Principles of Optics by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer have never been analysed seriously in any book. Because Michelson's interferometer is one of the important and fundamental optical experiments taught at both undergraduate and graduate levels, it would be appropriate to explain the localization of these fringes. In this paper, we analyse the localization of Michelson interferometer fringes using Fourier optics and temporal coherence, and show that they never localize at any plane even at infinity.
Relative humidity multi-point optical sensors system based on fast Fourier multiplexing technique
Lopez-Aldaba, A.; Lopez-Torres, D.; Elosua, C.; Auguste, J.-L.; Jamier, R.; Roy, P.; Arregui, F. J.; Lopez-Amo, M.
2017-04-01
In this paper, a new multipoint optical fiber system for relative humidity measurements based on SnO2-FP (Fabry-Pérot) sensing heads and an optical interrogator as single active device is presented and characterized. The interrogation of the sensing heads is carried out by monitoring the Fast Fourier Transform phase variations of the FP (Fabry-Pérot) interference frequencies. This method allows to multiplex several sensors with different wavelength spacing interference pattern. The sensors operate within a wide humidity range (20%-90% relative humidity) with low crosstalk between them. Five sensing heads have been measured using two different channels of the optical interrogator. The availability of four channels in the interrogator allows to multiplex a higher number of sensors, reducing proportionally the cost of each sensing point.
Advanced Optical Signal Processing using Time Lens based Optical Fourier Transformation
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Lillieholm, Mads
2016-01-01
An overview of recent progress on time lens based advanced optical signal processing is presented, with a special focus on all-optical ultrafast 640 Gbit/s all-channel serial-to-parallel conversion, and scalable WDM regeneration....
Wang, Yong-Ying; Wang, Yu-Rong; Wang, Yong; Li, Hui-Juan; Sun, Wen-Jia
2007-07-01
A new method of optical image encryption with binary Fourier transform computer-generated hologram (CGH) and pixel-scrambling technology is presented. In this method, the orders of the pixel scrambling, as well as the encrypted image, are used as the keys to decrypt the original image. Therefore, higher security is achieved. Furthermore, the encrypted image is binary, so it is easy to be fabricated and robust against noise and distortion. Computer simulation results are given to verify the feasibility of this method and its robustness against occlusion and additional noise.
Fourier transform acousto-optic imaging with a custom-designed CMOS smart-pixels array.
Barjean, Kinia; Contreras, Kevin; Laudereau, Jean-Baptiste; Tinet, Éric; Ettori, Dominique; Ramaz, François; Tualle, Jean-Michel
2015-03-01
We report acousto-optic imaging (AOI) into a scattering medium using a Fourier Transform (FT) analysis to achieve axial resolution. The measurement system was implemented using a CMOS smart-pixels sensor dedicated to the real-time analysis of speckle patterns. This first proof-of-principle of FT-AOI demonstrates some of its potential advantages, with a signal-to-noise ratio comparable to the one obtained without axial resolution, and with an acquisition rate compatible with a use on living biological tissue.
A modified split—step fourier method for optical pulse propagation with polarization mode dispersion
Institute of Scientific and Technical Information of China (English)
RaoMin; SunXiao-Han; ZhangMing-De
2003-01-01
A modified split-step Fourier method (SSFM) is presented to solve the coupled nonlinear Schroedinger equation (CNLS) that can be used to model high-speed pulse propagation in optical fibres with polarization mode dispersion (PMD). We compare our approach with the SSFM and demonstrate that our approach is much faster with no loss of pre-chirped RZ(CRZ) formats in the presence of high PMD through this approach. The simulation results show that CRZ pulses are the most tolerant to high PMD values and the extinct ratio has a great impact on the transmission performance.
Watanabe, Yuuki; Itagaki, Toshiki
2009-01-01
Fourier domain optical coherence tomography (FD-OCT) requires resampling of spectrally resolved depth information from wavelength to wave number, and the subsequent application of the inverse Fourier transform. The display rates of OCT images are much slower than the image acquisition rates due to processing speed limitations on most computers. We demonstrate a real-time display of processed OCT images using a linear-in-wave-number (linear-k) spectrometer and a graphics processing unit (GPU). We use the linear-k spectrometer with the combination of a diffractive grating with 1200 lines/mm and a F2 equilateral prism in the 840-nm spectral region to avoid calculating the resampling process. The calculations of the fast Fourier transform (FFT) are accelerated by the GPU with many stream processors, which realizes highly parallel processing. A display rate of 27.9 frames/sec for processed images (2048 FFT size x 1000 lateral A-scans) is achieved in our OCT system using a line scan CCD camera operated at 27.9 kHz.
Energy Technology Data Exchange (ETDEWEB)
Ritt, G.
2007-07-13
In this work a dissipationless asymmetrical optical potential for cold atoms was produced. In a first step a new type of optical lattice was generated, whose spatial periodicity only corresponds to a quarter of the wavelength of the light used for the generation. This corresponds to the half of the periodicity of a conventional optical lattice, which is formed by the light of the same wavelength. The generation of this new type of optical lattice was reached by the use of two degenerated raman transitions. Virtual processes occur, in which four photons are involved. In conventional optical lattices however virtual two-photon processes occur. By spatially superimposing this optical lattice with a conventional optical lattice an asymmetrical optical potential could be formed. By diffraction of a Bose Einstein condensate of rubidium atoms at the transient activated asymmetrical potential the asymmetrical structure was proven. (orig.)
DEFF Research Database (Denmark)
Guan, P.; Mulvad, Hans Christian Hansen; Kasai, K.
2010-01-01
We present a novel scheme for subharmonic clock recovery from an optical time-division-multiplexing signal using time-domain optical Fourier transformation and a narrowband optical filter. High-resolution 640-Gb/s clock recovery is successfully demonstrated with no pattern dependence. The clock...
Swept source optical coherence tomography based on non-uniform discrete fourier transform
Institute of Scientific and Technical Information of China (English)
Tong Wu; Zhihua Ding; Kai Wang; Chuan Wang
2009-01-01
A high-speed high-sensitivity swept source optical coherence tomography (SSOCT) system using a high speed swept laser source is developed.Non-uniform discrete fourier transform (NDFT) method is introduced in the SSOCT system for data processing.Frequency calibration method based on a Mach-Zender interferometer (MZI) and conventional data interpolation method is also adopted in the system for comparison.Optical coherence tomography (OCT) images from SSOCT based on the NDFT method,the MZI method,and the interpolation method are illustrated.The axial resolution of the SSOCT based on the NDFT method is comparable to that of the SSOCT system using MZI calibration method and conventional data interpolation method.The SSOCT system based on the NDFT method can achieve higher signal intensity than that of the system based on the MZI calibration method and conventional data interpolation method because of the better utilization of the power of source.
Broadband Fourier domain mode-locked laser for optical coherence tomography at 1060 nm
DEFF Research Database (Denmark)
Marschall, Sebastian; Klein, Thomas; Wieser, Wolfgang
2012-01-01
, enable acquisition of densely sampled three-dimensional datasets covering a wide field of view. However, semiconductor optical amplifiers (SOAs)-the typical laser gain media for swept sources-for the 1060nm band could until recently only provide relatively low output power and bandwidth. We have......Optical coherence tomography (OCT) in the 1060nm range is interesting for in vivo imaging of the human posterior eye segment (retina, choroid, sclera) due to low absorption in water and deep penetration into the tissue. Rapidly tunable light sources, such as Fourier domain mode-locked (FDML) lasers...... implemented an FDML laser using a new SOA featuring broad gain bandwidth and high output power. The output spectrum coincides with the wavelength range of minimal water absorption, making the light source ideal for OCT imaging of the posterior eye segment. With a moderate SOA current (270 mA) we achieve up...
Analyzing subcellular structure with optical Fourier filtering based on Gabor filters
Boustany, Nada N.; Sierra, Heidy
2013-02-01
Label-free measurement of subcellular morphology can be used to track dynamically cellular function under various conditions and has important applications in cellular monitoring and in vitro cell assays. We show that optical filtering of scattered light by two-dimensional Gabor filters allows for direct and highly sensitive measurement of sample structure. The Gabor filters, which are defined by their spatial frequency, orientation and Gaussian envelope, can be used to track locally and in situ the characteristic size and orientation of structures within the sample. Our method consists of sequentially implementing a set of Gabor filters via a spatial light modulator placed in a conjugate Fourier plane during optical imaging and identifying the filters that yield maximum signal. Using this setup, we show that Gabor filtering of light forward-scattered by spheres yields an optical response which varies linearly with diameter between 100nm and 2000nm. The optical filtering sensitivity to changes in diameter is on the order of 20nm and can be achieved at low image resolution. We use numerical simulations to demonstrate that this linear response can be predicted from scatter theory and does not vary significantly with changes in refractive index ratio. By applying this Fourier filtering method in samples consisting of diatoms and cells, we generate false-color images of the object that encode at each pixel the size of the local structures within the object. The resolution of these encoded size maps in on the order of 0.36μm. The pixel histograms of these encoded images directly provide 20nm resolved "size spectra", depicting the size distribution of structures within the analyzed object. We use these size spectra to differentiate the morphology of apoptosis-competent and bax/bak null apoptosis-resistant cells during cell death. We also utilize the sensitivity of the Gabor filters to object orientation to track changes in organelle morphology, and detect mitochondrial
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Mulvad, Hans Christian Hansen;
2014-01-01
We propose a DWDM-to-Nyquist channel conversion scheme based on complete Optical Fourier Transformation and optical Nyquist filtering. We demonstrate conversion from 50-GHz-grid 16×10 Gbit/s DPSK DWDM to a 160-Gbit/s Nyquist channel (0.9 symbol/s/Hz spectral efficiency) with 1.4 dB power penalty....
DEFF Research Database (Denmark)
Palushani, Evarist; Oxenløwe, Leif Katsuo; Galili, Michael;
2009-01-01
This paper reports on the generation of 1.6-ps fullwidth at half-maximum flat-top pulses by the optical Fourier transform technique, and the utilization of these pulses in a 320-Gb/s demultiplexing experiment. It is demonstrated how a narrow pulse having a 15-nm wide third-order super-Gaussian sp......This paper reports on the generation of 1.6-ps fullwidth at half-maximum flat-top pulses by the optical Fourier transform technique, and the utilization of these pulses in a 320-Gb/s demultiplexing experiment. It is demonstrated how a narrow pulse having a 15-nm wide third-order super......-Gaussian spectral intensity profile is mapped into a flat-top pulse resembling its spectrum by simple propagation in SMF. Theoretical and experimental descriptions are given on flat-top pulse generation, and an experimental validation of the systems performance of the pulses is carried out, demonstrating a benefit...
Seet, Katrina Y T; Nieminen, Timo A; Zvyagin, Andrei V
2009-01-01
The cell nucleus is the dominant optical scatterer in the cell. Neoplastic cells are characterized by cell nucleus polymorphism and polychromism-i.e., the nuclei exhibits an increase in the distribution of both size and refractive index. The relative size parameter, and its distribution, is proportional to the product of the nucleus size and its relative refractive index and is a useful discriminant between normal and abnormal (cancerous) cells. We demonstrate a recently introduced holographic technique, digital Fourier microscopy (DFM), to provide a sensitive measure of this relative size parameter. Fourier holograms were recorded and optical scatter of individual scatterers were extracted and modeled with Mie theory to determine the relative size parameter. The relative size parameter of individual melanocyte cell nuclei were found to be 16.5+/-0.2, which gives a cell nucleus refractive index of 1.38+/-0.01 and is in good agreement with previously reported data. The relative size parameters of individual malignant melanocyte cell nuclei are expected to be greater than 16.5.
Iterative Fourier transform algorithm: different approaches to diffractive optical element design
Skeren, Marek; Richter, Ivan; Fiala, Pavel
2002-10-01
This contribution focuses on the study and comparison of different design approaches for designing phase-only diffractive optical elements (PDOEs) for different possible applications in laser beam shaping. Especially, new results and approaches, concerning the iterative Fourier transform algorithm, are analyzed, implemented, and compared. Namely, various approaches within the iterative Fourier transform algorithm (IFTA) are analyzed for the case of phase-only diffractive optical elements with quantizied phase levels (either binary or multilevel structures). First, the general scheme of the IFTA iterative approach with partial quantization is briefly presented and discussed. Then, the special assortment of the general IFTA scheme is given with respect to quantization constraint strategies. Based on such a special classification, the three practically interesting approaches are chosen, further-analyzed, and compared to eachother. The performance of these algorithms is compared in detail in terms of the signal-to-noise ratio characteristic developments with respect to the numberof iterations, for various input diffusive-type objects chose. Also, the performance is documented on the complex spectra developments for typical computer reconstruction results. The advantages and drawbacks of all approaches are discussed, and a brief guide on the choice of a particular approach for typical design tasks is given. Finally, the two ways of amplitude elimination within the design procedure are considered, namely the direct elimination and partial elimination of the amplitude of the complex hologram function.
Van der Jeught, Sam; Bradu, Adrian; Podoleanu, Adrian Gh
2010-01-01
Fourier domain optical coherence tomography (FD-OCT) requires either a linear-in-wavenumber spectrometer or a computationally heavy software algorithm to recalibrate the acquired optical signal from wavelength to wavenumber. The first method is sensitive to the position of the prism in the spectrometer, while the second method drastically slows down the system speed when it is implemented on a serially oriented central processing unit. We implement the full resampling process on a commercial graphics processing unit (GPU), distributing the necessary calculations to many stream processors that operate in parallel. A comparison between several recalibration methods is made in terms of performance and image quality. The GPU is also used to accelerate the fast Fourier transform (FFT) and to remove the background noise, thereby achieving full GPU-based signal processing without the need for extra resampling hardware. A display rate of 25 framessec is achieved for processed images (1,024 x 1,024 pixels) using a line-scan charge-coupled device (CCD) camera operating at 25.6 kHz.
Subtle Solar Retinopathy Detected by Fourier-domain Optical Coherence Tomography
Directory of Open Access Journals (Sweden)
Ya-Hsin Kung
2010-07-01
Full Text Available Solar retinopathy is a retinal injury caused by direct or indirect sun-gazing and solar eclipse observation without protection. Subtle changes in the retinal damage might not be evident on fundus photography and fluorescein angiography. A 40-year-old veteran suffered from paracentral scotoma in his left eye shortly after unprotected solar eclipse observation about 1 month earlier. His visual acuity was 6/5 in the right eye and 6/6 in the left. Anterior segments were normal bilaterally. Dilated fundus examination, fluorescein angiography, and central visual field testing did not reveal any abnormal findings. Fourier-domain optical coherence tomography was used for evaluation, and a focal defect in the inner and outer segments of the photoreceptor layer band was noted in the paracentral region of the fovea in the left eye, with central foveal thickness of 198 μm. Solar retinopathy is preventable with adequate eye protection. Education should be reinforced to the public. In mildly affected individuals with subtle retinal damage, Fourier-domain optical coherence tomography could be a useful imaging tool to detect the disease.
Rugged optical mirrors for Fourier-Transform Spectrometers operated in harsh environments
Directory of Open Access Journals (Sweden)
D. G. Feist
2015-10-01
Full Text Available The Total Carbon Column Observing Network (TCCON and the Network for the Detection of Atmospheric Composition Change (NDACC operate a number of Fourier-Transform Spectrometers (FTSs that measure trace gases in the atmosphere by observing solar spectra. To guide the sunlight into the FTS, a solar tracker has to be placed outside. This device needs high-quality optical mirrors with good reflectivity in the near and mid infrared. More and more FTS stations are operated in remote locations with harsh environments. Optical mirrors are usually made for laboratory conditions and might not last very long there. At the MPI-BGC's TCCON site on Ascension Island, several mirrors from different optical manufacturers were destroyed within weeks. To continue operation, the MPI-BGC had to develop rugged mirrors that could sustain the harsh conditions for months or even years. While commercially available mirrors are typically made from a substrate coverered with a thin reflective coating, these rugged mirrors were made from stainless steel with no additional coating. Except for their lower reflectivity (which can easily be compensated for, their optical properties are comparable to existing mirrors. However, their rugged design makes them mostly immune to corrosion and scratching. Unlike most coated mirrors, they can also be cleaned easily.
Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states
dell'Anno, Fabio; de Siena, Silvio; Illuminati, Fabrizio
2004-03-01
We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local-oscillator angle; for n -mode systems they depend on n heterodyne mixing angles. The canonical formalism realizes nontrivial mixing of pairs of conjugate quadratures of the electromagnetic field in terms of homodyne variables for single-mode systems, and in terms of heterodyne variables for multimode systems. In the first instance the transformations yield nonquadratic model Hamiltonians of degenerate multiphoton processes and define a class of non-Gaussian, nonclassical multiphoton states that exhibit properties of coherence and squeezing. We show that such homodyne multiphoton squeezed states are generated by unitary operators with a nonlinear time evolution that realizes the homodyne mixing of a pair of conjugate quadratures. Tuning of the local-oscillator angle allows us to vary at will the statistical properties of such states. We discuss the relevance of the formalism for the study of degenerate (up-)down-conversion processes. In a companion paper [ F. Dell’Anno, S. De Siena, and F. Illuminati, 69, 033813 (2004) ], we provide the extension of the nonlinear canonical formalism to multimode systems, we introduce the associated heterodyne multiphoton squeezed states, and we discuss their possible experimental realization.
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-08
In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.
Study of Anterior Chamber Aqueous Tube Shunt by Fourier-Domain Optical Coherence Tomography
Directory of Open Access Journals (Sweden)
Chunhui Jiang
2012-01-01
Full Text Available Purpose. This cross-sectional, observational study used Fourier-domain optical coherence tomography (OCT to examine the position, patency, and the interior entrance site of anterior chamber (AC aqueous tube shunts. Methods. The OCT, slitlamp biomicroscopy, and gonioscopy findings of 23 eyes of 18 patients with AC shunts were collected and compared. Results. OCT images demonstrated the shunt position and patency in all 23 eyes, and the details of the AC entrance in 16 eyes. The position of the tube varied, with the majority (14/23 on the surface of the iris. The exact position of the AC entrance relative to Schwalbe’s line (SL could be determined in 9 eyes (posterior to SL in 7 eyes, anterior in 2 eyes. At the AC entrance, growth of fibrous scar tissue was present between the tube and the corneal endothelium in all 16 eyes in which the entrance could be clearly visualized. It’s a new finding that could not be visualized by slitlamp examination or lower resolution OCT. Conclusion. Compared to slitlamp examination, Fourier-domain OCT of AC tube shunts provided more detailed anatomic information regarding the insertion level relative to SL, scar tissue between the tube and the corneal endothelium, and patency of the tube opening.
Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states
Dell'Anno, F; Illuminati, F; Anno, Fabio Dell'; Siena, Silvio De; Illuminati, Fabrizio
2004-01-01
We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local oscillator angle; for n-mode systems they depend on n heterodyne mixing angles. The canonical formalism realizes nontrivial mixings of pairs of conjugate quadratures of the electromagnetic field in terms of homodyne variables for single-mode systems; and in terms of heterodyne variables for multimode systems. In the first instance the transformations yield nonquadratic model Hamiltonians of degenerate multiphoton processes and define a class of non Gaussian, nonclassical multiphoton states that exhibit properties of coherence and squeezing. We show that such homodyne multiphoton squeezed states are generated by unitary operators with a nonlinear time evolution that realizes the homodyne mixing of a pair of conjugate quadratures. Tuning of the local oscillator angle allows to vary at will the statist...
Common-optical axis Fourier transform profilometry for water surface waves
Ghadiri, Mahdi; Krechetnikov, Rouslan
2016-11-01
The Fourier transform profilometry - a single-shot optical profilometric measurement of surface deformation - has been widely used to visualize and measure water surface waves. This well-known method is based on an optical system composed of a video projector displaying a fringe pattern on the surface and a camera recording this pattern as the reference image. The deformed fringe pattern following deformation of the surface later is then recorded and compared to the reference image in order to produce a phase map, from which the height of the deformed surface is reconstructed through a phase-to-height relation. The biggest challenge encountered while applying this method for water surface is the light reflection which previously has been partially treated by enhancing the water light diffusivity with the addition of Titanium dioxide. As part of the effort to improve the accuracy and practical applicability of the method, in this talk we will present a new implementation of a common-optical axis geometry along with an appropriate phase-height relation. Furthermore, in the case of water surface waves, we introduce a proper light filtration, which removes all the reflections remaining after addition of Titanium dioxide. The proposed technique provides an order of magnitude improvement in the accuracy of detecting and reconstructing the surface deformation, which is crucial for studying small amplitude waves and bifurcation phenomena.
Characterization of polymer composites by fiber optic Fourier transform Raman spectroscopy
Farquharson, Stuart; Bhat, Sanmitra A.; Osbaldiston, Richard; DiTaranto, Marie B.; Smith, Wayne W.; Rose, Jennifer; Liu, Yong-Ming; Shaw, Montgomery
1999-01-01
The in-use performance of polymer composites is highly dependent on the polymeric structure, which in turn, is highly dependent on the processing conditions. We have been developing a Fourier transform Raman system capable of high temperature measurements within curing devices through the use of fiber optic probes. The goal is to use real-time spectral data to control heat schedules and ultimately, composite properties. This presentation will describe the development of cure models based on reaction mechanisms for an epoxy resin and a polyimide using IR and Raman spectroscopy. It will also describe correlations between molecular structure and mechanical properties obtained by simultaneous Raman and rheology measurements. In addition, new spectral methods to determine cure kinetics will be presented.
Verber, C. M.; Vahey, D. W.; Wood, V. E.; Kenan, R. P.; Hartman, N. F.
1977-01-01
The possibility of producing an integrated optics data processing device based upon Fourier transformations or other parallel processing techniques, and the ways in which such techniques may be used to upgrade the performance of present and projected NASA systems were investigated. Activities toward this goal include; (1) production of near-diffraction-limited geodesic lenses in glass waveguides; (2) development of grinding and polishing techniques for the production of geodesic lenses in LiNbO3 waveguides; (3) development of a characterization technique for waveguide lenses; and (4) development of a theory for corrected aspheric geodesic lenses. A holographic subtraction system was devised which should be capable of rapid on-board preprocessing of a large number of parallel data channels. The principle involved is validated in three demonstrations.
A modified split-step Fourier method for optical pulse propagation with polarization mode dispersion
Institute of Scientific and Technical Information of China (English)
饶敏; 孙小菡; 张明德
2003-01-01
A modified split-step Fourier method (SSFM) is presented to solve the coupled nonlinear Schrǒdinger equation (CNLS) that can be used to model high-speed pulse propagation in optical fibres with polarization mode dispersion (PMD). We compare our approach with the SSFM and démonstrate that our approach is much faster with no loss of accuracy. We discuss the pulse distortion and system Q-factor of non-return-to-zero (NRZ), return-to-zero (RZ) and pre-chirped RZ (CRZ) formats in the presence of high PMD through this approach. The simulation results show that CRZ pulses are the most tolerant to high PMD wlues and the extinct ratio has a great impact on the transmission performance.
Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography.
Wang, Yimin; Huang, David; Su, Ya; Yao, X Steve
2016-11-14
For phase-related imaging modalities using interferometric techniques, it is important to develop effective method to recover phase information that is mathematically wrapped. In this paper, we propose and demonstrate a two-dimensional (2D) method to achieve effective phase unwrapping in Doppler Fourier-domain (FD) optical coherence tomography (OCT), and recover the discontinuous phase distribution in retinal blood flow successfully for the first time in Doppler OCT studies. The proposed method is based on phase gradient approach in the axial dimension, with phase denoising performed through 2D window moving average in the sampled phase image using complex Doppler OCT data. The 2D unwrapping is carried out to correct phase discontinuities in the wrapped Doppler phase map, and the abrupt phase changes can be identified and corrected accurately. The proposed algorithm is computationally efficient and easy to be implemented.
Xia, Shaoyan; Huang, Yong; Peng, Shizhao; Wu, Yanfeng; Tan, Xiaodi
2016-08-01
Phase image in Fourier domain Doppler optical coherence tomography offers additional flow information of investigated samples, which provides valuable evidence towards accurate medical diagnosis. High quality phase images are thus desirable. We propose a noise reduction method for phase images by combining a synthetic noise estimation criteria based on local noise estimator (LNE) and distance median value (DMV) with anisotropic diffusion model. By identifying noise and signal pixels accurately and diffusing them with different coefficients respectively and adaptive iteration steps, we demonstrated the effectiveness of our proposed method in both phantom and mouse artery images. Comparison with other methods such as filtering method (mean, median filtering), wavelet method, probabilistic method and partial differential equation based methods in terms of peak signal-to-noise ratio (PSNR), equivalent number of looks (ENL) and contrast-to-noise ratio (CNR) showed the advantages of our method in reserving image energy and removing noise.
Johansson, Alexandra C; Khodabakhsh, Amir; Foltynowicz, Aleksandra
2016-01-01
We present a thorough analysis of the signal line shapes of Fourier transform-based noise-immune cavity-enhanced optical frequency comb spectroscopy (NICE-OFCS). We discuss the signal dependence on the ratio of the modulation frequency, f${_m}$, to the molecular line width, {\\Gamma}. We compare a full model of the signals and a simplified absorption-like analytical model that has high accuracy for low f${_m}$/{\\Gamma} ratios and is much faster to compute. We verify the theory experimentally by measuring and fitting NICE-OFCS spectra of CO${_2}$ at 1575 nm using a system based on an Er:fiber femtosecond laser and a cavity with a finesse of ~11000.
Muñoz Morales, Aarón A; Vázquez Y Montiel, Sergio
2012-10-01
The determination of optical parameters of biological tissues is essential for the application of optical techniques in the diagnosis and treatment of diseases. Diffuse Reflection Spectroscopy is a widely used technique to analyze the optical characteristics of biological tissues. In this paper we show that by using diffuse reflectance spectra and a new mathematical model we can retrieve the optical parameters by applying an adjustment of the data with nonlinear least squares. In our model we represent the spectra using a Fourier series expansion finding mathematical relations between the polynomial coefficients and the optical parameters. In this first paper we use spectra generated by the Monte Carlo Multilayered Technique to simulate the propagation of photons in turbid media. Using these spectra we determine the behavior of Fourier series coefficients when varying the optical parameters of the medium under study. With this procedure we find mathematical relations between Fourier series coefficients and optical parameters. Finally, the results show that our method can retrieve the optical parameters of biological tissues with accuracy that is adequate for medical applications.
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Palushani, Evarist; Hu, Hao
2011-01-01
We demonstrate conversion from 64 × 10 Gbit/s optical timedivision multiplexed (OTDM) data to dense wavelength division multiplexed (DWDM) data with 25 GHz spacing. The conversion is achieved by time-domain optical Fourier transformation (OFT) based on four-wave mixing (FWM) in a 3.6 mm long...
Tucher, Nico; Eisenlohr, Johannes; Gebrewold, Habtamu; Kiefel, Peter; Höhn, Oliver; Hauser, Hubert; Goldschmidt, Jan Christoph; Bläsi, Benedikt
2016-07-11
The OPTOS formalism is a matrix-based approach to determine the optical properties of textured optical sheets. It is extended within this work to enable the modelling of systems with an arbitrary number of textured, plane-parallel interfaces. A matrix-based system description is derived that accounts for the optical reflection and transmission interaction between all textured interfaces. Using OPTOS, we calculate reflectance and absorptance of complete photovoltaic module stacks, which consist of encapsulated silicon solar cells featuring textures that operate in different optical regimes. As exemplary systems, solar cells with and without module encapsulation are shown to exhibit a considerable absorptance gain if the random pyramid front side texture is combined with a diffractive rear side grating. A variation of the sunlight's angle of incidence reveals that the grating gain is almost not affected for incoming polar angles up to 60°. Considering as well the good agreement with alternative simulation techniques, OPTOS is demonstrated to be a versatile and efficient method for the optical analysis of photovoltaic modules.
A new way to characterize autostereoscopic 3D displays using Fourier optics instrument
Boher, P.; Leroux, T.; Bignon, T.; Collomb-Patton, V.
2009-02-01
Auto-stereoscopic 3D displays offer presently the most attractive solution for entertainment and media consumption. Despite many studies devoted to this type of technology, efficient characterization methods are still missing. We present here an innovative optical method based on high angular resolution viewing angle measurements with Fourier optics instrument. This type of instrument allows measuring the full viewing angle aperture of the display very rapidly and accurately. The system used in the study presents a very high angular resolution below 0.04 degree which is mandatory for this type of characterization. We can predict from the luminance or color viewing angle measurements of the different views of the 3D display what will be seen by an observer at any position in front of the display. Quality criteria are derived both for 3D and standard properties at any observer position and Qualified Stereo Viewing Space (QSVS) is determined. The use of viewing angle measurements at different locations on the display surface during the observer computation gives more realistic estimation of QSVS and ensures its validity for the entire display surface. Optimum viewing position, viewing freedom, color shifts and standard parameters are also quantified. Simulation of the moire issues can be made leading to a better understanding of their origin.
Baumann, Bernhard; Choi, WooJhon; Potsaid, Benjamin; Huang, David; Duker, Jay S; Fujimoto, James G
2012-04-23
Polarization sensitive optical coherence tomography (PS-OCT) is a functional imaging method that provides additional contrast using the light polarizing properties of a sample. This manuscript describes PS-OCT based on ultrahigh speed swept source / Fourier domain OCT operating at 1050 nm at 100 kHz axial scan rates using single mode fiber optics and a multiplexing approach. Unlike previously reported PS-OCT multiplexing schemes, the method uses a passive polarization delay unit and does not require active polarization modulating devices. This advance decreases system cost and avoids complex synchronization requirements. The polarization delay unit was implemented in the sample beam path in order to simultaneously illuminate the sample with two different polarization states. The orthogonal polarization components for the depth-multiplexed signals from the two input states were detected using dual balanced detection. PS-OCT images were computed using Jones calculus. 3D PS-OCT imaging was performed in the human and rat retina. In addition to standard OCT images, PS-OCT images were generated using contrast form birefringence and depolarization. Enhanced tissue discrimination as well as quantitative measurements of sample properties was demonstrated using the additional contrast and information contained in the PS-OCT images.
Zhang, Kang
2011-12-01
In this dissertation, real-time Fourier domain optical coherence tomography (FD-OCT) capable of multi-dimensional micrometer-resolution imaging targeted specifically for microsurgical intervention applications was developed and studied. As a part of this work several ultra-high speed real-time FD-OCT imaging and sensing systems were proposed and developed. A real-time 4D (3D+time) OCT system platform using the graphics processing unit (GPU) to accelerate OCT signal processing, the imaging reconstruction, visualization, and volume rendering was developed. Several GPU based algorithms such as non-uniform fast Fourier transform (NUFFT), numerical dispersion compensation, and multi-GPU implementation were developed to improve the impulse response, SNR roll-off and stability of the system. Full-range complex-conjugate-free FD-OCT was also implemented on the GPU architecture to achieve doubled image range and improved SNR. These technologies overcome the imaging reconstruction and visualization bottlenecks widely exist in current ultra-high speed FD-OCT systems and open the way to interventional OCT imaging for applications in guided microsurgery. A hand-held common-path optical coherence tomography (CP-OCT) distance-sensor based microsurgical tool was developed and validated. Through real-time signal processing, edge detection and feed-back control, the tool was shown to be capable of track target surface and compensate motion. The micro-incision test using a phantom was performed using a CP-OCT-sensor integrated hand-held tool, which showed an incision error less than +/-5 microns, comparing to >100 microns error by free-hand incision. The CP-OCT distance sensor has also been utilized to enhance the accuracy and safety of optical nerve stimulation. Finally, several experiments were conducted to validate the system for surgical applications. One of them involved 4D OCT guided micro-manipulation using a phantom. Multiple volume renderings of one 3D data set were
Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan
2012-02-15
Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.
DEFF Research Database (Denmark)
Hu, Hao; Kong, Deming; Palushani, Evarist;
2013-01-01
320 Gb/s Nyquist-OTDM is generated by rectangular filtering with a bandwidth of 320 GHz and received by polarization-insensitive time-domain optical Fourier transformation (TD-OFT) followed by passive filtering. After the time-to-frequency mapping in the TD-OFT, the Nyquist-OTDM is converted...
Fernández-Vigo, J I; Fernández-Vigo, C; Martínez de la Casa, J M; Sáenz-Francés, F; Santos-Bueso, E; García Feijóo, J; Fernández-Vigo, J A
2016-02-01
To study the structures of the iridocorneal angle using anterior segment optical coherence tomography (OCT) defining their tomographic characteristics and quantifying their identification frequency. A cross-sectional study was performed on 267 right eyes of 267 consecutive healthy patients. Fourier domain OCT RTVue (Optovue Inc, CA, EE. UU.) was used to examine the iridocorneal angle in the nasal and temporal sectors. The structures evaluated were: Sclerocorneal limbus, sclerocorneal transition, Schwalbe's line, trabecular meshwork, Schlemm's canal, scleral spur, and angular recess. Within and between agreements to identify structures were calculated using Cohen's kappa coefficient. The mean age was 41.3 ± 14.3 years (range 20-80), with 57% being women. The sclerocorneal limbus, sclerocorneal transition, and Schwalbe's line were identified by 98.7, 97 and 93.4% of the images, respectively, with the trabecular meshwork and Schlemm's canal being identified in 91% of cases. The scleral spur could be identified in 85.4%, and the angular recess in 74.5%. There was no difference in the identification between the temporal and nasal sectors. Within and between agreement was k=0.92 and k=0.88, respectively, in the identification of the structures of the total images studied. Fourier domain OCT is a reliable technique for the identification of the structures of the iridocorneal angle, among which can be highlighted are, the trabecular meshwork, Schlemm's canal, scleral spur, and Schwalbe's line. Copyright © 2015 Sociedad Española de Oftalmología. Published by Elsevier España, S.L.U. All rights reserved.
Rugged optical mirrors for the operation of Fourier-Transform Spectrometers in rough environments
Feist, Dietrich G.
2014-05-01
The Total Carbon Column Observing Network (TCCON) and the Network for the Detection of Atmospheric Composition Change (NDACC) operate a growing number of Fourier-Transform Spectrometers (FTS) that measure the total column of several atmospheric trace gases. For these measurements, the sun is used as a light source. This is typically achieved by a solar tracker that uses a pair of optical mirrors to guide the sunlight into the instrument. There is a growing demand to operate these instruments in remote locations that fill the gaps in the global observation network. Besides the logistical challenges of running a remote site, the environment at these locations can be very harsh compared to the sheltered environment of the instruments' home institutions. While the FTS itself is usually well protected inside a building or container, the solar tracker and especially its mirrors are exposed to the environment. There they may suffer from - temperature fluctuations - high humidity - sea salt corrosion at coastal sites - dirt and dust - air pollution from anthropogenic sources - deposition from plants or animals The Max Planck Institute for Biogeochemistry (MPI-BGC) operates a TCCON station on Ascension Island, about 200 m from the sea. Under the rough conditions at this site, typical optical mirrors that are made for laboratory conditions are destroyed by sea salt spray within a few weeks. Besides, typical gold-coated mirrors cannot be cleaned as their soft surface is easily scratched or damaged. To overcome these problems, the MPI-BGC has developed optical mirrors that - offer good reflectivity in the near and mid infrared - are highly resistant to salt and chlorine - have a hard surface so that they can be cleaned often and easily - are not affected by organic solvents - last for months in very harsh environments - can be reused after polishing These mirrors could be applied to most TCCON and NDACC sites. This way, the network could be expanded to regions where operation
Matrix formalism for light propagation and absorption in thick textured optical sheets.
Eisenlohr, Johannes; Tucher, Nico; Höhn, Oliver; Hauser, Hubert; Peters, Marius; Kiefel, Peter; Goldschmidt, Jan Christoph; Bläsi, Benedikt
2015-06-01
In this paper, we introduce a simulation formalism for determining the Optical Properties of Textured Optical Sheets (OPTOS). Our matrix-based method allows for the computationally-efficient calculation of non-coherent light propagation and absorption in thick textured sheets, especially solar cells, featuring different textures on front and rear side that may operate in different optical regimes. Within the simulated system, the angular power distribution is represented by a vector. This light distribution is modified by interaction with the surfaces of the textured sheets, which are described by redistribution matrices. These matrices can be calculated for each individual surface texture with the most appropriate technique. Depending on the feature size of the texture, for example, either ray- or wave-optical methods can be used. The comparison of the simulated absorption in a sheet of silicon for a variety of surface textures, both with the results from other simulation techniques and experimentally measured data, shows very good agreement. To demonstrate the versatility of this newly-developed approach, the absorption in silicon sheets with a large-scale structure (V-grooves) at the front side and a small-scale structure (diffraction grating) at the rear side is calculated. Moreover, with minimal computational effort, a thickness parameter variation is performed.
Directory of Open Access Journals (Sweden)
Saban Gonul
2014-12-01
Full Text Available Purpose: To compare the results of central corneal thickness (CCT measurements obtained using optical low-coherence reflectometry (OLCR, Fourier domain optical coherence tomography (FD-OCT, and a Scheimpflug camera (SC, combined with Placido corneal topography. Methods: A total of 25 healthy subjects were enrolled in the present study, and one eye of each subject was included. A detailed ophthalmic examination was performed in all cases following CCT measurements with OLCR, FD-OCT, and SC. The results were compared using an ANOVA test. Bland-Altman analysis was used to demonstrate agreement between methods. Intra-examiner repeatability was assessed by using intraclass correlation coefficients (ICCs. Results: Statistically significant differences were observed between the results of the CCT measurements obtained using the three different devices (p=0.009. Significant correlations were found between OLCR and FD-OCT (r=0.97; p0.98. Conclusion: Although the results of CCT measurements obtained from these three devices were highly correlated with one another and the mean differences between instruments were comparable with the reported diurnal CCT fluctuation, the measurements are not directly interchangeable in clinical practice because of the wide LOA values.
Wang, Xiaogang; Zhao, Daomu
2013-09-01
A nonlinear color and grayscale images cryptosystem based on phase-truncated fractional Fourier transform and optical superposition principle is proposed. In order to realize simultaneous encryption of color and grayscale images, each grayscale image is first converted into two phase masks by using an optical coherent superposition, one of which is treated as a part of input information that will be fractional Fourier transformed while the other in the form of a chaotic random phase mask (CRPM) is used as a decryption key. For the purpose of optical performance, all the processes are performed through three channels, i.e., red, green, and blue. Different from most asymmetric encryption methods, the decryption process is designed to be linear for the sake of effective decryption. The encryption level of a double random phase encryption based on phase-truncated Fourier transform is enhanced by extending it into fractional Fourier domain and the load of the keys management and transmission is lightened by using CRPMs. The security of the proposed cryptosystem is discussed and computer simulation results are presented to verify the validity of the proposed method.
Odinokov, Sergey; Zlokazov, Evgenii; Donchenko, Sergey; Verenikina, Nina
2017-09-01
The present article highlights the development results of archive memory holographic system based on application of computer generated Fourier holograms. The proposed idea allows realization of holographic principles of digital data record using simple and compact optical devices. Special interest is paid to synthesis and multiplexed record of one-dimensional Fourier transform holograms. The principal schemes of constructed prototypes of incoherent data recorder and coherent data reader are described in the present paper. The results of experimental implementation of the constructed devices are presented.
Foltynowicz, Aleksandra; Rutkowski, Lucile; Johanssson, Alexandra C.; Khodabakhsh, Amir; Maslowski, Piotr; Kowzan, Grzegorz; Lee, Kevin; Fermann, Martin
2015-06-01
Fourier transform spectrometers (FTS) based on optical frequency combs (OFC) allow detection of broadband molecular spectra with high signal-to-noise ratios within acquisition times orders of magnitude shorter than traditional FTIRs based on thermal sources. Due to the pulsed nature of OFCs the interferogram consists of a series of bursts rather than a single burst at zero optical path difference (OPD). The comb mode structure can be resolved by acquiring multiple bursts, in both mechanical FTS systems and dual-comb spectroscopy. However, in all existing demonstrations the resolution was ultimately limited either by the maximum available OPD between the interferometer arms or by the total acquisition time enabled by the storage memory. We present a method that provides spectral resolution exceeding the limit set by the maximum OPD using an interferogram containing only a single burst. The method allows measurements of absorption lines narrower than the OPD-limited resolution without any influence of the instrumental lineshape function. We demonstrate this by measuring undistorted CO2 and CO absorption lines with linewidth narrower than the OPD-limited resolution using OFC-based mechanical FTS in the near- and mid-infrared wavelength ranges. The near-infrared system is based on an Er:fiber femtosecond laser locked to a high finesse cavity, while the mid-infrared system is based on a Tm:fiber-laser-pumped optical parametric oscillator coupled to a multi-pass cell. We show that the method allows acquisition of high-resolution molecular spectra with interferometer length orders of magnitude shorter than traditional FTIR. Mandon, J., G. Guelachvili, and N. Picque, Nat. Phot., 2009. 3(2): p. 99-102. Zeitouny, M., et al., Ann. Phys., 2013. 525(6): p. 437-442. Zolot, A.M., et al., Opt. Lett., 2012. 37(4): p. 638-640.
Directory of Open Access Journals (Sweden)
Arash Hanifi
Full Text Available Hyaline cartilage and mechanically inferior fibrocartilage consisting of mixed collagen types are frequently found together in repairing articular cartilage. The present study seeks to develop methodology to identify collagen type and other tissue components using Fourier transform infrared (FTIR spectral evaluation of matrix composition in combination with multivariate analyses. FTIR spectra of the primary molecular components of repair cartilage, types I and II collagen, and aggrecan, were used to develop multivariate spectral models for discrimination of the matrix components of the tissues of interest. Infrared imaging data were collected from bovine bone, tendon, normal cartilage, meniscus and human repair cartilage tissues, and composition predicted using partial least squares analyses. Histology and immunohistochemistry results were used as standards for validation. Infrared fiber optic probe spectral data were also obtained from meniscus (a tissue with mixed collagen types to evaluate the potential of this method for identification of collagen type in a minimally-invasive clinical application. Concentration profiles of the tissue components obtained from multivariate analysis were in excellent agreement with histology and immunohistochemistry results. Bone and tendon showed a uniform distribution of predominantly type I collagen through the tissue. Normal cartilage showed a distribution of type II collagen and proteoglycan similar to the known composition, while in repair cartilage, the spectral distribution of both types I and II collagen were similar to that observed via immunohistochemistry. Using the probe, the outer and inner regions of the meniscus were shown to be primarily composed of type I and II collagen, respectively, in accordance with immunohistochemistry data. In summary, multivariate analysis of infrared spectra can indeed be used to differentiate collagen type I and type II, even in the presence of proteoglycan, in
Directory of Open Access Journals (Sweden)
Ricardo J. Cumba
2012-01-01
Full Text Available Purpose. To evaluate intraobserver and interobserver agreement in locating the scleral spur landmark (SSL and anterior chamber angle measurements obtained using Fourier Domain Anterior Segment Optical Coherence Tomography (ASOCT images. Methods. Two independent, masked observers (SR and AZC identified SSLs on ASOCT images from 31 eyes with open and nonopen angles. A third independent reader, NPB, adjudicated SSL placement if identifications differed by more than 80 μm. Nine months later, SR reidentified SSLs. Intraobserver and interobserver agreement in SSL placement, trabecular-iris space area (TISA750, and angle opening distance (AOD750 were calculated. Results. In 84% of quadrants, SR’s SSL placements during 2 sessions were within 80 μm in both the X- and Y-axes, and in 77% of quadrants, SR and AZC were within 80 μm in both axes. In adjudicated images, 90% of all quadrants were within 80 μm, 88% in nonopen-angle eyes, and 92% in open-angle eyes. The intraobserver and interobserver correlation coefficients (with and without adjudication were above 0.9 for TISA750 and AOD750 for all quadrants. Conclusions. Reproducible identification of the SSL from images obtained with FD-ASOCT is possible. The ability to identify the SSL allows reproducible measurement of the anterior chamber angle using TISA750 and AOD750.
Directory of Open Access Journals (Sweden)
Mohammed Rigi
2016-01-01
Full Text Available Purpose. To evaluate interobserver, intervisit, and interinstrument agreements for gonioscopy and Fourier domain anterior segment optical coherence tomography (FD ASOCT for classifying open and narrow angle eyes. Methods. Eighty-six eyes with open or narrow anterior chamber angles were included. The superior angle was classified open or narrow by 2 of 5 glaucoma specialists using gonioscopy and imaged by FD ASOCT in the dark. The superior angle of each FD ASOCT image was graded as open or narrow by 2 masked readers. The same procedures were repeated within 6 months. Kappas for interobserver and intervisit agreements for each instrument and interinstrument agreements were calculated. Results. The mean age was 50.9 (±18.4 years. Interobserver agreements were moderate to good for both gonioscopy (0.57 and 0.69 and FD ASOCT (0.58 and 0.75. Intervisit agreements were moderate to excellent for both gonioscopy (0.53 to 0.86 and FD ASOCT (0.57 and 0.85. Interinstrument agreements were fair to good (0.34 to 0.63, with FD ASOCT classifying more angles as narrow than gonioscopy. Conclusions. Both gonioscopy and FD ASOCT examiners were internally consistent with similar interobserver and intervisit agreements for angle classification. Agreement between instruments was fair to good, with FD ASOCT classifying more angles as narrow than gonioscopy.
Li, Jian; Bloch, Pavel; Xu, Jing; Sarunic, Marinko V; Shannon, Lesley
2011-05-01
Fourier domain optical coherence tomography (FD-OCT) provides faster line rates, better resolution, and higher sensitivity for noninvasive, in vivo biomedical imaging compared to traditional time domain OCT (TD-OCT). However, because the signal processing for FD-OCT is computationally intensive, real-time FD-OCT applications demand powerful computing platforms to deliver acceptable performance. Graphics processing units (GPUs) have been used as coprocessors to accelerate FD-OCT by leveraging their relatively simple programming model to exploit thread-level parallelism. Unfortunately, GPUs do not "share" memory with their host processors, requiring additional data transfers between the GPU and CPU. In this paper, we implement a complete FD-OCT accelerator on a consumer grade GPU/CPU platform. Our data acquisition system uses spectrometer-based detection and a dual-arm interferometer topology with numerical dispersion compensation for retinal imaging. We demonstrate that the maximum line rate is dictated by the memory transfer time and not the processing time due to the GPU platform's memory model. Finally, we discuss how the performance trends of GPU-based accelerators compare to the expected future requirements of FD-OCT data rates.
Huang, Yong; Tong, Dedi; Zhu, Shan; Wu, Lehao; Ibrahim, Zuhaib; Lee, WP Andrew; Brandacher, Gerald; Kang, Jin U.
2014-03-01
Vascular and microvascular anastomosis are critical components of reconstructive microsurgery, vascular surgery and transplant surgery. Imaging modality that provides immediate, real-time in-depth view and 3D structure and flow information of the surgical site can be a great valuable tool for the surgeon to evaluate surgical outcome following both conventional and innovative anastomosis techniques, thus potentially increase the surgical success rate. Microvascular anastomosis for vessels with outer diameter smaller than 1.0 mm is extremely challenging and effective evaluation of the outcome is very difficult if not impossible using computed tomography (CT) angiograms, magnetic resonance (MR) angiograms and ultrasound Doppler. Optical coherence tomography (OCT) is a non-invasive high-resolution (micron level), high-speed, 3D imaging modality that has been adopted widely in biomedical and clinical applications. Phaseresolved Doppler OCT that explores the phase information of OCT signals has been shown to be capable of characterizing dynamic blood flow clinically. In this work, we explore the capability of Fourier domain Doppler OCT as an evaluation tool to detect commonly encountered post-operative complications that will cause surgical failure and to confirm positive result with surgeon's observation. Both suture and cuff based techniques were evaluated on the femoral artery and vein in the rodent model.
Rigorous simulations of a helical core fiber by the use of transformation optics formalism.
Napiorkowski, Maciej; Urbanczyk, Waclaw
2014-09-22
We report for the first time on rigorous numerical simulations of a helical-core fiber by using a full vectorial method based on the transformation optics formalism. We modeled the dependence of circular birefringence of the fundamental mode on the helix pitch and analyzed the effect of a birefringence increase caused by the mode displacement induced by a core twist. Furthermore, we analyzed the complex field evolution versus the helix pitch in the first order modes, including polarization and intensity distribution. Finally, we show that the use of the rigorous vectorial method allows to better predict the confinement loss of the guided modes compared to approximate methods based on equivalent in-plane bending models.
Weatherbee, Andrew; Sugita, Mitsuro; Bizheva, Kostadinka; Popov, Ivan; Vitkin, Alex
2016-06-15
The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optical coherence tomography (OCT). It is shown that for low scatterer density, the governing statistics depart considerably from a Gaussian description and follow the K distribution for both OCT amplitude and intensity. The PDF formalism is shown to be independent of the scatterer flow conditions; this is expected from theory, and suggests robustness and motion independence of the OCT amplitude (and OCT intensity) PDF metrics in the context of potential biomedical applications.
Yang, J; Chan, E H W; Wang, X; Feng, X; Guan, B
2015-05-04
An all-optical photonic microwave phase shifter that can realize a continuous 360° phase shift over a wide frequency range is presented. It is based on the new concept of controlling the amplitude and phase of the two RF modulation sidebands via a Fourier-domain optical processor. The operating frequency range of the phase shifter is largely increased compared to the previously reported Fourier-domain optical processor based phase shifter that uses only one RF modulation sideband. This is due to the extension of the lower RF operating frequency by designing the amplitude and phase of one of the RF modulation sidebands while the other sideband is designed to realize the required RF signal phase shift. The two-sideband amplitude-and-phase-control based photonic microwave phase shifter has a simple structure as it only requires a single laser source, a phase modulator, a Fourier-domain optical processor and a single photodetector. Investigation on the bandwidth limitation problem in the conventional Fourier-domain optical processor based phase shifter is presented. Comparisons between the measured phase shifter output RF amplitude and phase responses with theory, which show excellent agreement, are also presented for the first time. Experimental results demonstrate the full -180° to + 180° phase shift with little RF signal amplitude variation of less than 3 dB and with a phase deviation of less than 4° over a 7.5 GHz to 26.5 GHz frequency range, and the phase shifter exhibits a long term stable performance.
DEFF Research Database (Denmark)
Guan, Pengyu; Mulvad, Hans Christian Hansen; Tomiyama, Yutaro
2011-01-01
developed an ultrafast timedomain optical Fourier transformation technique in a round-trip configuration. By applying this technique to subpicosecond pulses, transmission impairments were greatly reduced, and BER performance below FEC limit was obtained with increased system margin. Copyright © 2011...
Gan, Haiyong; Xu, Nan; Li, Jianwei; Xu, Tao; Wang, Yanping; Sun, Zhixu; Ma, Chong; Wang, Jinjin; Song, Feng; Sun, Ming; Li, Li; Sheng, Chuanxiang
2015-02-09
Self-diffraction can be induced using a biased photorefractive crystal in the Fourier plane of an imaging system where the light beam intensity is naturally high due to the concentration effect of an optical lens. The spatial frequency spectrum of the output image is proportional to the optical power density distribution in the Fourier plane. A photorefractive crystal with small size can be used and hence an reduced amount of biased voltage is needed to obtain significant diffraction effect in the image plane. When the input image is an overlay of a signal and a noise pattern, theoretic model reveals that the induced diffraction in the Fourier plane may be preferably applied on the noise pattern. In order to illustrate the effect experimentally, a signal from a weakly illuminated object is coupled with an overwhelming noise pattern and then the hidden signal is successfully recovered using a SBN61 crystal with an applied voltage of 800 V in the Fourier plane. Such technology can be employed in encrypted spatial communication systems for security purposes.
Polisetty, S.; Scheffler, J.; Sahoo, S.; Wang, Yi; Mukherjee, T.; He, Xi; Binek, Ch.
2008-05-01
We present a comparative study on an experimental and theoretical optimization of magneto-optical Kerr setups based on photoelastic modulation and phase sensitive detector methodology. The first and second harmonics, Iω ,2ω, of the reflected light intensity are measured for a CoO /Co magnetic reference film. The magnetic field dependence of the optical off-diagonal Fresnel reflection coefficients rps and rsp follows the sample magnetization. Different Kerr setups provide various dependencies of Iω ,2ω on the reflection coefficients and, hence, on the Kerr ellipticity ɛK and rotation θK. Jones matrix formalism has been used to analyze the impact of a systematic variation of relative analyzer and polarizer orientations with respect to each other and with respect to the retardation axis of the modulator involved in longitudinal Kerr setups for incoming s-polarized light. We find one particular setup which maximizes Iω as well as I2ω and maximizes the signal-to-noise ratio. Inefficient setups are characterized by Iω ,2ω intensities involving large nonmagnetic contributions of rp and rs.
Polisetty, S; Scheffler, J; Sahoo, S; Wang, Yi; Mukherjee, T; He, Xi; Binek, Ch
2008-05-01
We present a comparative study on an experimental and theoretical optimization of magneto-optical Kerr setups based on photoelastic modulation and phase sensitive detector methodology. The first and second harmonics, I omega,2 omega, of the reflected light intensity are measured for a CoO/Co magnetic reference film. The magnetic field dependence of the optical off-diagonal Fresnel reflection coefficients rps and rsp follows the sample magnetization. Different Kerr setups provide various dependencies of I omega,2 omega on the reflection coefficients and, hence, on the Kerr ellipticity epsilon K and rotation theta K. Jones matrix formalism has been used to analyze the impact of a systematic variation of relative analyzer and polarizer orientations with respect to each other and with respect to the retardation axis of the modulator involved in longitudinal Kerr setups for incoming s-polarized light. We find one particular setup which maximizes I(omega) as well as I2 omega and maximizes the signal-to-noise ratio. Inefficient setups are characterized by I omega,2 omega intensities involving large nonmagnetic contributions of rp and rs.
3D optical simulation formalism OPTOS for textured silicon solar cells.
Tucher, Nico; Eisenlohr, Johannes; Kiefel, Peter; Höhn, Oliver; Hauser, Hubert; Peters, Marius; Müller, Claas; Goldschmidt, Jan Christoph; Bläsi, Benedikt
2015-11-30
In this paper we introduce the three-dimensional formulation of the OPTOS formalism, a matrix-based method that allows for the efficient simulation of non-coherent light propagation and absorption in thick textured sheets. As application examples, we calculate the absorptance of solar cells featuring textures on front and rear side with different feature sizes operating in different optical regimes. A discretization of polar and azimuth angle enables a three-dimensional description of systems with arbitrary surface textures. We present redistribution matrices for 3D surface textures, including pyramidal textures, binary crossed gratings and a Lambertian scatterer. The results of the OPTOS simulations for silicon sheets with different combinations of these surfaces are in accordance with both optical measurements and results based on established simulation methods like ray tracing. Using OPTOS, we show that the integration of a diffractive grating at the rear side of a silicon solar cell featuring a pyramidal front side results in absorption close to the Yablonovitch Limit enhancing the photocurrent density by 0.6 mA/cm2 for a 200 µm thick cell.
Directory of Open Access Journals (Sweden)
Yong Huang
Full Text Available To demonstrate the feasibility of a miniature handheld optical coherence tomography (OCT imager for real time intraoperative vascular patency evaluation in the setting of super-microsurgical vessel anastomosis.A novel handheld imager Fourier domain Doppler optical coherence tomography based on a 1.3-µm central wavelength swept source for extravascular imaging was developed. The imager was minimized through the adoption of a 2.4-mm diameter microelectromechanical systems (MEMS scanning mirror, additionally a 12.7-mm diameter lens system was designed and combined with the MEMS mirror to achieve a small form factor that optimize functionality as a handheld extravascular OCT imager. To evaluate in-vivo applicability, super-microsurgical vessel anastomosis was performed in a mouse femoral vessel cut and repair model employing conventional interrupted suture technique as well as a novel non-suture cuff technique. Vascular anastomosis patency after clinically successful repair was evaluated using the novel handheld OCT imager.With an adjustable lateral image field of view up to 1.5 mm by 1.5 mm, high-resolution simultaneous structural and flow imaging of the blood vessels were successfully acquired for BALB/C mouse after orthotopic hind limb transplantation using a non-suture cuff technique and BALB/C mouse after femoral artery anastomosis using a suture technique. We experimentally quantify the axial and lateral resolution of the OCT to be 12.6 µm in air and 17.5 µm respectively. The OCT has a sensitivity of 84 dB and sensitivity roll-off of 5.7 dB/mm over an imaging range of 5 mm. Imaging with a frame rate of 36 Hz for an image size of 1000(lateral×512(axial pixels using a 50,000 A-lines per second swept source was achieved. Quantitative vessel lumen patency, lumen narrowing and thrombosis analysis were performed based on acquired structure and Doppler images.A miniature handheld OCT imager that can be used for intraoperative evaluation of
Gu, Ying
In this dissertation, Green's-function formalism (GFF) is developed to deal with the optical responses of arbitrary-shaped metallic clusters embedded in the infinite dielectric networks in the quasistatic limit. By the formalism, the resonance spectrum and the local field distribution for each eigenmode can be analytically obtained. We use the simple examples to describe the inhomogeneous local field in space around the metallic clusters due to the quasistatic resonance, which will be shown to give a large enhancement in the effective linear and nonlinear responses. Then, the GFF is applied to two systems. First, the optical responses of the dilute anisotropic networks are investigated for various applied fields, parallel or perpendicular to the direction of anisotropy. The large third order nonlinear enhancements are found to arise from the geometric anisotropy. The peaks of absorption and nonlinear enhancement overlap when the applied field is parallel to the anisotropy. In contrast, the absorption peak is separated from the nonlinear enhancement peak when the applied field is perpendicular to the anisotropy. In terms of the distribution of inverse participation ratios (IPR) with q = 2 and of the spectral density of linear and nonlinear optical responses, the above results can be understood. Secondly, the optical responses of two interacting clusters in composites are studied. The GFF of two clusters with central symmetry is derived. Compared with the optical responses of the isolated cluster, the red shifts and blue shifts occur, respectively, when the applied field is parallel and perpendicular to the central line of two clusters. We can explain these shifts completely by means of the local field distribution of two interacting single bonds. Finally, the statistics of the level spacing of resonance (or eigenvalues) and of the right eigenvectors of the Green's-matrix M of GFF is studied from the random matrix theory (RMT) for the disordered binary composites. In
DEFF Research Database (Denmark)
Palushani, Evarist; Mulvad, Hans Christian Hansen; Galili, Michael
2012-01-01
a dispersive medium followed by phase modulation; the latter being achieved by a four-wave mixing process with linearly chirped pump pulses. Both numerical and experimental investigations of the OTDM-to-WDM conversion technique are carried out. Experimental validations are performed on......This paper reports on the utilization of the timedomain optical Fourier transformation (OFT) technique for serial-to-parallel conversion of optical time division multiplexed (OTDM) data tributaries into dense wavelength division multiplexed (DWDM) channels. The OFT is implemented by using...
Fatome, Julien; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe
2016-04-01
Versatile and easy to implement methods to generate arbitrary optical waveforms at high repetition rates are of considerable interest with applications in optical communications, all-optical signal processing, instrumentation systems and microwave signal manipulation. While shaping sinusoidal, Gaussian or hyperbolic secant intensity profiles is commonly achieved by means of modulators or mode-locked lasers, other pulse profiles such as parabolic, triangular or flat-top shapes still remain challenging to synthesize. In this context, several strategies were already explored. First, the linear pulse shaping is a common method to carve an initial ultrashort pulse train into the desired shape. The line-by-line shaping of a coherent frequency comb made of tens of spectral components was also investigated to generate more complex structures whereas Fourier synthesis of a few discrete frequencies spectrum was exploited to efficiently generate high-fidelity ultrafast periodic intensity profiles. Besides linear shaping techniques, several nonlinear methods were implemented to benefit from the adiabatic evolution of the intensity pulse profile upon propagation in optical fibers. Other examples of efficient methods are based on the photonic generation involving specific Mach-Zehnder modulators, microwave photonic filters as well as frequency-to-time conversion. In this contribution, we theoretically and experimentally demonstrate a new approach enabling the synthesis of periodic high-repetition rate pulses with various intensity profiles ranging from parabola to triangular and flat-top pulses. More precisely by linear phase and amplitude shaping of only four spectral lines is it possible to reach the targeted temporal profile. Indeed, tailoring the input symmetric spectrum only requires the determination of two physical parameters: the phase difference between the inner and outer spectral sidebands and the ratio between the amplitude of these sidebands. Therefore, a systematic
Cheng, Mengfan; Deng, Lei; Li, Hao; Liu, Deming
2014-03-10
We propose a scheme whereby a time domain fractional Fourier transform (FRFT) is used to post process the optical chaotic carrier generated by an electro-optic oscillator. The time delay signature of the delay dynamics is successfully masked by the FRFT when some conditions are satisfied. Meanwhile the dimension space of the physical parameters is increased. Pseudo random binary sequence (PRBS) with low bit rate (hundreds of Mbps) is introduced to control the parameters of the FRFT. The chaotic optical carrier, FRFT parameters and the PRBS are covered by each other so that the eavesdropper has to search the whole key space to crack the system. The scheme allows enhancing the security of communication systems based on delay dynamics without modifying the chaotic source. In this way, the design of chaos based communication systems can be implemented in a modular manner.
Probing the dispersion properties of 1D nanophotonic waveguides with far-field Fourier optics
DEFF Research Database (Denmark)
Le Thomas, N.; Jágerská, J.; Houdré, R.
2008-01-01
We present an advanced Fourier space imaging technique to probe guided light in nanophotonic structures with an effective numerical aperture of 2.5. This superresolution technique allows us to successfully investigate the dispersive properties of 1D nanowaveguides such as photonic crystal W1...
Steiner, Patrick; Meier, Christoph; Koch, Volker M
2010-12-20
We demonstrate depth-resolved spectral absorption measurements in the wavelength range from 750 to 850 nm using a broadband light source consisting of three spectrally shifted superluminescent light-emitting diode modules and a low-cost spectrometer-based Fourier-domain optical coherence tomography system. We present the theoretical model and experimental verification of interferences between autocorrelation terms and the signal carrying cross-correlation terms, strongly affecting the absorption measurements. A simple background subtraction, minimizing the artifacts caused by the interferences of autocorrelation and cross-correlation terms, is presented.
Watanabe, Ryosuke; Yamaguchi, Kazuhiro; Sakamoto, Yuji
2016-01-20
Computer generated hologram (CGH) animations can be made by switching many CGHs on an electronic display. Some fast calculation methods for CGH animations have been proposed, but one for viewpoint movement has not been proposed. Therefore, we designed a fast calculation method of CGH animations for viewpoint parallel shifts and rotation. A Fourier transform optical system was adopted to expand the viewing angle. The results of experiments were that the calculation time of our method was over 6 times faster than that of the conventional method. Furthermore, the degradation in CGH animation quality was found to be sufficiently small.
Xu, Daguang; Huang, Yong; Kang, Jin U
2014-06-16
We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).
Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain
Liu, Xingbin; Mei, Wenbo; Du, Huiqian
2014-11-01
We propose a novel image encryption algorithm based on compressive sensing (CS) and chaos in the fractional Fourier domain. The original image is dimensionality reduction measured using CS. The measured values are then encrypted using chaotic-based double-random-phase encoding technique in the fractional Fourier transform domain. The measurement matrix and the random-phase masks used in the encryption process are formed from pseudo-random sequences generated by the chaotic map. In this proposed algorithm, the final result is compressed and encrypted. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys for distribution simultaneously. Numerical experiments verify the validity and security of the proposed algorithm.
SnO2-MOF-Fabry-Perot humidity optical sensor system based on fast Fourier transform technique
Lopez-Aldaba, A.; Lopez-Torres, D.; Ascorbe, J.; Rota-Rodrigo, S.; Elosua, C.; Lopez-Amo, M.; Arregui, F. J.; Corres, J. M.; Auguste, J.-L.; Jamier, R.; Roy, P.
2016-05-01
In this paper, a new sensor system for relative humidity measurements based on a SnO2 sputtering deposition on a microstructured optical fiber (MOF) low-finesse Fabry-Perot (FP) sensing head is presented and characterized. The interrogation of the sensing head is carried out by monitoring the Fast Fourier Transform phase variations of the FP interference frequency. This method is low-sensitive to signal amplitude variations and also avoids the necessity of tracking the evolution of peaks and valleys in the spectrum. The sensor is operated within a wide humidity range (20%-90% relative humidity) with a maximum sensitivity achieved of 0.14rad/%. The measurement method uses a commercial optical interrogator as the only active element, this compact solution allows real time analysis of the data.
Granieri, S; Del Carmen Lasprilla, M; Bolognini, N; Sicre, E E
1996-12-10
A space-variant optical correlator is proposed on the basis of the fractional Fourier transform. The optical device uses as a recording medium for the holographic filter a photorefractive Bi(12)GeO(2) (BGO) crystal. The experimental results confirm the shift-variance properties. Some limitations that arise from the volume diffraction are also considered.
Analyzing Fourier Transforms for NASA DFRC's Fiber Optic Strain Sensing System
Fiechtner, Kaitlyn Leann
2010-01-01
This document provides a basic overview of the fiber optic technology used for sensing stress, strain, and temperature. Also, the document summarizes the research concerning speed and accuracy of the possible mathematical algorithms that can be used for NASA DFRC's Fiber Optic Strain Sensing (FOSS) system.
Fourier's law on a one-dimensional optical random lattice
Energy Technology Data Exchange (ETDEWEB)
Platini, T [Department of Physics, Virginia Tech, Blacksburg, VA 24061 (United States); Harris, R J [School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom); Karevski, D [Institut Jean Lamour, Departement Physique de la Matiere et des Materiaux, Groupe de Physique Statistique, Nancy-Universite CNRS, BP 70239, F-54506 Vandoeuvre les Nancy Cedex (France)
2010-04-02
We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary-state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law j = -{kappa}({tau}){nabla}n where {tau} is a typical timescale of the lattice fluctuations and {nabla}n is the density gradient imposed by the reservoirs.
Pasternack, Robert M; Qian, Zhen; Zheng, Jing-Yi; Metaxas, Dimitris N; Boustany, Nada N
2009-07-06
We use optical Gabor-like filtering implemented with a digital micromirror device to achieve nanoscale sensitivity to changes in the size of finite and periodic objects imaged at low resolution. The method consists of applying an optical Fourier filter bank consisting of Gabor-like filters of varying periods and extracting the optimum filter period that maximizes the filtered object signal. Using this optimum filter period as a measure of object size, we show sensitivity to a 7.5 nm change in the period of a chirped phase mask with period around 1 microm. We also show 30 nm sensitivity to change in the size of polystyrene spheres with diameters around 500 nm. Unlike digital post-processing our optical processing method retains its sensitivity when implemented at low magnification in undersampled images. Furthermore, the optimum Gabor filter period found experimentally is linearly related to sphere diameter over the range 0.46 microm-1 microm and does not rely on a predictive scatter model such as Mie theory. The technique may have applications in high throughput optical analysis of subcellular morphology to study organelle function in living cells.
Huang, Yong; Zhang, Kang; Kang, Jin U.; Calogero, Don; James, Robert H.; Ilev, Ilko K.
2011-12-01
We propose a novel common-path Fourier domain optical coherence tomography (CP-FD-OCT) method for noncontact, accurate, and objective in vitro measurement of the dioptric power of intraocular lenses (IOLs) implants. The CP-FD-OCT method principle of operation is based on simple two-dimensional scanning common-path Fourier domain optical coherence tomography. By reconstructing the anterior and posterior IOL surfaces, the radii of the two surfaces, and thus the IOL dioptric power are determined. The CP-FD-OCT design provides high accuracy of IOL surface reconstruction. The axial position detection accuracy is calibrated at 1.22 μm in balanced saline solution used for simulation of in situ conditions. The lateral sampling rate is controlled by the step size of linear scanning systems. IOL samples with labeled dioptric power in the low-power (5D), mid-power (20D and 22D), and high-power (36D) ranges under in situ conditions are tested. We obtained a mean power of 4.95/20.11/22.09/36.25 D with high levels of repeatability estimated by a standard deviation of 0.10/0.18/0.2/0.58 D and a relative error of 2/0.9/0.9/1.6%, based on five measurements for each IOL respectively. The new CP-FD-OCT method provides an independent source of IOL power measurement data as well as information for evaluating other optical properties of IOLs such as refractive index, central thickness, and aberrations.
Silberman, Donn M.
2014-09-01
For the July 2013 issue of SPIE Professional Magazine, I was invited to and published an article related to this topic. This paper chronicles the progress made since that time and describes our direction towards bringing optics education from the informal programs we have provided for more than 10 years, to incorporating optics and photonics instruction into formal class curriculum. A major educational tool we are using was introduced at this conference two years ago and came to us from Eyestvzw. The Photonics Explorer Kit has been used as a foundation during some OptoBotics courses and it has been provided, a long with a teacher training session, to 10 local high school science teachers in Orange County, CA. The goal of this first phase is to obtain feedback from the teachers as they use the materials in their formal classroom settings and after-school activities; such as science classes and robotics club activities. Results of the teachers' initial feedback will be reviewed and future directions outlined. One clear direction is to understand the changes that will be required to the kits to formally gain acceptance as part of the California state high school science curriculum. Another is to use the Photonics Explorer kits (and other similar tools) to teach students in robotics clubs `how to give their robots eyes."
Leclerc, Arnaud
2015-01-01
A global solution of the Schr\\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is proposed in which, however, numerous integrals over time have to be evaluated. This internal work is done using a numerical integrator based on Fast Fourier Transforms (FFT). The case of a transition between two potential wells of a model molecule driven by intense laser pulses is used as an illustrative example. This application reveals some interesting features of the integration technique. Each iteration provides a global approximate solution on grid points regularly distributed over the full time propagation interval. Inside the convergence radius, the complete integration is competitive with standard algorithms, especially when high accuracy is required.
Institute of Scientific and Technical Information of China (English)
Chen Bao-Xin
2006-01-01
An elliptical Gaussian wave formalism model of a charged-particle beam is proposed by analogy with an elliptical Gaussian light beam.In the paraxial approximation.the charged-particle beam can be described as a whole by a complex radius of curvature in the real space domains.Therefore,the propagation and transform of charged-particle beam passing through a first-order optical system is represented by the ABCD-like law.As an example of the application of this model,the relation between the beam waist and the minimum beam spot at a fixed target is discussed.The result.well matches that from conventional phase space model,and proves that the Gaussian wave formalism model is highly effective and reasonable.
Montejo, Ludguier D.; Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2013-03-01
We apply the Fourier Transform to absorption and scattering coefficient images of proximal interphalangeal (PIP) joints and evaluate the performance of these coefficients as classifiers using receiver operator characteristic (ROC) curve analysis. We find 25 features that yield a Youden index over 0.7, 3 features that yield a Youden index over 0.8, and 1 feature that yields a Youden index over 0.9 (90.0% sensitivity and 100% specificity). In general, scattering coefficient images yield better one-dimensional classifiers compared to absorption coefficient images. Using features derived from scattering coefficient images we obtain an average Youden index of 0.58 +/- 0.16, and an average Youden index of 0.45 +/- 0.15 when using features from absorption coefficient images.
Rajput, Sudheesh K.; Nishchal, Naveen K.
2017-04-01
We propose a novel security scheme based on the double random phase fractional domain encoding (DRPE) and modified Gerchberg-Saxton (G-S) phase retrieval algorithm for securing two images simultaneously. Any one of the images to be encrypted is converted into a phase-only image using modified G-S algorithm and this function is used as a key for encrypting another image. The original images are retrieved employing the concept of known-plaintext attack and following the DRPE decryption steps with all correct keys. The proposed scheme is also used for encryption of two color images with the help of convolution theorem and phase-truncated fractional Fourier transform. With some modification, the scheme is extended for simultaneous encryption of gray-scale and color images. As a proof-of-concept, simulation results have been presented for securing two gray-scale images, two color images, and simultaneous gray-scale and color images.
Bagnaninchi, Pierre O
2010-04-01
To assess non-invasively and in real time the three- dimensional organization of cells within porous matrices by combining Fourier Domain Optical Coherence Tomography (FDOCT) and Impedance Spectroscopy (IS). Broadband interferences resulting from the recombination of in-depth light scattering events within the sample and light from a reference arm are measured as a modulation of the spectrum generated by a superluminescent laser diode (lambdao = 930nm, FWHM 90nm). Fourier transform allows in-depth localization of the scatterers, and the 3D microstructure of the sample is reconstructed by raster scanning. Simultaneously impedance spectroscopy is performed with a dielectric probe connected to an impedance analyzer to gather additional cellular information, and synchronized with FDOCT measurements. A combined IS-FDOCT system allowing an axial resolution of 5 micrometer in tissues and impedance measurements over the range 20MHz-1GHz has been developed. Alginate matrices have been characterized in terms of microstructure and impedance. Matrices seeded with adipose-derived stem cells have been monitored without the use of labeling agent. We have developed a multimodality system that will be instrumental to non-invasively monitor changes in total cell volume fraction and infer cell-specific dielectric properties in 3D structure.
Takasago, K; Takekawa, M; Shirakawa, A; Kannari, F
2000-05-10
A new, to our knowledge, space-variant optical interconnection system based on a spatial-phase code-division multiple-access technique with multiplexed Fourier holography is described. In this technique a signal beam is spread over wide spatial frequencies by an M-sequence pseudorandom phase code. At a receiver side a selected signal beam is properly decoded, and at the same time its spatial pattern is shaped with a Fourier hologram, which is recorded by light that is encoded with the same M-sequence phase mask as the desired signal beam and by light whose spatial beam pattern is shaped to a signal routing pattern. Using the multiplexed holography, we can simultaneously route multisignal flows into individually specified receiver elements. The routing pattern can also be varied by means of switching the encoding phase code or replacing the hologram. We demonstrated a proof-of-principle experiment with a doubly multiplexed hologram that enables simultaneous routing of two signal beams. Using a numerical model, we showed that the proposed scheme can manage more than 250 routing patterns for one signal flow with one multiplexed hologram at a signal-to-noise ratio of ~5.
Hermerschmidt, Andreas
2009-06-01
In close collaboration with four German universities, we have developed tutorials for experiments based on a transmissive liquid-crystal spatial light modulator (SLM). The experimental tutorials are grouped in six project modules, which cover a wide range of phenomena and have different levels of difficulty. At a basic level, students can investigate the SLM in its probably most well-known application as an image-generating element in a simple optical projector setup. At more advanced levels, the application as an adaptive optical element can be investigated in three different projects covering wave-optical phenomena. The fields covered include Fourier Optics using the SLM as a dynamic fan-out beam-splitter or kinoform, Computer-Generated Holography and basic Interferometry. For the support of these projects, software was developed which permits the generation of adaptive optical structures by the student with a user-friendly interface, while the underlying algorithms are explained in the theoretical tutorial. The modulation of the light by the twisted-neumatic liquid crystal cells of the SLM can be investigated in the two most advanced projects. In the first one, the parameters of the cell and the components of its Jones matrix can be derived from transmission measurements with rotatable polarizers at a number of different wavelengths. This project gives insight to the Jones matrix calculus at the level required for the analysis. In the second one, the complex-valued transmission of the SLM is determined by measuring the diffraction efficiency of dynamically addressed Ronchi gratings.
Optical-Path-Difference Linear Mechanism for the Panchromatic Fourier Transform Spectrometer
Blavier, Jean-Francois L.; Heverly, Matthew C.; Key, Richard W.; Sander, Stanley P.
2011-01-01
A document discusses a mechanism that uses flex-pivots in a parallelogram arrangement to provide frictionless motion with an unlimited lifetime. A voicecoil actuator drives the parallelogram over the required 5-cm travel. An optical position sensor provides feedback for a servo loop that keeps the velocity within 1 percent of expected value. Residual tip/tilt error is compensated for by a piezo actuator that drives the interferometer mirror. This mechanism builds on previous work that targeted ground-based measurements. The main novelty aspects include cryogenic and vacuum operation, high reliability for spaceflight, compactness of the design, optical layout compatible with the needs of an imaging FTS (i.e. wide overall field-of-view), and mirror optical coatings to cover very broad wavelength range (i.e., 0.26 to 15 m).
Peterseim, Tobias; Dressel, Martin
2017-01-01
The time-dependent optical properties of molecular systems are investigated by step-scan Fourier-transform spectroscopy in order to explore the dynamics at phase transitions and molecular orientation in the milli- and microsecond range. The electrical switching of liquid crystals traced by vibrational spectroscopy reveals a rotation of the molecules with a relaxation time of 2 ms. The photo-induced neutral-ionic transition in TTF-CA takes place by a suppression of the dimerization in the ionic phase and creation of neutral domains. The time-dependent infrared spectra, employed to investigate the domain-wall dynamics, depend on temperature and laser pulse intensity; the relaxation of the spectra follows a stretched-exponential decay with relaxation times in the microsecond range strongly dependent on temperature and laser intensity. We present all details of the experimental setups and thoroughly discuss the technical challenges.
Chen, Yu; Leach, Franklin E; Kaiser, Nathan K; Dang, Xibei; Ibrahim, Yehia M; Norheim, Randolph V; Anderson, Gordon A; Smith, Richard D; Marshall, Alan G
2015-01-01
Enhancements to the ion source and transfer optics of our 9.4 T Fourier transform ion cyclotron resonance (ICR) mass spectrometer have resulted in improved ion transmission efficiency for more sensitive mass measurement of complex mixtures at the MS and MS/MS levels. The tube lens/skimmer has been replaced by a dual ion funnel and the following octopole by a quadrupole for reduced ion cloud radial expansion before transmission into a mass-selective quadrupole. The number of ions that reach the ICR cell is increased by an order of magnitude for the funnel/quadrupole relative to the tube lens/skimmer/octopole. Copyright © 2015 John Wiley & Sons, Ltd.
Peterseim, Tobias; Dressel, Martin
2016-06-01
The time-dependent optical properties of molecular systems are investigated by step-scan Fourier-transform spectroscopy in order to explore the dynamics at phase transitions and molecular orientation in the milli- and microsecond range. The electrical switching of liquid crystals traced by vibrational spectroscopy reveals a rotation of the molecules with a relaxation time of 2 ms. The photo-induced neutral-ionic transition in TTF-CA takes place by a suppression of the dimerization in the ionic phase and creation of neutral domains. The time-dependent infrared spectra, employed to investigate the domain-wall dynamics, depend on temperature and laser pulse intensity; the relaxation of the spectra follows a stretched-exponential decay with relaxation times in the microsecond range strongly dependent on temperature and laser intensity. We present all details of the experimental setups and thoroughly discuss the technical challenges.
DEFF Research Database (Denmark)
Guan, P.; Mulvad, Hans Christian Hansen; Tomiyama, Y.;
2010-01-01
A single-channel 1.28 Tbit/s transmission over 525 km is demonstrated for the first time with a single-polarization DQPSK signal. Ultrafast time-domain optical Fourier transformation is successfully applied to DQPSK signals and results in improved performance and increased system margin.......A single-channel 1.28 Tbit/s transmission over 525 km is demonstrated for the first time with a single-polarization DQPSK signal. Ultrafast time-domain optical Fourier transformation is successfully applied to DQPSK signals and results in improved performance and increased system margin....
Doppler Fourier Domain Optical Coherence Tomography for Label-Free Tissue Angiography
Leitgeb, Rainer A.; Szkulmowski, Maciej; Blatter, Cedric; Wojtkowski, Maciej
Information about tissue perfusion and the vascular structure is certainly most important for assessment of tissue state or personal health and the diagnosis of any pathological conditions. It is therefore of key medical interest to have tools available for both quantitative blood flow assessment as well as qualitative vascular imaging. The strength of optical techniques is the unprecedented level of detail even for small capillary structures or microaneurysms and the possibility to combine different techniques for additional tissue spectroscopy giving insight into tissue metabolism. There is an immediate diagnostic and pharmacological demand for high-resolution, label-free, tissue angiography and flow assessment that in addition allow for precise depth gating of flow information. The most promising candidate is Doppler optical coherence tomography (DOCT) being noncontact, label free, and without employing hazardous radiation. DOCT provides fully quantitative volumetric information about blood flow together with the vascular and structural anatomy. Besides flow quantification, analysis of OCT signal fluctuations allows to contrast moving scatterers in tissue such as red blood cells from static tissue. This allows for non-invasive optical angiography and yields high resolution even for smallest capillaries. Because of the huge potential of DOCT and lable-free optical angiography for diagnosis, the last years saw a rapid increase of publications in this field with many different approaches. The present chapter gives an overview over existing Doppler OCT approaches and angiography techniques. It furthermore discusses limitations and noise issues, and gives examples for angiography in the eye and the skin.
Narayanamurthy, C. S.
2009-01-01
Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in "Principles of Optics" by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer…
Rogers, P D; Sirenko, A A
2011-01-01
Using 4x4 matrix formalism we analyzed electromagnetic wave propagation and Jones matrix components for reflectivity and transmittivity in bi-anisotropic materials. Analytic formulas for complex reflection and transmission coefficients for bi-anisotropic materials in both semi-infinite and thin-film configurations have been derived. The obtained results are applicable for analysis of the optical spectra of multiferroic crystals and metamaterials. The Adjusted Oscillator Strength Matching Condition (AOSM) for hybrid magnetic- and electric-dipole excitations in anisotropic multiferroics is derived for oblique angles of incidence. Mueller Matrices are used to simulate spectra of magneto-electric and chiral excitations and methods to distinguish them are discussed.
Fourier transform infrared (FTIR) fiber optic monitoring of composites during cure in an autoclave
Druy, Mark A.; Elandjian, Lucy; Stevenson, William A.; Driver, Richard D.; Leskowitz, Garett M.
1990-01-01
Real-time in situ monitoring of the chemical states of epoxy resins was investigated during cure in an autoclave using infrared evanescent spectroscopy. Fiber evanescent sensors were developed which may be sandwiched between the plies of the prepreg sample. A short length of sapphire fiber was used as the sensor cell portion of the fiber probe. Heavy metal fluoride glass optical fiber cables were designed for connecting the FTIR spectrometer to the sensor fiber within the autoclave. The sapphire fibers have outstanding mechanical thermal properties which should permit their use as an embedded link in all thermoset composites. The system is capable of operation at a temperature of 250 C for periods up to 8 hours without major changes to the fiber transmission. A discussion of the selection of suitable sensor fibers, the construction of a fiber-optic interface, and the interpretation of in situ infrared spectra of the curing process is presented.
Real-time all-optical OFDM transmission system based on time-domain optical fourier transformation
DEFF Research Database (Denmark)
Guan, Pengyu; Kong, Deming; Røge, Kasper Meldgaard
2014-01-01
We propose a novel simple all-optical OFDM transmission system based on time-domain OFT using time-lenses. A real-time 160 Gbit/s DPSK OFDM transmission with 16 decorrelated data subcarriers is successfully demonstrated over 100 km.......We propose a novel simple all-optical OFDM transmission system based on time-domain OFT using time-lenses. A real-time 160 Gbit/s DPSK OFDM transmission with 16 decorrelated data subcarriers is successfully demonstrated over 100 km....
Deparis, Olivier
2011-10-15
In spite of the fact that solutions to Maxwell's equations in stratified isotropic optical media are well known, it appears that an explicit expression of the Poynting vector flux spatial evolution inside such a medium has not been derived so far. Based on exact electromagnetic field solutions in the transfer-matrix formalism, I derive such an expression and show that, due to the presence of counterpropagating waves in the medium, an additional contribution to the flux appears that exists only in optically absorbing layers and arises from the interference between these waves. Based on this theory, the concept of incremental absorption is introduced for the calculation of the light absorption profile along the stratification direction. As an illustration of this concept, absorption profiles in a Si-based thin-film tandem solar cell are predicted at typical wavelengths.
Bradu, Adrian; Marques, Manuel J.; Bouchal, Petr; Podoleanu, Adrian Gh.
2013-03-01
The purpose of this study was to show how to favorably mix two e_ects to improve the sensitivity with depth in Fourier domain optical coherence tomography (OCT): Talbot bands (TB) and Gabor-based fusion (GF) technique. TB operation is achieved by directing the two beams, from the object arm and from the reference arm in the OCT interferometer, along parallel separate paths towards the spectrometer. By changing the lateral gap between the two beams in their path towards the spectrometer, the position for the maximum sensitivity versus the optical path difference in the interferometer is adjusted. For five values of the focus position, the gap between the two beams is readjusted to reach maximum sensitivity. Then, similar to the procedure employed in the GF technique, a composite image is formed by edging together the parts of the five images that exhibited maximum brightness. The combined procedure, TB/GF is examined for four different values of the beam diameters of the two beams. Also we demonstrate volumetric FD-OCT images with mirror term attenuation and sensitivity profile shifted towards higher OPD values by applying a Talbot bands configuration.
In vivo sweat film layer thickness measured with Fourier-domain optical coherence tomography
CSIR Research Space (South Africa)
Jonathan, E
2008-01-01
Full Text Available and pore can be located. In addition, other measure- ments of interest, for example, thickness of the SCL, diameter of an open sweat pore or depth position of DEJ can be performed. References [1] Weller AS. Body temperature and its regulation. Physiol... of tissue microstructure is achieved from operating in the optical low-coherence interferometry domain. 1. Introduction Sweat secretion in humans is accepted as a mechanism by which the body cools off [1,2]. Interest in sweat secretion in humans’ dates...
Werkmeister, René M.; Vietauer, Martin; Knopf, Corinna; Fürnsinn, Clemens; Leitgeb, Rainer A.; Reitsamer, Herbert; Gröschl, Martin; Garhöfer, Gerhard; Vilser, Walthard; Schmetterer, Leopold
2014-10-01
A wide variety of ocular diseases are associated with abnormalities in ocular circulation. As such, there is considerable interest in techniques for quantifying retinal blood flow, among which Doppler optical coherence tomography (OCT) may be the most promising. We present an approach to measure retinal blood flow in the rat using a new optical system that combines the measurement of blood flow velocities via Doppler Fourier-domain optical coherence tomography and the measurement of vessel diameters using a fundus camera-based technique. Relying on fundus images for extraction of retinal vessel diameters instead of OCT images improves the reliability of the technique. The system was operated with an 841-nm superluminescent diode and a charge-coupled device camera that could be operated at a line rate of 20 kHz. We show that the system is capable of quantifying the response of 100% oxygen breathing on the retinal blood flow. In six rats, we observed a decrease in retinal vessel diameters of 13.2% and a decrease in retinal blood velocity of 42.6%, leading to a decrease in retinal blood flow of 56.7%. Furthermore, in four rats, the response of retinal blood flow during stimulation with diffuse flicker light was assessed. Retinal vessel diameter and blood velocity increased by 3.4% and 28.1%, respectively, leading to a relative increase in blood flow of 36.2%;. The presented technique shows much promise to quantify early changes in retinal blood flow during provocation with various stimuli in rodent models of ocular diseases in rats.
Optical double image encryption employing a pseudo image technique in the Fourier domain
Guo, Changliang; Liu, Shi; Sheridan, John T.
2014-06-01
A novel optical encryption method is proposed involving double image encryption in which one image is introduced as the pseudo image while the other is the original object image. The Double Random Phase Encoding technique is used to encrypt both the pseudo and object images into complex images. A unique binary image is then employed to first generate the random phase key for the object image encryption and then to embed the encrypted object image into the encrypted pseudo image, which acts as host image. Both the second random phase mask used for encoding the pseudo image and the binary image act as encryption keys. If an attacker attempts to crack the random phase key and decrypt the original object image, the pseudo image will be obtained instead. Simulation results and robustness tests are performed which demonstrate the feasibility of the algorithm.
López-Miguel, Alberto; Calabuig-Goena, María; Marqués-Fernández, Victoria; Fernández, Itziar; Alió, Jorge L; Maldonado, Miguel J
2016-11-04
To assess the reliability of corneal epithelial thickness (CET), nonepithelial central corneal thickness (NECCT), and central corneal thickness (CCT) measurements using Cirrus high-definition optical coherence tomography (HD-OCT) in patients who did and did not undergo cataract surgery. Forty patients who underwent uneventful phacoemulsification and 40 healthy participants were recruited to evaluate the intraobserver repeatability and interobserver reproducibility of CET, NECCT, and CCT measurements using Cirrus HD-OCT. To analyze repeatability, one examiner obtained 5 consecutive scans in each participant; for interobserver reproducibility, another examiner randomly obtained another scan. Within-subject standard deviation, coefficient of variation (CV), limits of agreement, and intraclass correlation coefficient (ICC) data were obtained. For intraobserver repeatability, the intrasession CV (CVw) and ICC values of the CET in the operated and nonoperated groups were 3.7% and 0.80 and 3.8% and 0.73, respectively; for NECCT, 0.7% and 0.98 and 0.8% and 0.97; and for CCT, 0.6% and 0.99 and 0.7% and 0.98. For interobserver reproducibility, the CVw and ICC values for the CET in the operated and nonoperated groups were 2.6% and 0.82 and 2.3% and 0.62, respectively; for NECCT, 0.7% and 0.98 and 0.5% and 0.98; and for CCT, 0.5% and 0.99 and 0.4% and 0.99. The corneal sublayer thickness can be measured reliably using Cirrus HD-OCT in patients who underwent cataract surgery and elderly participants; however, the CET consistency is poorer than the NECCT. Corneal epithelial thickness modifications exceeding 4% reflect true thickness changes instead of random error variations using HD-OCT.
Real-time 3D Fourier-domain optical coherence tomography guided microvascular anastomosis
Huang, Yong; Ibrahim, Zuhaib; Lee, W. P. A.; Brandacher, Gerald; Kang, Jin U.
2013-03-01
Vascular and microvascular anastomosis is considered to be the foundation of plastic and reconstructive surgery, hand surgery, transplant surgery, vascular surgery and cardiac surgery. In the last two decades innovative techniques, such as vascular coupling devices, thermo-reversible poloxamers and suture-less cuff have been introduced. Intra-operative surgical guidance using a surgical imaging modality that provides in-depth view and 3D imaging can improve outcome following both conventional and innovative anastomosis techniques. Optical coherence tomography (OCT) is a noninvasive high-resolution (micron level), high-speed, 3D imaging modality that has been adopted widely in biomedical and clinical applications. In this work we performed a proof-of-concept evaluation study of OCT as an assisted intraoperative and post-operative imaging modality for microvascular anastomosis of rodent femoral vessels. The OCT imaging modality provided lateral resolution of 12 μm and 3.0 μm axial resolution in air and 0.27 volume/s imaging speed, which could provide the surgeon with clearly visualized vessel lumen wall and suture needle position relative to the vessel during intraoperative imaging. Graphics processing unit (GPU) accelerated phase-resolved Doppler OCT (PRDOCT) imaging of the surgical site was performed as a post-operative evaluation of the anastomosed vessels and to visualize the blood flow and thrombus formation. This information could help surgeons improve surgical precision in this highly challenging anastomosis of rodent vessels with diameter less than 0.5 mm. Our imaging modality could not only detect accidental suture through the back wall of lumen but also promptly diagnose and predict thrombosis immediately after reperfusion. Hence, real-time OCT can assist in decision-making process intra-operatively and avoid post-operative complications.
Directory of Open Access Journals (Sweden)
Tong Lin
2015-01-01
Full Text Available Dry eye is highly prevalent and has a significant impact on quality of life. Acupuncture was found to be effective to treat dry eye. However, little was known about the effect of acupuncture on different subtypes of dry eye. The objective of this study was to investigate the applicability of tear meniscus assessment by Fourier-domain optical coherence tomography in the evaluation of acupuncture treatment response in dry eye patients and to explore the effect of acupuncture on different subtypes of dry eye compared with artificial tear treatment. A total of 108 dry eye patients were randomized into acupuncture or artificial tear group. Each group was divided into three subgroups including lipid tear deficiency (LTD, Sjögren syndrome dry eye (SSDE, and non-Sjögren syndrome dry eye (Non-SSDE for data analysis. After 4-week treatment, the low tear meniscus parameters including tear meniscus height (TMH, tear meniscus depth (TMD, and tear meniscus area (TMA in the acupuncture group increased significantly for the LTD and Non-SSDE subgroups compared with both the baseline and the control groups (all P values < 0.05, but not for the SSDE. Acupuncture provided a measurable improvement of the tear meniscus dimensions for the Non-SSDE and LTD patients, but not for the SSDE patients.
Iizuka, Masayuki; Kariya, Makoto; Uehara, Shinobu; Nakashima, Yoshio; Takamatsu, Mamoru
2003-05-01
A blue white He-Cd laser composed of three R/G/B component beams in place of He-Ne laser is directly applied to fabricate the optical Fourier transform hologram (OFTH) using the red sensitive silver halide material (SO-253 film) for holography. As a result, the red beams play an important role as the coherent beams in the fabrication of OFTH. A green solid state laser is applied to fabricate the OFTH using the same film for holography. The visual appearance of reconstruted color images caused by He-Cd laser is discussed in contrast to that of an ordinary OFTH which can be made using the He-Ne laser and solid state laser. The visual color effect using the He-Cd laser is checked from the viewpoint of the relative real size and its place in the OFTH, and the visual depth sensation of overlapped ghost images called cross-talk in the Fresnel hologram. The purpose using a commercially available software such as HSL color model is to carry out the intuitive modification of overlapped and deteriorated color images in the digital reconstruction of OFTH and Fresnel hologram.
Directory of Open Access Journals (Sweden)
S. Catalan
2016-01-01
Full Text Available Purpose. To compare the characteristics of asymmetric keratoconic eyes and normal eyes by Fourier domain optical coherence tomography (OCT corneal mapping. Methods. Retrospective corneal and epithelial thickness OCT data for 74 patients were compared in three groups of eyes: keratoconic (n=22 and normal fellow eyes (n=22 in patients with asymmetric keratoconus and normal eyes (n=104 in healthy subjects. Areas under the curve (AUC of receiver operator characteristic (ROC curves for each variable were compared across groups to indicate their discrimination capacity. Results. Three variables were found to differ significantly between fellow eyes and normal eyes (all p<0.05: minimum corneal thickness, thinnest corneal point, and central corneal thickness. These variables combined showed a high discrimination power to differentiate fellow eyes from normal eyes indicated by an AUC of 0.840 (95% CI: 0.762–0.918. Conclusions. Our findings indicate that topographically normal fellow eyes in patients with very asymmetric keratoconus differ from the eyes of healthy individuals in terms of their corneal epithelial and pachymetry maps. This type of information could be useful for an early diagnosis of keratoconus in topographically normal eyes.
Fourier transform and Vernier spectroscopy using an optical frequency comb at 3-5.4 μm.
Khodabakhsh, Amir; Ramaiah-Badarla, Venkata; Rutkowski, Lucile; Johansson, Alexandra C; Lee, Kevin F; Jiang, Jie; Mohr, Christian; Fermann, Martin E; Foltynowicz, Aleksandra
2016-06-01
We present a versatile mid-infrared frequency comb spectroscopy system based on a doubly resonant optical parametric oscillator tunable in the 3-5.4 μm range and two detection methods: a Fourier transform spectrometer (FTS) and a continuous-filtering Vernier spectrometer (CF-VS). Using the FTS with a multipass cell, we measure high precision broadband absorption spectra of CH4 at 3.3 μm and NO at 5.25 μm, the latter for the first time with comb spectroscopy, and we detect atmospheric species (CH4, CO, CO2, and H2O) in air in the signal and idler ranges. Multiline fitting yields minimum detectable concentrations of 10-20 ppb Hz-1/2 for CH4, NO, and CO. For the first time in the mid-infrared, we perform CF-VS using an enhancement cavity, a grating, and a single detector, and we measure the absorption spectrum of CH4 and H2O in ambient air at ∼3.3 μm, reaching a 40 ppb concentration detection limit for CH4 in 2 ms.
Fourier transform and Vernier spectroscopy using an optical frequency comb at 3-54 μm
Khodabakhsh, Amir; Ramaiah-Badarla, Venkata; Rutkowski, Lucile; Johansson, Alexandra C.; Lee, Kevin F.; Jiang, Jie; Mohr, Christian; Fermann, Martin E.; Foltynowicz, Aleksandra
2016-06-01
We present a versatile mid-infrared frequency comb spectroscopy system based on a doubly resonant optical parametric oscillator tunable in the 3-5.4 {\\mu}m range and two detection methods, a Fourier transform spectrometer (FTS) and a Vernier spectrometer. Using the FTS with a multipass cell we measure high-precision broadband absorption spectra of CH$_4$ and NO at ~3.3 {\\mu}m and ~5.2 {\\mu}m, respectively, and of atmospheric species (CH$_4$, CO, CO$_2$ and H$_2$O) in air in the signal and idler wavelength range. The figure of merit of the system is on the order of 10$^{-8}$ cm$^{-1}$ Hz$^{-1/2}$ per spectral element, and multiline fitting yields minimum detectable concentrations of 10-20 ppb Hz$^{-1/2}$ for CH$_4$, NO and CO. For the first time in the mid-infrared, we perform continuous-filtering Vernier spectroscopy using a low finesse enhancement cavity, a grating and a single detector, and measure the absorption spectrum of CH$_4$ and H$_2$O in ambient air at ~3.3 {\\mu}m.
Miliani, C; Rosi, F; Borgia, I; Benedetti, P; Brunetti, B G; Sgamellotti, A
2007-03-01
A prototypical in situ noninvasive study of ancient mural painting materials has been carried out using an easily manageable fiber-optic Fourier transform mid-infrared (mid-FT-IR) reflectance spectrophotometer. The reported object of the study is the Renaissance fresco by Pietro Vannucci, called il Perugino, located in the church of Santa Maria delle Lacrime (1521, Trevi, Perugia Italy). For the first classification and interpretation of infrared spectra, principal components analysis was used. Spectral artifacts due to lacunas, restoration materials, or alteration products have been identified, as well as two different secco refinements bound in a tempera medium. For the characterization of inorganic pigments, mid-FT-IR spectra have been integrated with other data obtained through in situ X-ray fluorescence (XRF) elemental analysis. This complementary noninvasive approach led to the characterization of Perugino's pigments, even in the presence of complex mixtures. The mid-FT-IR noninvasive technique, in combination with XRF, is thus recommended as a valuable first approach for the examination of mural paintings, permitting the assessment of the execution technique as well as contributing to the evaluation of the conservation state.
Modeling cavities exhibiting strong lateral confinement using open geometry Fourier modal method
DEFF Research Database (Denmark)
Häyrynen, Teppo; Gregersen, Niels
2016-01-01
We have developed a computationally eﬃcient Fourier-Bessel expansion based open geometry formalism for modeling the optical properties of rotationally symmetric photonic nanostructures. The lateral computation domain is assumed inﬁnite so that no artiﬁcial boundary conditions are needed. Instead...
Nan, Nan; Bu, Peng; Guo, Xin; Wang, Xiangzhao
2012-03-01
A three dimensional full-range complex Fourier domain optical coherence tomography (complex FDOCT) system based on sinusoidal phase-modulating method is proposed. With the system, the range of imaging depth is doubled and the sensitivity degradation with the lateral scan distance is avoided. Fourier analysis of B-scan data along lateral scan distance is used for reconstructing the complex spectral interferograms. The B-scan based Fourier method improves the system tolerance of sample movement and makes data processing less time consuming. In vivo volumetric imaging of human skin with the proposed full-range FDOCT system is demonstrated. The mirror image rejection ratio is about 30 dB. The stratum corneum, the epidermis and the upper dermis of skin can be clearly identified in the reconstructed three dimensional FDOCT images.
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Quantum-optical states in finite-dimensional Hilbert space; 1, General formalism
Miranowicz, A; Imoto, N; Miranowicz, Adam; Leonski, Wieslaw; Imoto, Nobuyuki
2001-01-01
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation and measurement techniques, in particular, by the development of the discrete quantum-state tomography. In the first part of our review we present two essentially different approaches to define harmonic oscillator states in the finite-dimensional Hilbert spaces. One of them is related to the truncation scheme of Pegg, Phillips and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The second method corresponds to the truncation scheme of Leo\\'nski and Tana\\'s [Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states related to these truncation schemes and find their explicit forms in the Fock representation. We discuss finite-dimensional generalizations of coherent states, phase coherent states, displaced number states, Schr\\"odinger cats, and squeezed vacuum. We show some i...
Directory of Open Access Journals (Sweden)
Lucas Barasnevicius Quagliato
2014-08-01
Full Text Available Purpose: The goal of this cross-sectional observational study was to quantify the pattern-shift visual evoked potentials (VEP and the thickness as well as the volume of retinal layers using optical coherence tomography (OCT across a cohort of Parkinson's disease (PD patients and age-matched controls. Methods: Forty-three PD patients and 38 controls were enrolled. All participants underwent a detailed neurological and ophthalmologic evaluation. Idiopathic PD cases were included. Cases with glaucoma or increased intra-ocular pressure were excluded. Patients were assessed by VEP and high-resolution Fourier-domain OCT, which quantified the inner and outer thicknesses of the retinal layers. VEP latencies and the thicknesses of the retinal layers were the main outcome measures. Results: The mean age, with standard deviation (SD, of the PD patients and controls were 63.1 (7.5 and 62.4 (7.2 years, respectively. The patients were predominantly in the initial Hoehn-Yahr (HY disease stages (34.8% in stage 1 or 1.5, and 55.8 % in stage 2. The VEP latencies and the thicknesses as well as the volumes of the retinal inner and outer layers of the groups were similar. A negative correlation between the retinal thickness and the age was noted in both groups. The thickness of the retinal nerve fibre layer (RNFL was 102.7 μm in PD patients vs. 104.2 μm in controls. Conclusions: The thicknesses of retinal layers, VEP, and RNFL of PD patients were similar to those of the controls. Despite the use of a representative cohort of PD patients and high-resolution OCT in this study, further studies are required to establish the validity of using OCT and VEP measurements as the anatomic and functional biomarkers for the evaluation of retinal and visual pathways in PD patients.
Chen, Junyi; Huang, Haili; Zhang, Shenghai; Chen, Xueli; Sun, Xinghuai
2013-02-07
To determine the effect of travoprost 0.004% on Schlemm's canal (SC) in healthy human eyes using Fourier-domain optical coherence tomography (FD-OCT). Twelve healthy volunteers were recruited for a double-blind, placebo-controlled, randomized, and paired comparison study. Right eyes of subjects were randomly assigned to receive either travoprost 0.004% or placebo; the contralateral eye received the other treatment. FD-OCT imaging of SC and measurements of IOP were carried out before and at 1, 2, 4, 6, 8, 12, 24, 36, 48, 60, 72, and 84 hours after eye drop instillation. After instillation of travoprost eye drops, IOP gradually reduced, and the SC lumens expanded, while those values remained unchanged in placebo treated eyes. At 8 hours after the travoprost administration, the mean SC area increased 90.30% and 90.20%, respectively, in the nasal and temporal quadrant of the treated eyes as compared with the placebo group. The SC area and IOP showed a similar pattern of changes at most time points examined. In travoprost-treated eyes, a statistically significant correlation between SC area and IOP is observed (r = -0.2817; P = 0.0004). Measurements of the SC area showed sufficient repeatability and reproducibility. SC can be noninvasively imaged and quantitatively assessed in the living healthy human eye by FD-OCT. Travoprost treatment leads to SC lumen expansion accompanied by a drop of IOP in the healthy eye, likely as a result of the enhancement of pressure sensitive trabecular meshwork outflow induced by travoprost.
Stade, Eric
2005-01-01
A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of ap
Watanabe, Yuuki; Maeno, Seiya; Aoshima, Kenji; Hasegawa, Haruyuki; Koseki, Hitoshi
2010-09-01
The real-time display of full-range, 2048?axial pixelx1024?lateral pixel, Fourier-domain optical-coherence tomography (FD-OCT) images is demonstrated. The required speed was achieved by using dual graphic processing units (GPUs) with many stream processors to realize highly parallel processing. We used a zero-filling technique, including a forward Fourier transform, a zero padding to increase the axial data-array size to 8192, an inverse-Fourier transform back to the spectral domain, a linear interpolation from wavelength to wavenumber, a lateral Hilbert transform to obtain the complex spectrum, a Fourier transform to obtain the axial profiles, and a log scaling. The data-transfer time of the frame grabber was 15.73?ms, and the processing time, which includes the data transfer between the GPU memory and the host computer, was 14.75?ms, for a total time shorter than the 36.70?ms frame-interval time using a line-scan CCD camera operated at 27.9?kHz. That is, our OCT system achieved a processed-image display rate of 27.23 frames/s.
Scarfone, A. M.
2017-08-01
We present a new formulation of Fourier transform in the picture of the κ-algebra derived in the framework of the κ-generalized statistical mechanics. The κ-Fourier transform is obtained from a κ-Fourier series recently introduced by Scarfone (2013). The kernel of this transform, that reduces to the usual exponential phase in the κ → 0 limit, is composed by a κ-deformed phase and a damping factor that gives a wavelet-like behaviour. We show that the κ-Fourier transform is isomorph to the standard Fourier transform through a changing of time and frequency variables. Nevertheless, the new formalism is useful to study, according to Fourier analysis, those functions defined in the realm of the κ-algebra. As a relevant application, we discuss the central limit theorem for the κ-sum of n-iterate statistically independent random variables.
Hwang, Jungseek
2013-07-24
We propose a possible way to simulate a hump structure in the optical scattering rate. The optical scattering rate of correlated charge carriers can be defined within an extended Drude model formalism. When some electron- and hole-doped copper oxide systems are in spin density or charge density wave phases they show hump structures in their optical scattering rates. The hump structures have not yet been simulated or clearly understood. We are able to simulate the hump structure by using a peak followed by a dip feature in the normalized density of states within a generalized Allen formalism. We observe that reversing the order of the dip and peak gives completely different features in the optical scattering rate; a peak-dip (dip-peak) results in a hump (a valley) in the scattering rate. We also obtain the real parts of the optical conductivity and reflectance spectra from the simulated optical scattering rate and compare them with published experimental spectra. From these comparisons we conclude that the peak-dip order can give the hump structure that is observed experimentally in copper oxide systems. Finally we fit two published optical spectra with our new model and discuss our results and the possible origin of the dip or peak features in the normalized density of states.
Energy Technology Data Exchange (ETDEWEB)
Ramamoorthy, Sripriya [Oregon Hearing Research Center, Oregon Health & Science University, Portland, Oregon (United States); Zhang, Yuan; Jacques, Steven [Department of Biomedical Engineering, Oregon Health & Science University, Portland, Oregon (United States); Petrie, Tracy; Wang, Ruikang [Department of Bioengineering, University of Washington, Seattle, Washington (United States); Nuttall, Alfred L. [Oregon Hearing Research Center, Oregon Health & Science University, Portland, Oregon (United States); Kresge Hearing Research Institute, The University of Michigan, Ann Arbor, Michigan (United States)
2015-12-31
In this study, we have developed a phase-sensitive Fourier-domain optical coherence tomography system to simultaneously measure the in vivo inner ear vibrations in the hook area and second turn of the mouse cochlea. This technical development will enable measurement of intra-cochlear distortion products at ideal locations such as the distortion product generation site and reflection site. This information is necessary to un-mix the complex mixture of intra-cochlear waves comprising the DPOAE and thus leads to the non-invasive identification of the local region of cochlear damage.
Perston, Benjamin B; Hamilton, Michelle L; Williamson, Bryce E; Harland, Peter W; Thomson, Mary A; Melling, Peter J
2007-02-01
Fourier transform infrared reflection-absorption spectroscopy has been used with a fiber-optic grazing-angle reflectance probe as a rapid, in situ method for trace surface analysis of acetaminophen and aspirin at loadings of approximately 0-2 microg cm(-2) on glass. Partial least-squares multivariate regression permits the loadings to be quantified, simultaneously, with root-mean-squared errors of prediction of RMSEP approximately 0.1 microg cm(-2) for both compounds. The detection limits are estimated to be LD approximately 0.2 microg cm(-2).
Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Jacques, Steven; Wang, Ruikang; Nuttall, Alfred L.
2015-12-01
In this study, we have developed a phase-sensitive Fourier-domain optical coherence tomography system to simultaneously measure the in vivo inner ear vibrations in the hook area and second turn of the mouse cochlea. This technical development will enable measurement of intra-cochlear distortion products at ideal locations such as the distortion product generation site and reflection site. This information is necessary to un-mix the complex mixture of intra-cochlear waves comprising the DPOAE and thus leads to the non-invasive identification of the local region of cochlear damage.
Cheng, Kyle H Y; Standish, Beau A; Yang, Victor X D; Cheung, K K Y; Gu, Xijia; Lam, Edmund Y; Wong, K K Y
2010-02-01
We report the first Fourier domain modelocked (FDML) laser constructed using optical parametric amplifier (OPA) in conjunction with an erbium-doped fiber amplifier (EDFA), centered at approximately 1555 nm, to the best of our knowledge. We utilize a one-pump OPA and a C-band EDFA in serial configuration with a tunable Fabry-Perot interferometer to generate a hybrid FDML spectrum. Results demonstrate a substantially better spectral shape, output power and stability than individual configurations, with decreased sensitivity to polarization changes. We believe this technique has the potential to enable several amplifiers to complement individual deficiencies resulting in improved spectral shapes and power generation for imaging applications such as optical coherence tomography (OCT).
Su, Yonggang; Tang, Chen; Li, Biyuan; Chen, Xia; Xu, Wenjun; Cai, Yuanxue
2017-01-20
We propose an optical color image encryption system based on the single-lens Fourier transform, the Fresnel transform, and the chaotic random phase masks (CRPMs). The proposed encryption system contains only one optical lens, which makes it more efficient and concise to implement. The introduction of the Fresnel transform makes the first phase mask of the proposed system also act as the main secret key when the input image is a non-negative amplitude-only map. The two CRPMs generated by dual two-dimensional chaotic maps can provide more security to the proposed system. In the proposed system, the key management is more convenient and the transmission volume is reduced greatly. In addition, the secret keys can be updated conveniently in each encryption process to invalidate the chosen plaintext attack and the known plaintext attack. Numerical simulation results have demonstrated the feasibility and security of the proposed encryption system.
Krylov, Piotr
2017-01-01
This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a sol...
García-Muñoz, Víctor; Preciado, Miguel A; Muriel, Miguel A
2007-08-20
We propose an all-fiber method for the generation of ultrafast shaped pulse train bursts from a single pulse based on Fourier Series Developments (FDSs). The implementation of the FSD based filter only requires the use of a very simple non apodized Superimposed Fiber Bragg Grating (S-FBG) for the generation of the Shaped Output Pulse Train Burst (SOPTB). In this approach, the shape, the period and the temporal length of the generated SOPTB have no dependency on the input pulse rate.
Underwood, Kenneth J; Jones, Andrew M; Gopinath, Juliet T
2015-06-20
We present a new application of the stochastic parallel gradient descent (SPGD) algorithm to fast active phase control in a Fourier synthesis system. Pulses (4.9 ns) with an 80 MHz repetition rate are generated by feedback from a single phase-sensitive metric. Phase control is applied via fast current modulation of a tapered amplifier using an SPGD algorithm realized on a field-programmable gate array (FPGA). The waveforms are maintained by constant active feedback from the FPGA. We also discuss the extension of this technique to many more semiconductor laser emitters in a diode laser array.
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
Energy Technology Data Exchange (ETDEWEB)
Layton, E.G. (Joint Inst. for Lab. Astrophysics, Boulder, CO (United States)); Stade, E. (Colorado Univ., Boulder, CO (United States). Dept. of Mathematics)
1993-08-28
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author).
Watanabe, Yuuki
2012-05-01
The author presents a graphics processing unit (GPU) programming for real-time Fourier domain optical coherence tomography (FD-OCT) with fixed-pattern noise removal by subtracting mean and median. In general, the fixed-pattern noise can be removed by the averaged spectrum from the many spectra of an actual measurement. However, a mean-spectrum results in artifacts as residual lateral lines caused by a small number of high-reflective points on a sample surface. These artifacts can be eliminated from OCT images by using medians instead of means. However, median calculations that are based on a sorting algorithm can generate a large amount of computation time. With the developed GPU programming, highly reflective surface regions were obtained by calculating the standard deviation of the Fourier transformed data in the lateral direction. The medians and means were then subtracted at the observed regions and other regions, such as backgrounds. When the median calculation was less than 256 positions out of a total 512 depths in an OCT image with 1024 A-lines, the GPU processing rate was faster than that of the line scan camera (46.9 kHz). Therefore, processed OCT images can be displayed in real-time using partial medians.
Energy Technology Data Exchange (ETDEWEB)
Katsidis, C. C. [Department of Materials Science and Technology, University of Crete, P.O. Box 2208, 71003 Heraklion-Crete (Greece); Ajagunna, A. O.; Georgakilas, A. [Microelectronics Research Group, IESL, FORTH, P.O. Box 1385, 71110 Heraklion-Crete (Greece); Physics Department, University of Crete, P.O. Box 2208, 71003 Heraklion-Crete (Greece)
2013-02-21
Fourier Transform Infrared (FTIR) reflectance spectroscopy has been implemented as a non-destructive, non-invasive, tool for the optical characterization of a set of c-plane InN single heteroepitaxial layers spanning a wide range of thicknesses (30-2000 nm). The c-plane (0001) InN epilayers were grown by plasma-assisted molecular beam epitaxy (PAMBE) on GaN(0001) buffer layers which had been grown on Al{sub 2}O{sub 3}(0001) substrates. It is shown that for arbitrary multilayers with homogeneous anisotropic layers having their principal axes coincident with the laboratory coordinates, a 2 Multiplication-Sign 2 matrix algebra based on a general transfer-matrix method (GTMM) is adequate to interpret their optical response. Analysis of optical reflectance in the far and mid infrared spectral range has been found capable to discriminate between the bulk, the surface and interface contributions of free carriers in the InN epilayers revealing the existence of electron accumulation layers with carrier concentrations in mid 10{sup 19} cm{sup -3} at both the InN surface and the InN/GaN interface. The spectra could be fitted with a three-layer model, determining the different electron concentration and mobility values of the bulk and of the surface and the interface electron accumulation layers in the InN films. The variation of these values with increasing InN thickness could be also sensitively detected by the optical measurements. The comparison between the optically determined drift mobility and the Hall mobility of the thickest sample reveals a value of r{sub H} = 1.49 for the Hall factor of InN at a carrier concentration of 1.11 Multiplication-Sign 10{sup 19} cm{sup -3} at 300 Degree-Sign {Kappa}.
Shayesteh, S. Farjami; Dumelow, T.; Parker, T. J.; Benushis, T. I.; Ershov, S. N.; Vasilevskiy, M. I.
1995-04-01
Far infrared phase and amplitude reflectivity measurements have been made on two bulk CdxHg1-xTe mixed crystals with composition x=0.29 and x=0.22 by dispersive Fourier transform spectroscopy (DFTS). The results have been used to calculate the real and imaginary parts of the dielectric function (ɛ', ɛ″) from the Fresnel relations. A plasma contribution is observed in the spectra in addition to the phonon response. For both samples a broad but weak reflection band around 95 105 cm-1 is observed as well as the expected two-oscillator response from the HgTe-like and CdTe-like optical phonons. This feature is attributed to absorption due to phonon combination bands, but it is too broad to enable assignments to be made. There is no evidence of additional features in the CdTe region due to clustering.
Puvanathasan, Prabakar; Forbes, Peter; Ren, Zhao; Malchow, Doug; Boyd, Shelley; Bizheva, Kostadinka
2008-11-01
A high-speed (47,000 A-scans/s), ultrahigh axial resolution Fourier domain optical coherence tomography (OCT) system for retinal imaging at approximately 1060 nm, based on a 1024 pixel linear array, 47 kHz readout rate InGaAs camera is presented. When interfaced with a custom superluminescent diode (lambda(c) = 1020 nm, Deltalambda = 108 nm, Pout = 9 mW), the system provides 3.3 microm axial OCT resolution at the surface of biological tissue, approximately 4.5 microm in vivo in rat retina, approximately 5.7 microm in vivo in human retina, and 110 dB sensitivity for 870 microW incident power and 21 mus integration time. Retinal tomograms acquired in vivo from a human volunteer and a rat animal model show clear visualization of all intraretinal layer and increased penetration into the choroid.
Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Fridberger, Anders; Ren, Tianying; Wang, Ruikang; Jacques, Steven L.; Nuttall, Alfred L.
2015-02-01
In this study, we measure the in vivo apical-turn vibrations of the guinea pig organ of Corti in both axial and radial directions using phase-sensitive Fourier domain optical coherence tomography. The apical turn in guinea pig cochlea has best frequencies around 100 - 500 Hz which are relevant for human speech. Prior measurements of vibrations in the guinea pig apex involved opening the otic capsule, which has been questioned on the basis of the resulting changes to cochlear hydrodynamics. Here this limitation is overcome by measuring the vibrations through bone without opening the otic capsule. Furthermore, we have significantly reduced the surgery needed to access the guinea pig apex in the axial direction by introducing a miniature mirror inside the bulla. The method and preliminary data are discussed in this article.
Choudhury, Niloy; Zeng, Yaguang; Fridberger, Anders; Chen, Fangyi; Zha, Dingjun; Nuttall, Alfred L.; Wang, Ruikang K.
2011-03-01
Studying the sound stimulated vibrations of various membranes that form the complex structure of the organ of Corti in the cochlea of the inner ear is essential for understanding how the travelling sound wave of the basilar membrane couples its energy to the organ structures. In this paper we report the feasibility of using phase-sensitive Fourier domain optical coherence tomography (FD-OCT) to image the vibration of various micro-structures of the cochlea at the same time. An excised cochlea of a guinea pig was stimulated using sounds at various frequencies and vibration image was obtained. When measuring the apex area, vibration signal from different turns, which have different best response frequencies are obtained in the same image. The method has the potential to measure the response from a much wider region of the cochlea than any other currently used method. The noise floor for vibration image for the system at 200 Hz was ~0.3nm.
Shin, D. H.; Park, S. H.; Kim, B. Y.; Lee, M. Y.; Baik, H. K.; Seo, J. H.; Kang, J. U.; Song, C. G.
2013-03-01
The objective of this experiment is to evaluate the utility and limitations of optical coherence tomography (OCT) for real-time, high-resolution structural analysis. We monitored the degradation of the rat's articular cartilage inducing osteoarthritis (OA) and the change of the rat's articular cartilage recovery by treatment medication, using our developed common-path Fourier-domain (CP-FD) OCT. Also, we have done a comparative analysis the rat's articular cartilage and OA grade. To observe the progression of OA, we induced OA by injecting the monosodium iodoacetate (MIA) into the right knee joint. After the injection of MIA, we sacrificed the rats at intervals of 3 days and obtained OCT and histological images. OCT and histological images showed the OA progress of similar pattern. These results illustrated the potential for non-invasive diagnosis about the grade of OA using CP-FD OCT.
Caves, C. M.; Schumaker, B. L.
1985-01-01
A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).
Li, Xiaoli; Xu, Kaiwen; Zhang, Yuying; Sun, Chanjun; He, Yong
2017-01-01
The potential of Fourier transform infrared (FT-IR) transmission spectroscopy for determination of lead chrome green in green tea was investigated based on chemometric methods. Firstly, the qualitative analysis of lead chrome green in tea was performed based on partial least squares discriminant analysis (PLS-DA), and the correct rate of classification was 100%. And then, a hybrid method of interval partial least squares (iPLS) regression and successive projections algorithm (SPA) was proposed to select characteristic wavenumbers for the quantitative analysis of lead chrome green in green tea, and 19 wavenumbers were obtained finally. Among these wavenumbers, 1384 (C = C), 1456, 1438, 1419(C = N), and 1506 (CNH) cm-1 were the characteristic wavenumbers of lead chrome green. Then, these 19 wavenumbers were used to build determination models. The best model was achieved by least squares support vector machine (LS-SVM)algorithm with high coefficient of determination and low root-mean square error of prediction set (R2p = 0.864 and RMSEP = 0.291). All these results indicated the feasibility of IR spectra for detecting lead chrome green in green tea. PMID:28068348
Wise, Stephanie A.; Hardy, Robin C.; Dausch, David E.
1997-01-01
A new piezoelectric drive mechanism has been developed for optical translation in space-based spectrometer systems. The mechanism utilizes a stack of RAINBOW high displacement piezoelectric actuators to move optical components weighing less than 250 grams through a one centimeter travel. The mechanism uses the direct motion of the piezoelectric devices, stacked such that the displacement of the individual RAINBOW actuators is additive. A prototype device has been built which utilizes 21 RAINBOWs to accomplish the necessary travel. The mechanism weighs approximately 0.6 kilograms and uses less than 2 Watts of power at a scanning frequency of 0.5 Hertz, significantly less power than that required by state-of-the-art motor systems.
Diffusion formalism and applications
Dattagupta, Sushanta
2013-01-01
Within a unifying framework, Diffusion: Formalism and Applications covers both classical and quantum domains, along with numerous applications. The author explores the more than two centuries-old history of diffusion, expertly weaving together a variety of topics from physics, mathematics, chemistry, and biology. The book examines the two distinct paradigms of diffusion-physical and stochastic-introduced by Fourier and Laplace and later unified by Einstein in his groundbreaking work on Brownian motion. The author describes the role of diffusion in probability theory and stochastic calculus and
Hassan, Moinuddin; Ilev, Ilko
2016-03-01
Ophthalmic Viscosurgical Devices (OVDs) in clinical setting are a major health risk factor for potential endotoxin contamination in the eye, due to their extensive applications in cataract surgery for space creation, stabilization and protection of intraocular tissue and intraocular lens (IOL) during implantation. Endotoxin contamination of OVDs is implicated in toxic anterior syndrome (TASS), a severe complication of cataract surgery that leads to intraocular damage and even blindness. Current standard methods for endotoxin contamination detection utilize rabbit assay or Limulus amoebocyte lysate (LAL) assays. These endotoxin detection strategies are extremely difficult for gel-like type devices such as OVDs. To overcome the endotoxin detection limitations in OVDs, we have developed an alternative optical detection methodology for label-free and real-time sensing of bacterial endotoxin in OVDs, based on fiber-optic Fourier transform infrared (FO-FTIR) transmission spectrometry in the mid-IR spectral range from 2.5 micron to 12 micron. Endotoxin contaminated OVD test samples were prepared by serial dilutions of endotoxins on OVDs. The major results of this study revealed two salient spectral peak shifts (in the regions 2925 to 2890 cm^-1 and 1125 to 1100 cm^-1), which are associated with endotoxin in OVDs. In addition, FO-FTIR experimental results processed using a multivariate analysis confirmed the observed specific peak shifts associated with endotoxin contamination in OVDs. Thus, employing the FO-FTIR sensing methodology integrated with a multivariate analysis could potentially be used as an alternative endotoxin detection technique in OVD.
Huang, Yong; Song, Cheol; Liu, Xuan; Kang, Jin U.
2013-03-01
A motion-compensated hand-held common-path Fourier-domain optical coherence tomography imaging probe has been developed for image guided intervention during microsurgery. A hand-held prototype instrument was designed and fabricated by integrating an imaging fiber probe inside a stainless steel needle which is attached to the ceramic shaft of a piezoelectric motor housed in an aluminum handle. The fiber probe obtains A-scan images. The distance information was extracted from the A-scans to track the sample surface distance and a fixed distance was maintained by a feedback motor control which effectively compensated hand tremor and target movements in the axial direction. Graphical user interface, real-time data processing, and visualization based on a CPU-GPU hybrid programming architecture were developed and used in the implantation of this system. To validate the system, free-hand optical coherence tomography images using various samples were obtained. The system can be easily integrated into microsurgical tools and robotics for a wide range of clinical applications. Such tools could offer physicians the freedom to easily image sites of interest with reduced risk and higher image quality.
All-optical encrypted movie based on fractional Fourier transform%基于分数阶傅里叶变换的光学加密影片
Institute of Scientific and Technical Information of China (English)
杜翔军; 陶少华
2013-01-01
随着通信与网络的快速发展,能够包含大容量信息的影片得到了广泛应用.利用分数阶傅里叶变换的特点,提出了一种全光学加密解密影片的方法.将现有的影片加密密钥从二重变为了四重,显著增加了影片的安全性.通过改变振幅型正弦光栅的作用位置,将影片的加密解密次数由现有的每帧各一次减小为总共一次,优化了算法.仿真结果验证了该方法的有效性.%With fast developments of communications and internets, movies containing huge information are widely used. An optical encryption/decryption method based on fractional Fourier transform is proposed. The method increases number of the encryption keys for an all-optical encrypted movie from two to four. The security level of the all-optical encrypted movie is enhanced greatly. The interaction site of the amplitude sinusoidal grating is optmized. Encryption and decryption are needed once for a whole movie in the proposed method rather than for every frame of the movie in the previous methods. The implementation of the method is significantly simplified. The effectiveness of the method is verified with simulations.
Directory of Open Access Journals (Sweden)
Rolle T
2011-07-01
Full Text Available Teresa Rolle, Cristina Briamonte, Daniela Curto, Federico Maria GrignoloEye Clinic, Section of Ophthalmology, Department of Clinical Physiopathology, University of Torino, Torino, ItalyAims: To evaluate the capability of Fourier-domain optical coherence tomography (FD-OCT to detect structural damage in patients with preperimetric glaucoma.Methods: A total of 178 Caucasian subjects were enrolled in this cohort study: 116 preperimetric glaucoma patients and 52 healthy subjects. Using three-dimensional FD-OCT, the participants underwent imaging of the ganglion cell complex (GCC and the optic nerve head. Sensitivity, specificity, likelihood ratios, and predictive values were calculated for all parameters at the first and fifth percentiles. Areas under the curves (AUCs were generated for all parameters and were compared (Delong test. For both the GCC and the optic nerve head protocols, the OR logical disjunction (Boolean logic operator was calculated.Results: The AUCs didn’t significantly differ. Macular global loss volume had the largest AUC (0.81. Specificities were high at both the fifth and first percentiles (up to 97%, but sensitivities were low, especially at the first percentile (55%–27%.Conclusion: Macular and papillary diagnostic accuracies did not differ significantly based on the 95% confidence interval. The computation of the Boolean OR operator has been found to boost diagnostic accuracy. Using the software-provided classification, sensitivity and diagnostic accuracy were low for both the retinal nerve fiber layer and the GCC scans. FD-OCT does not seem to be decisive for early detection of structural damage in patients with no functional impairment. This suggests that there is a need for analysis software to be further refined to enhance glaucoma diagnostic capability.Keywords: OCT, RNFL, GCC, diagnostic accuracy
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
Joosten, Joost Johannes
2004-01-01
The dissertation is in the first place a treatment of mathematical interpretations. Interpretations themselves will be studied, but also shall they be used to study formal theories. Interpretations, when used in comparing theories, tell us, in a natural way, something about proof-strength of form
Schins, J.M.; Trinh, M.T.; Houtepen, A.J.; Siebbeles, L.D.A.
2009-01-01
The first two peaks of the optical extinction spectrum of PbSe nanocrystals in solution have been assigned in the literature to the 1Sh1Se and 1Ph1Pe transitions. In the present work we assign the transitions causing extinction in the energy region between these two lowest-energy peaks. Our femtosec
Directory of Open Access Journals (Sweden)
Mohammed Rigi
2014-01-01
Full Text Available Purpose. To introduce a new anterior segment optical coherence tomography parameter, trabecular-iris circumference volume (TICV, which measures the integrated volume of the peripheral angle, and establish a reference range in normal, open angle eyes. Methods. One eye of each participant with open angles and a normal anterior segment was imaged using 3D mode by the CASIA SS-1000 (Tomey, Nagoya, Japan. Trabecular-iris space area (TISA and TICV at 500 and 750 µm were calculated. Analysis of covariance was performed to examine the effect of age and its interaction with spherical equivalent. Results. The study included 100 participants with a mean age of 50 (±15 years (range 20–79. TICV showed a normal distribution with a mean (±SD value of 4.75 µL (±2.30 for TICV500 and a mean (±SD value of 8.90 µL (±3.88 for TICV750. Overall, TICV showed an age-related reduction (P=0.035. In addition, angle volume increased with increased myopia for all age groups, except for those older than 65 years. Conclusions. This study introduces a new parameter to measure peripheral angle volume, TICV, with age-adjusted normal ranges for open angle eyes. Further investigation is warranted to determine the clinical utility of this new parameter.
Fourier transforms in spectroscopy
Kauppinen, Jyrki
2000-01-01
This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi
Rethinking Formalisms in Formal Education
Nathan, Mitchell J.
2012-01-01
I explore a belief about learning and teaching that is commonly held in education and society at large that nonetheless is deeply flawed. The belief asserts that mastery of "formalisms"--specialized representations such as symbolic equations and diagrams with no inherent meaning except that which is established by convention--is prerequisite to…
Xiao, Qing; Hou, Jue; Fu, Ling
2012-06-01
A Fourier domain optical coherence tomography (OCT) system with 1310 nm light was demonstrated to study inflammatory human skin and the skin coated with a moisturizer in vivo. By using a graphics processing unit (GPU), the display rate could reach 20 frames/s with 1000 A-scans contained in one image. The field of view (FOV) of the cross-sectional image is 7 mm in the lateral direction and the penetration depth is ˜1 mm in skin. The result shows that, in inflammatory skin, the epidermis became thicker and had a decreased scattering; furthermore, the region of the severe lesion present an uneven thickness of the epidermis compared with the peripheral area. For the result of a finger tip coated with the moisturizer, the antireflection effect was significant and the stratum corneum became more transparent. In this letter, we demonstrated that real-time display with a large FOV could enable screening of a large tissue area; thereby increasing the dermatologic diagnostic potential of the method by permitting a comparison of the lesion and the normal peripheral region.
Owocki, Stanley P.; ud-Doula, Asif; Sundqvist, Jon O.; Petit, Veronique; Cohen, David H.; Townsend, Richard H. D.
2016-11-01
Slowly rotating magnetic massive stars develop `dynamical magnetospheres' (DMs), characterized by trapping of stellar wind outflow in closed magnetic loops, shock heating from collision of the upflow from opposite loop footpoints, and subsequent gravitational infall of radiatively cooled material. In 2D and 3D magnetohydrodynamic (MHD) simulations, the interplay among these three components is spatially complex and temporally variable, making it difficult to derive observational signatures and discern their overall scaling trends. Within a simplified, steady-state analysis based on overall conservation principles, we present here an `analytic dynamical magnetosphere' (ADM) model that provides explicit formulae for density, temperature, and flow speed in each of these three components - wind outflow, hot post-shock gas, and cooled inflow - as a function of colatitude and radius within the closed (presumed dipole) field lines of the magnetosphere. We compare these scalings with time-averaged results from MHD simulations, and provide initial examples of application of this ADM model for deriving two key observational diagnostics, namely hydrogen H α emission line profiles from the cooled infall, and X-ray emission from the hot post-shock gas. We conclude with a discussion of key issues and advantages in applying this ADM formalism towards derivation of a broader set of observational diagnostics and scaling trends for massive stars with such dynamical magnetospheres.
Denning, Peter J.
1991-01-01
The ongoing debate over the role of formalism and formal specifications in software features many speakers with diverse positions. Yet, in the end, they share the conviction that the requirements of a software system can be unambiguously specified, that acceptable software is a product demonstrably meeting the specifications, and that the design process can be carried out with little interaction between designers and users once the specification has been agreed to. This conviction is part of a larger paradigm prevalent in American management thinking, which holds that organizations are systems that can be precisely specified and optimized. This paradigm, which traces historically to the works of Frederick Taylor in the early 1900s, is no longer sufficient for organizations and software systems today. In the domain of software, a new paradigm, called user-centered design, overcomes the limitations of pure formalism. Pioneered in Scandinavia, user-centered design is spreading through Europe and is beginning to make its way into the U.S.
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Institute of Scientific and Technical Information of China (English)
周锦松; 相里斌; 魏儒义; 景娟娟
2011-01-01
对反射转镜式干涉光谱仪的原理进行了介绍,从马吕斯定律和角反射体的反射特性入手,选择转镜反射面的旋转中心作为入射光束和出射光束等波面的参考点,对反射转镜式干涉光谱仪的光程差进行了分析计算,给出反射转镜式干涉光谱仪任意时刻光程差及最大光程差的一般表达式,分析影响最大光程差和光程差变化周期的因素,为反射转镜式干涉光谱仪的设计与研制提供理论指导.%The principle of reflecting rotating Fourier transform spectrometer was introduced in the present paper. Based on the Malus law and reflecting characteristic of cube corner, the optic path difference of reflecting rotating Fourier transform spectrometer was analyzed and calculated by choosing the center of rotating mirror as a reference point of the aplanatic surface of incidence beam and return beam. General expression of optic path difference at any time and maximal optic path difference of reflecting rotating Fourier transform spectrometer was presented. The factors that influence the maximal optic path difference and the period of optic path difference were analyzed. The results provide a theoretical guidance for design and manufacture of reflecting rotating Fourier transform spectrometer.
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Samlan, C T; Naik, Dinesh N; Viswanathan, Nirmal K
2016-09-14
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena.
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-01-01
Discovered in 1813, the conoscopic interference pattern observed due to light propagating through a crystal, kept between crossed polarizers, shows isochromates and isogyres, respectively containing information about the dynamic and geometric phase acquired by the beam. We propose and demonstrate a closed-fringe Fourier analysis method to disentangle the isogyres from the isochromates, leading us to the azimuthally varying geometric phase and its manifestation as isogyres. This azimuthally varying geometric phase is shown to be the underlying mechanism for the spin-to-orbital angular momentum conversion observed in a diverging optical field propagating through a z-cut uniaxial crystal. We extend the formalism to study the optical activity mediated uniaxial-to-biaxial transformation due to a weak transverse electric field applied across the crystal. Closely associated with the phase and polarization singularities of the optical field, the formalism enables us to understand crystal optics in a new way, paving the way to anticipate several emerging phenomena. PMID:27625210
Institute of Scientific and Technical Information of China (English)
潘卫清; 朱勇建; 王建中
2009-01-01
在维格纳相空间中,通过将一阶光学系统的传输矩阵分解为坐标旋转、比例缩放和啁啾矩阵的组合,得到了一阶光学系统在空域的分数傅里叶表示.结果表明:任意一阶光学系统均可表示为经过比例缩放和二次相位调制的分数傅里叶变换.通过将输入输出光场在相空间中作π/2角旋转,得到了一阶光学系统在频域的传输矩阵和衍射积分公式,进而得到了一阶光学系统在频域的分数傅里叶表示.比较空域和频域一阶光学系统的相空间变换矩阵,说明2个系统本质上属同一变换在不同基坐标下的表示,并推导出了光学系统在空域和频域具有相同分数傅里叶变换的条件.%The fractional Fourier express of the first-order optical system was derived by decomposing the transfer matrices of firstorder optical system into coordinate rotation matrix, scale matrix and chirp matrix in Wigner phase space. The results show that an arbitrary first-order optical system can be expressed as the scaled and chirp modulation fractional Fourier transform. The transfer matrix and diffractive integral formula in frequency domain were acquired by rotating the input and output optical field π/2 in the phase space. Accordingly the fractional Fourier transforms of a first-order optical system in frequency domain were also obtained. By comparing the transfer matrices of two first-order optical systems in space and frequency domains respectively, it is found that the two first-order optical systems in different domain can be expressed as two different expressions of one and the same transfer based on different coordinates. At last the condition is derived for an optical system to implement the fractional Fourier transform in space and frequency domains with the same order.
Reflective Fourier ptychography.
Pacheco, Shaun; Zheng, Guoan; Liang, Rongguang
2016-02-01
The Fourier ptychography technique in reflection mode has great potential applications in tissue imaging and optical inspection, but the current configuration either has a limitation on cut-off frequency or is not practical. By placing the imaging aperture stop outside the illumination path, the illumination numerical aperture (NA) can be greater than the imaging NA of the objective lens. Thus, the cut-off frequency achieved in the proposed optical system is greater than twice the objective's NA divided by the wavelength (2NAobj/λ ), which is the diffraction limit for the cut-off frequency in an incoherent epi-illumination configuration. We experimentally demonstrated that the synthesized NA is increased by a factor of 4.5 using the proposed optical concept. The key advantage of the proposed system is that it can achieve high-resolution imaging over a large field of view with a simple objective. It will have a great potential for applications in endoscopy, biomedical imaging, surface metrology, and industrial inspection.
Fourier processing of quantum light
Poem, Eilon; Lahini, Yoav; Silberberg, Yaron
2012-01-01
It is shown that a classical optical Fourier processor can be used for the shaping of quantum correlations between two or more photons, and the class of Fourier masks applicable in the multiphoton Fourier space is identified. This concept is experimentally demonstrated using two types of periodic phase masks illuminated with path-entangled photon pairs, a highly non-classical state of light. Applied first were sinusoidal phase masks, emulating two-particle quantum walk on a periodic lattice, yielding intricate correlation patterns with various spatial bunching and anti-bunching effects depending on the initial state. Then, a periodic Zernike-like filter was applied on top of the sinusoidal phase masks. Using this filter, phase information lost in the original correlation measurements was retrieved.
Directory of Open Access Journals (Sweden)
Dave Odden
2013-02-01
Full Text Available Two problematic trends have dominated modern phonological theorizing: over-reliance on machinery of Universal Grammar, and reification of functional properties in grammar. The former trend leads to arbitrary postulation of grammatical principles because UG “has no cost”, which leads to a welter of contradictory and unresolvable claims. The latter trend amounts to rejection of phonology and indeed grammatical computation, as a legitimate independent area of scientific investigation. This paper outlines Formal Phonology, which is a metatheoretical approach rooted in an inductive epistemology, committed to seriously engaging the fundamental logic of the discipline, one which demands justification of claims and an integrated consideration of what is known about phonological grammars, eschewing ad libitum conjectures and isolated positing of novel claims without evaluating how the claim interacts with other aspects of phonology. Debate over the proper mechanism for apparent segment-transparency in harmony, or the binary vs. privative nature of features, is ultimately doomed if we do not have a clear awareness of what a “grammar” and a “phonology” are. Misconstruing the nature of a phonology as being a model of observed behavior negatively affects theoretical choices, leads to confusion over what could motivate a claim about the nature of grammar, and in general, a lack of developed epistemological foundation leads to confusion over how to approach theory-construction.
Fractional Fourier processing of quantum light.
Sun, Yifan; Tao, Ran; Zhang, Xiangdong
2014-01-13
We have extended Fourier transform of quantum light to a fractional Fourier processing, and demonstrated that a classical optical fractional Fourier processor can be used for the shaping of quantum correlations between two or more photons. Comparing the present method with that of Fourier processing, we find that fractional Fourier processing for quantum light possesses many advantages. Based on such a method, not only quantum correlations can be shaped more rich, but also the initial states can be easily identified. Moreover, the twisted phase information can be recovered and quantum states are easily controlled in performing quantum information experiments. Our findings open up new avenues for the manipulation of correlations between photons in optical quantum information processing.
Energy Technology Data Exchange (ETDEWEB)
Oliveira, N. de; Polack, F.; Vervloet, M.; Nahon, L. [Synchrotron Soleil, Orme des Merisiers, St AUBIN BP 48, 91192 GIF sur Yvette CEDEX (France); Joyeux, D.; Phalippou, D.; Rodier, J. C. [Laboratoire Charles Fabry de l' Institut d' Optique, RD 128, Campus Polytechnique, PALAISEAU cedex (France)
2009-04-15
We describe a Fourier transform (FT) spectrometer designed to operate down to 60 nm (20 eV) on a synchrotron radiation beamline for high resolution absorption spectrometry. As far as we know, such an instrument is not available below 140 nm mainly because manufacturing accurate and efficient beam splitters remains a major problem at these wavelengths, especially if a wide bandwidth operation is desired. In order to overcome this difficulty, we developed an interferometer based on wave front division instead of amplitude division. It relies on a modified Fresnel bimirror configuration that requires only flat mirrors. The instrument provides path difference scanning through the translation of one reflector. During the scanning, the moving reflector is controlled by an optical system that keeps its direction constant within a tolerable value and provides an accurate interferometric measurement of the path difference variation. Therefore, a regular interferogram sampling is obtained, producing a nominal spectral impulse response and an accurate spectral calibration. The first results presented in this paper show a measured spectral resolution of {delta}{sigma}=0.33 cm{sup -1} (interval between spectral samples). This was obtained with a sampling interval of 29 nm (path difference) and 512 K samples from a one-sided interferogram using a cosine FT. Such a sampling interval should allow the recording of large bandwidth spectra down to {lambda}=58 nm with an ultimate resolving power of 500 000 at this wavelength. In order to check the instrument performances, we first recorded an interferogram from a He-Ne stabilized laser. This provided the actual spectral impulse function, which was found to be fully satisfactory. The determination of the impulse response distortion and of the noise on the vacuum ultraviolet (VUV) spectral range provided accurate information in the sampling error profile over a typical scan. Finally, the instrument has been moved to the SU5 undulator
Transformadas Discretas de Fourier
Alpízar-Brenes, Geisel; Calderón-Arce, Cindy; Soto-Quirós, Juan Pablo
2015-01-01
Proyecto de Investigación (VIE-5402-1440-4301). Este proyecto presenta un marco matem atico-computacional para el desarrollo de un conjunto de de niciones derivadas de la transformada discreta de Fourier (TDF), que son la funci on discreta de ambig uedad, la transformada discreta de Zak, la transformada discreta de Fourier en tiempo corto, la transformada discreta chirp-Fourier, la transformada discreta de Fourier de quaterniones, la transformada discreta de Cohen, la transform...
Subharmonic Fourier domain mode locking.
Eigenwillig, Christoph M; Wieser, Wolfgang; Biedermann, Benjamin R; Huber, Robert
2009-03-15
We demonstrate a subharmonically Fourier domain mode-locked wavelength-swept laser source with a substantially reduced cavity fiber length. In contrast to a standard Fourier domain mode-locked configuration, light is recirculated repetitively in the delay line with the optical bandpass filter used as switch. The laser has a fundamental optical round trip frequency of 285 kHz and can be operated at integer fractions thereof (subharmonics). Sweep ranges up to 95 nm full width centred at 1317 nm are achieved at the 1/5th subharmonic. A maximum sensitivity of 116 dB and an axial resolution of 12 microm in air are measured at an average sweep power of 12 mW. A sensitivity roll-off of 11 dB over 4 mm and 25 dB over 10 mm is observed and optical coherence tomography imaging is demonstrated. Besides the advantage of a reduced fiber length, subharmonic Fourier domain mode locking (shFDML) enables simple scaling of the sweep speed by extracting light from the delay part of the resonator. A sweep rate of 570 kHz is achieved. Characteristic features of shFDML operation, such as power leakage during fly-back and cw breakthrough, are investigated.
Z. Jamil (Z.); G.J. Tearney (Guillermo); N. Bruining (Nico); K. Sihan (Kenji); G. van Soest (Gijs); J.M.R. Ligthart (Jürgen); R.T. van Domburg (Ron); B.E. Bouma (Brett); E.S. Regar (Eveline)
2013-01-01
textabstractRecently, Fourier domain OCT (FD-OCT) has been introduced for clinical use. This approach allows in vivo, high resolution (15 micron) imaging with very fast data acquisition, however, it requires brief flushing of the lumen during imaging. The reproducibility of such fast data acquisitio
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
Fourier transformation for pedestrians
Butz, Tilman
2006-01-01
Meant to serve an "entertaining textbook," this book belongs to a rare genre. It is written for all students and practitioners who deal with Fourier transformation. Fourier series as well as continuous and discrete Fourier transformation are covered, and particular emphasis is placed on window functions. Many illustrations and easy-to-solve exercises make the book especially accessible, and its humorous style will add to the pleasure of learning from it.
Fourier Series Operating Package
Charnow, Milton L.
1961-01-01
This report presents a computer program for multiplying, adding, differentiating, integrating, "barring" and scalarly multiplying "literal" Fourier series as such, and for extracting the coefficients of specified terms.
DEFF Research Database (Denmark)
Masses of Formal Philosophy is an outgrowth of Formal Philosophy. That book gathered the responses of some of the most prominent formal philosophers to five relatively open and broad questions initiating a discussion of metaphilosophical themes and problems surrounding the use of formal methods...... in philosophy. Including contributions from a wide range of philosophers, Masses of Formal Philosophy contains important new responses to the original five questions....
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
Fourier-Transform Infrared Spectrometer
Schindler, R. A.
1986-01-01
Fourier-transform spectrometer provides approximately hundredfold increase in luminosity at detector plane over that achievable with older instruments of this type. Used to analyze such weak sources as pollutants and other low-concentration substances in atmosphere. Interferometer creates fringe patterns on two distinct arrays of light detectors, which observe different wavelength bands. Objective lens focuses scene on image plane, which contains optical chopper. To make instrument less susceptible to variations in scene under observation, field and detector lenses focus entrance aperture, rather that image, onto detector array.
Boriakoff, Valentin
1994-01-01
The goal of this project was the feasibility study of a particular architecture of a digital signal processing machine operating in real time which could do in a pipeline fashion the computation of the fast Fourier transform (FFT) of a time-domain sampled complex digital data stream. The particular architecture makes use of simple identical processors (called inner product processors) in a linear organization called a systolic array. Through computer simulation the new architecture to compute the FFT with systolic arrays was proved to be viable, and computed the FFT correctly and with the predicted particulars of operation. Integrated circuits to compute the operations expected of the vital node of the systolic architecture were proven feasible, and even with a 2 micron VLSI technology can execute the required operations in the required time. Actual construction of the integrated circuits was successful in one variant (fixed point) and unsuccessful in the other (floating point).
Fourier analysis an introduction
Stein, Elias M
2003-01-01
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th
Indian Academy of Sciences (India)
P CHAKRABORTY; S K MANDAL; S C ROY
2016-07-01
Titanocene(III) Chloride mediated radical induced synthesis of 4-benzylidene substituted tetrahydrofuran, a typical lignan skeleton, has been accomplished in good yield through addition-elimination route in racemic as well as in optically active forms. The method has been applied to the synthesis of furano lignans, magnofargesin (1) and 7'-epimagnofargesin (2) in optically active forms.
Institute of Scientific and Technical Information of China (English)
2011-01-01
The advantages and disadvantages of formalization in philosophy are summarized. It is concluded that formalized philosophy is an endangered speciality that needs to be revitalized and to increase its interactions with non-formalized philosophy. The enigmatic style that is common in philosophical logic must give way to explicit discussions of the problematic relationship between formal models and the philosophical concepts and issues that motivated their development.
Debnath, Lokenath
2012-01-01
This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…
Fourier transformation for pedestrians
Butz, Tilman
2015-01-01
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
Fourier transform mass spectrometry.
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-07-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.
Research progress on discretization of fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
TAO Ran; ZHANG Feng; WANG Yue
2008-01-01
As the fractional Fourier transform has attracted a considerable amount of atten-tion in the area of optics and signal processing,the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier trans-form.Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain,the discre-tization of the fractional Fourier transform has been investigated recently.A sum-mary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper.The discretizations include sampling in the fractional Fourier domain,discrete-time fractional Fourier transform,frac-tional Fourier series,discrete fractional Fourier transform (including 3 main types:linear combination-type;sampling-type;and eigen decomposition-type),and other discrete fractional signal transform.It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.
On the Scaled Fractional Fourier Transformation Operator
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; HU Li-Yun
2008-01-01
Based on our previous study [Chin.Phys.Lett.24(2007)2238]in which the Fresnel operator corresponding to classical Fresnel transform was introduced,we derive the fractional Fourier transformation operator,and the optical operator method is then enriched.
Pragmatics for formal semantics
DEFF Research Database (Denmark)
Danvy, Olivier
2011-01-01
This tech talk describes how to write and how to inter-derive formal semantics for sequential programming languages. The progress reported here is (1) concrete guidelines to write each formal semantics to alleviate their proof obligations, and (2) simple calculational tools to obtain a formal...
Weinstock, B André; Guiney, Linda M; Loose, Christopher
2012-11-01
We have developed a rapid, nondestructive analytical method that estimates the thickness of a surface polymer layer with high precision but unknown accuracy using a single attenuated total reflection Fourier transform infrared (ATR FT-IR) measurement. Because the method is rapid, nondestructive, and requires no sample preparation, it is ideal as a process analytical technique. Prior to implementation, the ATR FT-IR spectrum of the substrate layer pure component and the ATR FT-IR and real refractive index spectra of the surface layer pure component must be known. From these three input spectra a synthetic mid-infrared spectral matrix of surface layers 0 nm to 10,000 nm thick on substrate is created de novo. A minimum statistical distance match between a process sample's ATR FT-IR spectrum and the synthetic spectral matrix provides the thickness of that sample. We show that this method can be used to successfully estimate the thickness of polysulfobetaine surface modification, a hydrated polymeric surface layer covalently bonded onto a polyetherurethane substrate. A database of 1850 sample spectra was examined. Spectrochemical matrix-effect unknowns, such as the nonuniform and molecularly novel polysulfobetaine-polyetherurethane interface, were found to be minimal. A partial least squares regression analysis of the database spectra versus their thicknesses as calculated by the method described yielded an estimate of precision of ±52 nm.
Directory of Open Access Journals (Sweden)
Nabanita Barua
2016-01-01
Full Text Available Context: Analysis of diagnostic ability of macular ganglionic cell complex and retinal nerve fiber layer (RNFL in glaucoma. Aim: To correlate functional and structural parameters and comparing predictive value of each of the structural parameters using Fourier-domain (FD optical coherence tomography (OCT among primary open angle glaucoma (POAG and ocular hypertension (OHT versus normal population. Setting and Design: Single centric, cross-sectional study done in 234 eyes. Materials and Methods: Patients were enrolled in three groups: POAG, ocular hypertensive and normal (40 patients in each group. After comprehensive ophthalmological examination, patients underwent standard automated perimetry and FD-OCT scan in optic nerve head and ganglion cell mode. The relationship was assessed by correlating ganglion cell complex (GCC parameters with mean deviation. Results were compared with RNFL parameters. Statistical Analysis: Data were analyzed with SPSS, analysis of variance, t-test, Pearson′s coefficient, and receiver operating curve. Results: All parameters showed strong correlation with visual field (P 0.5 when compared with other parameters. None of the parameters showed significant diagnostic capability to detect OHT from normal population. In diagnosing early glaucoma from OHT and normal population, only inferior GCC had statistically significant AUC value (0.715. Conclusion: In this study, GCC and RNFL parameters showed equal predictive capability in perimetric versus normal group. In early stage, inferior GCC was the best parameter. In OHT population, single day cross-sectional imaging was not valuable.
Weaving defect detection by Fourier imaging
Ciamberlini, Claudio; Francini, Franco; Longobardi, Giuseppe; Poggi, Pasquale; Sansoni, Paola; Tiribilli, Bruno
1996-08-01
An optical configuration for the detection of faults was developed and tested. The optical fourier transformation is the basic working principle of the system. When good fabric passes in front of the optical system the Fourier image, captured by the camera, shows well defined spots corresponding to the spatial frequencies of the tissue. If a defect occurs during production on the loom, the pattern changes significantly and a defect is easily detected in real time. A very simple electronic image processing based on thresholding and binary histograms allows to obtain very encouraging performance for its applicability to the looms. A compact device has been realized and tested in real working conditions on the loom.
Imaging Analysis by Means of Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Starting from the diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
Industrial use of formal methods formal verification
Boulanger, Jean-Louis
2012-01-01
At present the literature gives students and researchers of the very general books on the formal technics. The purpose of this book is to present in a single book, a return of experience on the used of the "formal technics" (such proof and model-checking) on industrial examples for the transportation domain. This book is based on the experience of people which are completely involved in the realization and the evaluation of safety critical system software based. The implication of the industrialists allows to raise the problems of confidentiality which could appear and so allow
Rudin, Walter
2011-01-01
In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.
Fourier analysis and synthesis tomography.
Energy Technology Data Exchange (ETDEWEB)
Wagner, Kelvin H. (University of Colorado at Boulder, Boulder, CO); Sinclair, Michael B.; Feldkuhn, Daniel (University of Colorado at Boulder, Boulder, CO)
2010-05-01
Most far-field optical imaging systems rely on a lens and spatially-resolved detection to probe distinct locations on the object. We describe and demonstrate a novel high-speed wide-field approach to imaging that instead measures the complex spatial Fourier transform of the object by detecting its spatially-integrated response to dynamic acousto-optically synthesized structured illumination. Tomographic filtered backprojection is applied to reconstruct the object in two or three dimensions. This technique decouples depth-of-field and working-distance from resolution, in contrast to conventional imaging, and can be used to image biological and synthetic structures in fluoresced or scattered light employing coherent or broadband illumination. We discuss the electronically programmable transfer function of the optical system and its implications for imaging dynamic processes. Finally, we present for the first time two-dimensional high-resolution image reconstructions demonstrating a three-orders-of-magnitude improvement in depth-of-field over conventional lens-based microscopy.
Fourier and Laplace Transforms
Beerends, R.J.; Morsche, ter H.G.; Berg, van den J.C.
2003-01-01
This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the a
Bilinear Fourier restriction theorems
Demeter, Ciprian
2012-01-01
We provide a general scheme for proving $L^p$ estimates for certain bilinear Fourier restrictions outside the locally $L^2$ setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior approaches, our argument avoids any use of the Rubio de Francia Littlewood--Paley inequality.
Fast Fourier Orthogonalization
Ducas, L.; Prest, T.; Abramov, S.A.; Zima, E.V.; Gao, X-S.
2016-01-01
The classical fast Fourier transform (FFT) allows to compute in quasi-linear time the product of two polynomials, in the {\\em circular convolution ring} R[x]/(x^d−1) --- a task that naively requires quadratic time. Equivalently, it allows to accelerate matrix-vector products when the matrix is *circ
DEFF Research Database (Denmark)
du Gay, Paul; Lopdrup-Hjorth, Thomas
Over recent decades, institutions exhibiting high degrees of formality have come in for severe criticism. From the private to the public sector, and across a whole spectrum of actors spanning from practitioners to academics, formal organization is viewed with increasing doubt and skepticism. In a...
Energy Technology Data Exchange (ETDEWEB)
Hassan, Moinuddin, E-mail: moinuddin.hassan@fda.hhs.gov; Ilev, Ilko [Optical Therapeutics and Medical Nanophotonics Laboratory, Division of Biomedical Physics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, Maryland 20993 (United States)
2014-10-15
Contamination of medical devices has become a critical and prevalent public health safety concern since medical devices are being increasingly used in clinical practices for diagnostics, therapeutics and medical implants. The development of effective sensing methods for real-time detection of pathogenic contamination is needed to prevent and reduce the spread of infections to patients and the healthcare community. In this study, a hollow-core fiber-optic Fourier transform infrared spectroscopy methodology employing a grazing incidence angle based sensing approach (FO-FTIR-GIA) was developed for detection of various biochemical contaminants on medical device surfaces. We demonstrated the sensitivity of FO-FTIR-GIA sensing approach for non-contact and label-free detection of contaminants such as lipopolysaccharide from various surface materials relevant to medical device. The proposed sensing system can detect at a minimum loading concentration of approximately 0.7 μg/cm{sup 2}. The FO-FTIR-GIA has the potential for the detection of unwanted pathogen in real time.
Unger, Miriam; Siesler, Heinz W
2009-12-01
In the present study, the orientation of a poly(3-hydroxybutyrate) (PHB)/poly(epsilon-caprolactone) (PCL) blend was monitored during uniaxial elongation by rheo-optical Fourier transform infrared (FT-IR) spectroscopy and analyzed by generalized two-dimensional correlation spectroscopy (2D-COS). The dichroism of the delta(CH(2)) absorption bands of PHB and PCL was employed to determine the polymer chain orientation in the PHB/PCL blend during the elongation up to 267% strain. From the PHB and PCL specific orientation functions it was derived that the PCL chains orient into the drawing direction while the PHB chains orient predominantly perpendicular to the applied strain. To extract more detailed information about the polymer orientation during uniaxial elongation, 2D-COS analysis was employed for the dichroic difference of the polarization spectra recorded during the drawing process. In the corresponding synchronous and asynchronous 2D correlation plots, absorption bands characteristic of the crystalline and amorphous regions of PHB and PCL were separated. Furthermore, the 2D-COS analysis revealed that during the mechanical treatment the PCL domains orient before the PHB domains.
Generic Quantum Fourier Transforms
Moore, Cristopher; Russell, A; Moore, Cristopher; Rockmore, Daniel; Russell, Alexander
2003-01-01
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the separation of variables technique that has been so successful in the study of classical Fourier transform computations. Specifically, this framework applies the existence of computable Bratteli diagrams, adapted factorizations, and Gel'fand-Tsetlin bases to offer efficient quantum circuits for the QFT over a wide variety a finite Abelian and non-Abelian groups, including all group families for which efficient QFTs are currently known and many new group families. Moreover, the method gives rise to the first subexponential-size quantum circuits for the QFT over the linear groups GL_k(q), SL_k(q), and the finite groups of Lie type, for any fixed prime power q.
Fourier analysis: from cloaking to imaging
Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping
2016-04-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.
Necessity of Integral Formalism
Institute of Scientific and Technical Information of China (English)
陶勇
2011-01-01
To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 （1974） 44fi], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 （1975） 3846]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schroedinger differential equation （i.e., differential formalism for wave function） shall lead to vanishing Berry phase and that the Schroedinger integral equation （i.e., integral formalism for wave function）, in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion： There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description.
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
Dependencies in Formal Mathematics
Alama, Jesse; Urban, Josef
2011-01-01
Dependencies in formal mathematical texts, large coherent formal libraries and proof assistants are introduced as an emerging research topic, analyzed from foundational, semantic, computational, and pragmatic perspectives, and put to practical use in computer-assisted mathematics. Two different approaches to dependency computation are implemented over two major proof assistants with different type disciplines, and a large-scale experimental comparison is provided based on large Coq and Mizar formal libraries. Apart from theoretical discussions, importance of dependency analysis for advanced automation of computer-assisted reasoning, and for efficient proof analysis and theory refactoring in substantial mathematical domains are experimentally demonstrated.
Local properties of Fourier series
Hüseyin Bor
2000-01-01
A theorem on local property of |N¯,pn|k summability of factored Fourier series, which generalizes some known results, and also a general theorem concerning the |N¯,pn|k summability factors of Fourier series have been proved.
Fourier transforms principles and applications
Hansen, Eric W
2014-01-01
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.
Real Clifford Windowed Fourier Transform
Institute of Scientific and Technical Information of China (English)
Mawardi BAHRI; Sriwulan ADJI; Ji Man ZHAO
2011-01-01
We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation,reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform (WFT) and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.
Institute of Scientific and Technical Information of China (English)
孔德照; 林超; 沈学举; 王昕; 周晗
2013-01-01
提出一种基于小波包变换(WPT)的分数阶光学图像加密方法.利用WPT能够对图像多层次分解的特性,结合分数傅里叶变换(FRFT)的灵活性,将双随机相位、小波函数的类型及尺度因子和分数阶次作为密钥,实现了图像的多重密钥加解密.同时,实现了图像小波域上的选择性加密,使加密样式变得更灵活多样,还增强了加密图像的抵抗恶意的攻击能力.数值模拟了加密和解密过程,分析了加密效果和解密图像质量,验证了本文方法的可行性.%A novel method for the optical image encryption is presented, which is based on the wavelet packet transform (WPT) and fractional Fourier transform (FRFT). The idea of combining WPT with FRFT comes from the study of properties of them. Images can be decomposed by wavelet packet transform. With the increase in the order of WPT,the image will be decomposed into more parts,of which each contains the essential information. Based on the good property of WPT and the flexibility of FRFT, the method implicates encryption and decryption of the image and produces many keys, consisting of double random phase masks,the order of WPT and the order of FRFT. Meanwhile,the selected-image-encryption in wavlet domain is realized in this paper,which varies the patterns of encryptioa The method improves the security,and the ability of resisting malicious attacks is also enhanced. The encryption and decryption are implicated by numerical simulation. The result of the simulation provides the requirement for analyzing the properties of encryption and decryptioa The feasibility and simplicity of the method are verified by numerical simulation,and a simple optical implication of the method is also proposed. Based on the numerical simulation and theroy analysis,it can be confluded that the method for the optical image encryption is novel and effective.
Specification of the Fast Fourier Transform algorithm as a term rewriting system
Rodenburg, P.H.; Hoekzema, D.J.
2008-01-01
We specify an algorithm for multiplying polynomials with complex coefficients incorporating, the Fast Fourier Transform algorithm of Cooley and Tukey [CT]. The specification formalism we use is a variant of the formalism ASF described in. [BHK]. The difference with ASF is essentially a matter of sem
Institute of Scientific and Technical Information of China (English)
伍柳
2002-01-01
This article intends to discuss one fundamental aspect of style…differences between formal and informal English with concrete examples through some specific features that distinquish these two types of English.
African Journals Online (AJOL)
Mohammad Saad Zaghloul Salem
2014-12-24
Dec 24, 2014 ... Abstract Formal genetic maps are databases, represented as text or graphic figures, that can be ..... cantly, to our current vague and scanty knowledge of many, ...... similar to reverse engineering techniques, might be worthy of.
Prinz, Andreas
2001-01-01
In dieser Habilitationsschrift wird die formale Semantik der standardisierten Spezifikationssprache SDL (Specification and Description Language) beschrieben. Da SDL eine sehr umfangreiche Sprache ist, wurde eine repräsentative eingeschränkte Sprache RSDL (Restricted SDL) ausgewählt, um die Konzepte der formalen Definition von SDL darzustellen. Die vorliegende Habilitationsschrift umfaßt zwei große Teile: die Definition der formalen Semantik von RSDL und ihre Implementierung. Die formale Def...
DEFF Research Database (Denmark)
Levinsen, Karin Tweddell; Sørensen, Birgitte Holm
2013-01-01
are examined and the relation between network society competences, learners’ informal learning strategies and ICT in formalized school settings over time is studied. The authors find that aspects of ICT like multimodality, intuitive interaction design and instant feedback invites an informal bricoleur approach....... When integrated into certain designs for teaching and learning, this allows for Formalized Informal Learning and support is found for network society competences building....
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
Higher Derivatives and Canonical Formalism
HAMAMOTO, Shinji
1995-01-01
A canonical formalism for higher-derivative theories is presented on the basis of Dirac's method for constrained systems. It is shown that this formalism shares a path integral expression with Ostrogradski's canonical formalism.
Fast Fourier transform telescope
Tegmark, Max; Zaldarriaga, Matias
2009-04-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore’s law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog2N rather than N2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Hackel, L.A.; Hermann, M.R.; Dane, C.B.; Tiszauer, D.H.
1995-12-12
A solid state laser is frequency tripled to 0.3 {micro}m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only about 1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power. 1 fig.
Hackel, Lloyd A.; Hermann, Mark R.; Dane, C. Brent; Tiszauer, Detlev H.
1995-01-01
A solid state laser is frequency tripled to 0.3 .mu.m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only .about.1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power.
Comparative analysis of imaging configurations and objectives for Fourier microscopy
Kurvits, Jonathan A; Zia, Rashid
2015-01-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes, which have been optimized for conventional real-space imaging. Here, we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we ide...
Thermal stabilization of static single-mirror Fourier transform spectrometers
Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.
2017-05-01
Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.
Formalizing Probabilistic Safety Claims
Herencia-Zapana, Heber; Hagen, George E.; Narkawicz, Anthony J.
2011-01-01
A safety claim for a system is a statement that the system, which is subject to hazardous conditions, satisfies a given set of properties. Following work by John Rushby and Bev Littlewood, this paper presents a mathematical framework that can be used to state and formally prove probabilistic safety claims. It also enables hazardous conditions, their uncertainties, and their interactions to be integrated into the safety claim. This framework provides a formal description of the probabilistic composition of an arbitrary number of hazardous conditions and their effects on system behavior. An example is given of a probabilistic safety claim for a conflict detection algorithm for aircraft in a 2D airspace. The motivation for developing this mathematical framework is that it can be used in an automated theorem prover to formally verify safety claims.
Institute of Scientific and Technical Information of China (English)
Cadence公司
2007-01-01
Incisive Formal Verifier为您的工作平台带来了形式分析的强大性能，能够令生产力大幅提高，并提升设计质量。作为Incisive平台的全套断言式验证解决方案的一个关键组件，Incisive Formal Verifier让你能够提前几个月开始验证，降低了重新投片的风险，加快了上市时间。
Žáček, Martin
2017-07-01
Ontology or formal ontology? Which word is correct? The aim of this article is to introduce correct terms and explain their basis. Ontology describes a particular area of interest (domain) in a formal way - defines the classes of objects that are in that area, and relationships that may exist between them. Meaning of ontology consists mainly in facilitating communication between people, improve collaboration of software systems and in the improvement of systems engineering. Ontology in all these areas offer the possibility of unification of view, maintaining consistency and unambiguity.
Dynamic measurement of deformation using Fourier transform digital holographic interferometry
Gao, Xinya; Wu, Sijin; Yang, Lianxiang
2013-10-01
Digital holographic interferometry (DHI) is a well-established optical technique for measurement of nano-scale deformations. It has become more and more important due to the rapid development of applications in aerospace engineering and biomedicine. Traditionally, phase shift technique is used to quantitatively measure the deformations in DHI. However, it cannot be applied in dynamic measurement. Fourier transform phase extraction method, which can determine the phase distribution from only a single hologram, becomes a promising method to extract transient phases in DHI. This paper introduces a digital holographic interferometric system based on 2D Fourier transform phase extraction method, with which deformations of objects can be measured quickly. In the optical setup, the object beam strikes a CCD via a lens and aperture, and the reference beam is projected on the CCD through a single-mode fiber. A small inclination angle between the diverging reference beam and optical axial is introduced in order to physically separate the Fourier components in frequency domain. Phase maps are then obtained by the utilization of Fourier transform and windowed inverse Fourier transform. The capability of the Fourier transform DHI is discussed by theoretical discussion as well as experiments.
Fourier Transform Spectrometer System
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Laser Field Imaging Through Fourier Transform Heterodyne
Energy Technology Data Exchange (ETDEWEB)
Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.
1999-04-05
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.
Digital Backpropagation in the Nonlinear Fourier Domain
Wahls, Sander; Prilepsky, Jaroslaw E; Poor, H Vincent; Turitsyn, Sergei K
2015-01-01
Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr\\"odinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the ...
Fourier Transform Fabry-Perot Interferometer
Snell, Hilary E.; Hays, Paul B.
1992-01-01
We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
du Gay, Paul; Lopdrup-Hjorth, Thomas
2016-01-01
term this ‘fear of the formal’, outlining key elements of its genealogy and exploring its contemporary manifestation in relation to recent and ongoing reforms of organisational life in a range of contexts. At the same time, we seek to indicate the continuing constitutive significance of formality...
DEFF Research Database (Denmark)
Garsten, Christina; Nyqvist, Anette
suits’ (Nyqvist 2013), and of doing ‘ethnography by failure’ (Garsten 2013). In this paper, we explore the layers of informality and formality in our fieldwork experiences among financial investors and policy experts, and discuss how to ethnographically represent embodied fieldwork practices. How do we...
Formal synthesis of (+)-discodermolide.
Francavilla, Charles; Chen, Weichun; Kinder, Frederick R
2003-04-17
[structure: see text] Herein we report the formal total synthesis of (+)-discodermolide in 21 steps (longest linear sequence) from commercially available Roche ester. This synthesis features the assembly of C(9-18) and C(19-24) fragments via a metal-chelated aldol coupling reaction.
DEFF Research Database (Denmark)
Rand, John; Torm, Nina Elisabeth
2012-01-01
factors and observable time-variant factors that may simultaneously influence the decision to formalize and subsequent firm performance, we find evidence that becoming officially registered leads to an increase in profits and investments, and a decrease in the use of casual labor (improved contract...
The Fourier U(2 Group and Separation of Discrete Variables
Directory of Open Access Journals (Sweden)
Kurt Bernardo Wolf
2011-06-01
Full Text Available The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R, whose maximal compact subgroup is the Fourier group U(2_F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4. Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle coordinates, thus realizing one case of separation in two discrete coordinates. The N^2-vectors in this space are digital (pixellated images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.
Twin image elimination in digital holography by combination of Fourier transformations
Choudhury, Debesh
2013-01-01
We present a new technique for removing twin image in in-line digital Fourier holography using a combination of Fourier transformations. Instead of recording only a Fourier transform hologram of the object, we propose to record a combined Fourier transform hologram by simultaneously recording the hologram of the Fourier transform and the inverse Fourier transform of the object with suitable weighting coefficients. Twin image is eliminated by appropriate inverse combined Fourier transformation and proper choice of the weighting coefficients. An optical configuration is presented for recording combined Fourier transform holograms. Simulations demonstrate the feasibility of twin image elimination. The hologram reconstruction is sensitive to phase aberrations of the object, thereby opening a way for holographic phase sensing.
Entangled Fractional Fourier Transform for the Multipartite Entangled State Representation
Institute of Scientific and Technical Information of China (English)
QIAN Xiao-Qing; SONG Tong-Qiang
2006-01-01
We deduce entangled fractional Fourier transformation (EFFT) for the multipartite entangled state representation, which was newly constructed with two mutually conjugate n-mode entangled states of continuum variables in n-mode Fock space. We establish a formalism of EFFT for quantum mechanical wave functions, which provides us a convenient way to derive some wave functions. We find that the eigenmode of EFFT is different from the usual Hermite Polynomials. We also derive the EFFT of the n-mode squeezed state.
Formal analogies in physics teacher education
DEFF Research Database (Denmark)
Avelar Sotomaior Karam, Ricardo; Ricardo, Elio
2012-01-01
the relevance of the subject, formal analogies are rarely systematically approached in physics education. In order to discuss this issue with pre-service physics teachers, we planned a lecture and designed a questionnaire with the goal of encouraging them to think about some “coincidences” in well known......Reasoning by similarities, especially the ones associated with formal aspects, is one of the most valuable sources for the development of physical theories. The essential role of formal analogies in science can be highlighted by the fact that several equations for different physical situations have...... the exact same appearance. Coulomb’s law’s similarity with Newton’s, Maxwell’s application of fluid theory to electromagnetism and Hamilton’s optical mechanical analogy are some among many other examples. These cases illustrate the power of mathematics in providing unifying structures for physics. Despite...
Formal analogies in physics teacher education
DEFF Research Database (Denmark)
Avelar Sotomaior Karam, Ricardo; Ricardo, Elio
2012-01-01
the relevance of the subject, formal analogies are rarely systematically approached in physics education. In order to discuss this issue with pre-service physics teachers, we planned a lecture and designed a questionnaire with the goal of encouraging them to think about some “coincidences” in well known......Reasoning by similarities, especially the ones associated with formal aspects, is one of the most valuable sources for the development of physical theories. The essential role of formal analogies in science can be highlighted by the fact that several equations for different physical situations have...... the exact same appearance. Coulomb’s law’s similarity with Newton’s, Maxwell’s application of fluid theory to electromagnetism and Hamilton’s optical mechanical analogy are some among many other examples. These cases illustrate the power of mathematics in providing unifying structures for physics. Despite...
Historical revision of the differential Stokes-Mueller formalism: discussion.
Arteaga, Oriol
2017-03-01
The differential Stokes-Mueller matrix formalism expresses the local evolution of the Mueller matrix or the Stokes parameters for light propagating through a homogeneous optical medium. This paper presents a historical revision of the development of the differential Stokes-Mueller matrix formalism and highlights several important early contributions that have been overlooked. Particularly relevant is that this formalism was pioneered as early as 1929 by Paul Soleillet, almost 50 years earlier than it has been usually assumed. This historical revision demonstrates that several different authors independently formulated the differential Stokes-Mueller formalism during the 20th century and they found equivalent results studying the propagation problem from different approaches.
Reconstruction in Fourier space
Burden, A.; Percival, W. J.; Howlett, C.
2015-10-01
We present a fast iterative fast Fourier transform (FFT) based reconstruction algorithm that allows for non-parallel redshift-space distortions (RSDs). We test our algorithm on both N-body dark matter simulations and mock distributions of galaxies designed to replicate galaxy survey conditions. We compare solenoidal and irrotational components of the redshift distortion and show that an approximation of this distortion leads to a better estimate of the real-space potential (and therefore faster convergence) than ignoring the RSD when estimating the displacement field. Our iterative reconstruction scheme converges in two iterations for the mock samples corresponding to Baryon Oscillation Spectroscopic Survey CMASS Data Release 11 when we start with an approximation of the RSD. The scheme takes six iterations when the initial estimate, measured from the redshift-space overdensity, has no RSD correction. Slower convergence would be expected for surveys covering a larger angle on the sky. We show that this FFT based method provides a better estimate of the real-space displacement field than a configuration space method that uses finite difference routines to compute the potential for the same grid resolution. Finally, we show that a lognormal transform of the overdensity, used as a proxy for the linear overdensity, is beneficial in estimating the full displacement field from a dense sample of tracers. However, the lognormal transform of the overdensity does not perform well when estimating the displacements from sparser simulations with a more realistic galaxy density.
Grafakos, Loukas
2014-01-01
This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews fr...
POINTWISE FOURIER INVERSION OF DISTRIBUTIONS
Institute of Scientific and Technical Information of China (English)
F.J.González Vieli
2008-01-01
We show that,given a tempered distribution T whose Fourier transform is a function of polynomial growth and a point x in Rn at which T has the value τ(in the sense of Lojasiewicz),the Fourier integral of T at x is summable in Bochner-Riesz means to τ.
Wavelet-fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
Readings in Formal Epistemology
DEFF Research Database (Denmark)
‘Formal epistemology’ is a term coined in the late 1990s for a new constellation of interests in philosophy,the roots of which are found in earlier works of epistemologists, philosophers of science, and logicians. It addresses a growing agenda of problems concerning knowledge, belief, certainty......, rationality, deliberation, decision, strategy, action and agent interaction – and it does so using methods from logic, probability, computability, decision, and game theory. This volume presents 42 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy...... and its neighbouring intellectual disciplines. The editors provide introductions to five basic subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactive Epistemology and Logics of Knowledge and Belief. The volume also includes a thorough index and suggestions for further reading...
Talebian-Ashkezari, Alireza; Abolhasani, Ali Akbar
2016-01-01
We study the evolution of the "non-perturbative" metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the "{\\delta}M formalism" for calculating the evolution of the tensor perturbations in anisotropic inflation models in almost similar way as the so-called {\\delta}N formula for the super-horizon dynamics of the curvature perturbations. Likewise its ancestor, {\\delta}N formalism, this new method can substantially reduce the amount of calculations related to the evolution of the tensor modes.
Formal groups and applications
Hazewinkel, Michiel
2012-01-01
This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
Digital Fourier analysis advanced techniques
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to advanced digital Fourier analysis for advanced undergraduate and graduate students. Assuming knowledge of the Fast Fourier Transform, this book covers advanced topics including the Hilbert transform, cepstrum analysis, and the two-dimensional Fourier transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Advanced Techniques" includes practice problems and thorough Appendices. As a central feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. The applet source code in Visual Basic is provided online, enabling advanced students to tweak and change the programs for more sophisticated results. A complete, intuitive guide, "Digital Fourier Analysis - Advanced Techniques" is an essential reference for students in science and engineering.
Institute of Scientific and Technical Information of China (English)
张海涛; 徐英英; 王保君; 朱红军
2011-01-01
Objective To assess visibility of scleral spur in images of anterior chamber angle measured by the CAM model of Fourier optic coherence tomography (OCT). Methods Subjects aged 40 years or older were selected from outpatients in our opthalmologic clinic. All participants underwent standard ocular examinations, and anterior chamber angle was measured by CAM-L model of RTVue-OCT (Optovue Inc,USA) and gonioscopy. Visibility of scleral spur in OCT images and its related factor were analyzed. Results 98 subjects (98 eyes) aged (63.3±10.5)y included 62 females (63.3%) were selected in this study. There were 286 in 392 quadrants (73.0%) with visualized scleral spur, which had significant difference among local bulbar conjunctiva thickened or not (P＜0.01). Logistic multiple regression showed that the visibility of scleral spur was not associated with gender, age, gonioscope grades (P＞0.05), but significant associated with local bulbar conjunctiva thickened (OR＝0.113, P＜0.01) and quadrants (OR of superior/temporal＝0.210, OR of inferior/temporal＝0.340, P＜0.01), of which there were different scleral spur visibility in superior and inferior quadrants compared with temporal(OR＝0.210, 0.340, P＜0.01). Angle status was still identified in 80.2% quadrants on condition that scleral spur was not visualized. Conclusions Fourier optic coherence tomography has good feasibility to detect anterior chamber angle as an alternative method, and may supply helpful information to estimate the pathogenesis of angle closure glaucoma.%目的 探讨傅立叶光学相干断层扫描仪CAM模块房角测量图像中巩膜突可见性及其影响因素.方法 连续选择本院眼科门诊40岁及以上患者,所有受试者均接受眼科常规项目检查,房角均分别接受Rtvue OCT(Optovue Inc,USA)CAM模块和房角镜检查.分析OCT图像中巩膜突的可见性及其影响因素.结果 受试者共98例(98眼),年龄(63.3±10.5)岁,其中女性62例(63.3%).在392
The Asymmetric Pupil Fourier Wavefront Sensor
Martinache, Frantz
2013-01-01
This paper introduces a novel wavefront sensing approach that relies on the Fourier analysis of a single conventional direct image. In the high Strehl ratio regime, the relation between the phase measured in the Fourier plane and the wavefront errors in the pupil can be linearized, as was shown in a previous work that introduced the notion of generalized closure-phase, or kernel-phase. The technique, to be usable as presented requires two conditions to be met: (1) the wavefront errors must be kept small (of the order of one radian or less) and (2) the pupil must include some asymmetry, that can be introduced with a mask, for the problem to become solvable. Simulations show that this asymmetric pupil Fourier wavefront sensing or APF-WFS technique can improve the Strehl ratio from 50 to over 90 % in just a few iterations, with excellent photon noise sensitivity properties, suggesting that on-sky close loop APF-WFS is possible with an extreme adaptive optics system.
Matrix isolation studies with Fourier transform IR
Energy Technology Data Exchange (ETDEWEB)
Green, David W.; Reedy, Gerald T.
1977-01-01
The combination of Fourier transform infrared (FT-IR) spectroscopy with the matrix-isolation techniques has advantages compared with the use of more conventional grating spectroscopy. Furthermore, the recent commercial availability of Fourier transform spectrometers has made FT-IR a practical alternative. Some advantages of the FT-IR spectrometer over the grating spectrometer are the result of the computerized data system that is a necessary part of the FT-IR spectrometer; other advantages are a consequence of the difference in optical arrangements and these represent the inherent advantages of the FT-IR method. In most applications with the matrix-isolation technique, the use of FT-IR spectroscopy results in either an improved signal-to-noise ratio or a shorter time for data collection compared with grating infrared spectroscopy. Fourier transform infrared spectroscopy has been used in the laboratory to study several molecular species in low-temperature matrices. Some species have been produced by high-temperature vaporization from Knudsen cells and others by sputtering. By sputtering, Ar and Kr matrices have been prepared which contain U atoms, UO, UO/sub 2/, UO/sub 3/, PuO, PuO/sub 2/, UN, or UN/sub 2/, depending upon the composition of the gas used to sputter as well as the identity of the metallic cathode. Infrared spectra of matrices containing these compounds are presented and discussed. (JRD)
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
Scenario testing using formal ontologies
CSIR Research Space (South Africa)
Harmse, HF
2014-09-01
Full Text Available . Recent research concerned with the formal validation of such UML class diagrams has focused on transforming UML class diagrams to various formalisms such as description logics. Description logics are desirable since they have reasoning support which can...
Formalizing the concept of sound.
Energy Technology Data Exchange (ETDEWEB)
Kaper, H. G.; Tipei, S.
1999-08-03
The notion of formalized music implies that a musical composition can be described in mathematical terms. In this article we explore some formal aspects of music and propose a framework for an abstract approach.
Directory of Open Access Journals (Sweden)
Alexei Serna A.
2012-12-01
Full Text Available The application of formal methods in industry has progressed extensively over the past decade and the results are promising. But despite these achievements and it have been documented in numerous studies, it is still very common the skepticism about its usefulness and applicability. The goal of this paper is to show that its evolution over the past decade exceeds all previous processes and each time they do a better job to satisfy industrial needs. This is achieved by the description of some experiments and the result of various applications in industry and through an analyzing of the needs of companies that must be satisfy the research community in this field.
DEFF Research Database (Denmark)
Levinsen, Karin; Sørensen, Birgitte Holm
2011-01-01
This paper presents findings from a large-scale longitudinal, qualitative study - Project ICT and Learning (PIL) - that engaged the participation of eight primary schools in Denmark, and was conducted between 2006 and 2008. The research design was based on action research, involving teachers and ...... in society, educational sector and technology....... and other relevant stakeholders, as well as participant observations in the classroom documented by thick descriptions, formal and informal interviews and focus group interviews. The aim of the study was to explore and identify relations between designs for teaching and learning and the students' learning...
Intelligence in formal machines
Vieira, Paulo Alexandre Andrade
2016-01-01
[ES]El objetivo de este trabajo es encontrar una forma de definir y medir la inteligencia en los sistemas formales computacionales. Para hacer esto yo hice varios tipos de consideraciones: en primer lugar, el concepto de ¿ ser inteligente ¿ asume nociones claras y se mide de manera aceptable sólo en el ser humano; segundo, hay una creciendo y salvaje uso del concepto ¿ ser inteligente¿ para el comportamiento de otros seres biológicos; tercero, hoy en día la palabra ¿inteligencia¿ a menudo se ...
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
Formal Methods in Knowledge Engineering
Harmelen, van F.A.H.; Fensel, D.
1995-01-01
This paper presents a general discussion of the role of formal methods in Knowledge Engineering. We give an historical account of the development of the field of Knowledge Engineering towards the use of formal methods. Subsequently, we discuss the pro's and cons of formal methods. We do this by summ
Formal Methods in Knowledge Engineering
Harmelen, van F.A.H.; Fensel, D.
1995-01-01
This paper presents a general discussion of the role of formal methods in Knowledge Engineering. We give an historical account of the development of the field of Knowledge Engineering towards the use of formal methods. Subsequently, we discuss the pro's and cons of formal methods. We do this by
Covariant Bardeen perturbation formalism
Vitenti, S. D. P.; Falciano, F. T.; Pinto-Neto, N.
2014-05-01
In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Discovery of Fourier-dependent time lags in cataclysmic variables
Scaringi, S.; Körding, E.; Groot, P.J.; Uttley, P.; Marsh, T.; Knigge, C.; Maccarone, T.; Dhillon, V.S.
2013-01-01
We report the first study of Fourier-frequency-dependent coherence and phase/time lags at optical wavelengths of cataclysmic variables (MV Lyr and LU Cam) displaying typical flickering variability in white light. Observations were performed on the William Herschel Telescope using ULTRACAM. Light
Grid-Independent Compressive Imaging and Fourier Phase Retrieval
Liao, Wenjing
2013-01-01
This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem. Many situations in optics, medical imaging and signal processing call…
Fourier series and orthogonal functions
Davis, Harry F
1963-01-01
This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging.
Guenther, B D
2015-01-01
Modern Optics is a fundamental study of the principles of optics using a rigorous physical approach based on Maxwell's Equations. The treatment provides the mathematical foundations needed to understand a number of applications such as laser optics, fiber optics and medical imaging covered in an engineering curriculum as well as the traditional topics covered in a physics based course in optics. In addition to treating the fundamentals in optical science, the student is given an exposure to actual optics engineering problems such as paraxial matrix optics, aberrations with experimental examples, Fourier transform optics (Fresnel-Kirchhoff formulation), Gaussian waves, thin films, photonic crystals, surface plasmons, and fiber optics. Through its many pictures, figures, and diagrams, the text provides a good physical insight into the topics covered. The course content can be modified to reflect the interests of the instructor as well as the student, through the selection of optional material provided in append...
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
Directory of Open Access Journals (Sweden)
Diana-Maria Drigă
2015-12-01
Full Text Available The concept of resilience has represented during the recent years a leading concern both in Romania, within the European Union and worldwide. Specialists in economics, management, finance, legal sciences, political sciences, sociology, psychology, grant a particular interest to this concept. Multidisciplinary research of resilience has materialized throughout the time in multiple conceptualizations and theorizing, but without being a consensus between specialists in terms of content, specificity and scope. Through this paper it is intended to clarify the concept of resilience, achieving an exploration of the evolution of this concept in ecological, social and economic environment. At the same time, the paper presents aspects of feedback mechanisms and proposes a formalization of resilience using the logic and mathematical analysis.
Comparative analysis of imaging configurations and objectives for Fourier microscopy.
Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid
2015-11-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.
Research progress of the fractional Fourier transform in signal processing
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.
An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.
Eastman, M. P.; And Others
1986-01-01
Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.
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.
On-chip photonic Fourier transform with surface plasmon polaritons
Institute of Scientific and Technical Information of China (English)
Shan Shan Kou; Guanghui Yuan; Qian wang; Luping Du; Eugeniu Balaur; Daohua Zhang; Dingyuan Tang
2016-01-01
The Fourier transform (FT),a cornerstone of optical processing,enables rapid evaluation of fundamental mathematical operations,such as derivatives and integrals.Conventionally,a converging lens performs an optical FT in free space when light passes through it.The speed of the transformation is limited by the thickness and the focal length of the lens.By usingthe wave nature of surface plasmon polaritons (SPPs),here we demonstrate that the FT can be implemented in a planar configuration with a minimal propagation distance of around 10 μm,resulting in an increase of speed by four to five orders of magnitude.The photonic FT was tested by synthesizing intricate SPP waves with their Fourier components.The reduced dimensionality in the minuscule device allows the future development of an ultrafast on-chip photonic information processing platform for large-scale optical computing.
Formal connections in deformation quantization
DEFF Research Database (Denmark)
Masulli, Paolo
attention on symplectic manifolds equipped with a family of star products, indexed by a parameter space. In this situation we can define a connection in the trivial bundle over the parameter space with fibres the formal smooth functions on the manifold, which relates the star products in the family...... and is called a formal connection. We study the question of classifying such formal connections. To each star product we can associate a certain cohomology class called the characteristic class. It turns out that a formal connection exists if and only if all the star products in the family have the same...... characteristic class, and that formal connections form an affine space over the derivations of the star products. Moreover, if the parameter space for the family of star products is contractible, we obtain that any two flat formal connections are gauge equivalent via a self-equivalence of the family of star...
Deep First Formal Concept Search
Directory of Open Access Journals (Sweden)
Tao Zhang
2014-01-01
Full Text Available The calculation of formal concepts is a very important part in the theory of formal concept analysis (FCA; however, within the framework of FCA, computing all formal concepts is the main challenge because of its exponential complexity and difficulty in visualizing the calculating process. With the basic idea of Depth First Search, this paper presents a visualization algorithm by the attribute topology of formal context. Limited by the constraints and calculation rules, all concepts are achieved by the visualization global formal concepts searching, based on the topology degenerated with the fixed start and end points, without repetition and omission. This method makes the calculation of formal concepts precise and easy to operate and reflects the integrity of the algorithm, which enables it to be suitable for visualization analysis.
Fourier-transform and global contrast interferometer alignment methods
Goldberg, Kenneth A.
2001-01-01
Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...
The Operator Manifold Formalism, 1
Ter-Kazarian, G T
1998-01-01
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the spacetime continuum and internal worlds, where the subquarks are defined implying the Confinement and Gauge principles. This formalism in Part II (hep-th/9812182) is used to develop further the microscopic approach to some key problems of particle physics.
Formalized Epistemology, Logic, and Grammar
Bitbol, Michel
The task of a formal epistemology is defined. It appears that a formal epistemology must be a generalization of "logic" in the sense of Wittgenstein's Tractatus. The generalization is required because, whereas logic presupposes a strict relation between activity and language, this relation may be broken in some domains of experimental enquiry (e.g., in microscopic physics). However, a formal epistemology should also retain a major feature of Wittgenstein's "logic": It must not be a discourse about scientific knowledge, but rather a way of making manifest the structures usually implicit in knowledge-gaining activity. This strategy is applied to the formalism of quantum mechanics.
DEFF Research Database (Denmark)
Bjørner, Dines; Havelund, Klaus
2014-01-01
In this "40 years of formal methods" essay we shall first delineate, Sect. 1, what we mean by method, formal method, computer science, computing science, software engineering, and model-oriented and algebraic methods. Based on this, we shall characterize a spectrum from specification-oriented met......In this "40 years of formal methods" essay we shall first delineate, Sect. 1, what we mean by method, formal method, computer science, computing science, software engineering, and model-oriented and algebraic methods. Based on this, we shall characterize a spectrum from specification...
Static Fourier transform infrared spectrometer.
Schardt, Michael; Murr, Patrik J; Rauscher, Markus S; Tremmel, Anton J; Wiesent, Benjamin R; Koch, Alexander W
2016-04-01
Fourier transform spectroscopy has established itself as the standard method for spectral analysis of infrared light. Here we present a robust and compact novel static Fourier transform spectrometer design without any moving parts. The design is well suited for measurements in the infrared as it works with extended light sources independent of their size. The design is experimentally evaluated in the mid-infrared wavelength region between 7.2 μm and 16 μm. Due to its large etendue, its low internal light loss, and its static design it enables high speed spectral analysis in the mid-infrared.
Formal, Non-Formal and Informal Learning in the Sciences
Ainsworth, Heather L.; Eaton, Sarah Elaine
2010-01-01
This research report investigates the links between formal, non-formal and informal learning and the differences between them. In particular, the report aims to link these notions of learning to the field of sciences and engineering in Canada and the United States, including professional development of adults working in these fields. It offers…
The Design of Lens Imaging System by Means of Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
CHEN Jiannong; XU Qiang; D.R.Selviah
2002-01-01
The relation between the 2nd fractional Fourier transform and the imaging process of an optical system is discussed. By changing the coordinate scales of the input plane in respect to the magnification of the optical imaging system, the fractional Fourier transform can be a powerful tool in designing specific imaging system. The Gaussian imaging formula of single lens is obtained by using the tool. Finally the procedures are generalized for designing a double-lens imaging system through an example.
Fourier-positivity constraints on QCD dipole models
Directory of Open Access Journals (Sweden)
Bertrand G. Giraud
2016-09-01
Full Text Available Fourier-positivity (F-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position space r. They are Bessel transforms of positive transverse momentum dependent gluon distributions. Using mathematical F-positivity constraints on the limit r→0 behavior of the dipole amplitudes, we identify the common origin of the violation of F-positivity for various, however phenomenologically convenient, dipole models. It is due to the behavior r2+ϵ, ϵ>0 softer, even slightly, than color transparency. F-positivity seems thus to conflict with the present dipole formalism when it includes a QCD running coupling constant α(r.
A Borderline Random Fourier Series
Talagrand, Michel
1995-01-01
Consider a mean zero random variable $X$, and an independent sequence $(X_n)$ distributed like $X$. We show that the random Fourier series $\\sum_{n\\geq 1} n^{-1} X_n \\exp(2i\\pi nt)$ converges uniformly almost surely if and only if $E(|X|\\log\\log(\\max(e^e, |X|))) < \\infty$.
Fourier Series and Elliptic Functions
Fay, Temple H.
2003-01-01
Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…
Fourier Lucas-Kanade algorithm.
Lucey, Simon; Navarathna, Rajitha; Ashraf, Ahmed Bilal; Sridharan, Sridha
2013-06-01
In this paper, we propose a framework for both gradient descent image and object alignment in the Fourier domain. Our method centers upon the classical Lucas & Kanade (LK) algorithm where we represent the source and template/model in the complex 2D Fourier domain rather than in the spatial 2D domain. We refer to our approach as the Fourier LK (FLK) algorithm. The FLK formulation is advantageous when one preprocesses the source image and template/model with a bank of filters (e.g., oriented edges, Gabor, etc.) as 1) it can handle substantial illumination variations, 2) the inefficient preprocessing filter bank step can be subsumed within the FLK algorithm as a sparse diagonal weighting matrix, 3) unlike traditional LK, the computational cost is invariant to the number of filters and as a result is far more efficient, and 4) this approach can be extended to the Inverse Compositional (IC) form of the LK algorithm where nearly all steps (including Fourier transform and filter bank preprocessing) can be precomputed, leading to an extremely efficient and robust approach to gradient descent image matching. Further, these computational savings translate to nonrigid object alignment tasks that are considered extensions of the LK algorithm, such as those found in Active Appearance Models (AAMs).
Fourier Analysis of Musical Intervals
LoPresto, Michael C.
2008-01-01
Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace. A recent article in "The Physics Teacher" aptly demonstrated the use of MacScope in just such a manner as a way to teach Fourier analysis. A logical continuation of this project is to…
A Formalization of Linkage Analysis
DEFF Research Database (Denmark)
Ingolfsdottir, Anna; Christensen, A.I.; Hansen, Jens A.
In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been ...
A Formalization of Linkage Analysis
DEFF Research Database (Denmark)
Ingolfsdottir, Anna; Christensen, A.I.; Hansen, Jens A.
In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been...
New procedure for departure formalities
HR & GS Departments
2011-01-01
As part of the process of simplifying procedures and rationalising administrative processes, the HR and GS Departments have introduced new personalised departure formalities on EDH. These new formalities have applied to students leaving CERN since last year and from 17 October 2011 this procedure will be extended to the following categories of CERN personnel: Staff members, Fellows and Associates. It is planned to extend this electronic procedure to the users in due course. What purpose do departure formalities serve? The departure formalities are designed to ensure that members of the personnel contact all the relevant services in order to return any necessary items (equipment, cards, keys, dosimeter, electronic equipment, books, etc.) and are aware of all the benefits to which they are entitled on termination of their contract. The new departure formalities on EDH have the advantage of tailoring the list of services that each member of the personnel must visit to suit his individual contractual and p...
Fourier analysis for rotating-element ellipsometers.
Cho, Yong Jai; Chegal, Won; Cho, Hyun Mo
2011-01-15
We introduce a Fourier analysis of the waveform of periodic light-irradiance variation to capture Fourier coefficients for multichannel rotating-element ellipsometers. In this analysis, the Fourier coefficients for a sample are obtained using a discrete Fourier transform on the exposures. The analysis gives a generic function that encompasses the discrete Fourier transform or the Hadamard transform, depending on the specific conditions. Unlike the Hadamard transform, a well-known data acquisition method that is used only for conventional multichannel rotating-element ellipsometers with line arrays with specific readout-mode timing, this Fourier analysis is applicable to various line arrays with either nonoverlap or overlap readout-mode timing. To assess the effects of the novel Fourier analysis, the Fourier coefficients for a sample were measured with a custom-built rotating-polarizer ellipsometer, using this Fourier analysis with various numbers of scans, integration times, and rotational speeds of the polarizer.
Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko
2013-12-01
The relation between a three-dimensional (3D) object and its diffracted wavefront in the 3D Fourier space is discussed at first and then a rigorous diffraction formula onto cylindrical surfaces is derived. The azimuthal direction and the spatial frequency direction corresponding to height can be expressed with a one-dimensional (1D) convolution integral and a 1D inverse Fourier transform in the 3D Fourier space, respectively, and fast Fourier transforms are available for fast calculation. A numerical simulation of a diffracted wavefront on cylindrical surfaces is presented. An alternative optical experiment equivalent of the optical reconstruction from cylindrical holograms is also demonstrated.
Formal verification - Robust and efficient code: Introduction to Formal Verification
CERN. Geneva
2016-01-01
In general, FV means "proving that certain properties hold for a given system using formal mathematics". This definition can certainly feel daunting, however, as we will learn, we can reap benefits from the paradigm without digging too deep into ...
Gåsvik, Kjell J
2003-01-01
New material on computerized optical processes, computerized ray tracing, and the fast Fourier transform, Bibre-Bragg sensors, and temporal phase unwrapping.* New introductory sections to all chapters.* Detailed discussion on lasers and laser principles, including an introduction to radiometry and photometry.* Thorough coverage of the CCD camera.
Image encryption techniques based on the fractional Fourier transform
Hennelly, B. M.; Sheridan, J. T.
2003-11-01
The fractional Fourier transform, (FRT), is a generalisation of the Fourier transform which allows domains of mixed spatial frequency and spatial information to be examined. A number of method have recently been proposed in the literature for the encryption of two dimensional information using optical systems based on the FRT. Typically, these methods require random phase screen keys to decrypt the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. We have proposed a new technique based on a random shifting or Jigsaw transformation. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in various FRT domains. The new method has been compared numerically with existing methods and shows comparable or superior robustness to blind decryption. An optical implementation is also proposed and the sensitivity of the various encryption keys to blind decryption is quantified. We also present a second image encryption technique, which is based on a recently proposed method of optical phase retrieval using the optical FRT and one of its discrete counterparts. Numerical simulations of the new algorithm indicates that the sensitivity of the keys is much greater than any of the techniques currently available. In fact the sensitivity appears to be so high that optical implementation, based on existing optical signal processing technology, may be impossible. However, the technique has been shown to be a powerful method of 2-D image data encryption.
Formal Component-Based Semantics
Madlener, Ken; van Eekelen, Marko; 10.4204/EPTCS.62.2
2011-01-01
One of the proposed solutions for improving the scalability of semantics of programming languages is Component-Based Semantics, introduced by Peter D. Mosses. It is expected that this framework can also be used effectively for modular meta theoretic reasoning. This paper presents a formalization of Component-Based Semantics in the theorem prover Coq. It is based on Modular SOS, a variant of SOS, and makes essential use of dependent types, while profiting from type classes. This formalization constitutes a contribution towards modular meta theoretic formalizations in theorem provers. As a small example, a modular proof of determinism of a mini-language is developed.
Formal Verification of NTRUEncrypt Scheme
Directory of Open Access Journals (Sweden)
Gholam Reza Moghissi
2016-04-01
Full Text Available In this paper we explore a mechanized verification of the NTRUEncrypt scheme, with the formal proof system Isabelle/HOL. More precisely, the functional correctness of this algorithm, in its reduced form, is formally verified with computer support. We show that this scheme is correct what is a necessary condition for the usefulness of any cryptographic encryption scheme. Besides, we present a convenient and application specific formalization of the NTRUEncrypt scheme in the Isabelle/HOL system that can be used in further study around the functional and security analysis of NTRUEncrypt family.
DEFF Research Database (Denmark)
Bjørner, Dines; Havelund, Klaus
2014-01-01
-oriented methods to analysis-oriented methods. Then, Sect. 2, we shall provide a "survey": which are the 'prerequisite works' that have enabled formal methods, Sect. 2.1, and which are, to us, the, by now, classical 'formal methods', Sect. 2.2. We then ask ourselves the question: have formal methods for software......" is complemented, in Sect. 3.4, by a "looking forward" at some promising developments-besides the alleviation of the (eighth or more) hindrances! © 2014 Springer International Publishing Switzerland....
Scalable Techniques for Formal Verification
Ray, Sandip
2010-01-01
This book presents state-of-the-art approaches to formal verification techniques to seamlessly integrate different formal verification methods within a single logical foundation. It should benefit researchers and practitioners looking to get a broad overview of the spectrum of formal verification techniques, as well as approaches to combining such techniques within a single framework. Coverage includes a range of case studies showing how such combination is fruitful in developing a scalable verification methodology for industrial designs. This book outlines both theoretical and practical issue
Motion-corrected Fourier ptychography
Bian, Liheng; Guo, Kaikai; Suo, Jinli; Yang, Changhuei; Chen, Feng; Dai, Qionghai
2016-01-01
Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the FP reconstruction and limits its practicability. In this paper, we propose a novel FP reconstruction method to efficiently correct for unknown sample motion. Specifically, we adaptively update the sample's Fourier spectrum from low spatial-frequency regions towards high spatial-frequency ones, with an additional motion recovery and phase-offset compensation procedure for each sub-spectrum. Benefiting from the phase retrieval redundancy theory, the required large overlap between adjacent sub-spectra offers an accurate guide for successful motion recovery. Experimental results on both simulated data and real captured data show that the proposed method can correct for unknown sample motion with its standard deviation being up to 10% of the field-of-view scale. We have released...
Fourier Analysis of Blazar Variability
Finke, Justin D
2014-01-01
Blazars display strong variability on multiple timescales and in multiple radiation bands. Their variability is often characterized by power spectral densities (PSDs) and time lags plotted as functions of the Fourier frequency. We develop a new theoretical model based on the analysis of the electron transport (continuity) equation, carried out in the Fourier domain. The continuity equation includes electron cooling and escape, and a derivation of the emission properties includes light travel time effects associated with a radiating blob in a relativistic jet. The model successfully reproduces the general shapes of the observed PSDs and predicts specific PSD and time lag behaviors associated with variability in the synchrotron, synchrotron self-Compton (SSC), and external Compton (EC) emission components, from sub-mm to gamma-rays. We discuss applications to BL Lacertae objects and to flat-spectrum radio quasars (FSRQs), where there are hints that some of the predicted features have already been observed. We a...
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Wide-field, high-resolution Fourier ptychographic microscopy
Zheng, Guoan; Yang, Changhuei
2014-01-01
In this article, we report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and digitally extend a microscope's depth-of-focus beyond the physical limitations of its optics. As a demonstration, we built a microscope prototype with a resolution of 0.78 um, a field-of-view of ~120 mm2, and a resolution-invariant depth-of-focus of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify FPM's successful operation. The reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one that is coupled to the physical limitations of the system's optics to one that is solvable through computation.
Canning plasmonic microscopy by image reconstruction from the Fourier space
Mollet, O; Drezet, A
2014-01-01
We demonstrate a simple scheme for high-resolution imaging of nanoplasmonic structures that basically removes most of the resolution limiting allowed light usually transmitted to the far field. This is achieved by implementing a Fourier lens in a near-field scanning optical microscope (NSOM) operating in the leakage-radiation microscopy (LRM) mode. The method consists of reconstructing optical images solely from the plasmonic `forbidden' light collected in the Fourier space. It is demonstrated by using a point-like nanodiamond-based tip that illuminates a thin gold film patterned with a sub-wavelength annular slit. The reconstructed image of the slit shows a spatial resolution enhanced by a factor $\\simeq 4$ compared to NSOM images acquired directly in the real space.
Fourier's Law in Quantum Mechanics
Seligman, Thomas H
2010-01-01
We derive Fourier's law for a completely coherent quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the length of the system.
A More Accurate Fourier Transform
Courtney, Elya
2015-01-01
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals (EI) that define Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric $\\mathrm{CO_2}$ concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT's FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability t...
An introduction to Fourier series and integrals
Seeley, Robert T
2006-01-01
This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Concepts of formal concept analysis
Žáček, Martin; Homola, Dan; Miarka, Rostislav
2017-07-01
The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.
El Salvador - Formal Technical Education
Millennium Challenge Corporation — With a budget of nearly $20 million, the Formal Technical Education Sub-Activity was designed to strengthen technical and vocational educational institutions in the...
Readings in Formal Epistemology : Sourcebook
Arló-Costa, H.; Hendricks, V.F.; van Benthem, J.
2016-01-01
This volume presents 38 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy and its neighbouring intellectual disciplines. The editors provide introductions to five subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactiv
Readings in Formal Epistemology: sourcebook
Arló-Costa, H.; Hendricks, V.F.; van Benthem, J.
2016-01-01
This volume presents 38 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy and its neighbouring intellectual disciplines. The editors provide introductions to five subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactiv
Formal Verification of UML Profil
DEFF Research Database (Denmark)
Bhutto, Arifa; Hussain, Dil Muhammad Akbar
2011-01-01
The Unified Modeling Language (UML) is based on the Model Driven Development (MDD) approach which capturing the system functionality using the platform-independent model (PMI) and appropriate domain-specific languages. In UML base system notations, structural view is model by the class, components...... and object diagrams and behavioral view model by the activity, use case, state, and sequence diagram. However, UML does not provide the formal syntax, therefore its semantics is not formally definable, so for assure of correctness, we need to incorporate semantic reasoning through verification, specification......, refinement, and incorporate into the development process. Our motivation of research is to make an easy structural view and suggest formal technique/ method which can be best applied or used for the UML based development system. We investigate the tools and methods, which broadly used for the formal...
Formal versus informal small businesses
African Journals Online (AJOL)
There is renewed interest in entrepreneurship, business formation and growth. ... acumen, while small formal businesses show higher levels of growth instigated by an ... Small business support strategies should focus on businesses with ...
Formalism and functionalism in linguistics.
Newmeyer, Frederick J
2010-05-01
Formalism and functionalism in linguistics are often taken to be diametrically opposed approaches. However, close examination of the relevant phenomena reveals that the two are complementary, rather than being irrevocably in opposition to each other. One can be a formal linguist and a functional linguist at the same time, without there being any contradiction. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.
Formal languages in dynamical systems
Troll, G
1993-01-01
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal language. However, in the special case of a symbolic dynamics, i.e. where the CA is just the shift map, one gets a stronger result: the identification map can be extended to a functor between the categories of symbolic dynamics and formal languages. This functor additionally maps topological conjugacies between subshifts to empty-string-limited generalized sequential machines between languages. If the periodic points form a dense set, a case which arises in a commonly used notion of chaotic dynamics, then an even more natural map to assign a formal language to a subshift is offered. This map extends to a functor, too. The Chomsky hierarchy measuring the complexity of formal languages can be transferred via either of these functors from formal languages to symbolic dynamics and p...
Fourier techniques in X-ray timing
M. van der Klis
1988-01-01
Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum
Dool, T.C. van den; Hamelinck, R.F.M.M.; Kruizinga, B.; Gielesen, W.L.M.; Braam, B.C.; Nijenhuis, J.R.; Loix, N.; Luyckx, S.; Loon, D. van; Kooijman, P.P.; Swinyard, B.M.
2010-01-01
TNO, together with its partners Micromega and SRON, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. The optics of the FTS scanning mechanism (FTSM) consists of two back-to-back cat's-eyes. The optics are mounted
Dool, T.C. van den; Hamelinck, R.F.M.M.; Kruizinga, B.; Gielesen, W.L.M.; Braam, B.C.; Nijenhuis, J.R.; Loix, N.; Luyckx, S.; Loon, D. van; Kooijman, P.P.; Swinyard, B.M.
2010-01-01
TNO, together with its partners Micromega and SRON, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. The optics of the FTS scanning mechanism (FTSM) consists of two back-to-back cat's-eyes. The optics are mounted o
Formalization of an environmental model using formal concept analysis - FCA
Bourdon-García, Rubén D.; Burgos-Salcedo, Javier D.
2016-08-01
Nowadays, there is a huge necessity to generate novel strategies for social-ecological systems analyses for resolving global sustainability problems. This paper has as main purpose the application of the formal concept analysis to formalize the theory of Augusto Ángel Maya, who without a doubt, was one of the most important environmental philosophers in South America; Ángel Maya proposed and established that Ecosystem-Culture relations, instead Human-Nature ones, are determinants in our understanding and management of natural resources. Based on this, a concept lattice, formal concepts, subconcept-superconcept relations, partially ordered sets, supremum and infimum of the lattice and implications between attributes (Duquenne-Guigues base), were determined for the ecosystem-culture relations.
Damin, Craig A; Sommer, André J
2013-11-01
Advances in fiber optic materials have allowed for the construction of fibers and waveguides capable of transmitting infrared radiation. An investigation of the transmission characteristics associated with two commonly used types of infrared-transmitting fibers/waveguides for prospective use in a fiber/waveguide-coupled attenuated total internal reflection (ATR) probe was performed. Characterization of silver halide polycrystalline fiber optics and hollow silica waveguides was done on the basis of the transmission of infrared light using a conventional fiber optic coupling accessory and an infrared microscope. Using the fiber optic coupling accessory, the average percent transmission for three silver halide fibers was 18.1 ± 6.1% relative to a benchtop reflection accessory. The average transmission for two hollow waveguides (HWGs) using the coupling accessory was 8.0 ± 0.3%. (Uncertainties in the relative percent transmission represent the standard deviations.) Reduced transmission observed for the HWGs was attributed to the high numerical aperture of the coupling accessory. Characterization of the fibers/waveguides using a zinc selenide lens objective on an infrared microscope indicated 24.1 ± 7.2% of the initial light input into the silver halide fibers was transmitted. Percent transmission obtained for the HWGs was 98.7 ± 0.1%. Increased transmission using the HWGs resulted from the absence or minimization of insertion and scattering losses due to the hollow air core and a better-matched numerical aperture. The effect of bending on the transmission characteristics of the fibers/waveguides was also investigated. Significant deviations in the transmission of infrared light by the solid-core silver halide fibers were observed for various bending angles. Percent transmission greater than 98% was consistently observed for the HWGs at the bending angles. The combined benefits of high percent transmission, reproducible instrument responses, and increased bending
Aperture scanning Fourier ptychographic microscopy
Ou, Xiaoze; Chung, Jaebum; Horstmeyer, Roarke; Yang, Changhuei
2016-01-01
Fourier ptychographic microscopy (FPM) is implemented through aperture scanning by an LCOS spatial light modulator at the back focal plane of the objective lens. This FPM configuration enables the capturing of the complex scattered field for a 3D sample both in the transmissive mode and the reflective mode. We further show that by combining with the compressive sensing theory, the reconstructed 2D complex scattered field can be used to recover the 3D sample scattering density. This implementation expands the scope of application for FPM and can be beneficial for areas such as tissue imaging and wafer inspection. PMID:27570705
Novel Micro Fourier Transform Spectrometers
Institute of Scientific and Technical Information of China (English)
KONG Yan-mei; LIANG Jing-qiu; LIANG Zhong-zhu; WANG-Bo; ZHANG Jun
2008-01-01
The miniaturization of spectrometer opens a new application area with real-time and on-site measurements. The Fourier transform spectrometer(FTS) is much attractive considering its particular advantages among the approaches. This paper reviews the current status of micro FTS in worldwide and describes its developments; In addition, analyzed are the key problems in designing and fabricating FTS to be settled during the miniaturization. Finally, a novel model of micro FTS with no moving parts is proposed and analyzed, which may provide new concepts for the design of spectrometers.
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
JPL Fourier transform ultraviolet spectrometer
Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.
1994-01-01
The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.
Fourier Transform Methods. Chapter 4
Kaplan, Simon G.; Quijada, Manuel A.
2015-01-01
This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..
Collier, Robert
2013-01-01
Optical Holography deals with the use of optical holography to solve technical problems, with emphasis on the properties of holograms formed with visible light. Topics covered include the Fourier transform, propagation and diffraction, pulsed-laser holography, and optical systems with spherical lenses. A geometric analysis of point-source holograms is also presented, and holograms and hologram spatial filters formed with spatially modulated reference waves are described. This book is comprised of 20 chapters and begins with an introduction to concepts that are basic to understanding hologr
Institute of Scientific and Technical Information of China (English)
冯明春; 徐亮; 高闽光; 焦洋; 魏秀丽; 金岭; 程巳阳; 李相贤; 冯书香
2012-01-01
使用傅里叶变换红外光谱(FTIR)技术,测量了两种不同浓度的枯草芽孢杆菌的红外透过率谱,根据朗伯-比尔定律计算出它们的质量消光截面,通过算出复折射率的虚部,再使用KK(Kramers-Kronig)关系,导出复折射率的实部,并对实验结果作了分析和讨论.通过研究枯草芽孢杆菌复折射率的测量和分析方法,对于进一步研究生物气溶胶的吸收和散射特性、拓宽生物气溶胶的测量和遥测技术方法,具有重要的意义.%The authors measured IR transmission spectra of two different concentrations of bacillus subtilis spores by using Fourier transform infrared spectroscopy (FTIR) technology. The mass extinction cross section k of bacillus subtilis spores was calculated according to Lambert-Beer law and the imaginary part n, of the complex refractive index was also calculated through k. The real part nr of the complex refractive index was derived from the KK (Kramers-Kronig) relationship and the experimental results were also analyzed and discussed with the study of measurement and analysis method of the complex refractive index on bacillus subtilis spores, it is of great significance to further research the absorption and scattering characteristics, and to broaden the measurement and remote sensing technology method of the biological aerosols.
Pointwise convergence of Fourier series
Arias de Reyna, Juan
2002-01-01
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
A Student's Guide to Fourier Transforms - 2nd Edition
James, J. F.
2002-09-01
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science. Expanded to include more emphasis on applications An established successful textbook for undergraduate and graduate students Includes worked examples and copious diagrams throughout
Formal Methods: Practice and Experience
DEFF Research Database (Denmark)
Woodcock, Jim; Larsen, Peter Gorm; Bicarregui, Juan
2009-01-01
Formal methods use mathematical models for analysis and verification at any part of the program life-cycle. We describe the state of the art in the industrial use of formal methods, concentrating on their increasing use at the earlier stages of specification and design. We do this by reporting...... on a new survey of industrial use, comparing the situation in 2009 with the most significant surveys carried out over the last 20 years. We describe some of the highlights of our survey by presenting a series of industrial projects, and we draw some observations from these surveys and records of experience....... Based on this, we discuss the issues surrounding the industrial adoption of formal methods. Finally, we look to the future and describe the development of a Verified Software Repository, part of the worldwide Verified Software Initiative. We introduce the initial projects being used to populate...
Leibniz' First Formalization of Syllogistics
DEFF Research Database (Denmark)
Robering, Klaus
2014-01-01
In his Dissertatio de Arte Combinatoria from 1666 Leibniz provides a formal presentation of syllogistics within the framework of his general-combinatoric program. He does not set up an axiomatic system for the derivation of all valid syllogistic mode, rather he formulates a set of rules which...... distinguish the valid modes among all possible ones. Leibniz' coding of syllogistic modi by combinations of letters and his distinction between possible and useful ("utiles") modes suggests to reconstruct the characterization of the valid modes as the problem of determining among the possible combination...... of letters just those which belong to the useful, i.e., valid, modes. The set of codes of valid modes turns out to be a so-called "regular" language (in the sense of formal-language-theory). Leibniz' formalization of syllogistics in his Dissertatio thus contains an estimation of the computational complexity...
DEFF Research Database (Denmark)
Villesèche, Florence; Josserand, Emmanuel
2017-01-01
implications: The paper contributes to research showing that the social structure of interactions and context can impact women’s standing in the workplace. Originality/value: The paper sheds light on the under-studied and under-theorised phenomenon of formal women-only business networks. Beyond the individual...... internal and external women-only networks and use the broader social capital and network literature to frame their arguments and develop propositions. Findings: Propositions are developed regarding how both internal and external formal women-only business networks can be of value for members, firms....../organisations and the wider social group of women in business. Research limitations/implications: The authors focus on the distinction between external and internal formal women-only networks while also acknowledging the broader diversity that can characterise such networks. Their review provides the reader with an insight...
Spin Glass Field Theory with Replica Fourier Transforms
Pimentel, Iveta R.; De Dominicis, Cirano
We develop a field theory for spin glasses using Replica Fourier Transforms (RFT). We present the formalism for the case of replica symmetry and the case of replica symmetry breaking on an ultrametric tree, with the number of replicas n and the number of replica symmetry breaking steps R generic integers. We show how the RFT applied to the two-replica fields allows to construct a new basis which block-diagonalizes the four-replica mass-matrix, into the replicon, anomalous and longitudinal modes. The eigenvalues are given in terms of the mass RFT and the propagators in the RFT space are obtained by inversion of the block-diagonal matrix. The formalism allows to express any i-replica vertex in the new RFT basis and hence enables to perform a standard perturbation expansion. We apply the formalism to calculate the contribution of the Gaussian fluctuations around the Parisi's solution for the free-energy of an Ising spin glass.
Formal Definition of Artificial Intelligence
Dobrev, Dimiter
2005-01-01
* This publication is partially supported by the KT-DigiCult-Bg project. A definition of Artificial Intelligence (AI) was proposed in [1] but this definition was not absolutely formal at least because the word "Human" was used. In this paper we will formalize the definition from [1]. The biggest problem in this definition was that the level of intelligence of AI is compared to the intelligence of a human being. In order to change this we will introduce some parameters to which AI ...
Formal Verification of UML Profil
DEFF Research Database (Denmark)
Bhutto, Arifa; Hussain, Dil Muhammad Akbar
2011-01-01
The Unified Modeling Language (UML) is based on the Model Driven Development (MDD) approach which capturing the system functionality using the platform-independent model (PMI) and appropriate domain-specific languages. In UML base system notations, structural view is model by the class, components...... and object diagrams and behavioral view model by the activity, use case, state, and sequence diagram. However, UML does not provide the formal syntax, therefore its semantics is not formally definable, so for assure of correctness, we need to incorporate semantic reasoning through verification, specification...
Worldline Formalism and Noncommutative Theories
Franchino-Viñas, Sebastián A
2015-01-01
The objective of this Ph.D. thesis is the implementation of the Worldline Formalism in the frame of Noncommutative Quantum Field Theories. The result is a master formula for the 1-loop effective action that is applied to a number of scalar models -- among them the Grosse-Wulkenhaar model. As a byproduct we find an expression for the small propertime expansion of general nonlocal operators' Heat Kernel. As an introduction, basic notions of spectral functions, Quantum Field Theories --path integrals and renormalization by means of spectral functions-- and the Worldline Formalism for commutative theories are given.
Observation of supersonic turbulent wakes by laser Fourier densitometry (LFD)
Gresillon, D.; Cabrit, B.; Bonnet, J. P.; Gemaux, G.
Laser Fourier Densitometry (LFD) is an optical method appropriate for turbulent flow observations. It uses the collective scattering of coherent light, by optical index inhomogeneities. The principle of this method is described. It provides a signal proportional to the space Fourier transform amplitude of index distribution for a wavevector k defined by the optical arrangement. For a fluctuating flow, this amplitude is a function of time, and its frequency spectrum can be observed. The spectrum shape provides elementary parameters of the flow, such as: direction, modulus of mean velocity, and local temperature. It also provides means to distinguish different kinds of density fluctuations, such as convected inhomogeneities, or acoustic waves. The respective level of these different fluctuations types can be measured, as well as their power scale-law and absolute level. A compact optical bench has been set on a nozzle flow. The results of measurements performed in two supersonic wake configurations are presented, for Mach numbers of 1.6 and 4.2. These include density fluctuation spectra in supersonic flows, acoustic waves, variations with position, and comparison with hot wire anemometry.
Rational formality of mapping spaces
Felix, Yves
2010-01-01
Let X and Y be finite nilpotent CW complexes with dimension of X less than the connectivity of Y. Generalizing results of Vigu\\'e-Poirrier and Yamaguchi, we prove that the mapping space Map(X,Y) is rationally formal if and only if Y has the rational homotopy type of a finite product of odd dimensional spheres.
The Role of Formal Instruction
Institute of Scientific and Technical Information of China (English)
Sun Yu
2011-01-01
This paper looks at second language acquisition in a classroom setting. It considers whether formal instruction makes a difference to SLA. This is an important issue, because it address the question of the role played by environmental factors in SLA. It is also an important educational issue, as language pedagogy has traditionally operated on the assumption that grammar can be taught.
Formal systems for persuasion dialogue
Prakken, Henry
This article reviews formal systems that regulate persuasion dialogues. In such dialogues two or more participants aim to resolve a difference of opinion, each trying to persuade the other participants to adopt their point of view. Systems for persuasion dialogue have found application in various
Formal Theories for Logspace Counting
Fontes, Lila
2010-01-01
We introduce two-sorted theories in the style of Cook and Nguyen for the complexity classes ParityL and DET, whose complete problems include determinants over GF(2) and Z, respectively. The definable functions in these theories are the functions in the corresponding complexity classes; thus each theory formalizes reasoning using concepts from its corresponding complexity class.
Formal-informal economy linkages
African Journals Online (AJOL)
Andries du Toit
poverty research and development of policy in South Africa and conclude the article .... disappear with development and growth, the informal sector has become a growing ...... the history and current challenges facing the economy. .... economy: including the more formal end of the SME”.50 Decent work is also a central.
Formal law and customary change
Cecchi, Francesco; Melesse, Mequanint Biset
2016-01-01
Do customary courts strategically adapt arbitration outcomes if they face increased competition by the formal law? Through a lab-in-field experiment with villagers and real customary judges in rural Ethiopia, we show that post-arbitration payouts to agents disfavored by the customary system are d
General Recursion and Formal Topology
Directory of Open Access Journals (Sweden)
Silvio Valentini
2010-12-01
Full Text Available It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In this work we propose a new approach to this problem based on the use of inductively generated formal topologies.
Automatic Testing with Formal Methods
Tretmans, G.J.; Belinfante, Axel
1999-01-01
The use of formal system specifications makes it possible to automate the derivation of test cases from specifications. This allows to automate the whole testing process, not only the test execution part of it. This paper presents the state of the art and future perspectives in testing based on
Cryogenic Scan Mechanism for Fourier Transform Spectrometer
Brasunas, John C.; Francis, John L.
2011-01-01
A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear
Quantum Fourier transform in computational basis
Zhou, S. S.; Loke, T.; Izaac, J. A.; Wang, J. B.
2017-03-01
The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ɛ for each Fourier coefficient. Its time complexity depends polynomially on log (N), where N is the problem size, and linearly on 1/δ and 1/ɛ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
The multiple-parameter fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
LANG Jun; TAO Ran; RAN QiWen; WANG Yue
2008-01-01
The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in frac-tional operator. A new source for the multiplicity of the weight-type fractional Fou-rier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters MN,∈ZM. Therefore a generalized frac-tional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.
The Fourier Transform on Quantum Euclidean Space
Directory of Open Access Journals (Sweden)
Kevin Coulembier
2011-05-01
Full Text Available We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.
Oversampling analysis in fractional Fourier domain
Institute of Scientific and Technical Information of China (English)
ZHANG Feng; TAO Ran; WANG Yue
2009-01-01
Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal Is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.
Implementing quantum Fourier transform with integrated photonic devices
Tabia, Gelo Noel
2014-03-01
Many quantum algorithms that exhibit exponential speedup over their classical counterparts employ the quantum Fourier transform, which is used to solve interesting problems such as prime factorization. Meanwhile, nonclassical interference of single photons achieved on integrated platforms holds the promise of achieving large-scale quantum computation with multiport devices. An optical multiport device can be built to realize any quantum circuit as a sequence of unitary operations performed by beam splitters and phase shifters on path-encoded qudits. In this talk, I will present a recursive scheme for implementing quantum Fourier transform with a multimode interference photonic integrated circuit. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Ultrafast ranging lidar based on real-time Fourier transformation.
Xia, Haiyun; Zhang, Chunxi
2009-07-15
Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the time delay between the two signals. The temporal interferograms are transformed from the time domain into the frequency domain using a time-to-frequency conversion function obtained in the calibration process. The Fourier transform is used in the data processing. A range resolution of 334 nm at a sampling rate of 48.6 MHz over a distance of 16 cm is demonstrated in the laboratory.
Time-frequency representation measurement based on temporal Fourier transformation
Suen, Yifan; Xiao, Shaoqiu; Hao, Sumin; Zhao, Xiaoxiang; Xiong, Yigao; Liu, Shenye
2016-10-01
We propose a new scheme to physically realize the short-time Fourier transform (STFT) of chirped optical pulse using time-lens array that enables us to get time-frequency representation without using FFT algorithm. The time-lens based upon the four-wave mixing is used to perform the process of temporal Fourier transformation. Pump pulse is used for both providing the quadratic phase and being the window function of STFT. The idea of STFT is physically realized in our scheme. Simulations have been done to investigate performance of the time-frequency representation scheme (TFRS) in comparison with STFT using FFT algorithm. Optimal measurement of resolution in time and frequency has been discussed.
THE FOURIER SERIES MODEL IN MAP ANALYSIS.
During the past several years the double Fourier Series has been applied to the analysis of contour-type maps as an alternative to the more commonly...used polynomial model. The double Fourier Series has high potential in the study of areal variations, inasmuch as a succession of trend maps based on...and it is shown that the double Fourier Series can be used to summarize the directional properties of areally-distributed data. An Appendix lists
Microscope system with on axis programmable Fourier transform filtering
Martínez, José Luis; García-Martínez, Pascuala; Moreno, Ignacio
2017-02-01
We propose an on-axis microscope optical system to implement programmable optical Fourier transform image processing operations, taking advantage of phase and polarization modulation of a liquid crystal on silicon (LCOS) display. We use a Hamamatsu spatial light modulator (SLM), free of flickering, which therefore can be tuned to fully eliminate the zero order component of the encoded diffractive filter. This allows the realization of filtering operation on axis (as opposed to other systems in the literature that require operating off axis), therefore making use of the full space bandwidth provided by the SLM. The system is first demonstrated by implementing different optical processing operations based on phase-only blazed gratings such as phase contrast, band-pass filtering, or additive and substractive imaging. Then, a simple Differential interference contrast (DIC) imaging is obtained changing to a polarization modulation scheme, achieved simply by selecting a different incident state of polarization on the incident beam.
Peterson, J R; Kahn, S M; Rasmussen, A P; Peng, E; Ahmad, Z; Bankert, J; Chang, C; Claver, C; Gilmore, D K; Grace, E; Hannel, M; Hodge, M; Lorenz, S; Lupu, A; Meert, A; Nagarajan, S; Todd, N; Winans, A; Young, M
2015-01-01
We present a comprehensive methodology for the simulation of astronomical images from optical survey telescopes. We use a photon Monte Carlo approach to construct images by sampling photons from models of astronomical source populations, and then simulating those photons through the system as they interact with the atmosphere, telescope, and camera. We demonstrate that all physical effects for optical light that determine the shapes, locations, and brightnesses of individual stars and galaxies can be accurately represented in this formalism. By using large scale grid computing, modern processors, and an efficient implementation that can produce 400,000 photons/second, we demonstrate that even very large optical surveys can be now be simulated. We demonstrate that we are able to: 1) construct kilometer scale phase screens necessary for wide-field telescopes, 2) reproduce atmospheric point-spread-function moments using a fast novel hybrid geometric/Fourier technique for non-diffraction limited telescopes, 3) ac...
Contextual approach to quantum formalism
Khrennikov, Andrei
2009-01-01
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems...
Formal Institutions and Subjective Wellbeing
DEFF Research Database (Denmark)
Bjørnskov, Christian; Dreher, Axel; Fischer, Justina A.V.
2010-01-01
cross-country studies on the institution-happiness association. Our findings suggest that their conclusions are qualitatively rather insensitive to the specific measure of 'happiness' used, while the associations between formal institutions and subjective well-being differ among poor and rich countries....... Separating different types of institutional quality, we find that in low-income countries the effects of economic-judicial institutions on happiness dominate those of political institutions, while analyses restricted to middle- and high-income countries show strong support for an additional beneficial effect......A long tradition in economics explores the association between the quality of formal institutions and economic performance. The literature on the relationship between such institutions and happiness is, however, rather limited, and inconclusive. In this paper, we revisit the findings from recent...
Informal work and formal plans
DEFF Research Database (Denmark)
Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm
2012-01-01
trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment...... and care. They initiated processes in the trajectories, and acquired information, which they used to form their trajectories. Patients presented problems to the healthcare professionals in order to get proper help when needed. DISCUSSION: Work done by patients was invisible and not perceived as work....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...
Musical Formalism and Political Performances
Directory of Open Access Journals (Sweden)
Jonathan A. Neufeld
2009-01-01
Full Text Available Musical formalism, which strictly limits the type of thing any description of the music can tell us, is ill-equipped to account for contemporary performance practice. If performative interpretations are in a position to tell us something about musical works—that is if performance is a kind of description, as Peter Kivy argues—then we have to loosen the restrictions on notions of musical relevance to make sense of performance. I argue that musical formalism, which strictly limits the type of thing any description of the music can tell us, is inconsistent with Kivy's quite compelling account of performance. This shows the difficulty that actual performances pose to overly rigid conceptions of music. Daniel Barenboim's unannounced performance of Wagner in Israel in 2001 shows that the problem of the boundaries of musical relevance is no mere philosophical puzzle. It is a pressing problem in the musical public sphere.
Informal work and formal plans
DEFF Research Database (Denmark)
Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm;
2012-01-01
trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment...... and care. They initiated processes in the trajectories, and acquired information, which they used to form their trajectories. Patients presented problems to the healthcare professionals in order to get proper help when needed. DISCUSSION: Work done by patients was invisible and not perceived as work....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...
Stroh formalism and Rayleigh waves
Tanuma, Kazumi
2008-01-01
Introduces a powerful and elegant mathematical method for the analysis of anisotropic elasticity equationsThe reader can grasp the essentials as quickly as possibleCan be used as a textbook, which presents compactly introduction and applications of the Stroh formalismAppeals to the people not only in mathematics but also in mechanics and engineering sciencePrerequisites are only basic linear algebra, calculus and fundamentals of differential equations
Formal aspects of component software
Sun, Meng; Schatz, B.
2014-01-01
This issue includes extended versions of selected best papers from the 7th International Workshop on Formal Aspects of Component Software (FACS 2010) held in Guimarães, Portugal on October 14–16, 2010. The component-based software development approach has emerged as a promising paradigm to cope with an ever increasing complexity of present-day software solutions by bringing sound production and engineering principles into software engineering. However, many conceptual and technological iss...
Indian Academy of Sciences (India)
Freek Wiedijk
2009-02-01
A small project in which I encoded a proof of Arrow’s theorem—probably the most famous results in the economics ﬁeld of social choice theory—in the computer using the Mizar system is presented here. The details of this speciﬁc project, as well as the process of formalization (encoding proofs in the computer) in general are discussed.
Formal modelling of cognitive interpretation
Rukšenas, R.; Curzon, P; Back, J.; Blandford, A.
2007-01-01
We formally specify the interpretation stage in a dual state space human-computer interaction cycle. This is done by extending/reorganising our previous cognitive architecture. In particular, we focus on shape related aspects of the interpretation process associated with device input prompts. A cash-point example illustrates our approach. Using the SAL model checking environment, we show how the extended cognitive architecture facilitates detection of prompt-shape induced human error. © Sprin...
Formal Verification under Unknown Constraints
Institute of Scientific and Technical Information of China (English)
LI Guang-hui; LI Xiao-wei
2005-01-01
We present a formal method of verifying designs with unknown constraints (e. g. , black boxes) using Boolean satisfiability (SAT). This method is based on a new encoding scheme of unknown constraints, and solves the corresponding conjunctive normal form (CNF) formulas. Furthermore, this method can avoid the potential memory explosion, which the binary decision diagram (BDD) based techniques maybe suffer from, thus it has the capacity of verifying large designs. Experimental results demonstrate the efficiency and feasibility of the proposed method.
Formal description of board games
Nowak, Stanislav
2011-01-01
The aim of thesis was to design a mathematical formalism that allows describing and exploring the properties of board games. The work benefits from the findings of automata theory and logic programming. First part of thesis deals with finite automata and their possible applications for the needs of board games. The result is an extension of finite-state automaton covering the specifics of board games called game automaton. Board games are a complex domain hight level tools should be used. Suc...
Formal Modeling of Communication Protocols.
1981-03-01
problems have been developed. 4 FORMAL MODELING OF COMMUNICATION PROTOCOLS The state machine model is motivated by the observation that protocols may be...simplest types of state machine model because they have only a single state variable (the state) which takes on a relatively small range of values. For...grammar, this correspondence is very apparent. For each state of the state machine model , we define a nonterminal symbol in the grammar. The inputs
Quantum Formalism: Brief Epistemological Considerations
Lynn, H; Caponigro, Michele; Lynn, Helen
2006-01-01
We argue about a conceptual approach to quantum formalism. Starting from philosophical conjectures (Platonism, Idealism and Realism) as basic ontic elements (namely: math world, data world, and state of matter), we will analyze the quantum superposition principle. This analysis bring us to demonstrate that the basic assumptions affect in different ways:(a) the general problem of the information and computability about a system, (b) the nature of the math tool utilized and (c) the correspondent physical reality.
Fractional Fourier transform of Cantor sets: further numerical study
Institute of Scientific and Technical Information of China (English)
Gao Qiong; Liao tian-He; Cui Yuan-Feng
2008-01-01
This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.
Charge reversal Fourier transform ion cyclotron resonance mass spectrometry.
Lobodin, Vladislav V; Savory, Joshua J; Kaiser, Nathan K; Dunk, Paul W; Marshall, Alan G
2013-02-01
We report the first charge reversal experiments performed by tandem-in-time rather than tandem-in-space MS/MS. Precursor odd-electron anions from fullerene C(60), and even-electron ions from 2,7-di-tert-butylfluorene-9-carboxylic acid and 3,3'-bicarbazole were converted into positive product ions ((-)CR(+)) inside the magnet of a Fourier transform ion cyclotron resonance mass spectrometer. Charge reversal was activated by irradiating precursor ions with high energy electrons or UV photons: the first reported use of those activation methods for charge reversal. We suggest that high energy electrons achieve charge reversal in one step as double electron transfer, whereas UV-activated (-)CR(+) takes place stepwise through two single electron transfers and formally corresponds to a neutralization-reionization ((-)NR(+)) experiment.
[Fourier Transform Spectrometer Based on Rotating Parallel-Mirror-Pair].
Zhao, Bao-wei; Xiangli, Bin; Cai, Qi-sheng; Lü, Qun-bo; Zhou, Jin-song
2015-11-01
In the temporally-modulated Fourier transform spectroscopy, the translational moving mirror is difficult to drive accurately, causing tilt and shear problems. While, a rotational moving mirror can solve these problems. A rotary Fourier transform spectrometer is recommanded in this paper. Its principle is analyzed and the optical path difference is deduced. Also, the constrains for engineering realization are presented. This spectrometer consists of one beamsplitter, two fixed mirrors, one rotating parallel mirror pair, a collimating lens, a collecting lens, and one detector. From it's principle, this spectrometer show a simple structure, and it is assembled and adjustmented easily because the two split light are interfered with each other after reflected through the same plane mirror; By calculating the expression of it's optical path difference, the spectrometer is easy to realize large optical path difference, meaning high spectral resolution; Through analyzing it's engineering design constraints and computer simulation, it is known that the spectrometer should get the high resolution sample by high-speed spinning motor, so it is easy to achieve precise motion control, good stability, fast measurement speed.
The multipliers of multiple trigonometric Fourier series
Ydyrys, Aizhan; Sarybekova, Lyazzat; Tleukhanova, Nazerke
2016-11-01
We study the multipliers of multiple Fourier series for a regular system on anisotropic Lorentz spaces. In particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Zn in order to make it a multiplier of multiple trigonometric Fourier series from Lp[0; 1]n to Lq[0; 1]n , p > q. These conditions include conditions Lizorkin theorem on multipliers.
1-Convergence of Complex Double Fourier Series
Indian Academy of Sciences (India)
Kulwinder Kaur; S S Bhatia; Babu Ram
2003-11-01
It is proved that the complex double Fourier series of an integrable function (, ) with coefficients {} satisfying certain conditions, will converge in 1-norm. The conditions used here are the combinations of Tauberian condition of Hardy–Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.
Two modified discrete chirp Fourier transform schemes
Institute of Scientific and Technical Information of China (English)
樊平毅; 夏香根
2001-01-01
This paper presents two modified discrete chirp Fourier transform (MDCFT) schemes.Some matched filter properties such as the optimal selection of the transform length, and its relationship to analog chirp-Fourier transform are studied. Compared to the DCFT proposed previously, theoretical and simulation results have shown that the two MDCFTs can further improve the chirp rate resolution of the detected signals.
A mathematical formalism for hyperspectral, multipoint plastic scintillation detectors.
Archambault, Louis; Therriault-Proulx, François; Beddar, Sam; Beaulieu, Luc
2012-11-07
The aim of this paper is to generalize and extend the mathematical formalism used with plastic scintillation detectors (PSDs). By doing so, we show the feasibility of multi-point PSD. The new formalism is based on the sole hypothesis that a PSD optical signal is a linear superposition of spectra. Two calibration scenarios were developed. Both involve solving a linear equation of the form Y = XB, but the process and input data depend on the information available on the detector system. Simulations were carried out to validate both scenarios and demonstrate the advantages of the new formalism. In this paper, we prove the following results. (1) Multi-point PSDs are feasible. Simulations have shown that six different spectra could be resolved accurately even in the presence of up to 10% Gaussian noise. (2) The new formalism leads to more precise PSD measurements. (3) By using the condition number of the measurement matrix, the ideal sets of calibration measurements can be identified. (4) By using principal component analysis it was possible to identify the best set of wavelength filters. We have shown through numerical simulations that multi-point detectors are feasible. This has potential for applications such as in vivo dose verification. Furthermore, our new formalism can be used to improve the robustness and ease of use of PSDs.
Formal Analysis of Meaning in Natural Languages
Directory of Open Access Journals (Sweden)
Ljiljana Saric
2006-06-01
Full Text Available Broadly, the subject of this paper is the relation between logic and linguistics. More narrowly, it concentrates on formal semantics. The first part of the text discusses the topics and methods of formal semantics, and the second part the history of formal semantics. Formal semantic analysis has not been widely known and applied in our research community, and formal methods have been applied extremely rarely in linguistic analyses. This is why it is useful to point out the significant achievements of formal semantics. This inspiring interdisciplinary field of research has been successfully connecting research in linguistics, logic and philosophy since the early 1970s.
From "Dirac combs" to Fourier-positivity
Giraud, Bertrand G
2015-01-01
Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms. A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed. As a practical application, we find simple and rapid analytic algorithms for checking Fourier-positivity in 1- and (radial) 2-dimensions among a large variety of real positive functions. This may provide a step towards a classification of positive positive-definite functions.
Double passing the Kitt Peak 1-m Fourier transform spectrometer
Jennings, D. E.; Hubbard, R.; Brault, J. W.
1985-01-01
Attention is given to a simple technique for performing the conversion of the Kitt Peak 1-m Fourier transform spectrometer's dual input/output optical configuration to a double pass configuration that improves spectral resolution by a factor of 2. The modification is made by placing a flat mirror in the output beam from each cat's eye, retroreflecting the beams back through the cat's eyes to the first beam splitter. A single detector is placed at the second input port, which then becomes the instrument's output.
Hyperspectral holographic Fourier-microscopy
Energy Technology Data Exchange (ETDEWEB)
Kalenkov, G S [Moscow Institute of Physics and Technology (State University), Moscow (Russian Federation); Kalenkov, S G [Moscow State University of Mechanical Engineering, Moscow (Russian Federation); Shtan' ko, A E [Moscow State University of Technology ' Stankin' , Moscow (Russian Federation)
2015-04-30
A detailed theory of the method of holographic recording of hyperspectral wave fields is developed. New experimentally obtained hyperspectral holographic images of microscopic objects are presented. The possibilities of the method are demonstrated experimentally using the examples of urgent microscopy problems: speckle noise suppression, obtaining hyperspectral image of a microscopic object, as well as synthesis of a colour image and obtaining an optical profile of a phase object. (holography)
Thin-film limit formalism applied to surface defect absorption
Holovsky, Jakub; Ballif, Christophe
2014-01-01
The thin-film limit is derived by a nonconventional approach and equations for transmittance, reflectance and absorptance are presented in highly versatile and accurate form. In the thin-film limit the optical properties do not depend on the absorption coefficient, thickness and refractive index individually, but only on their product. We show that this formalism is applicable to the problem of ultrathin defective layer e. g. on a top of a layer of amorphous silicon. We develop a new method o...
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
New families of Fourier eigenfunctions for steerable filtering.
Papari, Giuseppe; Campisi, Patrizio; Petkov, Nicolai
2012-06-01
A new diadic family of eigenfunctions of the 2-D Fourier transform has been discovered. Specifically, new wavelets are derived by steering the elongated Hermite-Gauss filters with respect to rotations, thus obtaining a natural generalization of the Laguerre-Gauss harmonics. Interestingly, these functions are also proportional to their 2-D Fourier transform. Their analytical expression is provided in a compact and treatable form, by means of a new ad hoc matrix notation in which the cases of even and odd orders of the Hermite polynomials are unified. Moreover, these functions can be efficiently implemented by means of a recursive formula that is derived in this paper. The proposed filters are applied to the problem of gradient estimation to improve the theoretical Canny tradeoff of position accuracy versus noise rejection that occurs in edge detection. Experimental results show considerable improvements in using the new wavelets over both isotropic Gaussian derivatives and other elongated steerable filters more recently introduced. Finally, being the proposed wavelets a set of Fourier eigenfunctions, they can be of interest in other fields of science, such as optics and quantum mechanics.
Vortex metrology using Fourier analysis techniques: vortex networks correlation fringes.
Angel-Toro, Luciano; Sierra-Sosa, Daniel; Tebaldi, Myrian; Bolognini, Néstor
2012-10-20
In this work, we introduce an alternative method of analysis in vortex metrology based on the application of the Fourier optics techniques. The first part of the procedure is conducted as is usual in vortex metrology for uniform in-plane displacement determination. On the basis of two recorded intensity speckled distributions, corresponding to two states of a diffuser coherently illuminated, we numerically generate an analytical signal from each recorded intensity pattern by using a version of the Riesz integral transform. Then, from each analytical signal, a two-dimensional pseudophase map is generated in which the vortices are located and characterized in terms of their topological charges and their core's structural properties. The second part of the procedure allows obtaining Young's interference fringes when Fourier transforming the light passing through a diffracting mask with multiple apertures at the locations of the homologous vortices. In fact, we use the Fourier transform as a mathematical operation to compute the far-field diffraction intensity pattern corresponding to the multiaperture set. Each aperture from the set is associated with a rectangular hole that coincides both in shape and size with a pixel from recorded images. We show that the fringe analysis can be conducted as in speckle photography in an extended range of displacement measurements. Effects related with speckled decorrelation are also considered. Our experimental results agree with those of speckle photography in the range in which both techniques are applicable.
Formal Inspection: A Tool for TQM
Welz, L.; Kelly, J.
1995-01-01
The goal of the Formal Inspection Program at the Jet Propulsion Laboratory (JPL) is to support projects wishing to use Formal Inspections to improve the quality of software and system level engineering products.
Energy Technology Data Exchange (ETDEWEB)
Patino, A [Universidad Technologica de Bolivar, Cartagena de Indias (Colombia); Durand, P-E; Fogret, E; Pellat-Finet, P, E-mail: alberto.patino-vanegas@univ-ubs.fr [Laboratoire de mathematiques et applications des mathematiques, Universite de Bretagne Sud, B P 92116, 56321 Lorient cedex (France)
2011-01-01
According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.
Coherence Enhancing Diffusion and Windowed Fourier Filtering for Fringe Patterns Denoising (II)
Wang, Haixia; Kemao, Qian
2010-04-01
Fringe patterns produced by various optical interferometric techniques encode the information of deformation, refractive index, vibration, etc. Noise as one of the key problems affects further processing of the fringe patterns and reduces the final measurement quality. Coherence enhancing diffusion (CED) is a partial differential equation based denoising model that suppresses the noise as well as preserves the flow-like structure. Windowed Fourier transform-based windowed Fourier filtering (WFF) is another useful fringe pattern denoising tool that removes noise by thresholding the windowed Fourier transform spectrum. An adaptive windowed Fourier filtering (AWFF) that denoises the fringe pattern based on pixels' local frequencies is proposed in this paper. The performance of AWFF is compared with WFF and CED by applying them to fringe patterns that contain speckle noise and different levels of frequencies. Quantitative results will be given on simulated fringe patterns. Experimental fringe pattern will also be tested to illustrate the performance of these methods.
Institute of Scientific and Technical Information of China (English)
南楠; 步鹏; 郭昕; 王向朝
2012-01-01
A three-dimensional (3D) full-range complex Fourier domain optical coherence tomography (FDOCT) system based on sinusoidal phase-modulating method is developed for vivo imaging of human skin. A complex spectral interferogram is retrieved based on Fourier transform analysis and bandpass filter of phase-modulated interference spectra, which is recorded with sinusoidal phase modulation introduced during lateral beam scanning. With the system, the depth imaging range is doubled and the signal-to-noise ratio degrading with the lateral scanning is avoided. Also the system is suitable for vivo imaging. 3D vivo full-range OCX images of human skin is achieved with the proposed system. In the images, the stratum corneum, the epidermis and the upper dermis can be clearly identified. By optimizing the sampling number in one modulation period, the complex conjugate rejection ratio is improved, which is about 36 dB.%基于正弦相位调制建立了用于人体皮肤在体三维成像的全深度复频域光学相干层析(FDOCT)成像系统.通过在不同横向位置获取的干涉谱信号中引入正弦相位调制,利用傅里叶变换结合带通滤波的方法重建复干涉谱信号,使成像深度范围扩大为原来的两倍,且适合对活体组织进行在体成像.通过优化相位调制周期内的采样点数,提高了镜像抑制比.基于该系统在体获得了人体皮肤的三维全深度层析图,图中角质层、表皮层及真皮乳突层等皮肤层状结构清晰可见,镜像消除比约为36dB.
Zharinov, V. V.
2013-02-01
We propose a formal construction generalizing the classic de Rham complex to a wide class of models in mathematical physics and analysis. The presentation is divided into a sequence of definitions and elementary, easily verified statements; proofs are therefore given only in the key case. Linear operations are everywhere performed over a fixed number field {F} = {R},{C}. All linear spaces, algebras, and modules, although not stipulated explicitly, are by definition or by construction endowed with natural locally convex topologies, and their morphisms are continuous.
Teleparallel formalism of galilean gravity
Ulhoa, S C; Santana, A E
2011-01-01
A pseudo-Riemannian manifold is introduced, with light-cone coordinates in (4+1) dimensional space-time, to describe a Galilei covariant gravity. The notion of 5-bein and torsion are developed and a galilean version of teleparallelism is constructed in this manifold. The formalism is applied to two spherically symmetric configurations. The first one is an ansatz which is inferred by following the Schwarzschild solution in general relativity. The second one is a solution of galilean covariant equations. In addition, this Galilei teleparallel approach provides a prescription to couple the 5-bein field to the galilean covariant Dirac field.
Mädler, Thomas
2016-01-01
The Bondi-Sachs formalism of General Relativity is a metric-based treatment of the Einstein equations in which the coordinates are adapted to the null geodesics of the spacetime. It provided the first convincing evidence that gravitational radiation is a nonlinear effect of general relativity and that the emission of gravitational waves from an isolated system is accompanied by a mass loss from the system. The asymptotic behaviour of the Bondi-Sachs metric revealed the existence of the symmetry group at null infinity, the Bondi-Metzner-Sachs group, which turned out to be larger than the Poincare group.
Formal Institutions and Subjective Wellbeing
DEFF Research Database (Denmark)
Bjørnskov, Christian; Dreher, Axel; Fischer, Justina
A long tradition in economics explores the association between the quality of formal institutions and economic performance. The literature on the relationship between such institutions and happiness is, however, rather limited. In this paper, we revisit the findings from recent cross......-country studies on the institutions-happiness association. Our findings suggest that the conclusions reached by previous studies are fairly sensitive to the specific measure of 'happiness' used. In addition, the results indicate that the welfare effects of policies may differ across phases of a country's economic...
Formal Institutions and Subjective Wellbeing
DEFF Research Database (Denmark)
Bjørnskov, Christian; Dreher, Axel; Fischer, Justina A.V.
2010-01-01
A long tradition in economics explores the association between the quality of formal institutions and economic performance. The literature on the relationship between such institutions and happiness is, however, rather limited, and inconclusive. In this paper, we revisit the findings from recent....... Separating different types of institutional quality, we find that in low-income countries the effects of economic-judicial institutions on happiness dominate those of political institutions, while analyses restricted to middle- and high-income countries show strong support for an additional beneficial effect...
Knowledge formalization of intelligent building
Žáček, Martin
2016-06-01
This article aim is understanding the basic knowledge about an intelligent building. The notion of the intelligent building can be called any building equipped with computer and communication technology, which can automatically respond to internal or external stimuli. The result of the intelligent building is an automated and foreseeing of activities that enable to reduce operating costs and increase comfort. The best way to use the intelligent building is for a low-energy building, a passive building, or for building with high savings. The output of this article is the formalization of basic knowledge of the intelligent building by RDF graph.
On Vasyliunas's equivalent conductivity formalism
Pontius, D. H., Jr.
1992-01-01
The Vasyliunas's (1972) equivalent conductivity formalism (ECF) for representing the coupling of the ionosphere and the magnetosphere is discussed, and a new, simpler, derivation is presented of the ECF, in which certain of the underlying assumptions and their implications are made transparent. The derivation presented indicates that the only role of the ions in the ECF is to insure quasi-neutrality. It is shown that the ECF is not as robust as usually assumed and that caution must be used to insure that reasonable results are obtained.
Formal analysis of design process dynamics
Bosse, T.; Jonker, C.M.; Treur, J.
2010-01-01
This paper presents a formal analysis of design process dynamics. Such a formal analysis is a prerequisite to come to a formal theory of design and for the development of automated support for the dynamics of design processes. The analysis was geared toward the identification of dynamic design
Fuzzy Set Approximations in Fuzzy Formal Contexts
Institute of Scientific and Technical Information of China (English)
Mingwen Shao; Shiqing Fan
2006-01-01
In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept, we present a pair of rough fuzzy set approximations within fuzzy formal contexts. By the proposed rough fuzzy set approximations, we can approximate a fuzzy set according to different precision level. We discuss the properties of the proposed approximation operators in detail.
Formalizing the concept phase of product development
Schuts, M.; Hooman, J.
2015-01-01
We discuss the use of formal techniques to improve the concept phase of product realisation. As an industrial application, a new concept of interventional X-ray systems has been formalized, using model checking techniques and the simulation of formal models. cop. Springer International Publishing Sw
Formal analysis of design process dynamics
Bosse, T.; Jonker, C.M.; Treur, J.
2010-01-01
This paper presents a formal analysis of design process dynamics. Such a formal analysis is a prerequisite to come to a formal theory of design and for the development of automated support for the dynamics of design processes. The analysis was geared toward the identification of dynamic design prope
Energy Technology Data Exchange (ETDEWEB)
Olivier, S S; Jones, S M; Chen, D C; Zawadzki, R J; Choi, S S; Laut, S P; Werner, J S
2006-01-05
Optical coherence tomography (OCT) sees the human retina sharply with adaptive optics. In vivo cellular visualization of the human retina at micrometer-scale resolution is possible by enhancing Fourier-domain optical-coherence tomography with adaptive optics, which compensate for the eye's optical aberrations.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Time domain ABCD matrix formalism is a useful model for analyzing the characteristics of actively modelocked fiber laser. Based on this model and given more consideration on the influences of optical fiber dispersion and optical fiber nonlinearity, the laser characteristic of actively modelocked fiber laser is analyzed, and the comparision of the theoretical analysis results with experimental ones is given.
Fourier transforms in radar and signal processing
Brandwood, David
2011-01-01
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit
Harmonic functions on groups and Fourier algebras
Chu, Cho-Ho
2002-01-01
This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
Formal Proofs for Nonlinear Optimization
Directory of Open Access Journals (Sweden)
Victor Magron
2015-01-01
Full Text Available We present a formally verified global optimization framework. Given a semialgebraic or transcendental function f and a compact semialgebraic domain K, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of f over K.This method allows to bound in a modular way some of the constituents of f by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent.The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.
Energy Technology Data Exchange (ETDEWEB)
Ritboon, Atirach, E-mail: atirach.3.14@gmail.com [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom); Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand); Daengngam, Chalongrat, E-mail: chalongrat.d@psu.ac.th [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand); Pengpan, Teparksorn, E-mail: teparksorn.p@psu.ac.th [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand)
2016-08-15
Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.
Short-time Fourier transform laser Doppler holography
Atlan, Michael
2012-01-01
We report a demonstration of laser Doppler holography at a sustained acquisition rate of 250 Hz on a 1 Megapixel complementary metal-oxide-semiconductor (CMOS) sensor array and image display at 10 Hz frame rate. The holograms are optically acquired in off-axis configuration, with a frequency-shifted reference beam. Wide-field imaging of optical fluctuations in a 250 Hz frequency band is achieved by turning time-domain samplings to the dual domain via short-time temporal Fourier transformation. The measurement band can be positioned freely within the low radio-frequency spectrum by tuning the frequency of the reference beam in real-time. Video-rate image rendering is achieved by streamline image processing with commodity computer graphics hardware. This experimental scheme is validated by a non-contact vibrometry experiment.
Interferometric measurement of charged particle spectra (Fourier-spectroscopy)
Energy Technology Data Exchange (ETDEWEB)
Hasselbach, F. [Tuebingen Univ. (Germany). Inst. fuer Angewandte Physik; Schaefer, A. [Tuebingen Univ. (Germany). Inst. fuer Angewandte Physik; Wachendorfer, H. [Tuebingen Univ. (Germany). Inst. fuer Angewandte Physik
1995-09-01
Fourier spectroscopy, the most fundamental and, at least in principle, the most precise spectroscopy method, has been introduced by A.A. Michelson at the end of the last century. The method was restricted to electromagnetic waves until an optical component to shift the interfering wave packets longitudinally was invented [G. Moellensted and G. Wohland, Electron Microscopy 1980, eds. P. Bredoro and G. Boom, 7th Europ. Congr. on Electron Microscopy Foundation, Leiden, Vol. 1, p. 28] and refined [H. Gauch, Diploma thesis, University Tuebingen (1983); I. Daberkow et al., Joint Meeting on Electron Microscopy, Antwerp, Belgium, 1983, Program and Abstract Book, p. 100] to such a degree of perfection that the longitudinal shift could be controlled to a fraction of a percent of the wavelength. The Fourier spectrometer for charged matter waves is made up by a wave front splitting electron optical biprism in combination with crossed electric and magnetic fields (Wien-filter) as a wave-packet-shifting device. The contrast of the interference fringes as a function of the longitudinal shift is recorded by a CCD-line-camera, transferred to a PC and Fourier analyzed subsequently. As an example the spectrum of a field emission electron source was analyzed. At an energy of the electrons of 1 keV about 12 000 fringes with a contrast exceeding 10% were recorded. The measured full width at half maximum was 0.6 eV{+-}80 meV. The total error of 80 meV contains 40 meV error due to insufficient sampling of data and 40 meV since about 2000 low contrast fringes were neglected. The action of crossed electric and magnetic fields on electron wave packets including the major problems arising from their weak focusing action for the new method of spectroscopy is discussed extensively. (orig.).
Formal Methods at Intel - An Overview
Harrison, John
2010-01-01
Since the 1990s, Intel has invested heavily in formal methods, which are now deployed in several domains: hardware, software, firmware, protocols etc. Many different formal methods tools and techniques are in active use, including symbolic trajectory evaluation, temporal logic model checking, SMT-style combined decision procedures, and interactive higher-order logic theorem proving. I will try to give a broad overview of some of the formal methods activities taking place at Intel, and describe the challenges of extending formal verification to new areas and of effectively using multiple formal techniques in combination
High Etendue Imaging Fourier Transform Spectrometer: initial results
Horton, Richard F.; Conger, Chris A.; Pelligrino, L. S.
1997-10-01
At the Denver meeting, last year, we presented the High Etendue Imaging Fourier Transform Spectrometer, (HEIFTS), theory and optical design. This device uses a new 'image plane interferometer' geometry to produce 'autocorrelation function modulation' in the image plane of a 2D imaging array, such that the phase offset of the modulation varies linearly across the image. As a 2D image is pushbroomed across the imaging, array, the record of an individual scene pixel is recorded for each autocorrelation phase offset. The 3D array of this data is processed to yield an 'autocorrelation function' data cube, which is Fourier transformed to yield a 'wavenumber' hyperspectral data curve. A phase I device has been demonstrated in the laboratory and initial results are presented. The significant increase in signal to noise ratio, which the HEIFTS optical design promises over conventional hyperspectral imaging schemes, has been simulated, and results will be discussed. A Phase II system is being prepared for initial field deployment, and will be described.
Fourier Series for Kample De Feriet Function
Directory of Open Access Journals (Sweden)
A. D. Wadhwa
1971-07-01
Full Text Available Some integrals involving Kampe de Feriet function have been evaluated. These integrals have further been employed to obtain some Fourier series for Kampe de Feriet functions. Some particular cases have also been discussed.
Fourier-Bessel rotational invariant eigenimages.
Zhao, Zhizhen; Singer, Amit
2013-05-01
We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-dimensional images and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are essentially band limited in the Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel-based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.
Composite Cyclotomic Fourier Transforms with Reduced Complexities
Wu, Xuebin; Chen, Ning; Yan, Zhiyuan; Wang, Ying
2010-01-01
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic fast Fourier transforms (CFFTs) are promising due to their low multiplicative complexities. Unfortunately, there are two issues with CFFTs: (1) they rely on efficient short cyclic convolution algorithms, which has not been investigated thoroughly yet, and (2) they have very high additive complexities when directly implemented. In this paper, we address both issues. One of the main contributions of this paper is efficient bilinear 11-point cyclic convolution algorithms, which allow us to construct CFFTs over GF$(2^{11})$. The other main contribution of this paper is that we propose composite cyclotomic Fourier transforms (CCFTs). In comparison to previously proposed fast Fourier transforms, our CCFTs achieve lower overall complexities for moderate to long lengths, and the imp...
Electronically-Scanned Fourier-Transform Spectrometer
Breckinridge, J. B.; Ocallaghan, F. G.
1984-01-01
Instrument efficient, lightweight, and stable. Fourier-transform spectrometer configuration uses electronic, instead of mechanical, scanning. Configuration insensitive to vibration-induced sampling errors introduced into mechanically scanned systems.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new me- thod of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
郑建斌; 张红权; 高鸿
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new method of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.