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....

Fourier optical cryptosystem using complex spatial modulation

International Nuclear Information System (INIS)

Sarkadi, T; Koppa, P

2014-01-01

Our goal is to enhance the security level of a Fourier optical encryption system. Therefore we propose a Mach–Zehnder interferometer based encryption setup. The input data is organized in a binary array, and it is encoded in the two wave fronts propagated in the arms of the interferometer. Both input wave fronts are independently encrypted by Fourier systems, hence the proposed method has two encryption keys. During decryption, the encrypted wave fronts are propagated through the interferometer setup. The interference pattern of the output shows the reconstructed data in cases where the correct decryption Fourier keys are used. We propose a novel input image modulation method with a user defined phase parameter. We show that the security level of the proposed cryptosystem can be enhanced by an optimally chosen phase parameter. (paper)

Fourier optics treatment of classical relativistic electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.

2006-08-15

In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)

Experimental display of Fourier analysis through the optical physics and its didatical utilization

International Nuclear Information System (INIS)

Oliveira, S.M.M. de.

1983-01-01

The properties of Fourier analysis through physical optics are displayed experimentally. Within physical optics topics that illustrate didactically Fourier analysis, a subject usually considered purely mathematical are selected. The most important properties of Fourier transform and their utilization in cleaning up images through spatial filtering are presented, in this way the properties of convolution to analyse image formation and characterize some diffraction patterns are also used. (Author) [pt

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....

Meso-optical Fourier transform microscope with double focusing

International Nuclear Information System (INIS)

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

1992-01-01

The meso-optical Fourier transform microscope (MFTM) with double focusing for particle tracks of low ionization level in the nuclear emulsion is described. It is shown experimentally that this device enables one to get high concentration of information about the position of the particle track in the nuclear emulsion and thus to increase the signal-to-noise ratio. It is shown that spreading of the meso-optical image of the particle track in the sagittal section of the MFTM can be eliminated completely in the frame of the diffraction limit. The number of the additional degrees of freedom in this new MFTM system along depth coordinate is equal to 20 in comparison to single degree of freedom in the Fourier transform microscope of the direct observation. 10 refs.; 15 figs

An OTDM-To-WDM Converter Using Optical Fourier Transformation

OpenAIRE

Khin Su Myat Min; Zaw Myo Lwin; Hla Myo Tun

2015-01-01

We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements ar...

High-resolution retinal imaging using adaptive optics and Fourier-domain optical coherence tomography

Science.gov (United States)

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.

An OTDM-To-WDM Converter Using Optical Fourier Transformation

Directory of Open Access Journals (Sweden)

Khin Su Myat Min

2015-08-01

Full Text Available We demonstrate serial-to-parallel conversion of 40 Gbps optical time division multiplexed OTDM signal to 4x10 Gbps wavelength division-multiplexed WDM individual channels by using Optical Fourier Transformation OFT method. OFT is also called time lens technique and it is implemented by the combination of dispersive fiber and phase modulation. In this research electro-optic phase modulator EOM is used as time lens. As our investigations simulation results and bit error rate BER measurements are expressed.

Fourier transform digital holographic adaptive optics imaging system

Science.gov (United States)

Liu, Changgeng; Yu, Xiao; Kim, Myung K.

2013-01-01

A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541

Development of an polarization sensitive Fourier domain optical coherence tomography and it utilization on the Mueller matrix determination

International Nuclear Information System (INIS)

Raele, Marcus Paulo

2009-01-01

This study approached theoretical and experimental aspects related with the development of a polarization sensitive, Fourier domain, optical coherence tomography system (PS-FD-OCT) and its utilization on the Mueller Matrix determination. This work began with a bibliographic revision, which describes since the early studies to the actual state of the art of the technique. The mathematical formalism of Fourier domain low coherence interferometry and light polarization was performed as well. Studies based on numerical simulations, of three different algorithm types, responsible to recover the scattering profile, were done. The implemented algorithms were: Direct Fourier Transform, Interpolation and zero-filling. By the end of the simulation study, was possible to conclude that the algorithm zero-filling 2N presented better characteristics when compared with the others. In the experimental part, firstly different OCT setups were assembled and measurements were done in order to verify aspects related with the theory. Then, using a polymeric sample, birefringence images were performed, which allowed determining the sample birefringence quantitatively. Finally, images taken of different polarization states were collected, and through then images related with the Mueller Matrix elements were calculated, which were analyzed individually. (author)

High Time-Resolution 640-Gb/s Clock Recovery Using Time-Domain Optical Fourier Transformation and Narrowband Optical Filter

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...

OTDM-WDM Conversion Based on Time-Domain Optical Fourier Transformation with Spectral Compression

DEFF Research Database (Denmark)

Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael

2011-01-01

We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown.......We propose a scheme enabling direct serial-to-parallel conversion of OTDM data tributaries onto a WDM grid, based on optical Fourier transformation with spectral compression. Demonstrations on 320 Gbit/s and 640 Gbit/s OTDM data are shown....

Pulse shaping using the optical Fourier transform technique - for ultra-high-speed signal processing

DEFF Research Database (Denmark)

Palushani, Evarist; Oxenløwe, Leif Katsuo; Galili, Michael

2009-01-01

This paper reports on the generation of a 1.6 ps FWHM flat-top pulse using the optical Fourier transform technique. The pulse is validated in a 320 Gbit/s demultiplexing experiment.......This paper reports on the generation of a 1.6 ps FWHM flat-top pulse using the optical Fourier transform technique. The pulse is validated in a 320 Gbit/s demultiplexing experiment....

Time lens based optical fourier transformation for advanced processing of spectrally-efficient OFDM and N-WDM signals

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....

Nonlinear Fourier transform for dual-polarization optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone

communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...

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 s Centre form the f th s pr t fi d id Keywords: Fourier-domain optical coherence tomography; Human sweat secretion; Sweat gland; Sweat duct; Hyperhidrosis growing list of triggers include cancer, glucose control disorder, mental stress, social..., that is, the gland, duct and pore(s). However, due to a slow imaging time, COCT is largely restricted to morphometry of human tissue and thickness measurement of biologic and biologic samples [12,13]. ARTICLE IN PRESS Fourier-domain optical coherence...

Simple example of track finding by Fourier transform and possibilities for vector or optical processors

International Nuclear Information System (INIS)

Underwood, D.

1986-01-01

Simple examples of finding tracks by Fourier transform with filter or correlation function are presented. Possibilities for using this method in more complicated real situations and the processing times which might be achieved are discussed. The method imitates the simplest examples in the literature on optical pattern recognition and optical processing. The possible benefits of the method are in speed of processing in the optical Fourier transform wherein an entire picture is processed simultaneously. The speed of a computer vector processor may be competitive with present electro-optical devices. 2 refs., 6 figs

Optical polarimeter based on Fourier analysis and electronic control

International Nuclear Information System (INIS)

Vilardy, J; Salas, V.; Torres, C.

2016-01-01

In this paper, we show the design and implementation of an optical polarimeter using electronic control and the Fourier analysis. The polarimeter prototype will be used as a main tool for the students of the Universidad Popular del Cesar that belong to the following university programs: Electronics engineering (optoelectronics area), Math and Physics degree and the Master in Physics Sciences, in order to learning the theory and experimental aspects of the state of optical polarization via the Stokes vector measurement. Using the electronic polarimeter proposed in this paper, the students will be able to observe (in an optical bench) and understand the different interactions of the states of optical polarization when the optical waves pass through to the polarizers and retarder waves plates. The electronic polarimeter has a software that captures the optical intensity measurement and evaluates the Stokes vector. (Author)

Dual-polarization nonlinear Fourier transform-based optical communication system

DEFF Research Database (Denmark)

Gaiarin, Simone; Perego, A. M.; da Silva, Edson Porto

2018-01-01

communication could potentially overcome these limitations. It relies on a mathematical technique called “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical...

Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs

Science.gov (United States)

Roychoudhuri, Chandrasekhar

2007-09-01

We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.

Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.

Science.gov (United States)

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.

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....

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...

Optically compressed sensing by under sampling the polar Fourier plane

International Nuclear Information System (INIS)

Stern, A; Levi, O; Rivenson, Y

2010-01-01

In a previous work we presented a compressed imaging approach that uses a row of rotating sensors to capture indirectly polar strips of the Fourier transform of the image. Here we present further developments of this technique and present new results. The advantages of our technique, compared to other optically compressed imaging techniques, is that its optical implementation is relatively easy, it does not require complicate calibrations and that it can be implemented in near-real time.

Topography description of thin films by optical Fourier Transform

International Nuclear Information System (INIS)

Jaglarz, Janusz

2008-01-01

In this work, the main problems concerning the scattering of light by real surfaces and films are presented in view of results obtained with the bidirectional reflection distribution function (BRDF) method and optical profilometry (OP). The BRDF and OP studies, being complementary to the atomic force microscopy (AFM), allow one to get information about surface topography. From the optical data, the surface power spectral density (PSD) functions for absorbing and transparent rough films have been found. Both functions have been evaluated from the Fourier transform (FT) of the surface profiles. The usefulness of BRDF-and OP methods in characterization of real surfaces is demonstrated when analyzing the optical data obtained for metallic TiN-and organic PVK thin films deposited on various substrates

Topography description of thin films by optical Fourier Transform

Energy Technology Data Exchange (ETDEWEB)

Jaglarz, Janusz [Institute of Physics, Cracow University of Technology, ul. Podchoraz.ych 1, 30-084 Krakow (Poland)], E-mail: pujaglar@cyfronet.krakow.pl

2008-09-30

In this work, the main problems concerning the scattering of light by real surfaces and films are presented in view of results obtained with the bidirectional reflection distribution function (BRDF) method and optical profilometry (OP). The BRDF and OP studies, being complementary to the atomic force microscopy (AFM), allow one to get information about surface topography. From the optical data, the surface power spectral density (PSD) functions for absorbing and transparent rough films have been found. Both functions have been evaluated from the Fourier transform (FT) of the surface profiles. The usefulness of BRDF-and OP methods in characterization of real surfaces is demonstrated when analyzing the optical data obtained for metallic TiN-and organic PVK thin films deposited on various substrates.

Universal discrete Fourier optics RF photonic integrated circuit architecture.

Science.gov (United States)

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.

All-Optical Ultra-High-Speed OFDM to Nyquist-WDM Conversion Based on Complete Optical Fourier Transformation

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...

Metasurface Enabled Wide-Angle Fourier Lens.

Science.gov (United States)

Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo

2018-06-01

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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...

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

OpenAIRE

Maj, Omar

2004-01-01

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

A planar waveguide optical discrete Fourier transformer design for 160 Gb/s all-optical OFDM systems

Science.gov (United States)

Li, Wei; Liang, Xiaojun; Ma, Weidong; Zhou, Tianhong; Huang, Benxiong; Liu, Deming

2010-01-01

A cost-effective all-optical discrete Fourier transformer (ODFT) is designed based on a silicon planar lightwave circuit (PLC), which can be applied to all-optical orthogonal frequency division multiplexing (OFDM) transmission systems and can be achieved by current techniques. It consists of 2 × 2 directional couplers, phase shifters and optical delay lines. Metal-film heaters are used as phase shifters, according to the thermooptic effect of SiO 2. Based on the ODFT, a 160 Gb/s OFDM system is set up. Simulation results show excellent bit error rate (BER) and optical signal-to-noise ratio (OSNR) performances after 400 km transmission.

Ultra-high-speed optical serial-to-parallel data conversion by time-domain optical Fourier transformation in a silicon nanowire

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...

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

Science.gov (United States)

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Retrieving the optical parameters of biological tissues using diffuse reflectance spectroscopy and Fourier series expansions. I. theory and application.

Science.gov (United States)

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.

Optical propagators in vector and spinor theories by path integral formalism

International Nuclear Information System (INIS)

Linares, J.

1993-01-01

The construction of an extended parabolic (wide-angle) vector and spinor wave theory is presented. For that, optical propagators in monochromatic vector light optics and monoenergetic spinor electron optics are evaluated by the path integral formalism. The auxiliary parameter method introduced by Fock and the Feynman-Dyson perturbative series are used. The proposed theory supplies, by a generalized Fermat's principle, the Mukunda-Simon-Sudarshan transformation for the passage from scalar to vector light (or spinor electron) optics in an asymptotic approximation. (author). 19 refs

Fourier optics along a hybrid optical fiber for Bessel-like beam generation and its applications in multiple-particle trapping.

Science.gov (United States)

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.

Flat-top pulse generation by the optical Fourier transform technique for ultrahigh speed signal processing

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...

Canonical formalism for coupled beam optics

International Nuclear Information System (INIS)

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

Tunable fractional-order Fourier transformer

International Nuclear Information System (INIS)

Malyutin, A A

2006-01-01

A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order a element of [0,1] in one of the mutually orthogonal planes corresponds to the transform order (2-a) in another plane, i.e., to inversion and inverse Fourier transform of the order a. (laser modes and beams)

Integration of LCoS-SLM and LabVIEW based software to simulate fundamental optics, wave optics, and Fourier optics

Science.gov (United States)

Lyu, Bo-Han; Wang, Chen; Tsai, Chun-Wei

2017-08-01

Jasper Display Corp. (JDC) offer high reflectivity, high resolution Liquid Crystal on Silicon - Spatial Light Modulator (LCoS-SLM) which include an associated controller ASIC and LabVIEW based modulation software. Based on this LCoS-SLM, also called Education Kit (EDK), we provide a training platform which includes a series of optical theory and experiments to university students. This EDK not only provides a LabVIEW based operation software to produce Computer Generated Holograms (CGH) to generate some basic diffraction image or holographic image, but also provides simulation software to verity the experiment results simultaneously. However, we believe that a robust LCoSSLM, operation software, simulation software, training system, and training course can help students to study the fundamental optics, wave optics, and Fourier optics more easily. Based on these fundamental knowledges, they could develop their unique skills and create their new innovations on the optoelectronic application in the future.

Isogyres - Manifestation of Spin-orbit interaction in uniaxial crystal: A closed-fringe Fourier analysis of conoscopic interference

Science.gov (United States)

Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.

2016-09-01

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.

Single-shot parallel full range complex Fourier-domain optical coherence tomography

International Nuclear Information System (INIS)

Huang Bingjie; Bu Peng; Nan Nan; Wang Xiangzhao

2011-01-01

We present a method of parallel full range complex Fourier-domain optical coherence tomography (FDOCT) that is capable of acquiring an artifacts-free two-dimensional (2-D) cross-sectional image, i.e. a full range B-scan tomogram, by a single shot of 2-D CCD camera. This method is based on a spatial carrier technique, in which the spatial carrier-frequency is instantaneously introduced into the 2-D spectral interferogram registered in parallel FDOCT by using a grating-generated reference beam. The spatial-carrier-contained 2-D spectral interferogram is processed through Fourier transformation to obtain a complex 2-D spectral interferogram. From the 2-D complex spectral interferomgram, a full range B-scan tomogram is reconstructed. The principle of our method is confirmed by imaging an onion sample.

Generating a Square Switching Window for Timing Jitter Tolerant 160 Gb/s Demultiplexing by the Optical Fourier Transform Technique

DEFF Research Database (Denmark)

Oxenløwe, Leif Katsuo; Galili, Michael; Clausen, A. T:

2006-01-01

A square spectrum is optically Fourier transformed into a square pulse in the time domain. This is used to demultiplex a 160 Gb/s data signal with a significant increase in jitter tolerance to 2.6 ps.......A square spectrum is optically Fourier transformed into a square pulse in the time domain. This is used to demultiplex a 160 Gb/s data signal with a significant increase in jitter tolerance to 2.6 ps....

Limitations in imaging common conjunctival and corneal pathologies with fourier-domain optical coherence tomography.

Science.gov (United States)

Demirci, Hakan; Steen, Daniel W

2014-01-01

To describe the limitations of Fourier-domain optical coherence tomography (OCT) in imaging common conjunctival and corneal pathology. Retrospective, single-center case series of 40 patients with conjunctival and cornea pathology. Fourier-domain OCT imaged laser in situ keratomileusis (LASIK) flaps in detail, including its relation to other corneal structures and abnormalities. Similarly, in infectious or degenerative corneal disorders, Fourier-domain OCT successfully showed the extent of infiltration or material deposition, which appeared as hyper-reflective areas. In cases with pterygium, the underlying cornea could not be imaged. All cases of common conjunctival pathologies, such as nevus or pinguecula, were successfully imaged in detail. Nevi, scleritis, pterygium, pinguecula, and subconjunctival hemorrhage were hyper-reflective lesions, while cysts and lymphangiectasia were hyporeflective. The details of the underlying sclera were not uniformly imaged in conjunctival pathologies. Fourier-domain OCT imaged the trabeculectomy bleb in detail, whereas the details of structures of the anterior chamber angle were not routinely visualized in all cases. Light scatter through vascularized, densely inflamed, or thick lesions limits the imaging capabilities of Fourier-domain anterior segment OCT.

1.28 Tbaud Nyquist Signal Transmission using Time-Domain Optical Fourier Transformation based Receiver

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....

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

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...

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,...... around a geometry specific dominant transverse wavenumber region. We will use the developed approach to investigate the Q factor and mode confinement in cavities where top DBR mirror has small rectangular defect confining the modes laterally on the defect region....

16 channel WDM regeneration in a single phase-sensitive amplifier through optical Fourier transformation

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...

Fourier path-integral Monte Carlo methods: Partial averaging

International Nuclear Information System (INIS)

Doll, J.D.; Coalson, R.D.; Freeman, D.L.

1985-01-01

Monte Carlo Fourier path-integral techniques are explored. It is shown that fluctuation renormalization techniques provide an effective means for treating the effects of high-order Fourier contributions. The resulting formalism is rapidly convergent, is computationally convenient, and has potentially useful variational aspects

1.28 Tbit/s/channel single-polarization DQPSK transmission over 525 km using ultrafast time-domain optical Fourier transformation

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....

Fourier duality as a quantization principle

International Nuclear Information System (INIS)

Aldrovandi, R.; Saeger, L.A.

1996-08-01

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs

Quasiparticle relaxation in Heavy Fermions studied using Inverse Fourier Transform of optical conductivity

International Nuclear Information System (INIS)

Dordevic, S.V.

2012-01-01

Inverse Fourier Transform of optical conductivity is used for studies of quasiparticle relaxation in Heavy Fermions in time domain. We demonstrate the usefulness of the procedure on model spectra and then use it to study quasiparticle relaxation in two Heavy Fermions YbFe 4 Sb 12 and CeRu 4 Sb 12 . Optical conductivity in time domain reveals details of quasiparticle relaxation close to the Fermi level, not readily accessible from the spectra in the frequency domain. In particular, we find that the relaxation of heavy quasiparticles does not start instantaneously, but typically after a few hundred femto-seconds.

Conversion of a DWDM signal to a single Nyquist channel based on a complete optical Fourier transformation

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....

Identification of persons by means of the Fourier spectra of the optical transmission binary models of the human irises

Czech Academy of Sciences Publication Activity Database

Muroň, A.; Koiš, P.; Pospíšil, Jaroslav

2001-01-01

Roč. 192, - (2001), s. 161-167 ISSN 0030-4018 Institutional research plan: CEZ:AV0Z1010921 Keywords : human iris * coherent optical Fourier transform * identification of persons Subject RIV: BH - Optics, Masers, Lasers Impact factor: 1.354, year: 2001

Research on FBG-based longitudinal-acousto-optic modulator with Fourier mode coupling method.

Science.gov (United States)

Li, Zhuoxuan; Pei, Li; Liu, Chao; Ning, Tigang; Yu, Shaowei

2012-10-20

Fourier mode coupling model was first applied to achieve the spectra property of a fiber Bragg grating (FBG)-based longitudinal-acousto-optic modulator. Compared with traditional analysis algorithms, such as the transfer matrix method, the Fourier mode coupling model could improve the computing efficiency up to 100 times with a guarantee of accuracy. In this paper, based on the theoretical analysis of this model, the spectra characteristics of the modulator in different frequencies and acoustically induced strains were numerically simulated. In the experiment, a uniform FBG was modulated by acoustic wave (AW) at 12 different frequencies. In particular, the modulator responses at 563 and 885.5 KHz with three different lead zirconate titanate (PZT) loads applied were plotted for illustration, and the linear fitting of experimental data demonstrated a good match with the simulation result. The acoustic excitation of the longitudinal wave is obtained using a conic silica horn attached to the surface of a shear-mode PZT plate paralleled to the fiber axis. This way of generating longitudinal AW with a transversal PZT may shed light on the optimal structural design for the FBG-based longitudinal-acousto-optic modulator.

Refractometry of melanocyte cell nuclei using optical scatter images recorded by digital Fourier microscopy.

Science.gov (United States)

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.

On the Cooley-Turkey Fast Fourier algorithm for arbitrary factors ...

African Journals Online (AJOL)

Atonuje and Okonta in [1] developed the Cooley-Turkey Fast Fourier transform algorithm and its application to the Fourier transform of discretely sampled data points N, expressed in terms of a power y of 2. In this paper, we extend the formalism of [1] Cookey-Turkey Fast Fourier transform algorithm. The method is developed ...

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

Science.gov (United States)

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-08-01

Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

Analysis of the localization of Michelson interferometer fringes using Fourier optics and temporal coherence

International Nuclear Information System (INIS)

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 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

Automatic Fourier transform and self-Fourier beams due to parabolic potential

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yiqi, E-mail: zhangyiqi@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Belić, Milivoj R., E-mail: milivoj.belic@qatar.tamu.edu [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Zhong, Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Shunde 528300 (China); Petrović, Milan S. [Institute of Physics, P.O. Box 68, 11001 Belgrade (Serbia); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

2015-12-15

We investigate the propagation of light beams including Hermite–Gauss, Bessel–Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams—that is, the beams whose Fourier transforms are the beams themselves.

Detection of 320 Gb/s Nyquist OTDM by polarization-insensitive time-domain optical Fourier transformation

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 into...

High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform

Science.gov (United States)

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

Repeatability of pachymetric mapping using fourier domain optical coherence tomography in corneas with opacities.

Science.gov (United States)

Samy El Gendy, Nehal M; Li, Yan; Zhang, Xinbo; Huang, David

2012-04-01

To evaluate the repeatability of Fourier domain optical coherence tomography (OCT) pachymetric mapping in patients with corneal opacities and to assess the reliability of Fourier domain OCT with 830 nm wavelength as a pachymetric measurement tool in opaque corneas. A Fourier domain OCT system was used to map the corneal thickness of patients with corneal scars or dystrophy. A retrospective study of a consecutive series was conducted. The repeatability was measured using pooled standard deviation of repeated measurements. A slit-scanning tomography device provided pachymetric mapping for comparison. Seventeen eyes of 12 patients with corneal scars (7 trauma and 3 post infection) or dystrophy (2 Reis-Bucklers and 5 granular dystrophy) were included. The posterior corneal boundary was detectable in all cases. The average corneal thickness measured by OCT was 536 ± 89 μm in central 2 mm area, 553 ± 76 μm in pericentral 2- to 5-mm area, and 508 ± 93 μm for the minimum corneal thickness. The slit-scanning tomography central corneal thickness, 433 ± 111 μm, was significantly lower than OCT readings (mean difference -91.1 ± 33.3 μm, P = 0.002). Repeatability of the OCT measurements was 2.1 μm centrally and 1.2 μm pericentrally. Pachymetric mapping with Fourier domain OCT was highly repeatable. Fourier domain OCT is a reliable pachymetric tool in opaque corneas. In comparison, corneal thickness measured by the slit-scanning tomography is significantly thinner than those measured by the Fourier domain OCT in the presence of corneal opacities.

Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

Science.gov (United States)

Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

2018-02-01

Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

Application of the fractional Fourier transform to the design of LCOS based optical interconnects and fiber switches.

Science.gov (United States)

Robertson, Brian; Zhang, Zichen; Yang, Haining; Redmond, Maura M; Collings, Neil; Liu, Jinsong; Lin, Ruisheng; Jeziorska-Chapman, Anna M; Moore, John R; Crossland, William A; Chu, D P

2012-04-20

It is shown that reflective liquid crystal on silicon (LCOS) spatial light modulator (SLM) based interconnects or fiber switches that use defocus to reduce crosstalk can be evaluated and optimized using a fractional Fourier transform if certain optical symmetry conditions are met. Theoretically the maximum allowable linear hologram phase error compared to a Fourier switch is increased by a factor of six before the target crosstalk for telecom applications of -40 dB is exceeded. A Gerchberg-Saxton algorithm incorporating a fractional Fourier transform modified for use with a reflective LCOS SLM is used to optimize multi-casting holograms in a prototype telecom switch. Experiments are in close agreement to predicted performance.

Reduced timing Sensitivity in all-optical switching using flat-top control pulses obtained by the optical fourier transform technique

DEFF Research Database (Denmark)

Oxenløwe, Leif Katsuo; Galili, Michael; Mulvad, Hans Christian Hansen

2006-01-01

into the time domain, referred to as the optical Fourier transform technique. A 3 ps flat-top pulse derived from a 3 nm wide square filter is obtained, and used to gate an all-optical OTDM demultiplexer, yielding an error-free timing jitter tolerance of 3 ps for 80 Gb/s and 160 Gb/s data signals.......For high-speed serial data, timing tolerance is crucial for switching and regeneration. We propose a novel scheme to generate flat-top pulses, for use as gating control pulses. The scheme relies on spectral shaping by a square-shaped filter, followed by a linear transformation of the spectral shape...

Propagation of a general-type beam through a truncated fractional Fourier transform optical system.

Science.gov (United States)

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.

Implementation of quantum and classical discrete fractional Fourier transforms

Science.gov (United States)

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

2016-01-01

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. PMID:27006089

Implementation of quantum and classical discrete fractional Fourier transforms.

Science.gov (United States)

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.

Differences between time domain and Fourier domain optical coherence tomography in imaging tissues.

Science.gov (United States)

Gao, W; Wu, X

2017-11-01

It has been numerously demonstrated that both time domain and Fourier domain optical coherence tomography (OCT) can generate high-resolution depth-resolved images of living tissues and cells. In this work, we compare the common points and differences between two methods when the continuous and random properties of live tissue are taken into account. It is found that when relationships that exist between the scattered light and tissue structures are taken into account, spectral interference measurements in Fourier domain OCT (FDOCT) is more advantageous than interference fringe envelope measurements in time domain OCT (TDOCT) in the cases where continuous property of tissue is taken into account. It is also demonstrated that when random property of tissue is taken into account FDOCT measures the Fourier transform of the spatial correlation function of the refractive index and speckle phenomena will limit the effective limiting imaging resolution in both TDOCT and FDOCT. Finally, the effective limiting resolution of both TDOCT and FDOCT are given which can be used to estimate the effective limiting resolution in various practical applications. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

Novel developments in Fourier domain optical coherence tomography and nonlinear tomographic interferometry

OpenAIRE

Mallat, Kamel

2014-01-01

In this thesis we present novel methods to improve the limitations in Optical Coherence Tomography (OCT). They are divided into two parts. The first part deals with the axial resolution limitation in OCT systems. We give a description of the Fourier Domain OCT (FDOCT), and then we show theoretically how to enhance the axial resolution in a particular case of a two-layer sample where one of the two layers is moving continuously, while these two layers are separated by a distance lower than the...

Beyond MOS and fibers: Optical Fourier-transform Imaging Unit for Cananea Observatory (OFIUCO)

Science.gov (United States)

Nieto-Suárez, M. A.; Rosales-Ortega, F. F.; Castillo, E.; García, P.; Escobedo, G.; Sánchez, S. F.; González, J.; Iglesias-Páramo, J.; Mollá, M.; Chávez, M.; Bertone, E.; et al.

2017-11-01

Many physical processes in astronomy are still hampered by the lack of spatial and spectral resolution, and also restricted to the field-of-view (FoV) of current 2D spectroscopy instruments available worldwide. It is due to that, many of the ongoing or proposed studies are based on large-scale imaging and/or spectroscopic surveys. Under this philosophy, large aperture telescopes are dedicated to the study of intrinsically faint and/or distance objects, covering small FoVs, with high spatial resolution, while smaller telescopes are devoted to wide-field explorations. However, future astronomical surveys, should be addressed by acquiring un-biases, spatially resolved, high-quality spectroscopic information for a wide FoV. Therefore, and in order to improve the current instrumental offer in the Observatorio Astrofísico Guillermo Haro (OAGH) in Cananea, Mexico (INAOE); and to explore a possible instrument for the future Telescopio San Pedro Mártir (6.5m), we are currently integrating at INAOE an instrument prototype that will provide us with un-biased wide-field (few arcmin) spectroscopic information, and with the flexibility of operating at different spectral resolutions (R 1-20000), with a spatial resolution limited by seeing, and therefore, to be used in a wide range of astronomical problems. This instrument called OFIUCO: Optical Fourier-transform Imaging Unit for Cananea Observatory, will make use of the Fourier Transform Spectroscopic technique, which has been proved to be feasible in the optical wavelength range (350-1000 nm) with designs such as SITELLE (CFHT). We describe here the basic technical description of a Fourier transform spectrograph with important modifications from previous astronomical versions, as well as the technical advantages and weakness, and the science cases in which this instrument can be implemented.

Hiding objects and creating illusions above a carpet filter using a Fourier optics approach.

Science.gov (United States)

Wu, Kedi; Wang, Guo Ping

2010-09-13

Invisibility carpet cloaks are usually used to hide an object beneath carpet. In this paper we propose and demonstrate a carpet filter to hide objects and create illusions above the filter by using a Fourier optics method. Instead of using transformation optics, we get electromagnetic parameters of the filter by optical transfer functions, which play the role of modulating the propagation of the scattering angular spectrum directly from an object above the filter. By further adding a functional layer onto the filter, we can even camouflage the object so that it appears to be a different object. The analytical results are confirmed by numerical simulations. Our method is completely different from the current coordinate transfer method and may provide another point of view to more clearly understand the mechanism of invisibility cloaks.

A simple formalism for diffusion coefficient calculations in cells having a small optical thickness

International Nuclear Information System (INIS)

Benoist, Pierre.

1980-04-01

A very simple formalism, using directionnal first flight collision probabilities, is established; it is assigned to the calculation of the diffusion coefficients in cells having a small optical thickness. This formalism can be used, at least as a first approximation, in lattices of sodium-cooled fast reactors or of light water reactors. However, due to the two assumptions -cylindricalization of the cell and restriction to the zeroth order term in B 2 (k)- this formalissm cannot be used for sodium-voided or gas-cooled fast reactor lattices [fr

Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states

Science.gov (United 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.

Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states

International Nuclear Information System (INIS)

Dell'Anno, Fabio; De Siena, Silvio; 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 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

Fourier domain optical coherence tomography achieves full range complex imaging in vivo by introducing a carrier frequency during scanning

International Nuclear Information System (INIS)

Wang, Ruikang K

2007-01-01

The author describes a Fourier domain optical coherence tomography (FDOCT) system that is capable of full range complex imaging in vivo. This is achieved by introducing a constant carrier frequency into the OCT spectral interferograms at the time when imaging is performed. The complex functions of the spatial interferograms formed by each single wavelength are constructed before performing the Fourier transformation to localize the scatters within a sample. Two algorithms, based on Fourier filtering and Hilbert transformation, respectively, are described to achieve the full range complex FDOCT imaging. It is shown that the Hilbert transformation approach delivers better performance than the Fourier filtering method does in terms of tolerating the sample movement in vivo. The author finally demonstrates experimentally the system and algorithms for true in vivo imaging at a rate of 20 000 axial scans per second

Handbook of Fourier analysis & its applications

CERN Document Server

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

Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus

International Nuclear Information System (INIS)

Aerts, Diederik; Czachor, Marek; Kuna, Maciej

2016-01-01

Highlights: • Fractal arithmetic allows to define Fourier transforms on Cantor-like sets. • General construction is illustrated on the example of a sawtooth signal. • The formalism is much simpler than the approaches discussed so far in the literature. - Abstract: Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.

Optical design and analysis of carbon dioxide laser fusion systems using interferometry and fast Fourier transform techniques

International Nuclear Information System (INIS)

Viswanathan, V.K.

1979-01-01

The optical design and analysis of the LASL carbon dioxide laser fusion systems required the use of techniques that are quite different from the currently used method in conventional optical design problems. The necessity for this is explored and the method that has been successfully used at Los Alamos to understand these systems is discussed with examples. This method involves characterization of the various optical components in their mounts by a Zernike polynomial set and using fast Fourier transform techniques to propagate the beam, taking diffraction and other nonlinear effects that occur in these types of systems into account. The various programs used for analysis are briefly discussed

Computing exact Fourier series coefficients of IC rectilinear polygons from low-resolution fast Fourier coefficients

Science.gov (United States)

Scheibler, Robin; Hurley, Paul

2012-03-01

We present a novel, accurate and fast algorithm to obtain Fourier series coefficients from an IC layer whose description consists of rectilinear polygons on a plane, and how to implement it using off-the-shelf hardware components. Based on properties of Fourier calculus, we derive a relationship between the Discrete Fourier Transforms of the sampled mask transmission function and its continuous Fourier series coefficients. The relationship leads to a straightforward algorithm for computing the continuous Fourier series coefficients where one samples the mask transmission function, compute its discrete Fourier transform and applies a frequency-dependent multiplicative factor. The algorithm is guaranteed to yield the exact continuous Fourier series coefficients for any sampling representing the mask function exactly. Computationally, this leads to significant saving by allowing to choose the maximal such pixel size and reducing the fast Fourier transform size by as much, without compromising accuracy. In addition, the continuous Fourier series is free from aliasing and follows closely the physical model of Fourier optics. We show that in some cases this can make a significant difference, especially in modern very low pitch technology nodes.

Meso-optical Fourier transform microscope - a new device for high energy physics

International Nuclear Information System (INIS)

Astakhov, A.Ya.; Batusov, Yu.A.; Bencze, G.L.; Farago, I.; Kisvaradi, A.; Molnar, L.; Soroko, L.M.; Vegh, J.

1989-01-01

A new device for high energy physics, the Meso-optical Fourier Transform Microscope (MFTM), designed for observation fo straight line particle tracks in nuclear research emulsion is described. The MFTM works without any mechanical or electronical depth scanning and can be considered as a selectivity viewing 'eye'. The computer controlled system containing MFTM as its main unit is given. This system can be used for a fast search for particle tracks and events produced by high energy neutrinos from particle accelerators. The results of the first experimental test of the computer controlled MFTM are presented. The performance of this system is described and discussed. It is shown that the angular resolution of the MFTM is 1 angular minute and the measurement time is equal to 30 ms per image. As all operations in the MFTM proceed without any depth scanning, this new evaluation system works at least two orders of magnitude faster than any known system with a traditional optical microscope. (orig.)

Imaging properties of the mesooptical Fourier transform microscope for nuclear research emulsion

International Nuclear Information System (INIS)

Bencze, Gy.L.; Soroko, L.M.

1987-01-01

The optical signal transformation in the Mesooptical Fourier Transform Microscope (MFTM) for nuclear emulsion is treated in terms of Fourier Optics. A continuous conversion of the traditional optical microscope into the MFTM is followed. The images of dot-like and straight line objects given by the MFTM are discussed

Design and calibration of a digital Fourier holographic microscope for particle sizing via goniometry and optical scatter imaging in transmission.

Science.gov (United States)

Rossi, Vincent M; Jacques, Steven L

2016-06-13

Goniometry and optical scatter imaging have been used for optical determination of particle size based upon optical scattering. Polystyrene microspheres in suspension serve as a standard for system validation purposes. The design and calibration of a digital Fourier holographic microscope (DFHM) are reported. Of crucial importance is the appropriate scaling of scattering angle space in the conjugate Fourier plane. A detailed description of this calibration process is described. Spatial filtering of the acquired digital hologram to use photons scattered within a restricted angular range produces an image. A pair of images, one using photons narrowly scattered within 8 - 15° (LNA), and one using photons broadly scattered within 8 - 39° (HNA), are produced. An image based on the ratio of these two images, OSIR = HNA/LNA, following Boustany et al. (2002), yields a 2D Optical Scatter Image (OSI) whose contrast is based on the angular dependence of photon scattering and is sensitive to the microsphere size, especially in the 0.5-1.0µm range. Goniometric results are also given for polystyrene microspheres in suspension as additional proof of principle for particle sizing via the DFHM.

Specification of the Fast Fourier Transform algorithm as a term rewriting system

NARCIS (Netherlands)

Rodenburg, P.H.; Hoekzema, D.J.

1987-01-01

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

Fourier Domain Optical Coherence Tomography integrated into a slit lamp; a novel technique combining anterior and posterior segment OCT

NARCIS (Netherlands)

Stehouwer, M.; Verbraak, F. D.; de Vries, H.; Kok, P. H. B.; van Leeuwen, T. G.

2010-01-01

Purpose Fourier Domain Optical Coherence Tomography (FD-OCT) provides high resolution cross-sectional images of the retina and the anterior segment. It has become an important tool in ophthalmology in the examination, diagnosis, and treatment of important and common diseases. Present OCT imaging

Change of Retinal Nerve Layer Thickness in Non-Arteritic Anterior Ischemic Optic Neuropathy Revealed by Fourier Domain Optical Coherence Tomography.

Science.gov (United States)

Han, Mei; Zhao, Chen; Han, Quan-Hong; Xie, Shiyong; Li, Yan

2016-08-01

To examine the changes of non-arteritic anterior ischemic optic neuropathy (NAION) by serial morphometry using Fourier domain optical coherence tomography (FD-OCT). Retrospective study in patients with newly diagnosed NAION (n=33, all unilateral) and controls (n=75 unilateral NAION patients with full contralateral eye vision) who underwent FD-OCT of the optic disk, optic nerve head (ONH), and macula within 1 week of onset and again 1, 3, 6, and 12 months later. The patients showed no improvement in vision during follow-up. Within 1 week of onset, all NAION eyes exhibited severe ONH fiber crowding and peripapillary retinal nerve fiber layer (RNFL) edema. Four had subretinal fluid accumulation and 12 had posterior vitreous detachment (PVD) at the optic disc surface. Ganglion cell complex (GCC) and RNFL thicknesses were reduced at 1 and 3 months (p < 0.05), with no deterioration thereafter. Initial RNFL/GCC contraction magnitude in the superior hemisphere correlated with the severity of inferior visual field deficits. NAION progression is characterized by an initial phase of accelerated RNFL and GCC deterioration. These results reveal that the kinetic change of neural retina in NAION and may have implication on the time window for treatment of NAION. FD-OCT is useful in the evaluation of NAION.

Multichannel Dynamic Fourier-Transform IR Spectrometer

Science.gov (United States)

Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.

2017-09-01

A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.

Pulse Propagation Effects in Optical 2D Fourier-Transform Spectroscopy: Theory.

Science.gov (United States)

Spencer, Austin P; Li, Hebin; Cundiff, Steven T; Jonas, David M

2015-04-30

A solution to Maxwell's equations in the three-dimensional frequency domain is used to calculate rephasing two-dimensional Fourier transform (2DFT) spectra of the D2 line of atomic rubidium vapor in argon buffer gas. Experimental distortions from the spatial propagation of pulses through the sample are simulated in 2DFT spectra calculated for the homogeneous Bloch line shape model. Spectral features that appear at optical densities of up to 3 are investigated. As optical density increases, absorptive and dispersive distortions start with peak shape broadening, progress to peak splitting, and ultimately result in a previously unexplored coherent transient twisting of the split peaks. In contrast to the low optical density limit, where the 2D peak shape for the Bloch model depends only on the total dephasing time, these distortions of the 2D peak shape at finite optical density vary with the waiting time and the excited state lifetime through coherent transient effects. Experiment-specific conditions are explored, demonstrating the effects of varying beam overlap within the sample and of pseudo-time domain filtering. For beam overlap starting at the sample entrance, decreasing the length of beam overlap reduces the line width along the ωτ axis but also reduces signal intensity. A pseudo-time domain filter, where signal prior to the center of the last excitation pulse is excluded from the FID-referenced 2D signal, reduces propagation distortions along the ωt axis. It is demonstrated that 2DFT rephasing spectra cannot take advantage of an excitation-detection transformation that can eliminate propagation distortions in 2DFT relaxation spectra. Finally, the high optical density experimental 2DFT spectrum of rubidium vapor in argon buffer gas [J. Phys. Chem. A 2013, 117, 6279-6287] is quantitatively compared, in line width, in depth of peak splitting, and in coherent transient peak twisting, to a simulation with optical density higher than that reported.

26 Tbit s-1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing

Science.gov (United States)

Hillerkuss, D.; Schmogrow, R.; Schellinger, T.; Jordan, M.; Winter, M.; Huber, G.; Vallaitis, T.; Bonk, R.; Kleinow, P.; Frey, F.; Roeger, M.; Koenig, S.; Ludwig, A.; Marculescu, A.; Li, J.; Hoh, M.; Dreschmann, M.; Meyer, J.; Ben Ezra, S.; Narkiss, N.; Nebendahl, B.; Parmigiani, F.; Petropoulos, P.; Resan, B.; Oehler, A.; Weingarten, K.; Ellermeyer, T.; Lutz, J.; Moeller, M.; Huebner, M.; Becker, J.; Koos, C.; Freude, W.; Leuthold, J.

2011-06-01

Optical transmission systems with terabit per second (Tbit s-1) single-channel line rates no longer seem to be too far-fetched. New services such as cloud computing, three-dimensional high-definition television and virtual-reality applications require unprecedented optical channel bandwidths. These high-capacity optical channels, however, are fed from lower-bitrate signals. The question then is whether the lower-bitrate tributary information can viably, energy-efficiently and effortlessly be encoded to and extracted from terabit per second data streams. We demonstrate an optical fast Fourier transform scheme that provides the necessary computing power to encode lower-bitrate tributaries into 10.8 and 26.0 Tbit s-1 line-rate orthogonal frequency-division multiplexing (OFDM) data streams and to decode them from fibre-transmitted OFDM data streams. Experiments show the feasibility and ease of handling terabit per second data with low energy consumption. To the best of our knowledge, this is the largest line rate ever encoded onto a single light source.

CMB in a box: Causal structure and the Fourier-Bessel expansion

International Nuclear Information System (INIS)

Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.

2010-01-01

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

Blind third-order dispersion estimation based on fractional Fourier transformation for coherent optical communication

Science.gov (United States)

Yang, Lin; Guo, Peng; Yang, Aiying; Qiao, Yaojun

2018-02-01

In this paper, we propose a blind third-order dispersion estimation method based on fractional Fourier transformation (FrFT) in optical fiber communication system. By measuring the chromatic dispersion (CD) at different wavelengths, this method can estimation dispersion slope and further calculate the third-order dispersion. The simulation results demonstrate that the estimation error is less than 2 % in 28GBaud dual polarization quadrature phase-shift keying (DP-QPSK) and 28GBaud dual polarization 16 quadrature amplitude modulation (DP-16QAM) system. Through simulations, the proposed third-order dispersion estimation method is shown to be robust against nonlinear and amplified spontaneous emission (ASE) noise. In addition, to reduce the computational complexity, searching step with coarse and fine granularity is chosen to search optimal order of FrFT. The third-order dispersion estimation method based on FrFT can be used to monitor the third-order dispersion in optical fiber system.

Fourier plane imaging microscopy

Energy Technology Data Exchange (ETDEWEB)

Dominguez, Daniel, E-mail: daniel.dominguez@ttu.edu; Peralta, Luis Grave de [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Alharbi, Nouf; Alhusain, Mdhaoui [Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States); Bernussi, Ayrton A. [Nano Tech Center, Texas Tech University, Lubbock, Texas 79409 (United States); Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)

2014-09-14

We show how the image of an unresolved photonic crystal can be reconstructed using a single Fourier plane (FP) image obtained with a second camera that was added to a traditional compound microscope. We discuss how Fourier plane imaging microscopy is an application of a remarkable property of the obtained FP images: they contain more information about the photonic crystals than the images recorded by the camera commonly placed at the real plane of the microscope. We argue that the experimental results support the hypothesis that surface waves, contributing to enhanced resolution abilities, were optically excited in the studied photonic crystals.

Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis

International Nuclear Information System (INIS)

Shimizu, Ryosuke; Edamatsu, Keiichi; Itoh, Tadashi

2006-01-01

We present one- and two-photon diffraction and interference experiments involving parametric down-converted photon pairs. By controlling the divergence of the pump beam in parametric down-conversion, the diffraction-interference pattern produced by an object changes from a quantum (perfectly correlated) case to a classical (uncorrelated) one. The observed diffraction and interference patterns are accurately reproduced by Fourier-optical analysis taking into account the quantum spatial correlation. We show that the relation between the spatial correlation and the object size plays a crucial role in the formation of both one- and two-photon diffraction-interference patterns

Modeling cavities exhibiting strong lateral confinement using open geometry Fourier modal method

Science.gov (United States)

Häyrynen, Teppo; Gregersen, Niels

2016-04-01

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, the leakage of the modes due to an imperfect field confinement is taken into account by using a basis functions that expand the whole infinite space. The computational efficiency is obtained by using a non-uniform discretization in the frequency space in which the lateral expansion modes are more densely sampled around a geometry specific dominant transverse wavenumber region. We will use the developed approach to investigate the Q factor and mode confinement in cavities where top DBR mirror has small rectangular defect confining the modes laterally on the defect region.

Miniaturized Fourier-plane fiber scanner for OCT endoscopy

International Nuclear Information System (INIS)

Vilches, Sergio; Kretschmer, Simon; Ataman, Çağlar; Zappe, Hans

2017-01-01

A forward-looking endoscopic optical coherence tomography (OCT) probe featuring a Fourier-plane fiber scanner is designed, manufactured and characterized. In contrast to common image-plane fiber scanners, the Fourier-plane scanner is a telecentric arrangement that eliminates vignetting and spatial resolution variations across the image plane. To scan the OCT beam in a spiral pattern, a tubular piezoelectric actuator is used to resonate an optical fiber bearing a collimating GRIN lens at its tip. The free-end of the GRIN lens sits at the back focal plane of an objective lens, such that its rotation replicates the beam angles in the collimated region of a classical telecentric 4f optical system. Such an optical arrangement inherently has a low numerical aperture combined with a relatively large field-of-view, rendering it particularly useful for endoscopic OCT imaging. Furthermore, the optical train of the Fourier-plane scanner is shorter than that of a comparable image-plane scanner by one focal length of the objective lens, significantly shortening the final arrangement. As a result, enclosed within a 3D printed housing of 2.5 mm outer diameter and 15 mm total length, the developed probe is the most compact forward-looking endoscopic OCT imager to date. Due to its compact form factor and compatibility with real-time OCT imaging, the developed probe is also ideal for use in the working channel of flexible endoscopes as a potential optical biopsy tool. (paper)

Miniaturized Fourier-plane fiber scanner for OCT endoscopy

Science.gov (United States)

Vilches, Sergio; Kretschmer, Simon; Ataman, Çağlar; Zappe, Hans

2017-10-01

A forward-looking endoscopic optical coherence tomography (OCT) probe featuring a Fourier-plane fiber scanner is designed, manufactured and characterized. In contrast to common image-plane fiber scanners, the Fourier-plane scanner is a telecentric arrangement that eliminates vignetting and spatial resolution variations across the image plane. To scan the OCT beam in a spiral pattern, a tubular piezoelectric actuator is used to resonate an optical fiber bearing a collimating GRIN lens at its tip. The free-end of the GRIN lens sits at the back focal plane of an objective lens, such that its rotation replicates the beam angles in the collimated region of a classical telecentric 4f optical system. Such an optical arrangement inherently has a low numerical aperture combined with a relatively large field-of-view, rendering it particularly useful for endoscopic OCT imaging. Furthermore, the optical train of the Fourier-plane scanner is shorter than that of a comparable image-plane scanner by one focal length of the objective lens, significantly shortening the final arrangement. As a result, enclosed within a 3D printed housing of 2.5 mm outer diameter and 15 mm total length, the developed probe is the most compact forward-looking endoscopic OCT imager to date. Due to its compact form factor and compatibility with real-time OCT imaging, the developed probe is also ideal for use in the working channel of flexible endoscopes as a potential optical biopsy tool.

Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units.

Science.gov (United States)

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.

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.

Glaucoma diagnosis by mapping macula with Fourier domain optical coherence tomography

Science.gov (United States)

Tan, Ou; Lu, Ake; Chopra, Vik; Varma, Rohit; Hiroshi, Ishikawa; Schuman, Joel; Huang, David

2008-03-01

A new image segmentation method was developed to detect macular retinal sub-layers boundary on newly-developed Fourier-Domain Optical Coherence Tomography (FD-OCT) with macular grid scan pattern. The segmentation results were used to create thickness map of macular ganglion cell complex (GCC), which contains the ganglion cell dendrites, cell bodies and axons. Overall average and several pattern analysis parameters were defined on the GCC thickness map and compared for the diagnosis of glaucoma. Intraclass correlation (ICC) is used to compare the reproducibility of the parameters. Area under receiving operative characteristic curve (AROC) was calculated to compare the diagnostic power. The result is also compared to the output of clinical time-domain OCT (TD-OCT). We found that GCC based parameters had good repeatability and comparable diagnostic power with circumpapillary nerve fiber layer (cpNFL) thickness. Parameters based on pattern analysis can increase the diagnostic power of GCC macular mapping.

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.

Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm.

Science.gov (United States)

Vogel, Curtis R; Yang, Qiang

2006-08-21

We present two different implementations of the Fourier domain preconditioned conjugate gradient algorithm (FD-PCG) to efficiently solve the large structured linear systems that arise in optimal volume turbulence estimation, or tomography, for multi-conjugate adaptive optics (MCAO). We describe how to deal with several critical technical issues, including the cone coordinate transformation problem and sensor subaperture grid spacing. We also extend the FD-PCG approach to handle the deformable mirror fitting problem for MCAO.

Connection between Fourier coefficient and Discretized Cartesian path integration

International Nuclear Information System (INIS)

Coalson, R.D.

1986-01-01

The relationship between so-called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier-like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on-diagonal statistical density matrix elements for a number of prototypical 1-d potentials. A consistent convergence order among these prescriptions is established

First order formalism for quantum gravity

International Nuclear Information System (INIS)

Gleiser, M.; Holman, R.; Neto, N.P.

1987-05-01

We develop a first order formalism for the quantization of gravity. We take as canonical variables both the induced metric and the extrinsic curvature of the (d - 1) -dimensional hypersurfaces obtained by the foliation of the d - dimensional spacetime. After solving the constraint algebra we use the Dirac formalism to quantize the theory and obtain a new representation for the Wheeler-DeWitt equation, defined in the functional space of the extrinsic curvature. We also show how to obtain several different representations of the Wheeler-DeWitt equation by considering actions differing by a total divergence. In particular, the intrinsic and extrinsic time approaches appear in a natural way, as do equivalent representations obtained by functional Fourier transforms of appropriate variables. We conclude with some remarks about the construction of the Hilbert space within the first order formalism. 10 refs

Comparative analysis of imaging configurations and objectives for Fourier microscopy.

Science.gov (United States)

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.

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.

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.

Image reconstruction from pairs of Fourier-transform magnitude

International Nuclear Information System (INIS)

Hunt, B.R.; Overman, T.L.; Gough, P.

1998-01-01

The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms. copyright 1998 Optical Society of America

Fourier analysis: from cloaking to imaging

Science.gov (United States)

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.

Fourier transform zero field NMR and NQR

International Nuclear Information System (INIS)

Zax, D.B.

1985-01-01

In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI

The Fourier-grid formalism: philosophy and application to scattering problems using R-matrix theory

International Nuclear Information System (INIS)

Layton, E.G.

1993-01-01

The Fourier-grid (FG) method is a recent L 2 variational treatment of the quantum mechanical eigenvalue problem that does not require the use of a set of basis functions; it is rather a discrete variable representation approach. In this article we restate the FG philosophy in more general terms, examine and compare this method with other approaches to the eigenvalue problem, and begin the development of an FG R-matrix method for scattering. The philosophy of the FG method is to use the simplest representation for each of the kinetic and potential energy operators of the Hamiltonian, and use a generalized Fourier transform to put the matrix elements of one of the above operators in the same representation as the other, so the Hamiltonian has a single representation. (author)

The use of Lorentz group formalism in solving polarization effects of a birefringent single mode optical fiber

International Nuclear Information System (INIS)

Ishiekwene, G.C.; Brown, C.S.; Mensah, S.Y.; Bak, A.E.

2000-07-01

A theoretical analysis on the polarization effects of a light beam propagating in a birefringent single-mode fiber is presented. We derive a system of differential equations representing the evolution of Stokes parameters and illustrate their application to polarization effects in a straight birefringent single mode optical fiber. The solutions to the set of equations are obtained using specifically the methods of the unified formalism for polarization optics which adopt the use of the Stokes-Mueller equation and the Lorentz group to model polarization phenomena in media such as optical fibers. The analytical results presented using this approach are identical to results obtained from other conventional methods. We observe the characteristic exponential decrease in the total intensity of the input light due to attenuation by the fiber. (author)

Improved Fourier-transform profilometry

International Nuclear Information System (INIS)

Mao Xianfu; Chen Wenjing; Su Xianyu

2007-01-01

An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object

Optical Frequency Comb Fourier Transform Spectroscopy with Resolution Exceeding the Limit Set by the Optical Path Difference

Science.gov (United States)

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.

On the Scaled Fractional Fourier Transformation Operator

International Nuclear Information System (INIS)

Hong-Yi, Fan; Li-Yun, Hu

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

Fourier analysis: from cloaking to imaging

International Nuclear Information System (INIS)

Wu, Kedi; Ping Wang, Guo; Cheng, Qiluan

2016-01-01

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. (review)

Compact Microwave Fourier Spectrum Analyzer

Science.gov (United States)

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.

Formal degrees of unipotent discrete series representations and the exotic Fourier transform

NARCIS (Netherlands)

Ciubotaru, D.; Opdam, E.

2015-01-01

We introduce a notion of elliptic fake degrees for unipotent elliptic representations of a semisimple p-adic group. We conjecture, and verify in some cases, that the relation between the formal degrees of unipotent discrete series representations of a semisimple p-adic group and the elliptic fake

Spatial-phase code-division multiple-access system with multiplexed Fourier holography switching for reconfigurable optical interconnection

Science.gov (United States)

Takasago, Kazuya; Takekawa, Makoto; Shirakawa, Atsushi; Kannari, Fumihiko

2000-05-01

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.

Fourier analysis of cell-wise Block-Jacobi splitting in two-dimensional geometry

International Nuclear Information System (INIS)

Rosa, M.; Warsa, J. S.; Kelley, T. M.

2009-01-01

A Fourier analysis is conducted in two-dimensional (2D) geometry for the discrete ordinates (S N ) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) using the cell-wise Block-Jacobi (BJ) algorithm. The results of the Fourier analysis show that convergence of cell-wise BJ can degrade, leading to a spectral radius equal to 1, in problems containing optically thin cells. For problems containing cells that are optically thick, instead, the spectral radius tends to 0. Hence, in the optically thick-cell regime, cell-wise BJ is rapidly convergent even for problems that are scattering dominated, with a scattering ratio c close to 1. (authors)

Anterior Chamber Angle Measurements Using Schwalbe's Line with High Resolution Fourier-Domain Optical Coherence Tomography

Science.gov (United States)

Qin, Bing; Francis, Brian A.; Li, Yan; Tang, Maolong; Zhang, Xinbo; Jiang, Chunhui; Cleary, Catherine; Huang, David

2012-01-01

Purpose To use Fourier-domain optical coherence tomography (OCT) to measure the angle opening distance at Schwalbe's line (AOD-SL) and determine its value in anterior chamber angle assessment. Methods Horizontal scans of the nasal and temporal anterior chamber angles in glaucoma subjects were performed by 830 nm wavelength Fourier-domain OCT. Images were graded by two ophthalmologists who assessed the visibility of Schwalbe’s line (SL), anterior limbus (AL), scleral spur (SS), and angle recess (AR). AOD-SL was measured with computer calipers. SL was manually identified by the termination of the corneal endothelium. Gonioscopy was used to classify anterior chamber angles according to a modified Shaffer system. Spearman's rho analysis was performed to assess correlation between AOD-SL and modified Shaffer grade. A cut-off value of AOD-SL for diagnosing occludable angles (modified Shaffer grade ≤1) was determined by receiver operating characteristic (ROC) analyses. Results Thirty-five glaucoma subjects (65 eyes) were enrolled. SL, AL, AR, and SS were visible by OCT in 97.7%, 99.2%, 87.3%, and 80.8% of eyes, respectively. Nasal and temporal AOD-SLs were 322.6 ± 200.2 µm and 341.4 ± 197.4 µm, respectively. Correlation coefficients between AOD-SL and modified Shaffer grade were 0.80 (nasal) and 0.81 (temporal). The diagnostic cut-off value of AOD-SL for occludable angles was 290 µm. The areas under the ROC curve, sensitivity, specificity values were 0.90, 0.80, 0.87 (nasal) and 0.90, 0.85, 0.77 (temporal). Conclusions The measurement of AOD-SL by Fourier-domain OCT is highly correlated with gonioscopy and may be a useful noncontact method of assessing angle closure risk. PMID:22827999

Polynomials formalism of quantum numbers

International Nuclear Information System (INIS)

Kazakov, K.V.

2005-01-01

Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru

A hybrid WDM/OCDMA ring with a dynamic add/drop function based on Fourier code for local area networks.

Science.gov (United States)

Choi, Yong-Kyu; Hosoya, Kenta; Lee, Chung Ghiu; Hanawa, Masanori; Park, Chang-Soo

2011-03-28

We propose and experimentally demonstrate a hybrid WDM/OCDMA ring with a dynamic add/drop function based on Fourier code for local area networks. Dynamic function is implemented by mechanically tuning the Fourier encoder/decoder for optical code division multiple access (OCDMA) encoding/decoding. Wavelength division multiplexing (WDM) is utilized for node assignment and 4-chip Fourier code recovers the matched signal from the codes. For an optical source well adapted to WDM channels and its short optical pulse generation, reflective semiconductor optical amplifiers (RSOAs) are used with a fiber Bragg grating (FBG) and gain-switched. To demonstrate we experimentally investigated a two-node hybrid WDM/OCDMA ring with a 4-chip Fourier encoder/decoder fabricated by cascading four FBGs with the bit error rate (BER) of <10(-9) for the node span of 10.64 km at 1.25 Gb/s.

Keratometric index obtained by Fourier-domain optical coherence tomography.

Directory of Open Access Journals (Sweden)

Yanjun Hua

Full Text Available To determine the keratometric indices calculated based on parameters obtained by Fourier-domain optical coherence tomography (FD-OCT.The ratio of anterior corneal curvature to posterior corneal curvature (Ratio and keratometric index (N were calculated within central 3 mm zone with the RTVue FD-OCT (RTVue, Optovue, Inc. in 186 untreated eyes, 60 post-LASIK/PRK eyes, and 39 keratoconus eyes. The total corneal powers were calculated using different keratometric indices: Kcal based on the mean calculated keratometric index, K1.3315 calculated by the keratometric index of 1.3315, and K1.3375 calculated by the keratometric index of 1.3375. In addition, the total corneal powers based on Gaussian optics formula (Kactual were calculated.The means for Ratio in untreated controls, post-LASIK/PRK group and keratoconus group were 1.176 ± 0.022 (95% confidence interval (CI, 1.172-1.179, 1.314 ± 0.042 (95%CI, 1.303-1.325 and 1.229 ± 0.118 (95%CI, 1.191-1.267, respectively. And the mean calculated keratometric index in untreated controls, post-LASIK/PRK group and keratoconus group were 1.3299 ± 0.00085 (95%CI, 1.3272-1.3308, 1.3242 ± 0.00171 (95%CI, 1.3238-1.3246 and 1.3277 ± 0.0046 (95%CI, 1.3263-1.3292, respectively. All the parameters were normally distributed. The differences between Kcal and Kactual, K1.3315 and Kactual, and K1.3375 and Kactual were 0.00 ± 0.11 D, 0.21 ± 0.11 D and 0.99 ± 0.12 D, respectively, in untreated controls; -0.01 ± 0.20 D, 0.85 ± 0.18 D and 1.56 ± 0.16 D, respectively, in post-LASIK/PRK group; and 0.03 ± 0.67 D, 0.56 ± 0.70 D and 1.40 ± 0.76 D, respectively, in keratoconus group.The calculated keratometric index is negatively related to the ratio of anterior corneal curvature to posterior corneal curvature in untreated, post-LASIK/PRK, and keratoconus eyes, respectively. Using the calculated keratometric index may improve the prediction accuracies of total corneal powers in untreated controls, but not in post

Aqueous contaminant detection via UiO-66 thin film optical fiber sensor platform with fast Fourier transform based spectrum analysis

Science.gov (United States)

Nazari, Marziyeh; Rubio-Martinez, Marta; Babarao, Ravichandar; Ayad Younis, Adel; Collins, Stephen F.; Hill, Matthew R.; Duke, Mikel C.

2018-01-01

Routine water quality monitoring is required in drinking and waste water management. A particular interest is to measure concentrations of a range of diverse contaminants on-site or remotely in real time. Here we present metal organic framework (MOF) integrated optical fiber sensor that allows for rapid optical measurement based on fast Fourier transform (FFT) spectrum analysis. The end-face of these glass optical fibers was modified with UiO-66(Zr) MOF thin film by in situ hydrothermal synthesis for the detection of the model contaminants, Rhodamine-B and 4-Aminopyridine, in water. The sensing mechanism is based on the change in the optical path length of the thin film induced by the adsorption of chemical molecules by UiO-66. Using FFT analysis, various modes of interaction (physical and chemical) became apparent, showing both irreversible changes upon contact with the contaminant, as well as reversible changes according to actual concentration. This was indicated by the second harmonic elevation to a certain level translating to high sensitivity detection.

Fourier transform wavefront control with adaptive prediction of the atmosphere.

Science.gov (United States)

Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre

2007-09-01

Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

Optical movie encryption based on a discrete multiple-parameter fractional Fourier transform

International Nuclear Information System (INIS)

Zhong, Zhi; Zhang, Yujie; Shan, Mingguang; Wang, Ying; Zhang, Yabin; Xie, Hong

2014-01-01

A movie encryption scheme is proposed using a discrete multiple-parameter fractional Fourier transform and theta modulation. After being modulated by sinusoidal amplitude grating, each frame of the movie is transformed by a filtering procedure and then multiplexed into a complex signal. The complex signal is multiplied by a pixel scrambling operation and random phase mask, and then encrypted by a discrete multiple-parameter fractional Fourier transform. The movie can be retrieved by using the correct keys, such as a random phase mask, a pixel scrambling operation, the parameters in a discrete multiple-parameter fractional Fourier transform and a time sequence. Numerical simulations have been performed to demonstrate the validity and the security of the proposed method. (paper)

Observation of superconducting fluxons by transmission electron microscopy: A Fourier space approach to calculate the electron optical phase shifts and images

International Nuclear Information System (INIS)

Beleggia, M.; Pozzi, G.

2001-01-01

An approach is presented for the calculation of the electron optical phase shift experienced by high-energy electrons in a transmission electron microscope, when they interact with the magnetic field associated with superconducting fluxons in a thin specimen tilted with respect to the beam. It is shown that by decomposing the vector potential in its Fourier components and by calculating the phase shift of each component separately, it is possible to obtain the Fourier transform of the electron optical phase shift, which can be inverted either analytically or numerically. It will be shown how this method can be used to recover the result, previously obtained by the real-space approach, relative to the case of a straight flux tube perpendicular to the specimen surfaces. Then the method is applied to the case of a London fluxon in a thin film, where the bending and the broadening of the magnetic-field lines due to the finite specimen thickness are now correctly taken into account and not treated approximately by means of a parabolic fit. Finally, it will be shown how simple models for the pancake structure of the fluxon can be analyzed within this framework and the main features of electron transmission images predicted

Fourier-muunnoksesta

OpenAIRE

NIEMELÄ, EERO

2008-01-01

Tutkielman aiheena on Fourier-muunnoksen esittely. Tarkoituksena on erityisesti johdatella lukija Fourier-sarjan ja -muunnoksen käsitteisiin. Fourier-muunnosten teoria kuuluu yleisempään Fourier-analyysin aihepiiriin. Fourier-analyysin keskiössä on tulos, jonka mukaan tietyt ehdot täyttävää funktiota voidaan approksimoida mielivaltaisen tarkasti niin sanotun Fourier-sarjan avulla. Osoitamme, että 2\\pi-jaksollisen funktion Lebesgue-neliöintegroituvuus takaa suppenevan Fourier-sarjakehitelm...

Fourier synthesis of asymmetrical optical potentials for atoms

International Nuclear Information System (INIS)

Ritt, G.

2007-01-01

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.)

Noise figure of amplified dispersive Fourier transformation

International Nuclear Information System (INIS)

Goda, Keisuke; Jalali, Bahram

2010-01-01

Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.

App. 1. Fourier series and Fourier transform

International Nuclear Information System (INIS)

Anon.

1977-01-01

Definitions, formulas and practical properties in quantum mechanics are presented: Fourier series (development of periodic function, Bessel-Parseval equality); Fourier transform (Parseval-Plancherel formula, Fourier transform in three-dimensional space) [fr

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

Science.gov (United States)

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…

Preparation and Characterization of Formalated Polyvinyl Alcohol Hydrogel Film

International Nuclear Information System (INIS)

Than Than Aye; Nyunt Win; San Myint

2011-12-01

A feasible hydrogen film was prepared from polyvinyl alcohol (PVA) sample. The effect of chemical grafting on polyvinyl alcohol film was studied. Polyvinyl alcohol sample was mixed with distilled water and autoclaved at 121C for 60 minutes. An aqueous solution of polyvinyl alcohol was casted into a steel plate and dried for a certain time at room temperature. The obtained PVA film was immersed in formalation bath containing aqueous formaldehyde, sulphuric acid, anhydrous sodium sulphate with a weight ratio of (64:95:300) and 1 liter of distilled water at 60C for various hours. Effect of formalation time was studied varying 6, 12, 24, 36 and 48 hours. Degree of formalation was also evaluated. Physical properties of the hydrogel film such as gel fraction, degree of swelling and mechanical properties such as tensile strength, elongation and hardness were determined before and after formalation of the PVA film. Fourier Transform Infrared Spectroscopic (FTIR) analysis, Thermogravimetric / Differential thermal analysis (DTA / TG) were also studied for characterization. It was found that the appropriate condition for formalation was occured at 24 hours formalation time of with the calculated degree of formalation 65.35% with the determined values (9.04 Mpa) for tensile strength, (241.92%) for elongation, (45.30 Shore D) for hardness, (280.36%) for degree of swelling and (68.32%) for gel fraction.

Rigorous simulations of a helical core fiber by the use of transformation optics formalism.

Science.gov (United States)

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.

Holographic memory system based on projection recording of computer-generated 1D Fourier holograms.

Science.gov (United States)

Betin, A Yu; Bobrinev, V I; Donchenko, S S; Odinokov, S B; Evtikhiev, N N; Starikov, R S; Starikov, S N; Zlokazov, E Yu

2014-10-01

Utilization of computer generation of holographic structures significantly simplifies the optical scheme that is used to record the microholograms in a holographic memory record system. Also digital holographic synthesis allows to account the nonlinear errors of the record system to improve the microholograms quality. The multiplexed record of holograms is a widespread technique to increase the data record density. In this article we represent the holographic memory system based on digital synthesis of amplitude one-dimensional (1D) Fourier transform holograms and the multiplexed record of these holograms onto the holographic carrier using optical projection scheme. 1D Fourier transform holograms are very sensitive to orientation of the anamorphic optical element (cylindrical lens) that is required for encoded data object reconstruction. The multiplex record of several holograms with different orientation in an optical projection scheme allowed reconstruction of the data object from each hologram by rotating the cylindrical lens on the corresponding angle. Also, we discuss two optical schemes for the recorded holograms readout: a full-page readout system and line-by-line readout system. We consider the benefits of both systems and present the results of experimental modeling of 1D Fourier holograms nonmultiplex and multiplex record and reconstruction.

Application of Fourier analysis to multispectral/spatial recognition

Science.gov (United States)

Hornung, R. J.; Smith, J. A.

1973-01-01

One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.

Spin and diamagnetism in linear and nonlinear optics

International Nuclear Information System (INIS)

Andersen, Torsten; Keller, Ole; Huebner, Wolfgang; Johansson, Boerje

2004-01-01

We present a local-field theory for spin and diamagnetism in linear and nonlinear optics. We examine all the processes contained in the Pauli Hamiltonian and its corresponding microscopic current density, including the terms depending on the electron spin. The resulting general real-space conductivities are presented and discussed. To quantify the implications of including the spin, we study the linear and nonlinear optical properties of free-electron metals, represented by the screened homogeneous electron gas. The real-space formalism is transformed into Fourier space, and the symmetries of the linear and nonlinear optical conductivities in a homogeneous electron gas are discussed. Numerical results are presented for the homogeneous electron gas, in which we treat ω and q as independent variables, thereby opening the theory to near-field optics and the study of evanescent waves. We show that in regions of the ω-q spectrum, the presence of diamagnetism and spin dynamics significantly alters the response in comparison to considering only the paramagnetic response. Additionally, we discuss the effects of screening, and we finish our treatment by a discussion of how to connect the present theory to existing methods in ab initio solid-state physics

Optical image-hiding method with false information disclosure based on the interference principle and partial-phase-truncation in the fractional Fourier domain

International Nuclear Information System (INIS)

Dai, Chaoqing; Wang, Xiaogang; Zhou, Guoquan; Chen, Junlang

2014-01-01

An image-hiding method based on the optical interference principle and partial-phase-truncation in the fractional Fourier domain is proposed. The primary image is converted into three phase-only masks (POMs) using an analytical algorithm involved partial-phase-truncation and a fast random pixel exchange process. A procedure of a fake silhouette for a decryption key is suggested to reinforce the encryption and give a hint of the position of the key. The fractional orders of FrFT effectively enhance the security of the system. In the decryption process, the POM with false information and the other two POMs are, respectively, placed in the input and fractional Fourier planes to recover the primary image. There are no unintended information disclosures and iterative computations involved in the proposed method. Simulation results are presented to verify the validity of the proposed approach. (letters)

Fourier transforms in spectroscopy

CERN Document Server

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

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....

Memory sparing, fast scattering formalism for rigorous diffraction modeling

Science.gov (United States)

Iff, W.; Kämpfe, T.; Jourlin, Y.; Tishchenko, A. V.

2017-07-01

The basics and algorithmic steps of a novel scattering formalism suited for memory sparing and fast electromagnetic calculations are presented. The formalism, called ‘S-vector algorithm’ (by analogy with the known scattering-matrix algorithm), allows the calculation of the collective scattering spectra of individual layered micro-structured scattering objects. A rigorous method of linear complexity is applied to model the scattering at individual layers; here the generalized source method (GSM) resorting to Fourier harmonics as basis functions is used as one possible method of linear complexity. The concatenation of the individual scattering events can be achieved sequentially or in parallel, both having pros and cons. The present development will largely concentrate on a consecutive approach based on the multiple reflection series. The latter will be reformulated into an implicit formalism which will be associated with an iterative solver, resulting in improved convergence. The examples will first refer to 1D grating diffraction for the sake of simplicity and intelligibility, with a final 2D application example.

Comparison of Fiber Optic and Conduit Attenuated Total Reflection (ATR) Fourier Transform Infrared (FT-IR) Setup for In-Line Fermentation Monitoring.

Science.gov (United States)

Koch, Cosima; Posch, Andreas E; Herwig, Christoph; Lendl, Bernhard

2016-12-01

The performance of a fiber optic and an optical conduit in-line attenuated total reflection mid-infrared (IR) probe during in situ monitoring of Penicillium chrysogenum fermentation were compared. The fiber optic probe was connected to a sealed, portable, Fourier transform infrared (FT-IR) process spectrometer via a plug-and-play interface. The optical conduit, on the other hand, was connected to a FT-IR process spectrometer via a knuckled probe with mirrors that had to be adjusted prior to each fermentation, which were purged with dry air. Penicillin V (PenV) and its precursor phenoxyacetic acid (POX) concentrations were determined by online high-performance liquid chromatography and the obtained concentrations were used as reference to build partial least squares regression models. Cross-validated root-mean-square errors of prediction were found to be 0.2 g L -1 (POX) and 0.19 g L -1 (PenV) for the fiber optic setup and 0.17 g L -1 (both POX and PenV) for the conduit setup. Higher noise-levels and spectrum-to-spectrum variations of the fiber optic setup lead to higher noise of estimated (i.e., unknown) POX and PenV concentrations than was found for the conduit setup. It seems that trade-off has to be made between ease of handling (fiber optic setup) and measurement accuracy (optical conduit setup) when choosing one of these systems for bioprocess monitoring. © The Author(s) 2016.

Iterative wave-front reconstruction in the Fourier domain.

Science.gov (United States)

Bond, Charlotte Z; Correia, Carlos M; Sauvage, Jean-François; Neichel, Benoit; Fusco, Thierry

2017-05-15

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

Rugged optical mirrors for the operation of Fourier-Transform Spectrometers in rough environments

Science.gov (United States)

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

Estimation of fringe orientation for optical fringe patterns with poor quality based on Fourier transform.

Science.gov (United States)

Tang, Chen; Wang, Zhifang; Wang, Linlin; Wu, Jian; Gao, Tao; Yan, Si

2010-02-01

Fringe orientation represents an important property of fringes. The estimation of orientation from a poor quality fringe image is still a challenging problem faced in this area. This paper introduces a new approach for estimating optical fringe orientation with a poor quality image. This approach is based on the power spectrum analysis of the Fourier transform. We evaluate the performance of this algorithm via application to a variety of test cases and comparison with the widely used gradient-based method and accumulate-differences method. The experimental results show that our method is capable of calculating fringe orientation robustly even when the quality of fringe images is considerably low because of high or low density, high noise, and low contrast. Under the same conditions, our accuracy is even better than that obtained with the gradient-based and accumulate-differences methods, especially for fringe images with poor quality.

Fourier series

CERN Document Server

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

Teaching stable two-mirror resonators through the fractional Fourier transform

International Nuclear Information System (INIS)

Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

2010-01-01

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects.

Fourier synthesis of asymmetrical optical potentials for atoms; Fourier-Synthese von asymmetrischen optischen Potentialen fuer Atome

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.)

Grid-Independent Compressive Imaging and Fourier Phase Retrieval

Science.gov (United States)

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…

Gas Measurement Using Static Fourier Transform Infrared Spectrometers.

Science.gov (United States)

Köhler, Michael H; Schardt, Michael; Rauscher, Markus S; Koch, Alexander W

2017-11-13

Online monitoring of gases in industrial processes is an ambitious task due to adverse conditions such as mechanical vibrations and temperature fluctuations. Whereas conventional Fourier transform infrared (FTIR) spectrometers use rather complex optical and mechanical designs to ensure stable operation, static FTIR spectrometers do not require moving parts and thus offer inherent stability at comparatively low costs. Therefore, we present a novel, compact gas measurement system using a static single-mirror Fourier transform spectrometer (sSMFTS). The system works in the mid-infrared range from 650 cm - 1 to 1250 cm - 1 and can be operated with a customized White cell, yielding optical path lengths of up to 120 cm for highly sensitive quantification of gas concentrations. To validate the system, we measure different concentrations of 1,1,1,2-Tetrafluoroethane (R134a) and perform a PLS regression analysis of the acquired infrared spectra. Thereby, the measured absorption spectra show good agreement with reference data. Since the system additionally permits measurement rates of up to 200 Hz and high signal-to-noise ratios, an application in process analysis appears promising.

In vivo monitoring laser tissue interaction using high resolution Fourier-domain optical coherence tomography

Science.gov (United States)

Jo, Hang Chan; Shin, Dong Jun; Ahn, Jin-Chul; Chung, Phil-Sang; Kim, DaeYu

2017-02-01

Laser-induced therapies include laser ablation to remove or cut target tissue by irradiating high-power focused laser beam. These laser treatments are widely used tools for minimally invasive surgery and retinal surgical procedures in clinical settings. In this study, we demonstrate laser tissue interaction images of various sample tissues using high resolution Fourier-domain optical coherence tomography (Fd-OCT). We use a Q-switch diode-pumped Nd:YVO4 nanosecond laser (532nm central wavelength) with a 4W maximum output power at a 20 kHz repetition rate to ablate in vitro and in vivo samples including chicken breast and mouse ear tissues. The Fd-OCT system acquires time-series Bscan images at the same location during the tissue ablation experiments with 532nm laser irradiation. The real-time series of OCT cross-sectional (B-scan) images compare structural changes of 532nm laser ablation using same and different laser output powers. Laser tissue ablation is demonstrated by the width and the depth of the tissue ablation from the B-scan images.

A FORMALISM FOR COVARIANT POLARIZED RADIATIVE TRANSPORT BY RAY TRACING

International Nuclear Information System (INIS)

Gammie, Charles F.; Leung, Po Kin

2012-01-01

We write down a covariant formalism for polarized radiative transfer appropriate for ray tracing through a turbulent plasma. The polarized radiation field is represented by the polarization tensor (coherency matrix) N αβ ≡ (a α k a* β k ), where a k is a Fourier coefficient for the vector potential. Using Maxwell's equations, the Liouville-Vlasov equation, and the WKB approximation, we show that the transport equation in vacuo is k μ ∇ μ N αβ = 0. We show that this is equivalent to Broderick and Blandford's formalism based on invariant Stokes parameters and a rotation coefficient, and suggest a modification that may reduce truncation error in some situations. Finally, we write down several alternative approaches to integrating the transfer equation.

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

NARCIS (Netherlands)

Bastiaans, M.J.

1979-01-01

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

Fourier fringe analysis and its application to metrology of extreme physical phenomena: a review [Invited].

Science.gov (United States)

Takeda, Mitsuo

2013-01-01

The paper reviews a technique for fringe analysis referred to as Fourier fringe analysis (FFA) or the Fourier transform method, with a particular focus on its application to metrology of extreme physical phenomena. Examples include the measurement of extremely small magnetic fields with subfluxon sensitivity by electron wave interferometry, subnanometer wavefront evaluation of projection optics for extreme UV lithography, the detection of sub-Ångstrom distortion of a crystal lattice, and the measurement of ultrashort optical pulses in the femotsecond to attosecond range, which show how the advantages of FFA are exploited in these cutting edge applications.

Limitations on continuous variable quantum algorithms with Fourier transforms

International Nuclear Information System (INIS)

Adcock, Mark R A; Hoeyer, Peter; Sanders, Barry C

2009-01-01

We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.

Common-path Fourier domain optical coherence tomography of irradiated human skin and ventilated isolated rabbit lungs

Science.gov (United States)

Popp, A.; Wendel, M.; Knels, L.; Knuschke, P.; Mehner, M.; Koch, T.; Boller, D.; Koch, P.; Koch, E.

2005-08-01

A compact common path Fourier domain optical coherence tomography (FD-OCT) system based on a broadband superluminescence diode is used for biomedical imaging. The epidermal thickening of human skin after exposure to ultraviolet radiation is measured to proof the feasibility of FD-OCT for future substitution of invasive biopsies in a long term study on natural UV skin protection. The FD-OCT system is also used for imaging lung parenchyma. FD-OCT images of a formalin fixated lung show the same alveolar structure as scanning electron microscopy images. In the ventilated and blood-free perfused isolated rabbit lung FD-OCT is used for real-time cross-sectional image capture of alveolar mechanics throughout tidal ventilation. The alveolar mechanics changing from alternating recruitment-derecruitment at zero positive end-expiratory pressure (PEEP) to persistent recruitment after applying a PEEP of 5 cm H2O is observed in the OCT images.

Beyond Fourier

Science.gov (United States)

Hoch, Jeffrey C.

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development.

Development of a phase-sensitive Fourier domain optical coherence tomography system to measure mouse organ of Corti vibrations in two cochlear turns

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.

Beyond Fourier.

Science.gov (United States)

Hoch, Jeffrey C

2017-10-01

Non-Fourier methods of spectrum analysis are gaining traction in NMR spectroscopy, driven by their utility for processing nonuniformly sampled data. These methods afford new opportunities for optimizing experiment time, resolution, and sensitivity of multidimensional NMR experiments, but they also pose significant challenges not encountered with the discrete Fourier transform. A brief history of non-Fourier methods in NMR serves to place different approaches in context. Non-Fourier methods reflect broader trends in the growing importance of computation in NMR, and offer insights for future software development. Copyright © 2017 Elsevier Inc. All rights reserved.

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

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.

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

International Nuclear Information System (INIS)

Ritboon, Atirach; Daengngam, Chalongrat; Pengpan, Teparksorn

2016-01-01

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.

Digital Fourier microscopy for soft matter dynamics

International Nuclear Information System (INIS)

Giavazzi, Fabio; Cerbino, Roberto

2014-01-01

Soft matter is studied with a large portfolio of methods. Light scattering and video microscopy are the most employed at optical wavelengths. Light scattering provides ensemble-averaged information on soft matter in the reciprocal space. The wave-vectors probed correspond to length scales ranging from a few nanometers to fractions of millimetre. Microscopy probes the sample directly in the real space, by offering a unique access to the local properties. However, optical resolution issues limit the access to length scales smaller than approximately 200 nm. We describe recent work that bridges the gap between scattering and microscopy. Several apparently unrelated techniques are found to share a simple basic idea: the correlation properties of the sample can be characterized in the reciprocal space via spatial Fourier analysis of images collected in the real space. We describe the main features of such digital Fourier microscopy (DFM), by providing examples of several possible experimental implementations of it, some of which not yet realized in practice. We also provide an overview of experimental results obtained with DFM for the study of the dynamics of soft materials. Finally, we outline possible future developments of DFM that would ease its adoption as a standard laboratory method. (topical review)

Spectral approach to optical resonator theory

International Nuclear Information System (INIS)

Feit, M.D.; Fleck, J.A. Jr.

1981-01-01

A new computational method for unloaded optical resonators is developed based on the discrete Fourier analysis of informaton generated by repated iterations of the optical field corresponding to transits between reflectors. The method is a straightforward extension of the propagating beam method developed earlier for optical fibers for extracting modal properties from numerical solutions to the paraxial scalar wave equation. The method requires computation of a field correlation function, whose Fourier transform reveals the eigenmodes as resonant peaks. Analysis of the location and breadth of these peaks determines the resonator eigenvalues When the eigenvalues are known, additional discrete Fourier transforms of the field are used to generate the mode eigenfunctions. This new method makes possible the unambiguous identification and accurate characterization of the entire spectrum of transverse resonator modes

Numerous applications of fiber optic evanescent wave Fourier transform infrared (FEW-FTIR) spectroscopy for subsurface structural analysis

Science.gov (United States)

Afanasyeva, Natalia I.; Welser, Leslie; Bruch, Reinhard F.; Kano, Angelique; Makhine, Volodymyr

1999-10-01

A new infrared (IR) interferometric method has been developed in conjunction with low-loss, flexible optical fibers, sensors, and probes. This combination of fiber optical sensors and Fourier Transform (FT) spectrometers can be applied to many fields, including (1) noninvasive medical diagnostics of cancer and other different diseases in vivo, (2) minimally invasive bulk diagnostics of tissue, (3) remote monitoring of tissue, chemical processes, and environment, (4) surface analysis of polymers and other materials, (5) characterization of the quality of food, pharmacological products, cosmetics, paper, and other wood-related products, as well as (6) agricultural, forensic, geological, mining, and archeological field measurements. In particular, our nondestructive, fast, compact, portable, remote and highly sensitive diagnostics tools are very promising for subsurface analysis at the molecular level without sample preparation. For example, this technique is ideal for different types of soft porous foams, rough polymers, and rock surfaces. Such surfaces, as well as living tissue, are very difficult to investigate by traditional FTIR methods. We present here FEW-FTIR spectra of polymers, banana and grapefruit peels, and living tissues detected directly at surfaces. In addition, results on the vibrational spectral analysis of normal and pathological skin tissue in the region of 850 - 4000 cm-1 are discussed.

Microvascular anastomosis in rodent model evaluated by Fourier domain Doppler optical coherence tomography

Science.gov (United States)

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.

Progress report of a static Fourier transform spectrometer breadboard

Science.gov (United States)

Rosak, A.; Tintó, F.

2017-11-01

MOLI instrument -for MOtionLess Interferometer- takes advantage of the new concept of static Fourier transform spectrometer. It is a high-resolution spectrometer working over a narrow bandwidth, which is adapted to a wide range of atmospheric sounding missions and compatible with micro-satellite platform. The core of this instrument is an echelette cube. Mirrors on the classical design are replaced by stepped mirrors -integrated into that interference cube- thus suppressing any moving part. The steps' directions being set over a perpendicular axis, the overlap of both stepped mirrors creates a cluster of so-called "echelettes", each one corresponding to a different optical path difference (OPD). Hence the Fourier transform of the incoming radiance is directly imaged on a CCD array in a single acquisition. The frequency domain of the measurements is selected by an interferential filter disposed on the incoming optical path. A rotating wheel equipped with several filters allows the successive measurement of spectra around some bands of interest, i.e. O2, CO2 and CO absorption bands.

Influence of age-related macular degeneration on macular thickness measurement made with fourier-domain optical coherence tomography.

Science.gov (United States)

Garas, Anita; Papp, András; Holló, Gábor

2013-03-01

To evaluate the influence of age-related macular degeneration (AMD) on macular thickness measurement made with Fourier-domain optical coherence tomography (RTVue-OCT) to detect glaucoma. : One nonglaucomatous eye of 79 white persons was imaged. This comprised 25 healthy eyes, 19 eyes with early/intermediate AMD (geographic atrophy excluded), 16 eyes with subfoveal choroidal neovascularization (CNV), and 19 CNV eyes after intravitreal antiangiogenic treatment [CNV-antivascular endothelial growth factor (VEGF)]. Compared with the age-matched controls, no difference in any nerve fiber layer and optic disc parameter was seen for any AMD group. No macular retinal segmentation error was detected in the control group. Localized inner retinal image segmentation errors topographically related to AMD were detected in 8 eyes with drusen (42.1%), all 16 CNV eyes (100%) and 17 eyes in the CNV-anti-VEGF group (89.5%; χ test, P0.05). In contrast, all pattern-based ganglion cell complex (GCC) parameters were significantly higher (more abnormal) in the CNV and CNV-anti-VEGF group than in the control eyes (Mann-Whitney test, Bonferroni correction, P<0.001). For GCC focal loss volume, the only pattern-based parameter classified by the software, the frequency of "borderline" and "outside normal limits" classifications was significantly greater in each AMD group than in the control group (χ test, Bonferroni correction, P ≤0.03). In nonglaucomatous eyes, AMD significantly influences the pattern-based inner macular thickness parameters of the RTVue optical coherence tomograph and the software-provided classification of GCC focal loss volume, for detection of glaucoma.

Orthonormal mode sets for the two-dimensional fractional Fourier transformation

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2007-01-01

A family of orthonormal mode sets arises when Hermite–Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an

Fourier transforms in NMR, optical, and mass spectrometry

International Nuclear Information System (INIS)

Marshall, A.G.; Verdun, F.R.; Ohio State Univ., Columbus, OH

1990-01-01

This book is a teaching and reference text for Fourier transform methods as they are applied in spectroscopy. It offers a unified treatment of the three most popular types of FT/spectroscopy. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g., use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance versus off-resonance response; interpolation; ultimate accuracy of discrete representation of an analog signal; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc. (author). refs.; figs.; tabs

Power filtering of n-th order in the fractional Fourier domain

NARCIS (Netherlands)

Alieva, T.; Calvo, M.L.; Bastiaans, M.J.

2002-01-01

The main properties of the power filtering operation in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of linear power filtering for solving the phase retrieval problem from only intensity distributions is proposed. The optical

Approximating the Analytic Fourier Transform with the Discrete Fourier Transform

OpenAIRE

Axelrod, Jeremy

2015-01-01

The Fourier transform is approximated over a finite domain using a Riemann sum. This Riemann sum is then expressed in terms of the discrete Fourier transform, which allows the sum to be computed with a fast Fourier transform algorithm more rapidly than via a direct matrix multiplication. Advantages and limitations of using this method to approximate the Fourier transform are discussed, and prototypical MATLAB codes implementing the method are presented.

Fiber-optic Fourier transform infrared spectroscopy for remote label-free sensing of medical device surface contamination

Science.gov (United States)

Hassan, Moinuddin; Tan, Xin; Welle, Elissa; Ilev, Ilko

2013-05-01

As a potential major source of biochemical contamination, medical device surfaces are of critical safety concerns in the clinical practice and public health. The development of innovative sensing methods for accurate and real-time detection of medical device surface contamination is essential to protect patients from high risk infection. In this paper, we demonstrate an alternative fiber-optic Fourier Transform Infrared (FTIR) spectroscopy based sensing approach for remote, non-contact, and label-free detection of biochemical contaminants in the mid-infrared (mid-IR) region. The sensing probe is designed using mid-IR hollow fibers and FTIR measurements are carried out in reflection mode. Bovine Serum Albumin (BSA) and bacterial endotoxin of different concentrations under thoroughly dry condition are used to evaluate the detection sensitivity. The devised system can identify ≤0.0025% (≤4 × 1011 molecules) BSA and 0.5% (0.5 EU/ml) endotoxin concentration. The developed sensing approach may be applied to detect various pathogens that pose public health threats.

Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

Science.gov (United States)

Barnett, Patrick D; Strange, K Alicia; Angel, S Michael

2017-06-01

This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics.

Science.gov (United States)

Monat, Christelle; Grillet, Christian; Corcoran, Bill; Moss, David J; Eggleton, Benjamin J; White, Thomas P; Krauss, Thomas F

2010-03-29

Using Fourier optics, we retrieve the wavevector dependence of the third-harmonic (green) light generated in a slow light silicon photonic crystal waveguide. We show that quasi-phase matching between the third-harmonic signal and the fundamental mode is provided in this geometry by coupling to the continuum of radiation modes above the light line. This process sustains third-harmonic generation with a relatively high efficiency and a substantial bandwidth limited only by the slow light window of the fundamental mode. The results give us insights into the physics of this nonlinear process in the presence of strong absorption and dispersion at visible wavelengths where bandstructure calculations are problematic. Since the characteristics (e.g. angular pattern) of the third-harmonic light primarily depend on the fundamental mode dispersion, they could be readily engineered.

Optical asymmetric cryptography based on elliptical polarized light linear truncation and a numerical reconstruction technique.

Science.gov (United States)

Lin, Chao; Shen, Xueju; Wang, Zhisong; Zhao, Cheng

2014-06-20

We demonstrate a novel optical asymmetric cryptosystem based on the principle of elliptical polarized light linear truncation and a numerical reconstruction technique. The device of an array of linear polarizers is introduced to achieve linear truncation on the spatially resolved elliptical polarization distribution during image encryption. This encoding process can be characterized as confusion-based optical cryptography that involves no Fourier lens and diffusion operation. Based on the Jones matrix formalism, the intensity transmittance for this truncation is deduced to perform elliptical polarized light reconstruction based on two intensity measurements. Use of a quick response code makes the proposed cryptosystem practical, with versatile key sensitivity and fault tolerance. Both simulation and preliminary experimental results that support theoretical analysis are presented. An analysis of the resistance of the proposed method on a known public key attack is also provided.

The application of an optical Fourier spectrum analyzer on detecting defects in mass-produced satellite photographs

Science.gov (United States)

Athale, R.; Lee, S. H.

1976-01-01

Various defects in mass-produced pictures transmitted to earth from a satellite are investigated. It is found that the following defects are readily detectable via Fourier spectrum analysis: (1) bit slip, (2) breakup causing loss of image, and (3) disabled track at the top of the imagery. The scratches made on the film during mass production, which are difficult to detect by visual observation, also show themselves readily in Fourier spectrum analysis. A relation is established between the number of scratches, their width and depth and the intensity of their Fourier spectra. Other defects that are found to be equally suitable for Fourier spectrum analysis or visual (image analysis) detection are synchronous loss without blurring of image, and density variation in gray scale. However, the Fourier spectrum analysis is found to be unsuitable for detection of such defects as pin holes, annotation error, synchronous loss with blurring of images, and missing image in the beginning of the work order. The design of an automated, real time system, which will reject defective films, is treated.

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

Science.gov (United States)

Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

2017-09-01

Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

Fourier-Hermite communications; where Fourier meets Hermite

NARCIS (Netherlands)

Korevaar, C.W.; Kokkeler, Andre B.J.; de Boer, Pieter-Tjerk; Smit, Gerardus Johannes Maria

A new signal set, based on the Fourier and Hermite signal bases, is introduced. It combines properties of the Fourier basis signals with the perfect time-frequency localization of the Hermite functions. The signal set is characterized by both a high spectral efficiency and good time-frequency

High resolution integral holography using Fourier ptychographic approach.

Science.gov (United States)

Li, Zhaohui; Zhang, Jianqi; Wang, Xiaorui; Liu, Delian

2014-12-29

An innovative approach is proposed for calculating high resolution computer generated integral holograms by using the Fourier Ptychographic (FP) algorithm. The approach initializes a high resolution complex hologram with a random guess, and then stitches together low resolution multi-view images, synthesized from the elemental images captured by integral imaging (II), to recover the high resolution hologram through an iterative retrieval with FP constrains. This paper begins with an analysis of the principle of hologram synthesis from multi-projections, followed by an accurate determination of the constrains required in the Fourier ptychographic integral-holography (FPIH). Next, the procedure of the approach is described in detail. Finally, optical reconstructions are performed and the results are demonstrated. Theoretical analysis and experiments show that our proposed approach can reconstruct 3D scenes with high resolution.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.

Science.gov (United States)

Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda

2017-09-13

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

Fourier transform NMR

International Nuclear Information System (INIS)

Hallenga, K.

1991-01-01

This paper discusses the concept of Fourier transformation one of the many precious legacies of the French mathematician Jean Baptiste Joseph Fourier, essential for understanding the link between continuous-wave (CW) and Fourier transform (FT) NMR. Although in modern FT NMR the methods used to obtain a frequency spectrum from the time-domain signal may vary greatly, from the efficient Cooley-Tukey algorithm to very elaborate iterative least-square methods based other maximum entropy method or on linear prediction, the principles for Fourier transformation are unchanged and give invaluable insight into the interconnection of many pairs of physical entities called Fourier pairs

Power filtering of nth order in the fractional Fourier domain

International Nuclear Information System (INIS)

Alieva, Tatiana; Calvo, Maria Luisa; Bastiaans, Martin J.

2002-01-01

The main properties of the power filtering operation in the fractional Fourier domain and its relationship to the differentiation operation are considered. The application of linear power filtering for solving the phase retrieval problem from intensity distributions only is proposed. The optical configuration for the experimental realization of the method is discussed. (author)

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

Science.gov (United States)

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

Color image cryptosystem using Fresnel diffraction and phase modulation in an expanded fractional Fourier transform domain

Science.gov (United States)

Chen, Hang; Liu, Zhengjun; Chen, Qi; Blondel, Walter; Varis, Pierre

2018-05-01

In this letter, what we believe is a new technique for optical color image encryption by using Fresnel diffraction and a phase modulation in an extended fractional Fourier transform domain is proposed. Different from the RGB component separation based method, the color image is converted into one component by improved Chirikov mapping. The encryption system is addressed with Fresnel diffraction and phase modulation. A pair of lenses is placed into the fractional Fourier transform system for the modulation of beam propagation. The structure parameters of the optical system and parameters in Chirikov mapping serve as extra keys. Some numerical simulations are given to test the validity of the proposed cryptosystem.

Numerical model of the influence function of deformable mirrors based on Bessel Fourier orthogonal functions

International Nuclear Information System (INIS)

Li Shun; Zhang Sijiong

2014-01-01

A numerical model is presented to simulate the influence function of deformable mirror actuators. The numerical model is formed by Bessel Fourier orthogonal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems. (research papers)

Suppression law of quantum states in a 3D photonic fast Fourier transform chip

Science.gov (United States)

Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio

2016-01-01

The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135

Quantum aspects of accelerator optics

International Nuclear Information System (INIS)

Khan, Sameen Ahmed

2003-01-01

Full text : Charged-particle optics, or the theory of transport of charged-particle beams through electromagnetic systems, is traditionally dealt with using classical mechanics. Though the classical treatment has been very successful, in designing and working of numerous charged-particle optical devices, it is natural to look for a prescription based on the quantum theory, since any system is quantum mechanical at the fundamental level. With this motivation the quantum theory of charged-particle beam optics, is being developed by Jagannathan et al. This formalism is specifically adapted to treat the problems of beam optics. It is found that the quantum theory gives rise to interesting additional contributions to the classical paraxial and aberrating behaviour. These contributions are directly proportional to the powers of the de Broglie wavelength. In the classical limit the quantum formalism reproduces the well-known Lie algebraic formalism of charged-particle beam optics. For spin-half particles, a treatment based on the Dirac equation is presented taking fully into account the spinor character of the wavefunction. The underlying powerful algebraic machinery of the formalism makes it possible to do computations to any degree of accuracy. This formalism is further applied to the study of the spin-dynamics of a Dirac particle with anomalous magnetic moment being transported through magnetic optical element. This naturally leads to a unified treatment of both the orbital (the Lorentz and Stem-Gerlach forces) and the spin (Thomas-Bargmann-Michel-Telegdi equation). This is illustrated, by computing the transfer maps for the phase-space and spin components in the cases of the normal and skew magnetic quadrupole lenses. The quantum mechanics of the concept of the spin-splitter devices, proposed recently for achieving polarized beams, is also understood using our formalisms

Expansions of general stationary stochastic optical fields: general formalism

International Nuclear Information System (INIS)

Martinez-Herrero, R.; Mejias, P.M.

1985-01-01

A new expansion of a general stationary stochastic optical field is derived. Each term of the series is seen to represent a recently defined new class of optical fields, the so-called spectrally quasi-factorizable fields. Alternative expansion in terms of nonstationary fields that obey the wave equation is also shown. A relationship between temporal and spatial features of stationary free optical fields is discussed

Engineering Optics

CERN Document Server

Iizuka, Keigo

2008-01-01

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

Optical-Correlator Neural Network Based On Neocognitron

Science.gov (United States)

Chao, Tien-Hsin; Stoner, William W.

1994-01-01

Multichannel optical correlator implements shift-invariant, high-discrimination pattern-recognizing neural network based on paradigm of neocognitron. Selected as basic building block of this neural network because invariance under shifts is inherent advantage of Fourier optics included in optical correlators in general. Neocognitron is conceptual electronic neural-network model for recognition of visual patterns. Multilayer processing achieved by iteratively feeding back output of feature correlator to input spatial light modulator and updating Fourier filters. Neural network trained by use of characteristic features extracted from target images. Multichannel implementation enables parallel processing of large number of selected features.

Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

International Nuclear Information System (INIS)

Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P

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.

On Fourier re-expansions

OpenAIRE

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.

Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects

International Nuclear Information System (INIS)

Miao, J.; Sayre, D.; Chapman, H.N.

1998-01-01

It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2x in each dimension (i.e., oversampling by 4x for 2D and 8x for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop. copyright 1998 Optical Society of America

The propagation of stochastic pixel noise into magnitude and phase values in the Fourier analysis of digital images

International Nuclear Information System (INIS)

Holden, J.E.; Halama, J.R.; Hasegawa, B.H.

1986-01-01

The use of Fourier analysis in nuclear medicine gated blood ventriculography provides a useful example of the application of Fourier methods to digital medical imaging. In particular, the nuclear medicine experience demonstrates that there is diagnostic significance not only in the pixel averages of temporal Fourier magnitude and phase computed in various image regions, but also in the distributions of the individual pixel values about those averages. However, a region containing pixels that are perfectly synchronous on average would still yield a finite distribution of calculated Fourier coefficients due to the propagation of stochastic pixel noise into the calculated values. The authors have studied this noise component of both the magnitude and phase distributions using phantom studies and computer simulation. In both approaches, several thousand one-pixel 'ventriculograms' were generated, all identical to each other except for stochastic noise. Fourier magnitudes and phases at several frequencies were calculated and histograms generated. A theoretical prediction of the distributions was developed and shown to fit the experimental results well. The authors' formalism can be used to estimate study count requirements or, for fixed study counts, to assess the stochastic noise contribution in the interpretation of measured phase and magnitude distributions. (author)

Principles of Fourier analysis

CERN Document Server

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 ...

Reminder of Lagrange-Hamilton formalism and of the corpuscular optics invariants

International Nuclear Information System (INIS)

Griess, F.

1958-01-01

Hamiltonian formalism - Canonical transformations - Invariants of Liouville, Helmholtz-Lagrange, Busch, Stoermer and Lagrange - Synchrotron's Hamiltonian - Betatron oscillation damping. (author) [fr

Optical Two Dimensional Fourier Transform Spectroscopy of Layered Metal Dichalcogenides

Science.gov (United States)

Dey, P.; Paul, J.; Stevens, C. E.; Kovalyuk, Z. D.; Kudrynskyi, Z. R.; Romero, A. H.; Cantarero, A.; Hilton, D. J.; Shan, J.; Karaiskaj, D.; Z. D. Kovalyuk; Z. R. Kudrynskyi Collaboration; A. H. Romero Collaboration; A. Cantarero Collaboration; D. J. Hilton Collaboration; J. Shan Collaboration

2015-03-01

Nonlinear two-dimensional Fourier transform (2DFT) measurements were used to study the mechanism of excitonic dephasing and probe the electronic structure of the excitonic ground state in layered metal dichalcogenides. Temperature-dependent 2DFT measurements were performed to probe exciton-phonon interactions. Excitation density dependent 2DFT measurements reveal exciton-exciton and exciton-carrier scattering, and the lower limit for the homogeneous linewidth of excitons on positively and negatively doped samples. U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0012635.

Optical holography

CERN Document Server

Collier, Robert J; Lin, Lawrence H

1971-01-01

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

IMAGING WITH MULTIMODAL ADAPTIVE-OPTICS OPTICAL COHERENCE TOMOGRAPHY IN MULTIPLE EVANESCENT WHITE DOT SYNDROME: THE STRUCTURE AND FUNCTIONAL RELATIONSHIP.

Science.gov (United States)

Labriola, Leanne T; Legarreta, Andrew D; Legarreta, John E; Nadler, Zach; Gallagher, Denise; Hammer, Daniel X; Ferguson, R Daniel; Iftimia, Nicusor; Wollstein, Gadi; Schuman, Joel S

2016-01-01

To elucidate the location of pathological changes in multiple evanescent white dot syndrome (MEWDS) with the use of multimodal adaptive optics (AO) imaging. A 5-year observational case study of a 24-year-old female with recurrent MEWDS. Full examination included history, Snellen chart visual acuity, pupil assessment, intraocular pressures, slit lamp evaluation, dilated fundoscopic exam, imaging with Fourier-domain optical coherence tomography (FD-OCT), blue-light fundus autofluorescence (FAF), fundus photography, fluorescein angiography, and adaptive-optics optical coherence tomography. Three distinct acute episodes of MEWDS occurred during the period of follow-up. Fourier-domain optical coherence tomography and adaptive-optics imaging showed disturbance in the photoreceptor outer segments (PR OS) in the posterior pole with each flare. The degree of disturbance at the photoreceptor level corresponded to size and extent of the visual field changes. All findings were transient with delineation of the photoreceptor recovery from the outer edges of the lesion inward. Hyperautofluorescence was seen during acute flares. Increase in choroidal thickness did occur with each active flare but resolved. Although changes in the choroid and RPE can be observed in MEWDS, Fourier-domain optical coherence tomography, and multimodal adaptive optics imaging localized the visually significant changes seen in this disease at the level of the photoreceptors. These transient retinal changes specifically occur at the level of the inner segment ellipsoid and OS/RPE line. En face optical coherence tomography imaging provides a detailed, yet noninvasive method for following the convalescence of MEWDS and provides insight into the structural and functional relationship of this transient inflammatory retinal disease.

Nonlinear Fourier transform for dual-polarization optical communication system

OpenAIRE

Gaiarin, Simone

2018-01-01

New services and applications are causing an exponential increase in the internet traffic. In a few years, the current fiber-optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically limits the information transmission rate. Eigenvalue communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering trans...

MEMS-based handheld fourier domain Doppler optical coherence tomography for intraoperative microvascular anastomosis imaging.

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

Electronic structure of antiferromagnetic UN and UPtGe single crystals from optical and magneto-optical spectroscopy

International Nuclear Information System (INIS)

Marutzky, M.

2006-01-01

In this thesis the study of the magneto-optical Kerr effect and the determination of the optical constants by means of ellipsometry and Fourier-transformation infrared spectroscopy of UN and UPtGe is described. In UPtGe an optical anisotropy was detected over a spectral range from 6 meV to 32 eV. (HSI)

Influences of overlap index on Fourier ptychography imaging

Science.gov (United States)

Wang, Honghong; Rong, Lu; Wang, Dayong; Zhang, Xu; Zhai, Changchao; Panezai, Spozmai; Wang, Yunxin; Zhao, Jie

2018-01-01

Fourier ptychography is a new type of synthetic aperture imaging technique based on phase retrieval method which can improve microscopeic imaging performance beyond the diffraction limit of the employed optical components by illuminating the object with oblique waves of different incident angles where the field of view remains unchanged. illumination angle and the overlap rate of spectrum will have a certain impact on the quality of reconstruction. In this paper, we study the effects of illumination angle and spectral overlap rate on the image quality of Fourier ptychography. The simulation results show that increasing the illumination angle and spectral overlap can improve the resolution, but there is a threshold for the key parameters of spectral overlap rate. The convergence rate decreases when the overlap rate exceeds 70%, and the reconstruction process is more time-consuming due to the high overlap rate. However the results of proposed study shows that an overlap of 60% is the optimal choice to acquire a high-quality recovery with high speed.

Use of Fourier-Domain Optical Coherence Tomography to Evaluate Anterior Stromal Opacities in Donor Corneas

Directory of Open Access Journals (Sweden)

Matthew R. Bald

2013-01-01

Full Text Available Purpose. To evaluate Fourier-domain optical coherence tomography (FD-OCT as an adjunct to traditional slit lamp examination of donor corneas with suspected Anterior Stromal Opacities. Methods. Seven corneas suspected of having anterior stromal opacities by slit lamp examination were evaluated with FD-OCT. Each cornea was evaluated to confirm the presence of opacity and, if present, the depth of opacity was measured. Results. The opacity depth ranged from 82 μm to 624 μm. The initial slit lamp impressions of five of the seven corneas were confirmed by OCT. In two corneas, the OCT findings were different from the initial slit lamp impressions. Slit lamp examination of the first cornea gave the impression of anterior stromal scarring, but OCT showed that the opacity was limited to the epithelium. Slit lamp examination of the second cornea suggested opacity limited to the epithelium, but OCT identified significant sub-Bowman's scarring. In all cases, the Eye Bank Technicians reported that the location and depth of corneal opacity were more sharply defined by OCT than by slit lamp. Conclusion. The high resolution of OCT makes it easier to determine the location of corneal opacities compared to slit lamp examinations. This enhanced visualization can improve decisions regarding transplant suitability of donor corneas.

Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval

Science.gov (United States)

Smith, Jeffrey Scott

2006-01-01

Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.

Fourier transform infrared spectroscopy of peptides.

Science.gov (United States)

Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell

2014-01-01

Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data.

Application of Fourier elastodynamics to direct and inverse problems for the scattering of elastic waves from flaws near surfaces

International Nuclear Information System (INIS)

Richardson, J.M.; Fertig, K.W. Jr.

1983-01-01

In order to inspect flaws which lie too close to the surface a Fourier elastodynamic formalism is proposed which enables one to decompose the elastodynamic system into separately charterizable parts by means of planes perpendicular to the z-axis. The process can be represented by a generalized transfer function relating the near-field scattered waves to the waves incident on a slab of material containing the flaw. The Fourier elastodynamics are applied to the characterization of the total scattering process involving a flaw at various distances from a plastic-water interface. An abbreviated discussion of Fourier elastodynamics is presented, and the results specialized to the case of spherical voids and inclusions bear an interface. Finally, the computational results for several ranges of temporal frequency and for a sequence of values of the distance from the flaw center to the interface are discussed

Fourier domain mode-locked swept source at 1050 nm based on a tapered amplifier

DEFF Research Database (Denmark)

Marschall, Sebastian; Klein, Thomas; Wieser, Wolfgang

2010-01-01

While swept source optical coherence tomography (OCT) in the 1050 nm range is promising for retinal imaging, there are certain challenges. Conventional semiconductor gain media have limited output power, and the performance of high-speed Fourier domain mode-locked (FDML) lasers suffers from...

Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions.

Science.gov (United States)

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho; Poon, Ting-Chung

2008-07-01

We propose a novel optical sectioning method for optical scanning holography, which is performed in phase space by using Wigner distribution functions together with the fractional Fourier transform. The principle of phase-space optical sectioning for one-dimensional signals, such as slit objects, and two-dimensional signals, such as rectangular objects, is first discussed. Computer simulation results are then presented to substantiate the proposed idea.

A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods

International Nuclear Information System (INIS)

Choi, Kihwan; Li, Ruijiang; Nam, Haewon; Xing, Lei

2014-01-01

As a solution to iterative CT image reconstruction, first-order methods are prominent for the large-scale capability and the fast convergence rate O(1/k 2 ). In practice, the CT system matrix with a large condition number may lead to slow convergence speed despite the theoretically promising upper bound. The aim of this study is to develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods applied to CT image reconstruction. Instead of working in the projection domain, we transform the projection data and construct a data fidelity model in Fourier space. Inspired by the filtered backprojection formalism, the data are appropriately weighted in Fourier space. We formulate an optimization problem based on weighted least-squares in the Fourier space and total-variation (TV) regularization in image space for parallel-beam, fan-beam and cone-beam CT geometry. To achieve the maximum computational speed, the optimization problem is solved using a fast iterative shrinkage-thresholding algorithm with backtracking line search and GPU implementation of projection/backprojection. The performance of the proposed algorithm is demonstrated through a series of digital simulation and experimental phantom studies. The results are compared with the existing TV regularized techniques based on statistics-based weighted least-squares as well as basic algebraic reconstruction technique. The proposed Fourier-based compressed sensing (CS) method significantly improves both the image quality and the convergence rate compared to the existing CS techniques. (paper)

A Fourier-based compressed sensing technique for accelerated CT image reconstruction using first-order methods.

Science.gov (United States)

Choi, Kihwan; Li, Ruijiang; Nam, Haewon; Xing, Lei

2014-06-21

As a solution to iterative CT image reconstruction, first-order methods are prominent for the large-scale capability and the fast convergence rate [Formula: see text]. In practice, the CT system matrix with a large condition number may lead to slow convergence speed despite the theoretically promising upper bound. The aim of this study is to develop a Fourier-based scaling technique to enhance the convergence speed of first-order methods applied to CT image reconstruction. Instead of working in the projection domain, we transform the projection data and construct a data fidelity model in Fourier space. Inspired by the filtered backprojection formalism, the data are appropriately weighted in Fourier space. We formulate an optimization problem based on weighted least-squares in the Fourier space and total-variation (TV) regularization in image space for parallel-beam, fan-beam and cone-beam CT geometry. To achieve the maximum computational speed, the optimization problem is solved using a fast iterative shrinkage-thresholding algorithm with backtracking line search and GPU implementation of projection/backprojection. The performance of the proposed algorithm is demonstrated through a series of digital simulation and experimental phantom studies. The results are compared with the existing TV regularized techniques based on statistics-based weighted least-squares as well as basic algebraic reconstruction technique. The proposed Fourier-based compressed sensing (CS) method significantly improves both the image quality and the convergence rate compared to the existing CS techniques.

Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens.

Science.gov (United States)

Urs, Raksha; Ho, Arthur; Manns, Fabrice; Parel, Jean-Marie

2010-06-01

To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205 microm. The age-dependent equations provide a reliable lens model for ages 20-60 years. The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Fractional Fourier transform for confluent hypergeometric beams

International Nuclear Information System (INIS)

Tang, Bin; Jiang, Chun; Zhu, Haibin

2012-01-01

Based on the definition of the fractional Fourier transform (FRFT) in the cylindrical coordinate system, the propagation properties of a new family of paraxial laser beams named confluent hypergeometric (HyG) beams, of which intensity profile is similar to that for the Bessel modes, passing through FRFT optical systems have been studied in detail by some typical numerical examples. The results indicate that the normalized intensity distribution of a HyG beam in the FRFT plane is closely related to not only the fractional order p but also the beam parameters m,n, and focal length f. -- Highlights: ► We study the propagation of a HyG beam through FRFT optical systems. ► The intensity of the beam in the FRFT plane is closely related to some parameters. ► We can control the properties of HyG beams by properly choosing the parameters.

Estimating the Spectral Width of a Narrowband Optical Signal

DEFF Research Database (Denmark)

Lading, Lars; Skov Jensen, A.

1980-01-01

Methods for estimating the spectral width of a narrowband optical signal are investigated. Spectral analysis and Fourier spectroscopy are compared. Optimum and close-to-optimum estimators are developed under the constraint of having only one photodetector.......Methods for estimating the spectral width of a narrowband optical signal are investigated. Spectral analysis and Fourier spectroscopy are compared. Optimum and close-to-optimum estimators are developed under the constraint of having only one photodetector....

Linear optics and quantum maps

International Nuclear Information System (INIS)

Aiello, A.; Puentes, G.; Woerdman, J. P.

2007-01-01

We present a theoretical analysis of the connection between classical polarization optics and quantum mechanics of two-level systems. First, we review the matrix formalism of classical polarization optics from a quantum information perspective. In this manner the passage from the Stokes-Jones-Mueller description of classical optical processes to the representation of one- and two-qubit quantum operations, becomes straightforward. Second, as a practical application of our classical-vs-quantum formalism, we show how two-qubit maximally entangled mixed states can be generated by using polarization and spatial modes of photons generated via spontaneous parametric down conversion

Asymmetric Formal Synthesis of Azadirachtin.

Science.gov (United States)

Mori, Naoki; Kitahara, Takeshi; Mori, Kenji; Watanabe, Hidenori

2015-12-01

An asymmetric formal synthesis of azadirachtin, a potent insect antifeedant, was accomplished in 30 steps to Ley's synthetic intermediate (longest linear sequence). The synthesis features: 1) rapid access to the optically active right-hand segment starting from the known 5-hydroxymethyl-2-cyclopentenone scaffold; 2) construction of the B and E rings by a key intramolecular tandem radical cyclization; 3) formation of the hemiacetal moiety in the C ring through the α-oxidation of the six-membered lactone followed by methanolysis. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Evaluation of Macular Ganglion Cell Complex and Peripapillary Retinal Nerve Fiber Layer in Primary Craniopharyngioma by Fourier-Domain Optical Coherence Tomography.

Science.gov (United States)

Yang, Liu; Qu, Yuanzhen; Lu, Wen; Liu, Fengjun

2016-07-03

BACKGROUND The aim of this study was to compare the differences in macular ganglion cell complex (GCC) and peripapillary retinal nerve fiber layer (pRNFL) in child and adult patients with primary craniopharyngioma by Fourier-domain optical coherence tomography (FD-OCT) and to evaluate their significance in the diagnosis of primary craniopharyngioma. MATERIAL AND METHODS Ninety-six participants were divided into 3 groups: 32 in the child craniopharyngioma group (CCG) and 32 in the adult craniopharyngioma group (ACG) who were treated in Beijing Tiantan Hospital between November 2013 and October 2014, and 32 in the normal group (NG). All subjects were scanned by FD-OCT to map GCC and pRNFL thicknesses. Spearman correlation coefficient was used to assess the correlation between GCC and pRNFL thickness, and pRNFL thickness and optic nerve head (ONH) parameters, including horizontal cup-disc ratio (HCDR), vertical cup-disc ratio (VCDR), optic disc area (ODA), and cup area (CA), respectively. RESULTS The correlation between GCC and pRNFL thickness in the CCG was slightly stronger compared with the ACG. A significant difference in GCC thickness was observed among the CCG, ACG, and NG. Although the pRNFL thickness in both the CCG and ACG was significantly higher than that in NG, no significant difference in pRNFL thickness was detected between the 2 craniopharyngioma groups. The average, superior, and inferior pRNFL thicknesses were negatively correlated with VCDR in the CCG (in double eyes) and ACG (only in left eyes). CONCLUSIONS GCC was more sensitive than pRNFL in detecting optic nerve damage in the eyes of craniopharyngioma patients. A thinner pRNFL was especially correlated with VCDR in child craniopharyngioma patients.

Spectral analysis of the UFBG-based acousto—optical modulator in V-I transmission matrix formalism

Science.gov (United States)

Wu, Liang-Ying; Pei, Li; Liu, Chao; Wang, Yi-Qun; Weng, Si-Jun; Wang, Jian-Shuai

2014-11-01

In this study, the V-I transmission matrix formalism (V-I method) is proposed to analyze the spectrum characteristics of the uniform fiber Bragg grating (FBG)-based acousto—optic modulators (UFBG-AOM). The simulation results demonstrate that both the amplitude of the acoustically induced strain and the frequency of the acoustic wave (AW) have an effect on the spectrum. Additionally, the wavelength spacing between the primary reflectivity peak and the secondary reflectivity peak is proportional to the acoustic frequency with the ratio 0.1425 nm/MHz. Meanwhile, we compare the amount of calculation. For the FBG whose period is M, the calculation of the V-I method is 4 × (2M-1) in addition/subtraction, 8 × (2M - 1) in multiply/division and 2M in exponent arithmetic, which is almost a quarter of the multi-film method and transfer matrix (TM) method. The detailed analysis indicates that, compared with the conventional multi-film method and transfer matrix (TM) method, the V-I method is faster and less complex.

Spectral analysis of the UFBG-based acousto—optical modulator in V–I transmission matrix formalism

International Nuclear Information System (INIS)

Wu Liang-Ying; Pei Li; Liu Chao; Wang Yi-Qun; Weng Si-Jun; Wang Jian-Shuai

2014-01-01

In this study, the V–I transmission matrix formalism (V–I method) is proposed to analyze the spectrum characteristics of the uniform fiber Bragg grating (FBG)-based acousto—optic modulators (UFBG-AOM). The simulation results demonstrate that both the amplitude of the acoustically induced strain and the frequency of the acoustic wave (AW) have an effect on the spectrum. Additionally, the wavelength spacing between the primary reflectivity peak and the secondary reflectivity peak is proportional to the acoustic frequency with the ratio 0.1425 nm/MHz. Meanwhile, we compare the amount of calculation. For the FBG whose period is M, the calculation of the V–I method is 4 × (2M–1) in addition/subtraction, 8 × (2M – 1) in multiply/division and 2M in exponent arithmetic, which is almost a quarter of the multi-film method and transfer matrix (TM) method. The detailed analysis indicates that, compared with the conventional multi-film method and transfer matrix (TM) method, the V–I method is faster and less complex. (general)

A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.

Science.gov (United States)

Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei

2015-09-01

A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress.

Fractional finite Fourier transform.

Science.gov (United States)

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Fourier series, Fourier transform and their applications to mathematical physics

CERN Document Server

Serov, Valery

2017-01-01

This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences.  Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing.  The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations.  The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

DEFF Research Database (Denmark)

Pedersen, Anders Filsøe; Simons, Hugh; Detlefs, Carsten

2018-01-01

The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing...... the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown...

Reconstruction of Optical Thickness from Hoffman Modulation Contrast Images

DEFF Research Database (Denmark)

Olsen, Niels Holm; Sporring, Jon; Nielsen, Mads

2003-01-01

Hoffman microscopy imaging systems are part of numerous fertility clinics world-wide. We discuss the physics of the Hoffman imaging system from optical thickness to image intensity, implement a simple, yet fast, reconstruction algorithm using Fast Fourier Transformation and discuss the usability...... of the method on a number of cells from a human embryo. Novelty is identifying the non-linearity of a typical Hoffman imaging system, and the application of Fourier Transformation to reconstruct the optical thickness....

Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

Science.gov (United States)

Ma, Q.; Boulet, C.; Tipping, R. H.

2014-01-01

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Fourier transform infrared imaging and infrared fiber optic probe spectroscopy identify collagen type in connective tissues.

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

Rotational Fourier tracking of diffusing polygons.

Science.gov (United States)

Mayoral, Kenny; Kennair, Terry P; Zhu, Xiaoming; Milazzo, James; Ngo, Kathy; Fryd, Michael M; Mason, Thomas G

2011-11-01

We use optical microscopy to measure the rotational Brownian motion of polygonal platelets that are dispersed in a liquid and confined by depletion attractions near a wall. The depletion attraction inhibits out-of-plane translational and rotational Brownian fluctuations, thereby facilitating in-plane imaging and video analysis. By taking fast Fourier transforms (FFTs) of the images and analyzing the angular position of rays in the FFTs, we determine an isolated particle's rotational trajectory, independent of its position. The measured in-plane rotational diffusion coefficients are significantly smaller than estimates for the bulk; this difference is likely due to the close proximity of the particles to the wall arising from the depletion attraction.

Optical metrology

CERN Document Server

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.

Agreement between Gonioscopic Examination and Swept Source Fourier Domain Anterior Segment Optical Coherence Tomography Imaging

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.

Agreement between Gonioscopic Examination and Swept Source Fourier Domain Anterior Segment Optical Coherence Tomography Imaging

Science.gov (United States)

Nguyen, Donna; Minnal, Vandana R.

2016-01-01

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. PMID:27990300

Visualization of hair follicles using high-speed optical coherence tomography based on a Fourier domain mode locking laser

Science.gov (United States)

Tsai, M.-T.; Chang, F.-Y.

2012-04-01

In this study, a swept-source optical coherence tomography (SS-OCT) system with a Fourier domain mode locking (FDML) laser is proposed for a dermatology study. The homemade FDML laser is one kind of frequency-sweeping light source, which can provide output power of >20 mW and an output spectrum of 65 nm in bandwidth centered at 1300 nm, enabling imaging with an axial resolution of 12 μm in the OCT system. To eliminate the forward scans from the laser output and insert the delayed backward scans, a Mach-Zehnder configuration is implemented. Compared with conventional frequency-sweeping light sources, the FDML laser can achieve much higher scan rates, as high as ˜240 kHz, which can provide a three-dimensional imaging rate of 4 volumes/s. Furthermore, the proposed high-speed SS-OCT system can provide three-dimensional (3D) images with reduced motion artifacts. Finally, a high-speed SS-OCT system is used to visualize hair follicles, demonstrating the potential of this technology as a tool for noninvasive diagnosis of alopecia.

Fourier-based automatic alignment for improved Visual Cryptography schemes.

Science.gov (United States)

Machizaud, Jacques; Chavel, Pierre; Fournel, Thierry

2011-11-07

In Visual Cryptography, several images, called "shadow images", that separately contain no information, are overlapped to reveal a shared secret message. We develop a method to digitally register one printed shadow image acquired by a camera with a purely digital shadow image, stored in memory. Using Fourier techniques derived from Fourier Optics concepts, the idea is to enhance and exploit the quasi periodicity of the shadow images, composed by a random distribution of black and white patterns on a periodic sampling grid. The advantage is to speed up the security control or the access time to the message, in particular in the cases of a small pixel size or of large numbers of pixels. Furthermore, the interest of visual cryptography can be increased by embedding the initial message in two shadow images that do not have identical mathematical supports, making manual registration impractical. Experimental results demonstrate the successful operation of the method, including the possibility to directly project the result onto the printed shadow image.

Optical configuration with fixed transverse magnification for self-interference incoherent digital holography.

Science.gov (United States)

Imbe, Masatoshi

2018-03-20

The optical configuration proposed in this paper consists of a 4-f optical setup with the wavefront modulation device on the Fourier plane, such as a concave mirror and a spatial light modulator. The transverse magnification of reconstructed images with the proposed configuration is independent of locations of an object and an image sensor; therefore, reconstructed images of object(s) at different distances can be scaled with a fixed transverse magnification. It is yielded based on Fourier optics and mathematically verified with the optical matrix method. Numerical simulation results and experimental results are also given to confirm the fixity of the reconstructed images.

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

Science.gov (United States)

Dean, Bruce H. (Inventor)

2012-01-01

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Calculations of the transport properties within the PAW formalism

Energy Technology Data Exchange (ETDEWEB)

Mazevet, S.; Torrent, M.; Recoules, V.; Jollet, F. [CEA Bruyeres-le-Chatel, DIF, 91 (France)

2010-07-01

We implemented the calculation of the transport properties within the PAW formalism in the ABINIT code. This feature allows the calculation of the electrical and optical properties, including the XANES spectrum, as well as the electronic contribution to the thermal conductivity. We present here the details of the implementation and results obtained for warm dense aluminum plasma. (authors)

Optical surfacing via linear ion source

International Nuclear Information System (INIS)

Wu, Lixiang; Wei, Chaoyang; Shao, Jianda

2017-01-01

We present a concept of surface decomposition extended from double Fourier series to nonnegative sinusoidal wave surfaces, on the basis of which linear ion sources apply to the ultra-precision fabrication of complex surfaces and diffractive optics. The modified Fourier series, or sinusoidal wave surfaces, build a relationship between the fabrication process of optical surfaces and the surface characterization based on power spectral density (PSD) analysis. Also, we demonstrate that the one-dimensional scanning of linear ion source is applicable to the removal of mid-spatial frequency (MSF) errors caused by small-tool polishing in raster scan mode as well as the fabrication of beam sampling grating of high diffractive uniformity without a post-processing procedure. The simulation results show that optical fabrication with linear ion source is feasible and even of higher output efficiency compared with the conventional approach.

Optical surfacing via linear ion source

Energy Technology Data Exchange (ETDEWEB)

Wu, Lixiang, E-mail: wulx@hdu.edu.cn [Key Lab of RF Circuits and Systems of Ministry of Education, Zhejiang Provincial Key Lab of LSI Design, Microelectronics CAD Center, College of Electronics and Information, Hangzhou Dianzi University, Hangzhou (China); Wei, Chaoyang, E-mail: siomwei@siom.ac.cn [Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China); Shao, Jianda, E-mail: jdshao@siom.ac.cn [Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800 (China)

2017-04-15

We present a concept of surface decomposition extended from double Fourier series to nonnegative sinusoidal wave surfaces, on the basis of which linear ion sources apply to the ultra-precision fabrication of complex surfaces and diffractive optics. The modified Fourier series, or sinusoidal wave surfaces, build a relationship between the fabrication process of optical surfaces and the surface characterization based on power spectral density (PSD) analysis. Also, we demonstrate that the one-dimensional scanning of linear ion source is applicable to the removal of mid-spatial frequency (MSF) errors caused by small-tool polishing in raster scan mode as well as the fabrication of beam sampling grating of high diffractive uniformity without a post-processing procedure. The simulation results show that optical fabrication with linear ion source is feasible and even of higher output efficiency compared with the conventional approach.

Two dimensional vibrations of the guinea pig apex organ of Corti measured in vivo using phase sensitive Fourier domain optical coherence tomography

Science.gov (United States)

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.

Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems.

Science.gov (United States)

Brunel, Marc; Shen, Huanhuan; Coetmellec, Sebastien; Lebrun, Denis

2012-03-10

We present a new model to predict diffraction patterns of femtosecond pulses through complex optical systems. The model is based on the extension of an ABCD matrix formalism combined with generalized Huygens-Fresnel transforms (already used in the CW regime) to the femtosecond regime. The model is tested to describe femtosecond digital in-line holography experiments realized in situ through a cylindrical Plexiglas pipe. The model allows us to establish analytical relations that link the holographic reconstruction process to the experimental parameters of the pipe and of the incident beam itself. Simulations and experimental results are in good concordance. Femtosecond digital in-line holography is shown to allow significant coherent noise reduction, and this model will be particularly efficient to describe a wide range of optical geometries. More generally, the model developed can be easily used in any experiment where the knowledge of the precise evolution of femtosecond transverse patterns is required.

Tidal generation of gravitational waves from orbiting Newtonian stars. I. General formalism

International Nuclear Information System (INIS)

Turner, M.

1977-01-01

A linearized formalism is presented for the calculation of the tidally produced gravitational radiation potential h/sup TT/ from binary systems with arbitrary orbits. The stars are Newtonian, isentropic, and nonrotating. Normal-mode analysis is used to calculate the tidally generated internal motions; the resulting radiation potential h/sup TT/ and its Fourier decomposition are calculated in the Newtonian limit of the multipole formalism. The tidal radiation potential is weaker than that produced by the orbital motion by a factor of order [(stellar radius)/(periastron distance)] 5 . If we assume that the time scale of the tidal perturbation is always much less than the damping time of the star, then if in addition the damping time is much less than the time between periastron passages, the radiation spectrum consists of the l=2 eigenfrequencies of the star near the fundamental l=2 eigenfrequency; if the reverse is true (damping time >> time between periastrons), the spectrum is similar to the orbital gravitational radiation specturm

Quantum Optics

CERN Document Server

Walls, D F

2007-01-01

Quantum Optics gives a comprehensive coverage of developments in quantum optics over the past years. In the early chapters the formalism of quantum optics is elucidated and the main techniques are introduced. These are applied in the later chapters to problems such as squeezed states of light, resonance fluorescence, laser theory, quantum theory of four-wave mixing, quantum non-demolition measurements, Bell's inequalities, and atom optics. Experimental results are used to illustrate the theory throughout. This yields the most comprehensive and up-to-date coverage of experiment and theory in quantum optics in any textbook. More than 40 exercises helps readers test their understanding and provide practice in quantitative problem solving.

Imaging vibration of the cochlear partition of an excised guinea pig cochlea using phase-sensitive Fourier domain optical coherence tomography

Science.gov (United States)

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.

Fourier transforms principles and applications

CERN Document Server

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.

Agreement of Anterior Segment Parameters Obtained From Swept-Source Fourier-Domain and Time-Domain Anterior Segment Optical Coherence Tomography.

Science.gov (United States)

Chansangpetch, Sunee; Nguyen, Anwell; Mora, Marta; Badr, Mai; He, Mingguang; Porco, Travis C; Lin, Shan C

2018-03-01

To assess the interdevice agreement between swept-source Fourier-domain and time-domain anterior segment optical coherence tomography (AS-OCT). Fifty-three eyes from 41 subjects underwent CASIA2 and Visante OCT imaging. One hundred eighty-degree axis images were measured with the built-in two-dimensional analysis software for the swept-source Fourier-domain AS-OCT (CASIA2) and a customized program for the time-domain AS-OCT (Visante OCT). In both devices, we examined the angle opening distance (AOD), trabecular iris space area (TISA), angle recess area (ARA), anterior chamber depth (ACD), anterior chamber width (ACW), and lens vault (LV). Bland-Altman plots and intraclass correlation (ICC) were performed. Orthogonal linear regression assessed any proportional bias. ICC showed strong correlation for LV (0.925) and ACD (0.992) and moderate agreement for ACW (0.801). ICC suggested good agreement for all angle parameters (0.771-0.878) except temporal AOD500 (0.743) and ARA750 (nasal 0.481; temporal 0.481). There was a proportional bias in nasal ARA750 (slope 2.44, 95% confidence interval [CI]: 1.95-3.18), temporal ARA750 (slope 2.57, 95% CI: 2.04-3.40), and nasal TISA500 (slope 1.30, 95% CI: 1.12-1.54). Bland-Altman plots demonstrated in all measured parameters a minimal mean difference between the two devices (-0.089 to 0.063); however, evidence of constant bias was found in nasal AOD250, nasal AOD500, nasal AOD750, nasal ARA750, temporal AOD500, temporal AOD750, temporal ARA750, and ACD. Among the parameters with constant biases, CASIA2 tends to give the larger numbers. Both devices had generally good agreement. However, there were proportional and constant biases in most angle parameters. Thus, it is not recommended that values be used interchangeably.

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...

Optimization of sampling pattern and the design of Fourier ptychographic illuminator.

Science.gov (United States)

Guo, Kaikai; Dong, Siyuan; Nanda, Pariksheet; Zheng, Guoan

2015-03-09

Fourier ptychography (FP) is a recently developed imaging approach that facilitates high-resolution imaging beyond the cutoff frequency of the employed optics. In the original FP approach, a periodic LED array is used for sample illumination, and therefore, the scanning pattern is a uniform grid in the Fourier space. Such a uniform sampling scheme leads to 3 major problems for FP, namely: 1) it requires a large number of raw images, 2) it introduces the raster grid artefacts in the reconstruction process, and 3) it requires a high-dynamic-range detector. Here, we investigate scanning sequences and sampling patterns to optimize the FP approach. For most biological samples, signal energy is concentrated at low-frequency region, and as such, we can perform non-uniform Fourier sampling in FP by considering the signal structure. In contrast, conventional ptychography perform uniform sampling over the entire real space. To implement the non-uniform Fourier sampling scheme in FP, we have designed and built an illuminator using LEDs mounted on a 3D-printed plastic case. The advantages of this illuminator are threefold in that: 1) it reduces the number of image acquisitions by at least 50% (68 raw images versus 137 in the original FP setup), 2) it departs from the translational symmetry of sampling to solve the raster grid artifact problem, and 3) it reduces the dynamic range of the captured images 6 fold. The results reported in this paper significantly shortened acquisition time and improved quality of FP reconstructions. It may provide new insights for developing Fourier ptychographic imaging platforms and find important applications in digital pathology.

Formal matrices

CERN Document Server

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...

Direct fourier method reconstruction based on unequally spaced fast fourier transform

International Nuclear Information System (INIS)

Wu Xiaofeng; Zhao Ming; Liu Li

2003-01-01

First, We give an Unequally Spaced Fast Fourier Transform (USFFT) method, which is more exact and theoretically more comprehensible than its former counterpart. Then, with an interesting interpolation scheme, we discusse how to apply USFFT to Direct Fourier Method (DFM) reconstruction of parallel projection data. At last, an emulation experiment result is given. (authors)

The Wigner distribution function applied to optical signals and systems

NARCIS (Netherlands)

Bastiaans, M.J.

1978-01-01

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

On the Fourier integral theorem

NARCIS (Netherlands)

Koekoek, J.

1987-01-01

Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the

Subwavelength Fourier-transform imaging without a lens or a beamsplitter

International Nuclear Information System (INIS)

Liu Rui-Feng; Yuan Xin-Xing; Fang Yi-Zhen; Zhang Pei; Zhou Yu; Gao Hong; Li Fu-Li

2014-01-01

The fourier-transform patterns of an object are usually observed in the far-field region or obtained in the near-field region with the help of lenses. Here we propose and experimentally demonstrate a scheme of Fourier-transform patterns in the Fresnel diffraction region with thermal light. In this scheme, neither a lens nor a beamsplitter is used, and only one single charge coupled device (CCD) is employed. It means that dividing one beam out of a light source into signal and reference beams is not as necessary as the one done by the use of a beamsplitter in usual ghost interference experiments. Moreover, the coincidence measurement of two point detectors is not necessary and data recorded on a single CCD are sufficient for reconstructing the ghost diffraction patterns. The feature of the scheme promises a great potential application in the fields of X-ray and neutron diffraction imaging processes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Cross sections for electron-impact excitation of argon by fourier transform spectroscopy

International Nuclear Information System (INIS)

Chilton, J.E.; Boffard, J.B.; Chun C.L.

1996-01-01

The authors report absolute measurements of electron-impact excitation cross sections out of the ground level to the ten levels in the 3p 5 4p configuration of argon. The apparent excitation cross sections are determined by measuring the optical cross sections for the emission lines in the 3p 5 4p → 3p 5 4s manifold. For cascade corrections the authors measured the optical cross sections for the various 3p 5 5s → 3p 5 4p and 3p 5 4p infrared lines using a Fourier transform weak emission spectrometer to obtain the direct excitation cross sections from the optical data. Although the optical cross sections vary with pressure in the regime of 0.1 to 6 mTorr, the direct cross sections remain invariant. These pressure effects are understood within the framework of a radiation-reabsorption model. The excitation functions for the different transitions are also found to show considerable variation in shape

Reproducibility of Scleral Spur Identification and Angle Measurements Using Fourier Domain Anterior Segment Optical Coherence Tomography

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.

Analyzing Fourier Transforms for NASA DFRC's Fiber Optic Strain Sensing System

Science.gov (United States)

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.

Compression of fiber supercontinuum pulses to the Fourier-limit in a high-numerical-aperture focus

DEFF Research Database (Denmark)

Tu, Haohua; Liu, Yuan; Turchinovich, Dmitry

2011-01-01

A multiphoton intrapulse interference phase scan (MIIPS) adaptively and automatically compensates the combined phase distortion from a fiber supercontinuum source, a spatial light modulator pulse shaper, and a high-NA microscope objective, allowing Fourier-transform-limited compression of the sup......A multiphoton intrapulse interference phase scan (MIIPS) adaptively and automatically compensates the combined phase distortion from a fiber supercontinuum source, a spatial light modulator pulse shaper, and a high-NA microscope objective, allowing Fourier-transform-limited compression...... power of 18–70mW, and a repetition rate of 76MHz, permitting the application of this source to nonlinear optical microscopy and coherently controlled microspectroscopy....

Assessment of Corneal Epithelial Thickness in Asymmetric Keratoconic Eyes and Normal Eyes Using Fourier Domain Optical Coherence Tomography

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 transformation for engineering and natural science

International Nuclear Information System (INIS)

Klingen, B.

2001-01-01

The following topics are covered: functions, Dirac delta function, Fourier operators, Fourier integrals, Fourier transformation and periodic functions, discrete Fourier transformations and discrete filters, applications. (WL)

Fourier analysis an introduction

CERN Document Server

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

Spinor formalism and complex-vector formalism of general relativity

International Nuclear Information System (INIS)

Han-ying, G.; Yong-shi, W.; Gendao, L.

1974-01-01

In this paper, using E. Cartan's exterior calculus, we give the spinor form of the structure equations, which leads naturally to the Newman--Penrose equations. Furthermore, starting from the spinor spaces and the el (2C) algebra, we construct the general complex-vector formalism of general relativity. We find that both the Cahen--Debever--Defrise complex-vector formalism and that of Brans are its special cases. Thus, the spinor formalism and the complex-vector formalism of general relativity are unified on the basis of the uni-modular group SL(2C) and its Lie algebra

Optical characterization of free electron concentration in heteroepitaxial InN layers using Fourier transform infrared spectroscopy and a 2 × 2 transfer-matrix algebra

International Nuclear Information System (INIS)

Katsidis, C. C.; Ajagunna, A. O.; Georgakilas, A.

2013-01-01

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 2 O 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 × 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 19 cm −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 H = 1.49 for the Hall factor of InN at a carrier concentration of 1.11 × 10 19 cm −3 at 300°Κ.

Quantum optical properties in plasmonic systems

Energy Technology Data Exchange (ETDEWEB)

Ooi, C. H. Raymond [Department of Physics, University of Malaya, 50603, Kuala Lumpur (Malaysia)

2015-04-24

Plasmonic metallic particle (MP) can affect the optical properties of a quantum system (QS) in a remarkable way. We develop a general quantum nonlinear formalism with exact vectorial description for the scattered photons by the QS. The formalism enables us to study the variations of the dielectric function and photon spectrum of the QS with the particle distance between QS and MP, exciting laser direction, polarization and phase in the presence of surface plasmon resonance (SPR) in the MP. The quantum formalism also serves as a powerful tool for studying the effects of these parameters on the nonclassical properties of the scattered photons. The plasmonic effect of nanoparticles has promising possibilities as it provides a new way for manipulating quantum optical properties of light in nanophotonic systems.

SBME : Exploring boundaries between formal, non-formal, and informal learning

OpenAIRE

Shahoumian, Armineh; Parchoma, Gale; Saunders, Murray; Hanson, Jacky; Dickinson, Mike; Pimblett, Mark

2013-01-01

In medical education learning extends beyond university settings into practice. Non-formal and informal learning support learners’ efforts to meet externally set and learner-identified objectives. In SBME research, boundaries between formal, non-formal, and informal learning have not been widely explored. Whether SBME fits within or challenges these categories can make a contribution. Formal learning is described in relation to educational settings, planning, assessment, and accreditation. In...

Jean Baptiste Joseph Fourier

Science.gov (United States)

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.

Fourier Transform Mass Spectrometry

Science.gov (United States)

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-01-01

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. PMID:21742802

Digital Fourier analysis fundamentals

CERN Document Server

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 nuclear magnetic resonance

International Nuclear Information System (INIS)

Geick, R.

1981-01-01

This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author)

Formalization of Database Systems -- and a Formal Definition of {IMS}

DEFF Research Database (Denmark)

Bjørner, Dines; Løvengreen, Hans Henrik

1982-01-01

Drawing upon an analogy between Programming Language Systems and Database Systems we outline the requirements that architectural specifications of database systems must futfitl, and argue that only formal, mathematical definitions may 6atisfy these. Then we illustrate home aspects and touch upon...... come ueee of formal definitions of data models and databaee management systems. A formal model of INS will carry this discussion. Finally we survey some of the exkting literature on formal definitions of database systems. The emphasis will be on constructive definitions in the denotationul semantics...... style of the VCM: Vienna Development Nethd. The role of formal definitions in international standardiaation efforts is briefly mentioned....

Double peak-induced distance error in short-time-Fourier-transform-Brillouin optical time domain reflectometers event detection and the recovery method.

Science.gov (United States)

Yu, Yifei; Luo, Linqing; Li, Bo; Guo, Linfeng; Yan, Jize; Soga, Kenichi

2015-10-01

The measured distance error caused by double peaks in the BOTDRs (Brillouin optical time domain reflectometers) system is a kind of Brillouin scattering spectrum (BSS) deformation, discussed and simulated for the first time in the paper, to the best of the authors' knowledge. Double peak, as a kind of Brillouin spectrum deformation, is important in the enhancement of spatial resolution, measurement accuracy, and crack detection. Due to the variances of the peak powers of the BSS along the fiber, the measured starting point of a step-shape frequency transition region is shifted and results in distance errors. Zero-padded short-time-Fourier-transform (STFT) can restore the transition-induced double peaks in the asymmetric and deformed BSS, thus offering more accurate and quicker measurements than the conventional Lorentz-fitting method. The recovering method based on the double-peak detection and corresponding BSS deformation can be applied to calculate the real starting point, which can improve the distance accuracy of the STFT-based BOTDR system.

Snapshot polarization-sensitive plug-in optical module for a Fourier-domain optical coherence tomography system

Science.gov (United States)

Marques, Manuel J.; Rivet, Sylvain; Bradu, Adrian; Podoleanu, Adrian

2018-02-01

In this communication, we present a proof-of-concept polarization-sensitive Optical Coherence Tomography (PS-OCT) which can be used to characterize the retardance and the axis orientation of a linear birefringent sample. This module configuration is an improvement from our previous work1, 2 since it encodes the two polarization channels on the optical path difference, effectively carrying out the polarization measurements simultaneously (snapshot measurement), whilst retaining all the advantages (namely the insensitivity to environmental parameters when using SM fibers) of these two previous configurations. Further progress consists in employing Master Slave OCT technology,3 which is used to automatically compensate for the dispersion mismatch introduced by the elements in the module. This is essential given the encoding of the polarization states on two different optical path lengths, each of them having dissimilar dispersive properties. By utilizing this method instead of the commonly used re-linearization and numerical dispersion compensation methods an improvement in terms of the calculation time required can be achieved.

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...

Tutorial on Fourier space coverage for scattering experiments, with application to SAR

Science.gov (United States)

Deming, Ross W.

2010-04-01

The Fourier Diffraction Theorem relates the data measured during electromagnetic, optical, or acoustic scattering experiments to the spatial Fourier transform of the object under test. The theorem is well-known, but since it is based on integral equations and complicated mathematical expansions, the typical derivation may be difficult for the non-specialist. In this paper, the theorem is derived and presented using simple geometry, plus undergraduatelevel physics and mathematics. For practitioners of synthetic aperture radar (SAR) imaging, the theorem is important to understand because it leads to a simple geometric and graphical understanding of image resolution and sampling requirements, and how they are affected by radar system parameters and experimental geometry. Also, the theorem can be used as a starting point for imaging algorithms and motion compensation methods. Several examples are given in this paper for realistic scenarios.

SELF-EFFICACY OF FORMALLY AND NON-FORMALLY TRAINED PUBLIC SECTOR TEACHERS

Directory of Open Access Journals (Sweden)

Muhammad Nadeem ANWAR

2009-07-01

Full Text Available The main objective of the study was to compare the formally and non-formally trained in-service public sector teachers’ Self-efficacy. Five hypotheses were developed describing no difference in the self-efficacy of formally and non-formally trained teachers to influence decision making, influence school resources, instructional self-efficacy, disciplinary self-efficacy and create positive school climate. Teacher Efficacy Instrument (TSES developed by Bandura (2001 consisting of thirty 9-point items was used in the study. 342 formally trained and 255 non-formally trained respondents’ questionnaires were received out of 1500 mailed. The analysis of data revealed that the formally trained public sector teachers are high in their self-efficacy on all the five categories: to influence decision making, to influence school resources, instructional self-efficacy, disciplinary self-efficacy and self-efficacy to create positive school climate.

Masses of Formal Philosophy

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 i...... in philosophy. Including contributions from a wide range of philosophers, Masses of Formal Philosophy contains important new responses to the original five questions.......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...

Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform.

Science.gov (United States)

Mendlovic, D; Ozaktas, H M; Lohmann, A W

1994-09-10

Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.

More twists on optical twisters: of helico-conical beams, superpositions and combinations

DEFF Research Database (Denmark)

Glückstad, Jesper; Palima, Darwin

We have previously demonstrated so-called optical twisters that can steer microparticles along spiral trajectories during optical micromanipulation. These optical twisters may be created using Fourier holograms ofthe helicoconical form, exp[ i l 8 (K- r/r0)], which is characterized by non...

General Correlation Theorem for Trinion Fourier Transform

OpenAIRE

Bahri, Mawardi

2017-01-01

- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.

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...

Optical-Path-Difference Linear Mechanism for the Panchromatic Fourier Transform Spectrometer

Science.gov (United States)

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).

Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer

Energy Technology Data Exchange (ETDEWEB)

Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.

1993-10-01

We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.

Fourier techniques in X-ray timing

NARCIS (Netherlands)

van der Klis, M.

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

Visual optics under the wavefront perspective

Directory of Open Access Journals (Sweden)

Sidney Júlio Faria-E-Sousa

2014-08-01

Full Text Available Some intriguing concepts of visual optics cannot be explained by ray tracing. However, they can be clarified using wavefront formalism. Its main advantage is in the use of the concept of vergence, which is very helpful in interpreting the optical phenomena involved in the neutralization of the ametropias. In this line of thinking, the major role of a lens is in the creation of a new light source (the image point that orientates the refracted waves. Once the nature and position of this source is known, one can easily predict the behavior of the wavefronts. The formalism also allows for an easier understanding on how wavefronts relate to light rays and on how algebraic signs are assigned to optical distances.

Side-chain liquid crystalline polyesters for optical information storage

DEFF Research Database (Denmark)

Ramanujam, P.S.; Holme, Christian; Hvilsted, Søren

1996-01-01

and holographic storage in one particular polyester are described in detail and polarized Fourier transform infrared spectroscopic data complementing the optical data are presented. Optical and atomic force microscope investigations point to a laser-induced aggregation as responsible for permanent optical storage.......Azobenzene side-chain liquid crystalline polyester structures suitable for permanent optical storage are described. The synthesis and characterization of the polyesters together with differential scanning calorimetry and X-ray investigations are discussed. Optical anisotropic investigations...

Anisotropic resonator analysis using the Fourier-Bessel mode solver

Science.gov (United States)

Gauthier, Robert C.

2018-03-01

A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.

Quadrature formulas for Fourier coefficients

KAUST Repository

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.

The fractional Fourier transform and applications

Science.gov (United States)

Bailey, David H.; Swarztrauber, Paul N.

1991-01-01

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Fourier-Domain Optical Coherence Tomography for Monitoring the Lower Tear Meniscus in Dry Eye after Acupuncture Treatment

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.

Fourier Series Optimization Opportunity

Science.gov (United States)

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…

Advances in hyperspectral remote sensing I: The visible Fourier transform hyperspectral imager

Directory of Open Access Journals (Sweden)

J. Bruce Rafert

2015-05-01

Full Text Available We discuss early hyperspectral research and development activities during the 1990s that led to the deployment of aircraft and satellite payloads whose heritage was based on the use of visible, spatially modulated, imaging Fourier transform spectrometers, beginning with early experiments at the Florida Institute of Technology, through successful launch and deployment of the Visible Fourier Transform Hyperspectral Imager on MightySat II.1 on 19 July 2000. In addition to a brief chronological overview, we also discuss several of the most interesting optical engineering challenges that were addressed over this timeframe, present some as-yet un-exploited features of field-widened (slit-less SMIFTS instruments, and present some images from ground-based, aircraft-based and satellite-based instruments that helped provide the impetus for the proliferation and development of entire new families of instruments and countless new applications for hyperspectral imaging.

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....

Classical Fourier analysis

CERN Document Server

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...

Formalizing Informal Logic

Directory of Open Access Journals (Sweden)

Douglas Walton

2015-12-01

Full Text Available This paper presents a formalization of informal logic using the Carneades Argumentation System (CAS, a formal, computational model of argument that consists of a formal model of argument graphs and audiences. Conflicts between pro and con arguments are resolved using proof standards, such as preponderance of the evidence. CAS also formalizes argumentation schemes. Schemes can be used to check whether a given argument instantiates the types of argument deemed normatively appropriate for the type of dialogue.

New method of contour image processing based on the formalism of spiral light beams

International Nuclear Information System (INIS)

Volostnikov, Vladimir G; Kishkin, S A; Kotova, S P

2013-01-01

The possibility of applying the mathematical formalism of spiral light beams to the problems of contour image recognition is theoretically studied. The advantages and disadvantages of the proposed approach are evaluated; the results of numerical modelling are presented. (optical image processing)

Vector frequency-comb Fourier-transform spectroscopy for characterizing metamaterials

International Nuclear Information System (INIS)

Ganz, T; Brehm, M; Von Ribbeck, H G; Keilmann, F; Van der Weide, D W

2008-01-01

We determine infrared transmission amplitude and phase spectra of metamaterial samples at well-defined incidence and polarization with a vector ('asymmetric') frequency-comb Fourier-transform spectrometer (c-FTS) that uses no moving elements. The metamaterials are free-standing metallic hole arrays; we study their resonances in the 7-13 μm and 100-1000 μm wavelength regions due both to interaction with bulk waves (Wood anomaly) and with leaky surface plasmon polaritons (near-unity transmittance, coupling features and dispersion). Such complex-valued transmission and reflection spectra could be used to compute a metamaterial's complex dielectric function directly, as well as its magnetic and magneto-optical permeability functions.

Optical absorption spectra of Ag-11 isomers

DEFF Research Database (Denmark)

Martinez, Jose Ignacio; Fernandez, E. M.

2009-01-01

The optical absorption spectra of the three most; stable structural isomers of the Ag-11 cluster were calculated using the time-dependent, density functional theory within the Casida formalism. The slightly different, spectra, of the isomers may permit the identification of the ground-stale confi......The optical absorption spectra of the three most; stable structural isomers of the Ag-11 cluster were calculated using the time-dependent, density functional theory within the Casida formalism. The slightly different, spectra, of the isomers may permit the identification of the ground...

Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy*

OpenAIRE

Liu, Yan-de; Ying, Yi-bin; Fu, Xia-ping

2005-01-01

To develop nondestructive acidity prediction for intact Fuji apples, the potential of Fourier transform near infrared (FT-NIR) method with fiber optics in interactance mode was investigated. Interactance in the 800 nm to 2619 nm region was measured for intact apples, harvested from early to late maturity stages. Spectral data were analyzed by two multivariate calibration techniques including partial least squares (PLS) and principal component regression (PCR) methods. A total of 120 Fuji appl...

On coherent optical evaluation of autoradiographs

International Nuclear Information System (INIS)

Birkholz, W.; Freyer, K.

1978-01-01

The autoradiography imaging process can be described through the imaging equation s(y 1 ,y 2 ) = ∫ a(x 1 ,y 2 )h(y 1 ,y 2 ,x 1 ,x 2 )dx 1 dx 2 where s(y 1 ,y 2 ) in the density distribution of the autoradiograph, a(x 1 ,x 2 ) is the activity distribution over a plane sample and h(y 1 ,y 2 ,x 1 ,x 2 ) transfer fuction of the system. Light transfer through a lens system may be characterized in an analogous way. By application of the Fourier transformation to the imaging equation, the autoradiographic imaging process becomes a filter process with the function H (= Fourier transformer of h). If autoradiographs are imaged through a lens system by means of coherent light the Fourier transform of the autoradiograph is formed in the Fourier plane. Through suitable arrangement of filters in the Fourier plane, systematic imaging errors can be corrected or the autoradiographic imaging be changed. The possibilities of coherent-optical filtration in the evaluation of autoradiographs are considered. (author)

Modeling open nanophotonic systems using the Fourier modal method: generalization to 3D Cartesian coordinates.

Science.gov (United States)

Häyrynen, Teppo; Osterkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels

2017-09-01

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform k-space discretization was introduced for rotationally symmetric structures, providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)JOAOD61084-752910.1364/JOSAA.33.001298]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates, allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier k space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence, enabling more accurate and efficient modeling of open 3D nanophotonic structures.

Picosecond pulses from wavelength-swept continuous-wave Fourier domain mode-locked lasers.

Science.gov (United States)

Eigenwillig, Christoph M; Wieser, Wolfgang; Todor, Sebastian; Biedermann, Benjamin R; Klein, Thomas; Jirauschek, Christian; Huber, Robert

2013-01-01

Ultrafast lasers have a crucial function in many fields of science; however, up to now, high-energy pulses directly from compact, efficient and low-power semiconductor lasers are not available. Therefore, we introduce a new approach based on temporal compression of the continuous-wave, wavelength-swept output of Fourier domain mode-locked lasers, where a narrowband optical filter is tuned synchronously to the round-trip time of light in a kilometre-long laser cavity. So far, these rapidly swept lasers enabled orders-of-magnitude speed increase in optical coherence tomography. Here we report on the generation of ~60-70 ps pulses at 390 kHz repetition rate. As energy is stored optically in the long-fibre delay line and not as population inversion in the laser-gain medium, high-energy pulses can now be generated directly from a low-power, compact semiconductor-based oscillator. Our theory predicts subpicosecond pulses with this new technique in the future.

Statistical analysis of polarization-inhomogeneous Fourier spectra of laser radiation scattered by human skin in the tasks of differentiation of benign and malignant formations

Science.gov (United States)

Ushenko, Alexander G.; Dubolazov, Alexander V.; Ushenko, Vladimir A.; Novakovskaya, Olga Y.

2016-07-01

The optical model of formation of polarization structure of laser radiation scattered by polycrystalline networks of human skin in Fourier plane was elaborated. The results of investigation of the values of statistical (statistical moments of the 1st to 4th order) parameters of polarization-inhomogeneous images of skin surface in Fourier plane were presented. The diagnostic criteria of pathological process in human skin and its severity degree differentiation were determined.

Two-dimensional Fourier analysis of the spongy medullary keratin of structurally coloured feather barbs

Science.gov (United States)

Prum, R. O.; Torres, R.; Williamson, S.; Dyck, J.

1999-01-01

We conducted two-dimensional (2D) discrete Fourier analyses of the spatial variation in refractive index of the spongy medullary keratin from four different colours of structurally coloured feather barbs from three species of bird: the rose-faced lovebird, Agapornis roseicollis (Psittacidae), the budgerigar, Melopsittacus undulatus (Psittacidae), and the Gouldian finch, Poephila guttata (Estrildidae). These results indicate that the spongy medullary keratin is a nanostructured tissue that functions as an array of coherent scatterers. The nanostructure of the medullary keratin is nearly uniform in all directions. The largest Fourier components of spatial variation in refractive index in the tissue are of the appropriate size to produce the observed colours by constructive interference alone. The peaks of the predicted reflectance spectra calculated from the 2D Fourier power spectra are congruent with the reflectance spectra measured by using microspectrophotometry. The alternative physical models for the production of these colours, the Rayleigh and Mie theories, hypothesize that medullary keratin is an incoherent array and that scattered waves are independent in phase. This assumption is falsified by the ring-like Fourier power spectra of these feathers, and the spacing of the scattering air vacuoles in the medullary keratin. Structural colours of avian feather barbs are produced by constructive interference of coherently scattered light waves from the optically heterogeneous matrix of keratin and air in the spongy medullary layer.

X-ray interferometric Fourier holography

International Nuclear Information System (INIS)

Balyan, M.K.

2016-01-01

The X-ray interferometric Fourier holography is proposed and theoretically investigated. Fourier The X-ray interferometric Young fringes and object image reconstruction are investigated. It is shown that the interference pattern of two slits formed on the exit surface of the crystal-analyzer (the third plate of the interferometer) is the X-ray interferometric Young fringes. An expression for X-ray interferometric Young fringes period is obtained. The subsequent reconstruction of the slit image as an object is performed by means of Fourier transform of the intensity distribution on the hologram. Three methods of reconstruction of the amplitude transmission complex function of the object are presented: analytical - approximate method, method of iteration and step by step method. As an example the X-ray Fourier interferometric hologram recording and the complex amplitude transmission function reconstruction for a beryllium circular wire are considered

Wigner distribution function and its application to first-order optics

NARCIS (Netherlands)

Bastiaans, M.J.

1979-01-01

The Wigner distribution function of optical signals and systems has been introduced. The concept of such functions is not restricted to deterministic signals, but can be applied to partially coherent light as well. Although derived from Fourier optics, the description of signals and systems by means

A fast method for linear waves based on geometrical optics

NARCIS (Netherlands)

Stolk, C.C.

2009-01-01

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

Optical Pattern Recognition

Science.gov (United States)

Yu, Francis T. S.; Jutamulia, Suganda

2008-10-01

Contributors; Preface; 1. Pattern recognition with optics Francis T. S. Yu and Don A. Gregory; 2. Hybrid neural networks for nonlinear pattern recognition Taiwei Lu; 3. Wavelets, optics, and pattern recognition Yao Li and Yunglong Sheng; 4. Applications of the fractional Fourier transform to optical pattern recognition David Mendlovic, Zeev Zalesky and Haldum M. Oxaktas; 5. Optical implementation of mathematical morphology Tien-Hsin Chao; 6. Nonlinear optical correlators with improved discrimination capability for object location and recognition Leonid P. Yaroslavsky; 7. Distortion-invariant quadratic filters Gregory Gheen; 8. Composite filter synthesis as applied to pattern recognition Shizhou Yin and Guowen Lu; 9. Iterative procedures in electro-optical pattern recognition Joseph Shamir; 10. Optoelectronic hybrid system for three-dimensional object pattern recognition Guoguang Mu, Mingzhe Lu and Ying Sun; 11. Applications of photrefractive devices in optical pattern recognition Ziangyang Yang; 12. Optical pattern recognition with microlasers Eung-Gi Paek; 13. Optical properties and applications of bacteriorhodopsin Q. Wang Song and Yu-He Zhang; 14. Liquid-crystal spatial light modulators Aris Tanone and Suganda Jutamulia; 15. Representations of fully complex functions on real-time spatial light modulators Robert W. Cohn and Laurence G. Hassbrook; Index.

Automatic target recognition using a feature-based optical neural network

Science.gov (United States)

Chao, Tien-Hsin

1992-01-01

An optical neural network based upon the Neocognitron paradigm (K. Fukushima et al. 1983) is introduced. A novel aspect of the architectural design is shift-invariant multichannel Fourier optical correlation within each processing layer. Multilayer processing is achieved by iteratively feeding back the output of the feature correlator to the input spatial light modulator and updating the Fourier filters. By training the neural net with characteristic features extracted from the target images, successful pattern recognition with intra-class fault tolerance and inter-class discrimination is achieved. A detailed system description is provided. Experimental demonstration of a two-layer neural network for space objects discrimination is also presented.

Observation of Biological Tissues Using Common Path Optical Coherence Tomography with Gold Coated Conical Tip Lens Fiber

International Nuclear Information System (INIS)

Taguchi, K; Sugiyama, J; Totsuka, M; Imanaka, S

2012-01-01

In this paper, we proposed a high lateral resolution common-path Fourier domain optical coherence tomography(OCT) system with the use of a chemically etched single mode fiber. In our experiments, single mode optical fiber for 1310nm was used for preparing the tapered tips. Our system used a conical microlens that was chemically etched by selective chemical etching technique using an etching solution of buffered hydrofluoric acid (BHF). From experimental results, we verified that our proposed optical coherence tomography system could operate as a common-path Fourier domain OCT system and conical tip lens fiber was very useful for a high lateral resolution common-path Fourier domain OCT system. Furthermore, we could observe a surface of paramecium bursaria and symbiotic chlorella in the paramecium bursaria using gold coated conical-tip fiber in the water.

On fractional Fourier transform moments

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2000-01-01

Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their

Optics learning by computing, with examples using Maple, MathCad, Mathematica, and MATLAB

CERN Document Server

Moeller, Karl Dieter

2007-01-01

This new edition is intended for a one semester course in optics for juniors and seniors in science and engineering; it uses scripts from Maple, MathCad, Mathematica, and MATLAB provide a simulated laboratory where students can learn by exploration and discovery instead of passive absorption. The text covers all the standard topics of a traditional optics course, including: geometrical optics and aberration, interference and diffraction, coherence, Maxwell's equations, wave guides and propagating modes, blackbody radiation, atomic emission and lasers, optical properties of materials, Fourier transforms and FT spectroscopy, image formation, and holography. It contains step by step derivations of all basic formulas in geometrical, wave and Fourier optics. The basic text is supplemented by over 170 files in Maple, MathCad, Mathematica, and MATLAB (many of which are in the text, each suggesting programs to solve a particular problem, and each linked to a topic in or application of optics. The computer files are d...

Fourier analysis and stochastic processes

CERN Document Server

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...

Performing derivative and integral operations for optical waves with optical metamaterials

Energy Technology Data Exchange (ETDEWEB)

Dai, Cun-Li [College of Engineering, Nanjing Agriculture University, Nanjing Jiangsu, 210031 (China); College of Science, Nanjing Agriculture University, Nanjing Jiangsu, 210095 (China); Zhao, Zhi-Gang; Li, Xiao-Lin [College of Engineering, Nanjing Agriculture University, Nanjing Jiangsu, 210031 (China); Yang, Hong-Wei, E-mail: phd_hwyang@njau.edu.cn [College of Science, Nanjing Agriculture University, Nanjing Jiangsu, 210095 (China)

2016-12-01

The graded refractive index waveguides can perform Fourier transform for an optical wave. According to this characteristic, simpler optical metamaterials with three waveguides are theoretically proposed, in which all of the waveguides are materials with a positive refractive index. By selecting the appropriate refractive index and structure size, the theory and simulations demonstrated that these metamaterials can perform mathematical operations for the outline of incident optical waves, including the first-order derivative, second-order derivative and the integral. - Highlights: • The derivative and integral operations of optical waves are achieved with a simpler model. • Both negative and positive refractive index boast the same functions. • The mathematical operations can be implemented only by changing the refractive index of the intermediate material. • The results will greatly expand the possible applications, including photon computers, picture processing, video displays and data storage.

A simple approach to Fourier aliasing

International Nuclear Information System (INIS)

Foadi, James

2007-01-01

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and structured, introductions to the topic, commonly met in advanced, specialized books

High-Throughput Screening Using Fourier-Transform Infrared Imaging

Directory of Open Access Journals (Sweden)

Erdem Sasmaz

2015-06-01

Full Text Available Efficient parallel screening of combinatorial libraries is one of the most challenging aspects of the high-throughput (HT heterogeneous catalysis workflow. Today, a number of methods have been used in HT catalyst studies, including various optical, mass-spectrometry, and gas-chromatography techniques. Of these, rapid-scanning Fourier-transform infrared (FTIR imaging is one of the fastest and most versatile screening techniques. Here, the new design of the 16-channel HT reactor is presented and test results for its accuracy and reproducibility are shown. The performance of the system was evaluated through the oxidation of CO over commercial Pd/Al2O3 and cobalt oxide nanoparticles synthesized with different reducer-reductant molar ratios, surfactant types, metal and surfactant concentrations, synthesis temperatures, and ramp rates.

Resonator memories and optical novelty filters

Science.gov (United States)

Anderson, Dana Z.; Erle, Marie C.

Optical resonators having holographic elements are potential candidates for storing information that can be accessed through content addressable or associative recall. Closely related to the resonator memory is the optical novelty filter, which can detect the differences between a test object and a set of reference objects. We discuss implementations of these devices using continuous optical media such as photorefractive materials. The discussion is framed in the context of neural network models. There are both formal and qualitative similarities between the resonator memory and optical novelty filter and network models. Mode competition arises in the theory of the resonator memory, much as it does in some network models. We show that the role of the phenomena of "daydreaming" in the real-time programmable optical resonator is very much akin to the role of "unlearning" in neural network memories. The theory of programming the real-time memory for a single mode is given in detail. This leads to a discussion of the optical novelty filter. Experimental results for the resonator memory, the real-time programmable memory, and the optical tracking novelty filter are reviewed. We also point to several issues that need to be addressed in order to implement more formal models of neural networks.

Fabry-Perot confocal resonator optical associative memory

Science.gov (United States)

Burns, Thomas J.; Rogers, Steven K.; Vogel, George A.

1993-03-01

A unique optical associative memory architecture is presented that combines the optical processing environment of a Fabry-Perot confocal resonator with the dynamic storage and recall properties of volume holograms. The confocal resonator reduces the size and complexity of previous associative memory architectures by folding a large number of discrete optical components into an integrated, compact optical processing environment. Experimental results demonstrate the system is capable of recalling a complete object from memory when presented with partial information about the object. A Fourier optics model of the system's operation shows it implements a spatially continuous version of a discrete, binary Hopfield neural network associative memory.

Realistic ion optical transfer maps for Super-FRS magnets from numerical field data

Energy Technology Data Exchange (ETDEWEB)

Kazantseva, Erika; Boine-Frankenheim, Oliver [Technische Universitaet Darmstadt (Germany)

2016-07-01

In large aperture accelerators such as Super-FRS, the non-linearity of the magnetic field in bending elements leads to the non-linear beam dynamics, which cannot be described by means of linear ion optics. Existing non-linear approach is based on the Fourier harmonics formalism and is not working if horizontal aperture is bigger as vertical or vice versa. In Super-FRS dipole the horizontal aperture is much bigger than the vertical. Hence, it is necessary to find a way to create the higher order transfer map for this dipole to accurately predict the particle dynamics in the realistic magnetic fields in the whole aperture. The aim of this work is to generate an accurate high order transfer map of magnetic elements from measured or simulated 3D magnetic field data. Using differential algebraic formalism allows generating transfer maps automatically via numerical integration of ODEs of motion in beam physics coordinates along the reference path. To make the transfer map accurate for all particles in the beam, the magnetic field along the integration path should be represented by analytical function, matching with the real field distribution in the volume of interest. Within this work the steps of high order realistic transfer map production starting from the field values on closed box, covering the volume of interest, will be analyzed in detail.

The derivative-free Fourier shell identity for photoacoustics.

Science.gov (United States)

Baddour, Natalie

2016-01-01

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

Formality in Brackets

DEFF Research Database (Denmark)

Garsten, Christina; Nyqvist, Anette

Ethnographic work in formal organizations involves learning to recognize the many layers of front stage and back stage of organized life, and to bracket formality. It means to be alert to the fact that what is formal and front stage for one some actors, and in some situations, may in fact be back...... stage and informal for others. Walking the talk, donning the appropriate attire, wearing the proper suit, may be part of what is takes to figure out the code of formal organizational settings – an entrance ticket to the backstage, as it were. Oftentimes, it involves a degree of mimicry, of ‘following...... 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...

Optical simulation of quantum algorithms using programmable liquid-crystal displays

International Nuclear Information System (INIS)

Puentes, Graciana; La Mela, Cecilia; Ledesma, Silvia; Iemmi, Claudio; Paz, Juan Pablo; Saraceno, Marcos

2004-01-01

We present a scheme to perform an all optical simulation of quantum algorithms and maps. The main components are lenses to efficiently implement the Fourier transform and programmable liquid-crystal displays to introduce space dependent phase changes on a classical optical beam. We show how to simulate Deutsch-Jozsa and Grover's quantum algorithms using essentially the same optical array programmed in two different ways

Techniques for Handling and Removal of Spectral Channels in Fourier Transform Synchrotron-Based Spectra

International Nuclear Information System (INIS)

Ibrahim, Amr; Predoi-Cross, Adriana; Teillet, Philippe M.

2010-01-01

Channel spectra are a big problem for those attempting to use synchrotron-based Fourier transform spectra for spectral lineshape studies. Due to the layout of the optical system at the CLS far-infrared beamline, the synchrotron beam undergoes unavoidable multiple reflections on the steering mirrors, beam splitter, several sets of windows, and filters. We present a method for eliminating channel spectra and compare the results of our technique with other methods available in the literature.

Characterization of local fluid flow in 3D porous construct characterized by Fourier domain Doppler optical coherence tomography

Science.gov (United States)

Bagnaninchi, P. O.; Yang, Y.; El Haj, A.; Hinds, M. T.; Wang, R. K.

2007-02-01

In order to achieve functional tissue with the correct biomechanical properties it is critical to stimulate mechanically the cells. Perfusion bioreactor induces fluid shear stress that has been well characterized for two-dimensional culture where both simulation and experimental data are available. However these results can't be directly translated to tissue engineering that makes use of complex three-dimensional porous scaffold. Moreover, stimulated cells produce extensive extra-cellular matrix (ECM) that alter dramatically the micro-architecture of the constructs, changing the local flow dynamic. In this study a Fourier domain Doppler optical coherent tomography (FD-DOCT) system working at 1300nm with a bandwidth of 50nm has been used to determine the local flow rate inside different types of porous scaffolds used in tissue engineering. Local flow rates can then be linearly related, for Newtonian fluid, to the fluid shear stress occurring on the pores wall. Porous chitosan scaffolds (\\fgr 1.5mm x 3mm) with and without a central 250 μm microchannel have been produced by a freeze-drying technique. This techniques allow us to determine the actual shear stress applied to the cells and to optimise the input flow rate consequently, but also to relate the change of the flow distribution to the amount of ECM production allowing the monitoring of tissue formation.

Formal description of the jumpstart just-in-time signaling protocol using EFSM

Science.gov (United States)

Zaim, A. H.; Baldine, Ilia; Cassada, Mark; Rouskas, George N.; Perros, Harry G.; Stevenson, Daniel S.

2002-07-01

We present a formal protocol description for a Just-In-Time (JIT) signaling scheme running over a core dWDM network which utilizes Optical Burst Switches (OBS). We apply an eight-tuple extended finite state machine (EFSM) model to formally specify the protocol. Using the EFSM model, we define the communication between a source client node and a destination client node through an ingress and one or multiple intermediate switches. We worked on single burst connections that means setting up the connection just before sending a single burst and then closing the connection as soon as the burst is sent. The communication between the EFSMs is handled through message transfer between protocol entities.

Applications of Fourier transforms to generalized functions

CERN Document Server

Rahman, M

2011-01-01

This book explains how Fourier transforms can be applied to generalized functions. The generalized function is one of the important branches of mathematics and is applicable in many practical fields. Its applications to the theory of distribution and signal processing are especially important. The Fourier transform is a mathematical procedure that can be thought of as transforming a function from its time domain to the frequency domain.The book contains six chapters and three appendices. Chapter 1 deals with preliminary remarks on Fourier series from a general point of view and also contains an introduction to the first generalized function. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. The author has stated and proved 18 formulas dealing with the Fourier transforms of generalized functions, and demonstrated some important problems of practical interest. Chapter 4 deals with the asymptotic esti...

Software Formal Inspections Guidebook

Science.gov (United States)

1993-01-01

The Software Formal Inspections Guidebook is designed to support the inspection process of software developed by and for NASA. This document provides information on how to implement a recommended and proven method for conducting formal inspections of NASA software. This Guidebook is a companion document to NASA Standard 2202-93, Software Formal Inspections Standard, approved April 1993, which provides the rules, procedures, and specific requirements for conducting software formal inspections. Application of the Formal Inspections Standard is optional to NASA program or project management. In cases where program or project management decide to use the formal inspections method, this Guidebook provides additional information on how to establish and implement the process. The goal of the formal inspections process as documented in the above-mentioned Standard and this Guidebook is to provide a framework and model for an inspection process that will enable the detection and elimination of defects as early as possible in the software life cycle. An ancillary aspect of the formal inspection process incorporates the collection and analysis of inspection data to effect continual improvement in the inspection process and the quality of the software subjected to the process.

Harnessing mode-selective nonlinear optics for on-chip multi-channel all-optical signal processing

Directory of Open Access Journals (Sweden)

Ming Ma

2016-11-01

Full Text Available All-optical signal processing based on nonlinear optical effects allows for the realization of important functions in telecommunications including wavelength conversion, optical multiplexing/demultiplexing, Fourier transformation, and regeneration, amongst others, on ultrafast time scales to support high data rate transmission. In integrated photonic subsystems, the majority of all-optical signal processing systems demonstrated to date typically process only a single channel at a time or perform a single processing function, which imposes a serious limitation on the functionality of integrated solutions. Here, we demonstrate how nonlinear optical effects can be harnessed in a mode-selective manner to perform simultaneous multi-channel (two and multi-functional optical signal processing (i.e., regenerative wavelength conversion in an integrated silicon photonic device. This approach, which can be scaled to a higher number of channels, opens up a new degree of freedom for performing a broad range of multi-channel nonlinear optical signal processing functions using a single integrated photonic device.

Optical geometry across the horizon

International Nuclear Information System (INIS)

Jonsson, Rickard

2006-01-01

In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

Adaption of optical Fresnel transform to optical Wigner transform

International Nuclear Information System (INIS)

Lv Cuihong; Fan Hongyi

2010-01-01

Enlightened by the algorithmic isomorphism between the rotation of the Wigner distribution function (WDF) and the αth fractional Fourier transform, we show that the optical Fresnel transform performed on the input through an ABCD system makes the output naturally adapting to the associated Wigner transform, i.e. there exists algorithmic isomorphism between ABCD transformation of the WDF and the optical Fresnel transform. We prove this adaption in the context of operator language. Both the single-mode and the two-mode Fresnel operators as the image of classical Fresnel transform are introduced in our discussions, while the two-mode Wigner operator in the entangled state representation is introduced for fitting the two-mode Fresnel operator.

Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform.

Science.gov (United States)

Tang, Heng-He; Liu, Pu-Kun

2015-09-07

A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances.

Fourier Series

Indian Academy of Sciences (India)

The theory of Fourier series deals with periodic functions. By a periodic ..... including Dirichlet, Riemann and Cantor occupied themselves with the problem of ... to converge only on a set which is negligible in a certain sense (Le. of measure ...

Alternating multivariate trigonometric functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2008-01-01

We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel

Fourier transform n.m.r. spectroscopy

International Nuclear Information System (INIS)

Shaw, D.

1976-01-01

This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques

Fourier transform n. m. r. spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Shaw, D [Varian Ltd., Walton (UK)

1976-01-01

This book is orientated to techniques rather than applications. The basic theory of n.m.r. is dealt with in a unified approach to the Fourier theory. The middle section of the book concentrates on the practical aspects of Fourier n.m.r., both instrumental and experimental. The final chapters briefly cover general application of n.m.r., but concentrate strongly on those areas where Fourier n.m.r. can give information which is not available by conventional techniques.

Pion-nucleus scattering in the isobar formalism

International Nuclear Information System (INIS)

Moniz, E.J.

1978-06-01

Lectures on the isobar-hole model for pion reactions include the isobar as an explicit degree of freedom and the connection with a purely pion and nucleon system, the formalism and its relation to the pion optical potential, the extended schematic model for pion scattering, a simple spinless s-wave model, application to pion-oxygen 16 scattering and comparison with elastic scattering data. In this way the extent is shown to which microscopic treatment of the many-body dynamics explains the data and the extent to which additional physical input is required. Another test is the various inelastic processes. Inclusive reactions are briefly discussed. 37 references

Properties of the distributional finite Fourier transform

OpenAIRE

Carmichael, Richard D.

2016-01-01

The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.

Analyzing Seasonal Variations in Suicide With Fourier Poisson Time-Series Regression: A Registry-Based Study From Norway, 1969-2007.

Science.gov (United States)

Bramness, Jørgen G; Walby, Fredrik A; Morken, Gunnar; Røislien, Jo

2015-08-01

Seasonal variation in the number of suicides has long been acknowledged. It has been suggested that this seasonality has declined in recent years, but studies have generally used statistical methods incapable of confirming this. We examined all suicides occurring in Norway during 1969-2007 (more than 20,000 suicides in total) to establish whether seasonality decreased over time. Fitting of additive Fourier Poisson time-series regression models allowed for formal testing of a possible linear decrease in seasonality, or a reduction at a specific point in time, while adjusting for a possible smooth nonlinear long-term change without having to categorize time into discrete yearly units. The models were compared using Akaike's Information Criterion and analysis of variance. A model with a seasonal pattern was significantly superior to a model without one. There was a reduction in seasonality during the period. Both the model assuming a linear decrease in seasonality and the model assuming a change at a specific point in time were both superior to a model assuming constant seasonality, thus confirming by formal statistical testing that the magnitude of the seasonality in suicides has diminished. The additive Fourier Poisson time-series regression model would also be useful for studying other temporal phenomena with seasonal components. © The Author 2015. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

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 foll...... follows that integral transform with kernels which are products of a Bessel and a Hankel function or which is of a certain general hypergeometric type have inverse transforms of the same structure....

Formal, Non-Formal and Informal Learning in the Sciences

Science.gov (United States)

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…

Miniaturised optical sensors for industrial applications

DEFF Research Database (Denmark)

Jakobsen, Michael Linde; Hanson, Steen Grüner

2010-01-01

. The technology is based on compact and low-cost laser sources such as Vertical Cavity Surface Emitting Lasers (VCSELs). The methods characterise the object motion by speckle translation in the near field (imaging) or far field (optical Fourier transform) by optical spatial filtering velocimetry. The volume...... of the two optical solutions is less than 1 cm3, including the application specific integrated circuit (ASIC), which processes the data and interfaces a PC/Laptop directly via a USB driver. The sensors are designed for working distances of 2 and 12 mm for near field and far field, respectively. We...

Mapped Fourier Methods for stiff problems in toroidal geometry

OpenAIRE

Guillard , Herve

2014-01-01

Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates the use of mapped Fourier method as a way to circumvent this problem. Mapped Fourier method uses instead of the usual Fourier interpolant the compositio...

Electronic structure of antiferromagnetic UN and UPtGe single crystals from optical and magneto-optical spectroscopy; Elektronische Struktur von antiferromagnetischen UN- und UPtGe-Einkristallen aus optischer und magnetooptischer Spektroskopie

Energy Technology Data Exchange (ETDEWEB)

Marutzky, M.

2006-10-12

In this thesis the study of the magneto-optical Kerr effect and the determination of the optical constants by means of ellipsometry and Fourier-transformation infrared spectroscopy of UN and UPtGe is described. In UPtGe an optical anisotropy was detected over a spectral range from 6 meV to 32 eV. (HSI)

Fear of the Formal

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 “Schumpetarian world” (Teece et al., 1997: 509) of dynamic competition and incessant reform, formal organization appears as well suited to survival as a fish out of water. Indeed, formal organization, and its closely overlapping semantic twin bureaucracy, are not only represented as ill suited to the realities...... is that formal organization is an obstacle to be overcome. For that very reason, critics, intellectuals and reformers alike have urged public and private organizations to break out of the stifling straightjacket of formality, to dispense with bureaucracy, and to tear down hierarchies. This could either be done...

Proposal of AAA-battery-size one-shot ATR Fourier spectroscopic imager for on-site analysis: Simultaneous measurement of multi-components with high accuracy

Science.gov (United States)

Hosono, Satsuki; Qi, Wei; Sato, Shun; Suzuki, Yo; Fujiwara, Masaru; Hiramatsu, Hiroyuki; Suzuki, Satoru; Abeygunawardhana, P. K. W.; Wada, Kenji; Nishiyama, Akira; Ishimaru, Ichiro

2015-03-01

For simultaneous measurement of multi-components on-site like factories, the ultra-compact (diameter: 9[mm], length: 45[mm], weight: 200[g]) one-shot ATR (Attenuated Total Reflection) Fourier spectroscopic imager was proposed. Because the proposed one-shot Fourier spectroscopic imaging is based on spatial-phase-shift interferometer, interferograms could be obtained with simple optical configurations. We introduced the transmission-type relativeinclined phase-shifter, that was constructed with a cuboid prism and a wedge prism, onto the optical Fourier transform plane of infinity corrected optical systems. And also, small light-sources and cameras in the mid-infrared light region, whose size are several millimeter on a side, are essential components for the ultra-compact spectroscopic configuration. We selected the Graphite light source (light source area: 1.7×1.7[mm], maker: Hawkeye technologies) whose radiation factor was high. Fortunately, in these days we could apply the cost-effective 2-dimensional light receiving device for smartphone (e.g. product name: LEPTON, maker: FLIR, price: around 400USD). In the case of alcoholic drinks factory, conventionally workers measure glucose and ethanol concentrations by bringing liquid solution back to laboratories every day. The high portable spectroscopy will make it possible to measure multi-components simultaneously on manufacturing scene. But we found experimentally that absorption spectrum of glucose and water and ethanol were overlapped each other in near infrared light region. But for mid-infrared light region, we could distinguish specific absorption peaks of glucose (@10.5[μm]) and ethanol (@11.5[μm]) independently from water absorption. We obtained standard curve between absorption (@9.6[μm]) and ethanol concentration with high correlation coefficient 0.98 successfully by ATR imaging-type 2-dimensional Fourier spectroscopy (wavelength resolution: 0.057[μm]) with the graphite light source (maker: Hawkeye

Statistical optics

Science.gov (United States)

Goodman, J. W.

This book is based on the thesis that some training in the area of statistical optics should be included as a standard part of any advanced optics curriculum. Random variables are discussed, taking into account definitions of probability and random variables, distribution functions and density functions, an extension to two or more random variables, statistical averages, transformations of random variables, sums of real random variables, Gaussian random variables, complex-valued random variables, and random phasor sums. Other subjects examined are related to random processes, some first-order properties of light waves, the coherence of optical waves, some problems involving high-order coherence, effects of partial coherence on imaging systems, imaging in the presence of randomly inhomogeneous media, and fundamental limits in photoelectric detection of light. Attention is given to deterministic versus statistical phenomena and models, the Fourier transform, and the fourth-order moment of the spectrum of a detected speckle image.

OPTICAL correlation identification technology applied in underwater laser imaging target identification

Science.gov (United States)

Yao, Guang-tao; Zhang, Xiao-hui; Ge, Wei-long

2012-01-01

The underwater laser imaging detection is an effective method of detecting short distance target underwater as an important complement of sonar detection. With the development of underwater laser imaging technology and underwater vehicle technology, the underwater automatic target identification has gotten more and more attention, and is a research difficulty in the area of underwater optical imaging information processing. Today, underwater automatic target identification based on optical imaging is usually realized with the method of digital circuit software programming. The algorithm realization and control of this method is very flexible. However, the optical imaging information is 2D image even 3D image, the amount of imaging processing information is abundant, so the electronic hardware with pure digital algorithm will need long identification time and is hard to meet the demands of real-time identification. If adopt computer parallel processing, the identification speed can be improved, but it will increase complexity, size and power consumption. This paper attempts to apply optical correlation identification technology to realize underwater automatic target identification. The optics correlation identification technology utilizes the Fourier transform characteristic of Fourier lens which can accomplish Fourier transform of image information in the level of nanosecond, and optical space interconnection calculation has the features of parallel, high speed, large capacity and high resolution, combines the flexibility of calculation and control of digital circuit method to realize optoelectronic hybrid identification mode. We reduce theoretical formulation of correlation identification and analyze the principle of optical correlation identification, and write MATLAB simulation program. We adopt single frame image obtained in underwater range gating laser imaging to identify, and through identifying and locating the different positions of target, we can improve

Self-Fourier functions and coherent laser combination

International Nuclear Information System (INIS)

Corcoran, C J; Pasch, K A

2004-01-01

The Gaussian and Comb functions are generally quoted as being the two basic functions that are their own Fourier transforms. In 1991, Caola presented a recipe for generating functions that are their own Fourier transforms by symmetrizing any transformable function and then adding its own Fourier transform to it. In this letter, we present a new method for generating a set of functions that are exactly their own Fourier transforms, and which have direct application to laser cavity design for a wide variety of applications. The generated set includes the Gaussian and Comb functions as special cases and forms a continuous bridge of functions between them. The new generating method uses the Gaussian and Comb functions as bases and does not rely on the Fourier operator itself. This self-Fourier function promises to be particularly useful in high-power laser design through coherent laser beam combination. Although these results are presented in a single dimension as with a linear array, the results are equally valid in two dimensions. (letter to the editor)

Content adaptive illumination for Fourier ptychography.

Science.gov (United States)

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%.

High-resolution Fourier-Domain Optical Coherence Tomography and Microperimetric Findings After Macula-off Retinal Detachment Repair

Science.gov (United States)

Smith, Allison J.; Telander, David G.; Zawadzki, Robert J.; Choi, Stacey S.; Morse, Lawrence S.; Werner, John S.; Park, Susanna S.

2009-01-01

Objective To evaluate the morphologic changes in the macula of subjects with repaired macula-off retinal detachment (RD) using high-resolution Fourier-domain optical coherence tomography (FD OCT) and to perform functional correlation in a subset of patients using microperimetry (MP-1). Design Prospective observational case series. Participants Seventeen eyes from 17 subjects who had undergone anatomically successful repair for macula-off, rhegmatogenous RD at least 3 months earlier and without visually significant maculopathy on funduscopy. Methods FD OCT with axial and transverse resolution of 4.5 μm and 10 to 15 μm, respectively, was used to obtain rapid serial B-scans of the macula, which were compared with that from Stratus OCT. The FD OCT B-scans were used to create a 3-dimensional volume, from which en face C-scans were created. Among 11 patients, MP-1 was performed to correlate morphologic changes with visual function. Main Outcome Measures Stratus OCT scans, FD OCT scans, and MP-1 data. Results Stratus OCT and FD OCT images of the macula were obtained 3 to 30 months (mean 7 months) postoperatively in all eyes. Although Stratus OCT revealed photoreceptor disruption in 2 eyes (12%), FD OCT showed photoreceptor disruption in 13 eyes (76%). This difference was statistically significant (Pmacula-off RD repair is a common abnormality in the macula that is detected better with FD OCT than Stratus OCT. A good correlation between MP-1 abnormality and presence of photoreceptor disruption or subretinal fluid on FD OCT demonstrates that these anatomic abnormalities contribute to decreased visual function after successful repair. PMID:18672289

The structure of polarization maps of skin histological sections in the Fourier domain for the tasks of benign and malignant formations differentiation

Science.gov (United States)

Ushenko, V. A.; Dubolazov, A. V.; Savich, V. O.; Novakovskaya, O. Y.; Olar, O. V.; Marchuk, Y. F.

2015-02-01

The optical model of birefringent networks of biological tissues is presented. The technique of Fourier polarimetry for selection of manifestations of linear and circular birefringence of protein fibrils is suggested. The results of investigations of statistical (statistical moments of the 1st-4th orders), correlation (dispersion and excess of autocorrelation functions) and scalar-self-similar (logarithmic dependencies of power spectra) structure of Fourier spectra of polarization azimuths distribution of laser images of skin samples are presented. The criteria of differentiation of postoperative biopsy of benign (keratoma) and malignant (adenocarcinoma) skin tumors are determined.

Optical properties of graphene superlattices.

Science.gov (United States)

Le, H Anh; Ho, S Ta; Nguyen, D Chien; Do, V Nam

2014-10-08

In this work, the optical responses of graphene superlattices, i.e. graphene subjected to a periodic scalar potential, are theoretically reported. The optical properties were studied by investigating the optical conductivity, which was calculated using the Kubo formalism. It was found that the optical conductivity becomes dependent on the photon polarization and is suppressed in the photon energy range of (0, Ub), where Ub is the potential barrier height. In the higher photon energy range, i.e. Ω > Ub, the optical conductivity is, however, almost identical to that of pristine graphene. Such behaviors of the optical conductivity are explained microscopically through the analysis of the elements of optical matrices and effectively through a simple model, which is based on the Pauli blocking mechanism.

Optical systems for synchrotron radiation. Lecture 1. Introductory topics. Revision

International Nuclear Information System (INIS)

Howells, M.R.

1986-02-01

Various fundamental topics are considered which underlie the design and use of optical systems for synchrotron radiation. The point of view of linear system theory is chosen which acts as a unifying concept throughout the series. In this context the important optical quantities usually appear as either impulse response functions (Green's functions) or frequency transfer functions (Fourier Transforms of the Green's functions). Topics include the damped harmonic oscillator, free-space optical field propagation, optical properties of materials, dispersion, and the Kramers-Kronig relations

(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

International Nuclear Information System (INIS)

Klimyk, A U; Patera, J

2007-01-01

We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found

Necessity of Integral Formalism

International Nuclear Information System (INIS)

Tao Yong

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) 445], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 (1975) 3845]. 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 Schrödinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schrödinger 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. (general)

Optical coherence techniques for plasma doppler spectroscopy

International Nuclear Information System (INIS)

Howard, J.; Michael, C.; Glass, F.; Cheetham, A.D.

2000-01-01

A new electro-optically Modulated Optical Solid-State (MOSS) interferometer has been constructed for measurement of the low order spectral moments of line emission from optically thin radiant media. The instrument, which is based on the principle of the Fourier transform spectrometer, has high etendue and is rugged, compact and inexpensive. By employing electro-optical path-length modulation techniques, the spectral information is transferred to the temporal frequency domain and can be obtained using a single photodetector. Specifically, the zeroth moment (brightness) is given by the average signal level, the first moment (shift) by the modulation phase and the second moment (line width) by the modulation amplitude. (author)

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...

Diffractive optical elements for transformation of modes in lasers

Science.gov (United States)

Sridharan, Arun K.; Pax, Paul H.; Heebner, John E.; Drachenberg, Derrek R.; Armstrong, James P.; Dawson, Jay W.

2015-09-01

Spatial mode conversion modules are described, with the capability of efficiently transforming a given optical beam profile, at one plane in space into another well-defined optical beam profile at a different plane in space, whose detailed spatial features and symmetry properties can, in general, differ significantly. The modules are comprised of passive, high-efficiency, low-loss diffractive optical elements, combined with Fourier transform optics. Design rules are described that employ phase retrieval techniques and associated algorithms to determine the necessary profiles of the diffractive optical components. System augmentations are described that utilize real-time adaptive optical techniques for enhanced performance as well as power scaling.

Randomly displaced phase distribution design and its advantage in page-data recording of Fourier transform holograms.

Science.gov (United States)

Emoto, Akira; Fukuda, Takashi

2013-02-20

For Fourier transform holography, an effective random phase distribution with randomly displaced phase segments is proposed for obtaining a smooth finite optical intensity distribution in the Fourier transform plane. Since unitary phase segments are randomly distributed in-plane, the blanks give various spatial frequency components to an image, and thus smooth the spectrum. Moreover, by randomly changing the phase segment size, spike generation from the unitary phase segment size in the spectrum can be reduced significantly. As a result, a smooth spectrum including sidebands can be formed at a relatively narrow extent. The proposed phase distribution sustains the primary functions of a random phase mask for holographic-data recording and reconstruction. Therefore, this distribution is expected to find applications in high-density holographic memory systems, replacing conventional random phase mask patterns.

Fourier phasing with phase-uncertain mask

International Nuclear Information System (INIS)

Fannjiang, Albert; Liao, Wenjing

2013-01-01

Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)

Finite-mode analysis by means of intensity information in fractional optical systems

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2002-01-01

It is shown how a coherent optical signal that contains only a finite number of Hermite-Gauss modes, can be reconstructed from the knowledge of its Radon-Wigner transform -- associated with the intensity distribution in a fractional Fourier transform optical system -- at only two transversal points.

Industrial use of formal methods formal verification

CERN Document Server

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

Imaging retinal degeneration in mice by combining Fourier domain optical coherence tomography and fluorescent scanning laser ophthalmoscopy

Science.gov (United States)

Hossein-Javaheri, Nima; Molday, Laurie L.; Xu, Jing; Molday, Robert S.; Sarunic, Marinko V.

2009-02-01

Visualization of the internal structures of the retina is critical for clinical diagnosis and monitoring of pathology as well as for medical research investigating the root causes of retinal degeneration. Optical Coherence Tomography (OCT) is emerging as the preferred technique for non-contact sub-surface depth-resolved imaging of the retina. The high resolution cross sectional images acquired in vivo by OCT can be compared to histology to visually delineate the retinal layers. The recent demonstration of the significant sensitivity increase obtained through use of Fourier domain (FD) detection with OCT has been used to facilitate high speed scanning for volumetric reconstruction of the retina in software. The images acquired by OCT are purely structural, relying on refractive index differences in the tissue for contrast, and do not provide information on the molecular content of the sample. We have constructed a FDOCT prototype and combined it with a fluorescent Scanning Laser Ophthalmoscope (fSLO) to permit real time alignment of the field of view on the retina. The alignment of the FDOCT system to the specimen is crucial for the registration of measurements taken throughout longitudinal studies. In addition, fluorescence detection has been integrated with the SLO to enable the en face localization of a molecular contrast signal, which is important for retinal angiography, and also for detection of autofluorescence associated with some forms of retinal degeneration, for example autofluorescence lipofuscin accumulations are associated with Stargardt's Macular Dystrophy. The integrated FD OCT/fSLO system was investigated for imaging the retina of the mice in vivo.

Group-invariant finite Fourier transforms

International Nuclear Information System (INIS)

Shenefelt, M.H.

1988-01-01

The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible

Performance of a MEMS-based AO-OCT system using Fourier Reconstruction

Energy Technology Data Exchange (ETDEWEB)

Evans, J; Zawadzki, R; Jones, S; Olivier, S; Werner, J S

2009-01-21

Adaptive optics (AO) and optical coherence tomography (OCT) are powerful imaging modalities that, when combined, can provide high-resolution (3.5 {micro}m isotropic), 3-D images of the retina. The AO-OCT system at UC Davis has demonstrated the utility of this technology for microscopic, volumetric, in vivo retinal imaging. The current system uses an AOptix bimorph deformable mirror (DM) for low-order, high-stroke correction and a 140-actuator Boston Micromachines DM for high-order correction. Developments to improve performance or functionality of the instrument are on-going. Based on previous work in system characterization we have focused on improved AO control. We present preliminary results and remaining challenges for a newly implemented Fourier transform reconstructor (FTR). The previously reported error budget analysis is also reviewed and updated, with consideration of how to improve both the amount of residual error and the robustness of the system. Careful characterization of the AO system will lead to improved performance and inform the design of future systems.

Formal Verification -26 ...

Indian Academy of Sciences (India)

by testing of the components and successful testing leads to the software being ... Formal verification is based on formal methods which are mathematically based ..... scenario under which a similar error could occur. There are various other ...

On the inverse windowed Fourier transform

OpenAIRE

Rebollo Neira, Laura; Fernández Rubio, Juan Antonio

1999-01-01

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

Science.gov (United States)

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

Science.gov (United States)

Grimm, C. A.

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

PFS: the Planetary Fourier Spectrometer for Mars Express

Science.gov (United States)

Formisano, V.; Grassi, D.; Orfei, R.; Biondi, D.; Mencarelli, E.; Mattana, A.; Nespoli, F.; Maturilli, A.; Giuranna, M.; Rossi, M.; Maggi, M.; Baldetti, P.; Chionchio, G.; Saggin, B.; Angrilli, F.; Bianchini, G.; Piccioni, G.; di Lellis, A.; Cerroni, P.; Capaccioni, F.; Capria, M. T.; Coradini, A.; Fonti, S.; Orofino, V.; Blanco, A.; Colangeli, L.; Palomba, E.; Esposito, F.; Patsaev, D.; Moroz, V.; Zasova, L.; Ignatiev, N.; Khatuntsev, I.; Moshkin, B.; Ekonomov, A.; Grigoriev, A.; Nechaev, V.; Kiselev, A.; Nikolsky, Y.; Gnedykh, V.; Titov, D.; Orleanski, P.; Rataj, M.; Malgoska, M.; Jurewicz, A.; Blecka, M. I.; Hirsh, H.; Arnold, G.; Lellouch, E.; Marten, A.; Encrenaz, T.; Lopez Moreno, J.; Atreya, S., Gobbi, P.

2004-08-01

The Planetary Fourier Spectrometer (PFS) for the Mars Express mission is optimised for atmospheric studies, covering the IR range of 1.2-45 μm in two channels. The apodised spectral resolution is 2 cm-1, while the sampling is 1 cm-1. The FOV is about 2° for the short wavelength (SW) channel and 4° for the long wavelength (LW) channel, corresponding to spatial resolutions of 10 km and 20 km, respectively, from an altitude of 300 km. PFS will also provide unique data on the surface-atmosphere interaction and the mineralogical composition of the surface. It will be the first Fourier spectrometer covering 1-5 μm to orbit the Earth or Mars. The experiment has real-time onboard Fast Fourier Transform (FFT) in order to select the spectral range of interest for data transmission to ground. Measurement of the 15-μm CO2 band is very important. Its profile gives, via a complex temperature-profile retrieval technique, the vertical pressure temperature relation, which is the basis of the global atmospheric study. The SW channel uses a PbSe detector cooled to 200-220K, while the LW channel is based on a pyroelectric (LiTaO3) device working at room temperature. The interferogram is measured at every 150 nm displacement step of the corner cube retroreflectors (corresponding to 600 nm optical path difference) via a laser diode monochromatic interferogram (a sine wave), with the zero crossings controlling the double pendulum motion. PFS will operate for about 1.5 h around the pericentre of the orbit. With a measurement every 10 s, 600 measurements per orbit will be acquired, corresponding to 224 Mbit. Onboard compression will reduce it to 125 Mbit or less, depending on the allocated data volume per day. An important requirement is to observe at all local times in order to include night-side vertical temperature profiles. Total instrument mass is 31.2 kg.

Radon-Wigner transform for optical field analysis

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Nijhawan, O.P.; Gupta, A.K.; Musla, A.K.; Singh, Kehar

1998-01-01

The Radon-Wigner transform, associated with the intensity distribution in the fractional Fourier transform system, is used for the analysis of complex structures of coherent as well as partially coherent optical fields. The application of the Radon-Wigner transform to the analysis of fractal fields

A Note on Fourier and the Greenhouse Effect

OpenAIRE

Postma, Joseph E.

2015-01-01

Joseph Fourier's discovery of the greenhouse effect is discussed and is compared to the modern conception of the greenhouse effect. It is confirmed that what Fourier discovered is analogous to the modern concept of the greenhouse effect. However, the modern concept of the greenhouse effect is found to be based on a paradoxical analogy to Fourier's greenhouse work and so either Fourier's greenhouse work, the modern conception of the greenhouse effect, or the modern definition of heat is incorr...

Optical properties of graphene superlattices

International Nuclear Information System (INIS)

Le, H Anh; Do, V Nam; Ho, S Ta; Nguyen, D Chien

2014-01-01

In this work, the optical responses of graphene superlattices, i.e. graphene subjected to a periodic scalar potential, are theoretically reported. The optical properties were studied by investigating the optical conductivity, which was calculated using the Kubo formalism. It was found that the optical conductivity becomes dependent on the photon polarization and is suppressed in the photon energy range of (0, U b ), where U b is the potential barrier height. In the higher photon energy range, i.e. Ω > U b , the optical conductivity is, however, almost identical to that of pristine graphene. Such behaviors of the optical conductivity are explained microscopically through the analysis of the elements of optical matrices and effectively through a simple model, which is based on the Pauli blocking mechanism. (paper)

Three dimensional image reconstruction in the Fourier domain

International Nuclear Information System (INIS)

Stearns, C.W.; Chesler, D.A.; Brownell, G.L.

1987-01-01

Filtered backprojection reconstruction algorithms are based upon the relationship between the Fourier transform of the imaged object and the Fourier transforms of its projections. A new reconstruction algorithm has been developed which performs the image assembly operation in Fourier space, rather than in image space by backprojection. This represents a significant decrease in the number of operations required to assemble the image. The new Fourier domain algorithm has resolution comparable to the filtered backprojection algorithm, and, after correction by a pointwise multiplication, demonstrates proper recovery throughout image space. Although originally intended for three-dimensional imaging applications, the Fourier domain algorithm can also be developed for two-dimensional imaging applications such as planar positron imaging systems

A Comparison of Participation Patterns in Selected Formal, Non-Formal, and Informal Online Learning Environments

Science.gov (United States)

Schwier, Richard A.; Seaton, J. X.

2013-01-01

Does learner participation vary depending on the learning context? Are there characteristic features of participation evident in formal, non-formal, and informal online learning environments? Six online learning environments were chosen as epitomes of formal, non-formal, and informal learning contexts and compared. Transcripts of online…

Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism ( S-quantization)

Science.gov (United States)

Ivanov, K. A.; Nikolaev, V. V.; Gubaydullin, A. R.; Kaliteevski, M. A.

2017-10-01

Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures ( S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate

Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding.

Science.gov (United States)

Wang, Xiaogang; Chen, Wen; Chen, Xudong

2014-09-22

We present a novel image hiding method based on phase retrieval algorithm under the framework of nonlinear double random phase encoding in fractional Fourier domain. Two phase-only masks (POMs) are efficiently determined by using the phase retrieval algorithm, in which two cascaded phase-truncated fractional Fourier transforms (FrFTs) are involved. No undesired information disclosure, post-processing of the POMs or digital inverse computation appears in our proposed method. In order to achieve the reduction in key transmission, a modified image hiding method based on the modified phase retrieval algorithm and logistic map is further proposed in this paper, in which the fractional orders and the parameters with respect to the logistic map are regarded as encryption keys. Numerical results have demonstrated the feasibility and effectiveness of the proposed algorithms.

Non linear optical studies on semiorganic single crystal: L-arginine 4-nitrophenalate 4-nitrophenol dihydrate (LAPP)

Science.gov (United States)

Mahadevan, M.; Sankar, P. K.; Vinitha, G.; Arivanandhan, M.; Ramachandran, K.; Anandan, P.

2017-07-01

L-arginine 4-nitrophenalate 4-nitrophenol dihydrate (LAPP) has been synthesized and grown by solution growth at room temperature using deionized water as a solvent. The various functional groups of the sample were identified by Fourier transform infra-red and Fourier transforms - Raman spectroscopic analyses. The Laser damage threshold of LAPP has been studied. Refractive index of LAPP single crystal was measured using Metricon prism coupler Instrument. The etching studies were carried out to study the quality of the grown crystals. The third order nonlinear optical properties of LAPP sample was analyzed by the Z-scan technique using 532 nm diode pumped CW Nd: YAG laser. The LAPP material exhibits negative optical nonlinearity. The results show that LAPP sample has potential applications in nonlinear optics and it can be exploited for optical limiting or switching.

Optical implementation of a feature-based neural network with application to automatic target recognition

Science.gov (United States)

Chao, Tien-Hsin; Stoner, William W.

1993-01-01

An optical neural network based on the neocognitron paradigm is introduced. A novel aspect of the architecture design is shift-invariant multichannel Fourier optical correlation within each processing layer. Multilayer processing is achieved by feeding back the ouput of the feature correlator interatively to the input spatial light modulator and by updating the Fourier filters. By training the neural net with characteristic features extracted from the target images, successful pattern recognition with intraclass fault tolerance and interclass discrimination is achieved. A detailed system description is provided. Experimental demonstrations of a two-layer neural network for space-object discrimination is also presented.

Fourier techniques and applications

CERN Document Server

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...

Improving Learner Outcomes in Lifelong Education: Formal Pedagogies in Non-Formal Learning Contexts?

Science.gov (United States)

Zepke, Nick; Leach, Linda

2006-01-01

This article explores how far research findings about successful pedagogies in formal post-school education might be used in non-formal learning contexts--settings where learning may not lead to formal qualifications. It does this by examining a learner outcomes model adapted from a synthesis of research into retention. The article first…

Real-time quantitative Schlieren imaging by fast Fourier demodulation of a checkered backdrop

Science.gov (United States)

Wildeman, Sander

2018-06-01

A quantitative synthetic Schlieren imaging (SSI) method based on fast Fourier demodulation is presented. Instead of a random dot pattern (as usually employed in SSI), a 2D periodic pattern (such as a checkerboard) is used as a backdrop to the refractive object of interest. The range of validity and accuracy of this "Fast Checkerboard Demodulation" (FCD) method are assessed using both synthetic data and experimental recordings of patterns optically distorted by small waves on a water surface. It is found that the FCD method is at least as accurate as sophisticated, multi-stage, digital image correlation (DIC) or optical flow (OF) techniques used with random dot patterns, and it is significantly faster. Efficient, fully vectorized, implementations of both the FCD and DIC/OF schemes developed for this study are made available as open source Matlab scripts.

A new twist to fourier transforms

CERN Document Server

Meikle, Hamish D

2004-01-01

Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs

First-order optical systems with unimodular eigenvalues

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2006-01-01

It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues, is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the

Combining Formal, Non-Formal and Informal Learning for Workforce Skill Development

Science.gov (United States)

Misko, Josie

2008-01-01

This literature review, undertaken for Australian Industry Group, shows how multiple variations and combinations of formal, informal and non-formal learning, accompanied by various government incentives and organisational initiatives (including job redesign, cross-skilling, multi-skilling, diversified career pathways, action learning projects,…

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Boashash, B.

2003-01-01

We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

Fourier analysis of parallel block-Jacobi splitting with transport synthetic acceleration in two-dimensional geometry

International Nuclear Information System (INIS)

Rosa, M.; Warsa, J. S.; Chang, J. H.

2007-01-01

A Fourier analysis is conducted in two-dimensional (2D) Cartesian geometry for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. The results for the un-accelerated algorithm show that convergence of PBJ can degrade, leading in particular to stagnation of GMRES(m) in problems containing optically thin sub-domains. The results for the accelerated algorithm indicate that TSA can be used to efficiently precondition an iterative method in the optically thin case when implemented in the 'modified' version MTSA, in which only the scattering in the low order equations is reduced by some non-negative factor β<1. (authors)

X-ray Fourier-transform holographic microscope

International Nuclear Information System (INIS)

Haddad, W.S.; Cullen, D.; Solem, J.C.; Boyer, K.; Rhodes, C.K.

1988-01-01

The properties of an x-ray Fourier-transform holographic instrument suitable for imaging hydrated biological samples are described. Recent advances in coherent x-ray source technology are making diffraction-limited holograms of microscopic structures, with corresponding high spatial resolution, a reality. A high priority application of snapshot x-ray holography is the study of microscopic biological structures in the hydrated living state. X-rays offer both high resolution and high contrast for important structures within living organisms, thereby rendering unnecessary the staining of specimens, essential for optical and electron microscopy. If the wavelength is properly chosen. Furthermore, the snapshot feature, arising from picosecond or subpicosecond exposure times, eliminates blurring occurring from either thermal heating or normal biological activity of the sample. Finally, with sufficiently high photon fluxes, such as those available from x-ray lasers, the x-ray snapshot can be accomplished with a single pulse, thereby yielding complete three-dimensional information on a sample having normal biological integrity at the moment of exposure. 10 refs., 6 figs

Replica Fourier Transform: Properties and applications

International Nuclear Information System (INIS)

Crisanti, A.; De Dominicis, C.

2015-01-01

The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically

An introduction to Fourier series and integrals

CERN Document Server

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.

The morphing of geographical features by Fourier transformation.

Science.gov (United States)

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

Fourier Series

Indian Academy of Sciences (India)

polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.

Adaptive optics stochastic optical reconstruction microscopy (AO-STORM) by particle swarm optimization.

Science.gov (United States)

Tehrani, Kayvan F; Zhang, Yiwen; Shen, Ping; Kner, Peter

2017-11-01

Stochastic optical reconstruction microscopy (STORM) can achieve resolutions of better than 20nm imaging single fluorescently labeled cells. However, when optical aberrations induced by larger biological samples degrade the point spread function (PSF), the localization accuracy and number of localizations are both reduced, destroying the resolution of STORM. Adaptive optics (AO) can be used to correct the wavefront, restoring the high resolution of STORM. A challenge for AO-STORM microscopy is the development of robust optimization algorithms which can efficiently correct the wavefront from stochastic raw STORM images. Here we present the implementation of a particle swarm optimization (PSO) approach with a Fourier metric for real-time correction of wavefront aberrations during STORM acquisition. We apply our approach to imaging boutons 100 μm deep inside the central nervous system (CNS) of Drosophila melanogaster larvae achieving a resolution of 146 nm.

Some Applications of Fourier's Great Discovery for Beginners

Science.gov (United States)

Kraftmakher, Yaakov

2012-01-01

Nearly two centuries ago, Fourier discovered that any periodic function of period T can be presented as a sum of sine waveforms of frequencies equal to an integer times the fundamental frequency [omega] = 2[pi]/T (Fourier's series). It is impossible to overestimate the importance of Fourier's discovery, and all physics or engineering students…

Beyond formalism

Science.gov (United States)

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.

The measurement and analysis of wavefront structure from large aperture ICF optics

International Nuclear Information System (INIS)

Wolfe, C.R.; Lawson, J.K.

1995-01-01

This paper discusses the techniques, developed over the past year, for high spatial resolution measurement and analysis of the transmitted and/or reflected wavefront of large aperture ICF optical components. Parts up to 400 mm x 750 mm have been measured and include: laser slabs, windows, KDP crystals and lenses. The measurements were performed using state-of-the-art commercial phase shifting interferometers at a wavelength of 633 μm. Both 1 and 2-D Fourier analysis have been used to characterize the wavefront; specifically the Power Spectral Density, (PSD), function was calculated. The PSDs of several precision optical components will be shown. The PSD(V) is proportional to the (amplitude) 2 of components of the Fourier frequency spectrum. The PSD describes the scattered intensity and direction as a function of scattering angle in the wavefront. The capability of commercial software is limited to 1-D Fourier analysis only. We are developing our own 2-D analysis capability in support of work to revise specifications for NIF optics. 2-D analysis uses the entire wavefront phase map to construct 2D PSD functions. We have been able to increase the signal-to-noise relative to 1-D and can observe very subtle wavefront structure

Quantum optical predictions in Q representation for Bell's type experiments

International Nuclear Information System (INIS)

Ferrero, M.; Marshall, T.W.

1991-01-01

Using the Q representation, the authors study the disagreement between quantum optical formalism and local realism and they show that the phenomenon of enhancement, first revealed by the local realist analysis, could receive a simple explanation if they use this particular version of the quantum formalism. Nevertheless, some fundamental difficulties remain

Improvement in spatial frequency characteristics of magneto-optical Kerr microscopy

Science.gov (United States)

Ogasawara, Takeshi

2017-10-01

The spatial resolution of a conventional magneto-optical Kerr microscope, compared with those of conventional optical microscopes, inevitably deteriorates owing to oblique illumination. An approach to obtaining the maximum spatial resolution using multiple images with different illumination directions is demonstrated here. The method was implemented by rotating the illumination path around the optical axis using a motorized stage. The Fourier transform image of the observed magnetic domain indicates that the spatial frequency component that is lost in the conventional method is restored.

Integrated formal operations plan

Energy Technology Data Exchange (ETDEWEB)

Cort, G.; Dearholt, W.; Donahue, S.; Frank, J.; Perkins, B.; Tyler, R.; Wrye, J.

1994-01-05

The concept of formal operations (that is, a collection of business practices to assure effective, accountable operations) has vexed the Laboratory for many years. To date most attempts at developing such programs have been based upon rigid, compliance-based interpretations of a veritable mountain of Department of Energy (DOE) orders, directives, notices, and standards. These DOE dictates seldom take the broad view but focus on highly specialized programs isolated from the overall context of formal operations. The result is a confusing array of specific, and often contradictory, requirements that produce a patchwork of overlapping niche programs. This unnecessary duplication wastes precious resources, dramatically increases the complexity of our work processes, and communicates a sense of confusion to our customers and regulators. Coupled with the artificial divisions that have historically existed among the Laboratory`s formal operations organizations (quality assurance, configuration management, records management, training, etc.), this approach has produced layers of increasingly vague and complex formal operations plans, each of which interprets its parent and adds additional requirements of its own. Organizational gridlock ensues whenever an activity attempts to implement these bureaucratic monstrosities. The integrated formal operations plan presented is to establish a set of requirements that must be met by an integrated formal operations program, assign responsibilities for implementation and operation of the program, and specify criteria against which the performance of the program will be measured. The accountable line manager specifies the items, processes, and information (the controlled elements) to which the formal operations program specified applies. The formal operations program is implemented using a graded approach based on the level of importance of the various controlled elements and the scope of the activities in which they are involved.

Electro-optical properties of tetragonal KNbO 3

Indian Academy of Sciences (India)

Linear electro-optical tensor coefficients and optical susceptibility of tetragonal KNbO3 are calculated using a formalism based on bond charge theory. Results are in close agreement with the experimental data. The covalent Nb–O bonding network comprising the distorted NbO6 octahedral groups in the structure is found to ...

Surface Fourier-transform lens using a metasurface

International Nuclear Information System (INIS)

Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun

2015-01-01

We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)

Dynamic changes of photorecrptor layer in eyes with acute central serous chorioretinopathy after laser treatment by fourier-domain optical coherence tomography

Directory of Open Access Journals (Sweden)

Li-Qin Zhou

2014-10-01

Full Text Available AIM: To dynamically observe the feeling change of the photorecrptor layer in the eyes with acute central serous chorioretinopathy(CSCRkrypton laser treatment by fourier-domain optical coherence tomography(FD-OCT, and to study their correlation with the chang of vision.METHODS: This is a retrospective case series study. The clinical diagnosis of 52 patients with monocular initial onset of central serous chorioretinopathy, krypton laser photocoagulation before treatment, after 1, 2, 4, 6, 8wk, 6mo, FD-OCT were performed to observe the morphological changes characteristic of photoreceptor layer and changes in vision. RESULTS: After 1wk treatment, all cases were improved; 2wk, 6 cases were cured; 4wk, 38 cases were cured; 6wk, 41 cases were cured; 8wk, 45 cases were cured, the OCT showed macular retinal neuroepithelial layer(RNLfrom fully absorbed; 6mo with the same 8wk. Before and after treatment in patients with best corrected visual acuity and from the height difference between the macular region of RNL was statistically significant(PPPCONCLUSION: FD-OCT can dynamicaly observed acute central serous chorioretinopathy krypton laser treatment of photoreceptor ultrastruture changes. Photoreceptor layer of complete and incomplete best corrected visual acuity difference was statistically significant(P<0.01.

Polarization Optics in Telecommunications

CERN Document Server

Damask, Jay N

2005-01-01

The strong investments into optical telecommunications in the late 1990s resulted in a wealth of new research, techniques, component designs, and understanding of polarization effects in fiber. Polarization Optics in Telecommunications brings together recent advances in the field to create a standard, practical reference for component designers and optical fiber communication engineers. Beginning with a sound foundation in electromagnetism, the author offers a dissertation of the spin-vector formalism of polarization and the interaction of light with media. Applications discussed include optical isolators, optical circulators, fiber collimators, and a variety of applied waveplate and prism combinations. Also included in an extended discussion of polarization-mode dispersion (PMD) and polarization-dependent loss (PDL), their representation, behavior, statistical properties, and measurement. This book draws extensively from the technical and patent literature and is an up-to-date reference for researchers and c...

Projective Fourier duality and Weyl quantization

International Nuclear Information System (INIS)

Aldrovandi, R.; Saeger, L.A.

1996-08-01

The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs

Integrating semi-formal and formal requirements

NARCIS (Netherlands)

Wieringa, Roelf J.; Olivé, Antoni; Dubois, Eric; Pastor, Joan Antoni; Huyts, Sander

1997-01-01

In this paper, we report on the integration of informal, semiformal and formal requirements specification techniques. We present a framework for requirements specification called TRADE, within which several well-known semiformal specification techniques are placed. TRADE is based on an analysis of

Quantitative Fourier Domain Optical Coherence Tomography Imaging of the Ocular Anterior Segment

Science.gov (United States)

McNabb, Ryan Palmer

Clinical imaging within ophthalmology has had transformative effects on ocular health over the last century. Imaging has guided clinicians in their pharmaceutical and surgical treatments of macular degeneration, glaucoma, cataracts and numerous other pathologies. Many of the imaging techniques currently used are photography based and are limited to imaging the surface of ocular structures. This limitation forces clinicians to make assumptions about the underlying tissue which may reduce the efficacy of their diagnoses. Optical coherence tomography (OCT) is a non-invasive, non-ionizing imaging modality that has been widely adopted within the field of ophthalmology in the last 15 years. As an optical imaging technique, OCT utilizes low-coherence interferometry to produce micron-scale three-dimensional datasets of a tissue's structure. Much of the human body consists of tissues that significantly scatter and attenuate optical signals limiting the imaging depth of OCT in those tissues to only 1-2mm. However, the ocular anterior segment is unique among human tissue in that it is primarily transparent or translucent. This allows for relatively deep imaging of tissue structure with OCT and is no longer limited by the optical scattering properties of the tissue. This goal of this work is to develop methods utilizing OCT that offer the potential to reduce the assumptions made by clinicians in their evaluations of their patients' ocular anterior segments. We achieved this by first developing a method to reduce the effects of patient motion during OCT volume acquisitions allowing for accurate, three dimensional measurements of corneal shape. Having accurate corneal shape measurements then allowed us to determine corneal spherical and astigmatic refractive contribution in a given individual. This was then validated in a clinical study that showed OCT better measured refractive change due to surgery than other clinical devices. Additionally, a method was developed to combine

Generalized Fourier slice theorem for cone-beam image reconstruction.

Science.gov (United States)

Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang

2015-01-01

The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).

Corrected Fourier series and its application to function approximation

Directory of Open Access Journals (Sweden)

Qing-Hua Zhang

2005-01-01

Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.

Formal System Verification - Extension 2

Science.gov (United States)

2012-08-08

vision of truly trustworthy systems has been to provide a formally verified microkernel basis. We have previously developed the seL4 microkernel...together with a formal proof (in the theorem prover Isabelle/HOL) of its functional correctness [6]. This means that all the behaviours of the seL4 C...source code are included in the high-level, formal specification of the kernel. This work enabled us to provide further formal guarantees about seL4 , in

Psychologist in non-formal education

OpenAIRE

Pavićević Miljana S.

2011-01-01

Learning is not limited to school time. It starts at birth and continues throughout the entire life. Equally important as formal education there are also non-formal and informal education. Any kind of learning outside the traditional school can be called informal. However, it is not easy to define non-formal education because it is being described differently, for example as an education movement, process, system… Projects and programs implemented under the name of non-formal education are of...

Fourier transforms in radar and signal processing

CERN Document Server

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

Study of Fourier transform spectrometer based on Michelson interferometer wave-meter

Science.gov (United States)

Peng, Yuexiang; Wang, Liqiang; Lin, Li

2008-03-01

A wave-meter based on Michelson interferometer consists of a reference and a measurement channel. The voice-coiled motor using PID means can realize to move in stable motion. The wavelength of a measurement laser can be obtained by counting interference fringes of reference and measurement laser. Reference laser with frequency stabilization creates a cosine interferogram signal whose frequency is proportional to velocity of the moving motor. The interferogram of the reference laser is converted to pulse signal, and it is subdivided into 16 times. In order to get optical spectrum, the analog signal of measurement channel should be collected. The Analog-to-Digital Converter (ADC) for measurement channel is triggered by the 16-times pulse signal of reference laser. So the sampling rate is constant only depending on frequency of reference laser and irrelative to the motor velocity. This means the sampling rate of measurement channel signals is on a uniform time-scale. The optical spectrum of measurement channel can be processed with Fast Fourier Transform (FFT) method by DSP and displayed on LCD.

Topical Roots of Formal Dialectic

NARCIS (Netherlands)

Krabbe, Erik C. W.

Formal dialectic has its roots in ancient dialectic. We can trace this influence in Charles Hamblin's book on fallacies, in which he introduced his first formal dialectical systems. Earlier, Paul Lorenzen proposed systems of dialogical logic, which were in fact formal dialectical systems avant la

Level 0 to 1 processing of the imaging Fourier transform spectrometer GLORIA: generation of radiometrically and spectrally calibrated spectra

Directory of Open Access Journals (Sweden)

A. Kleinert

2014-12-01

Full Text Available The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA is an imaging Fourier transform spectrometer that is capable of operating on various high-altitude research aircraft. It measures the atmospheric emission in the thermal infrared spectral region in limb and nadir geometry. GLORIA consists of a classical Michelson interferometer combined with an infrared camera. The infrared detector has a usable area of 128 × 128 pixels, measuring up to 16 384 interferograms simultaneously. Imaging Fourier transform spectrometers impose a number of challenges with respect to instrument calibration and algorithm development. The optical setup with extremely high optical throughput requires the development of new methods and algorithms for spectral and radiometric calibration. Due to the vast amount of data there is a high demand for scientifically intelligent optimisation of the data processing. This paper outlines the characterisation and processing steps required for the generation of radiometrically and spectrally calibrated spectra. Methods for performance optimisation of the processing algorithm are presented. The performance of the data processing and the quality of the calibrated spectra are demonstrated for measurements collected during the first deployments of GLORIA on aircraft.

System Design, Implementation, and Evaluation of the Optical Broadband Correlator

Science.gov (United States)

1994-09-20

shear-mode TeO2 , Model No. N45075-6-20, manufactured by Newport Electro- Optic Systems with a length of 75 pjs, acoustic direction 1110], optical...optical aperture (or useful length) TOA of our cells are shown in Table 3. The Bragg cells are shear-mode TeO2 , Model No. N45075-6-20, manufactured by...focusing or integrating (Fourier transform) lens is a laser diode glass doublet Model 06LAI013/076, from Melles Griot. Its focal length is 145 nun at 830

Transformation de Fourier et moments invariants appliqués à la reconnaissance des caractères Tifinaghe

Directory of Open Access Journals (Sweden)

Rachid El Ayachi

2012-03-01

Full Text Available Optical Character Recognition OCR is a tool that aims to provide opportunities for computers to read characters without human intervention. The objective of OCR is characterization of a character by invariant descriptors in translation, rotation and scaling. In this paper, the OCR developed use invariant moments and Fourier transform in extraction phase. In the recognition phase, dynamic programming and neural network are adopted. All tests are applied on Tifinaghe printed characters.

Revisiting the Fourier expansion of Mie scattering matrices in generalized spherical functions

International Nuclear Information System (INIS)

Sanghavi, Suniti

2014-01-01

Mie computations of the scattering properties of large particles are a time consuming step in the radiative transfer modeling of aerosol and clouds. Currently, there exist two methods based on the use of spherical functions for computing the Fourier moments of the phase matrix of a given spherical particle or particulate polydispersion: The first, developed over the years before being presented in a convenient form by Siewert [31], required an intermediate computation of the phase matrix over which numerical integration was performed to deliver the required Fourier components. The second, suggested by Domke [9], promised a direct computation of the Fourier moments using Wigner 3-j symbols. While the former was relatively easy to implement and is thus the most commonly used to date, its numerical implementation using an arbitrary user choice of angular quadrature (NAI-1) can produce inaccurate results. Numerical integration using quadrature points as recommended by de Rooij and van der Stap [5] (NAI-2) delivers accurate results with high computational efficiency. Domke's method enables a direct computation of the exact number of required Fourier components. However, the original manuscript contained several misprints, many of which were subsequently corrected by de Rooij and van der Stap [5]. Unfortunately, the main recurrence relationship used in Domke [9] remained uncorrected. In this paper, the corrected relationship is presented along with other minor corrections. de Rooij and van der Stap [5] had found the straightforward application of Domke's method viable only for size parameters smaller than ∼120 due to issues involving computer storage. A means of implementing the corrected Domke formalism using precomputed tabulations of Wigner 3-j symbols (PCW) is presented here, making it more computationally economical and applicable over much broader particle size ranges. The accuracy of PCW is only limited by machine precision. For a single particle, NAI-2 is found

Fan beam image reconstruction with generalized Fourier slice theorem.

Science.gov (United States)

Zhao, Shuangren; Yang, Kang; Yang, Kevin

2014-01-01

For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.

Fourier spectral simulations for wake fields in conducting cavities

International Nuclear Information System (INIS)

Min, M.; Chin, Y.-H.; Fischer, P.F.; Chae, Y.-Chul; Kim, K.-J.

2007-01-01

We investigate Fourier spectral time-domain simulations applied to wake field calculations in two-dimensional cylindrical structures. The scheme involves second-order explicit leap-frogging in time and Fourier spectral approximation in space, which is obtained from simply replacing the spatial differentiation operator of the YEE scheme by the Fourier differentiation operator on nonstaggered grids. This is a first step toward investigating high-order computational techniques with the Fourier spectral method, which is relatively simple to implement.

Lending Policies of Informal, Formal, and Semi-formal Lenders: Evidence from Vietnam

NARCIS (Netherlands)

Lensink, B.W.; Pham, T.T.T.

2007-01-01

This paper compares lending policies of formal, informal and semiformal lenders with respect to household lending in Vietnam. The analysis suggests that the probability of using formal or semiformal credit increases if borrowers provide collateral, a guarantor and/or borrow for business-related

Grazing incidence angle based sensing approach integrated with fiber-optic Fourier transform infrared (FO-FTIR) spectroscopy for remote and label-free detection of medical device contaminations

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.

Numerical Investigation of Vertical Cavity Lasers With High-Contrast Gratings Using the Fourier Modal Method

DEFF Research Database (Denmark)

Taghizadeh, Alireza; Mørk, Jesper; Chung, Il-Sug

2016-01-01

We explore the use of a modal expansion technique, Fourier modal method (FMM), for investigating the optical properties of vertical cavities employing high-contrast gratings (HCGs). Three techniques for determining the resonance frequency and quality factor (Q-factor) of a cavity mode are compared......, the scattering losses of several HCG-based vertical cavities with inplane heterostructures which have promising prospects for fundamental physics studies and on-chip laser applications, are investigated. This type of parametric study of 3D structures would be numerically very demanding using spatial...

Fourier series and orthogonal polynomials

CERN Document Server

Jackson, Dunham

2004-01-01

This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe

Concepciones acerca de la maternidad en la educación formal y no formal

Directory of Open Access Journals (Sweden)

Alvarado Calderón, Kathia

2005-06-01

Full Text Available Este artículo presenta algunos resultados de la investigación desarrollada en el Instituto de Investigación en Educación (INIE, bajo el nombre "Construcción del concepto de maternidad en la educación formal y no formal". Utilizando un enfoque cualitativo de investigación, recurrimos a las técnicas de elaboración de dibujos, entrevistas y grupo focal como recursos para la recolección de la información. De esta manera, podemos acercarnos a las concepciones de la maternidad que utilizan los participantes de las diferentes instancias educativas (formal y no formal con quienes se trabajó. This article presents some results the research developed in the Instituto de Investigación en Educación (INIE, named "Construcción del concepto de maternidad en la educación formal y no formal". It begins with a theoretical analysis about social conceptions regarding motherhood in the occidental societies. Among the techniques for gathering information were thematic drawing, interview and focus group, using a qualitative approach research method. This is followed by a brief summary of main findings. The article concludes with a proposal of future working lines for the deconstruction of the motherhood concept in formal and informal education contexts.

q-Generalization of the inverse Fourier transform

International Nuclear Information System (INIS)

Jauregui, M.; Tsallis, C.

2011-01-01

A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.

Fast Fourier single-pixel imaging via binary illumination.

Science.gov (United States)

Zhang, Zibang; Wang, Xueying; Zheng, Guoan; Zhong, Jingang

2017-09-20

Fourier single-pixel imaging (FSI) employs Fourier basis patterns for encoding spatial information and is capable of reconstructing high-quality two-dimensional and three-dimensional images. Fourier-domain sparsity in natural scenes allows FSI to recover sharp images from undersampled data. The original FSI demonstration, however, requires grayscale Fourier basis patterns for illumination. This requirement imposes a limitation on the imaging speed as digital micro-mirror devices (DMDs) generate grayscale patterns at a low refreshing rate. In this paper, we report a new strategy to increase the speed of FSI by two orders of magnitude. In this strategy, we binarize the Fourier basis patterns based on upsampling and error diffusion dithering. We demonstrate a 20,000 Hz projection rate using a DMD and capture 256-by-256-pixel dynamic scenes at a speed of 10 frames per second. The reported technique substantially accelerates image acquisition speed of FSI. It may find broad imaging applications at wavebands that are not accessible using conventional two-dimensional image sensors.

Electron tomography, three-dimensional Fourier analysis and colour prediction of a three-dimensional amorphous biophotonic nanostructure

Science.gov (United States)

Shawkey, Matthew D.; Saranathan, Vinodkumar; Pálsdóttir, Hildur; Crum, John; Ellisman, Mark H.; Auer, Manfred; Prum, Richard O.

2009-01-01

Organismal colour can be created by selective absorption of light by pigments or light scattering by photonic nanostructures. Photonic nanostructures may vary in refractive index over one, two or three dimensions and may be periodic over large spatial scales or amorphous with short-range order. Theoretical optical analysis of three-dimensional amorphous nanostructures has been challenging because these structures are difficult to describe accurately from conventional two-dimensional electron microscopy alone. Intermediate voltage electron microscopy (IVEM) with tomographic reconstruction adds three-dimensional data by using a high-power electron beam to penetrate and image sections of material sufficiently thick to contain a significant portion of the structure. Here, we use IVEM tomography to characterize a non-iridescent, three-dimensional biophotonic nanostructure: the spongy medullary layer from eastern bluebird Sialia sialis feather barbs. Tomography and three-dimensional Fourier analysis reveal that it is an amorphous, interconnected bicontinuous matrix that is appropriately ordered at local spatial scales in all three dimensions to coherently scatter light. The predicted reflectance spectra from the three-dimensional Fourier analysis are more precise than those predicted by previous two-dimensional Fourier analysis of transmission electron microscopy sections. These results highlight the usefulness, and obstacles, of tomography in the description and analysis of three-dimensional photonic structures. PMID:19158016

Elements of quantum optics

CERN Document Server

Meystre, Pierre

2007-01-01

Elements of Quantum Optics gives a self-contained and broad coverage of the basic elements necessary to understand and carry out research in laser physics and quantum optics, including a review of basic quantum mechanics and pedagogical introductions to system-reservoir interactions and to second quantization. The text reveals the close connection between many seemingly unrelated topics, such as probe absorption, four-wave mixing, optical instabilities, resonance fluorescence and squeezing. It also comprises discussions of cavity quantum electrodynamics and atom optics. The 4th edition includes a new chapter on quantum entanglement and quantum information, as well as added discussions of the quantum beam splitter, electromagnetically induced transparency, slow light, and the input-output formalism needed to understand many problems in quantum optics. It also provides an expanded treatment of the minimum-coupling Hamiltonian and a simple derivation of the Gross-Pitaevskii equation, an important gateway to rese...

Optical pulsation from the HZ Her/Her X-1 system

International Nuclear Information System (INIS)

Chester, T.J.

1977-01-01

A theoretical model for the observed optical pulsation from the x-ray binary HZ Her/Her X-1 is presented. Its foundation is a general computer code for an x-ray illuminated stellar atmosphere. Detailed results are given for several atmospheres applicable to HZ Her. A formalism is developed to calculate the amount of pulsed optical radiation emergent from these atmospheres if they are exposed to pulsed x rays. This formalism is used to calculate the pulsed and unpulsed optical light curves for HZ Her. The calculated optical pulsation agrees with the observed amplitude. A nonuniform x-ray beam can cause the amplitude and velocity of the optical pulsation to vary by more than a factor of two for fixed system parameters. The presence of soft x rays (0.1 to 1 keV) can significantly affect the calculated pulsation amplitude. The model places explicit limits on the system parameters; in particular, if corotation is assumed, 0.8 M/sub sun/ less than or equal to M/sub Her X-1/ less than or equal to 1.7 M/sub sun/

Optimal defocus selection based on normed Fourier transform for digital fringe pattern profilometry.

Science.gov (United States)

Kamagara, Abel; Wang, Xiangzhao; Li, Sikun

2017-10-01

Owing to gamma-effect robustness and high-speed imaging capabilities, projector defocusing of binary-coded fringe patterns is by far the most widely used and effective technique in generating sinusoidal fringe patterns for three-dimensional optical topography measurement with digital fringe projection techniques. However, this technique is not trouble-free. It is borne with uncertainty and challenges mainly because it remains somewhat difficult to quantify and ascertain the level of defocus required for desired fidelity in sinuousness of the projected fringe pattern. Too much or too little defocusing will affect the sinuosity accuracy of fringe patterns and consequently jeopardize the quality of the measurement results. In this paper, by combining intrinsic phase spectral sensitivities and normed Fourier transform, a method to quantify the amount of defocus and subsequently select the optimal degree of sinuosity for generating digital sinusoidal fringe patterns with projector defocusing for fringe pattern optical three-dimensional profilometry is proposed. Numerical simulations plus experiments give evidence of the feasibility and validity of the proposed method in enabling an improved digital binary defocusing technique for optical phase-shift profilometry using the digital fringe projection technique.

Image encryption based on fractal-structured phase mask in fractional Fourier transform domain

Science.gov (United States)

Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-04-01

We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.

Formalized Informal Learning

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....

Double Fourier analysis for Emotion Identification in Voiced Speech

International Nuclear Information System (INIS)

Sierra-Sosa, D.; Bastidas, M.; Ortiz P, D.; Quintero, O.L.

2016-01-01

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented. (paper)

Optical chirp z-transform processor with a simplified architecture.

Science.gov (United States)

Ngo, Nam Quoc

2014-12-29

Using a simplified chirp z-transform (CZT) algorithm based on the discrete-time convolution method, this paper presents the synthesis of a simplified architecture of a reconfigurable optical chirp z-transform (OCZT) processor based on the silica-based planar lightwave circuit (PLC) technology. In the simplified architecture of the reconfigurable OCZT, the required number of optical components is small and there are no waveguide crossings which make fabrication easy. The design of a novel type of optical discrete Fourier transform (ODFT) processor as a special case of the synthesized OCZT is then presented to demonstrate its effectiveness. The designed ODFT can be potentially used as an optical demultiplexer at the receiver of an optical fiber orthogonal frequency division multiplexing (OFDM) transmission system.

The base of the iceberg: informal learning and its impact on formal and non-formal learning

OpenAIRE

Rogers, Alan

2014-01-01

The author looks at learning (formal, non-formal and informal) and examines the hidden world of informal (unconscious, unplanned) learning. He points out the importance of informal learning for creating tacit attitudes and values, knowledge and skills which influence (conscious, planned) learning - formal and non-formal. Moreover, he explores the implications of informal learning for educational planners and teachers in the context of lifelong learning. While mainly aimed at adult educators, ...

Fourier transform and its application to 1D and 2D NMR

International Nuclear Information System (INIS)

Canet, D.

1988-01-01

In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr

Parameterization using Fourier series expansion of the diffuse reflectance of human skin to vary the concentration of the melanocytes

Science.gov (United States)

Narea, J. Freddy; Muñoz, Aarón A.; Castro, Jorge; Muñoz, Rafael A.; Villalba, Caroleny E.; Martinez, María. F.; Bravo, Kelly D.

2013-11-01

Human skin has been studied in numerous investigations, given the interest in knowing information about physiology, morphology and chemical composition. These parameters can be determined using non invasively optical techniques in vivo, such as the diffuse reflectance spectroscopy. The human skin color is determined by many factors, but primarily by the amount and distribution of the pigment melanin. The melanin is produced by the melanocytes in the basal layer of the epidermis. This research characterize the spectral response of the human skin using the coefficients of Fourier series expansion. Simulating the radiative transfer equation for the Monte Carlo method to vary the concentration of the melanocytes (fme) in a simplified model of human skin. It fits relating the Fourier series coefficient a0 with fme. Therefore it is possible to recover the skin biophysical parameter.

Classical optics representation of the quantum mechanical translation operator via ABCD matrices

International Nuclear Information System (INIS)

Ornigotti, Marco; Aiello, Andrea

2013-01-01

The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix formalism presented here and the quantum mechanical translation operator is established. (paper)

A Microfluidic Device with an Integrated Waveguide Beam Splitter for Velocity Measurements of Flowing Particles by Fourier Transformation

DEFF Research Database (Denmark)

Mogensen, Klaus Bo; Kwok, Y.C.; Eijkel, J.C.T.

2003-01-01

A microfabricated capillary electrophoresis device for velocity measurements of flowing particles is presented. It consists of a 1 x 128 planar waveguide beam splitter monolithically integrated with an electrically insulated fluidic channel network for fluorescence excitation at multiple points...... optics. The integrated planar waveguide beam splitter was, furthermore, permanently connected to the light source by a glued-on optical fiber, to achieve a robust and alignment-free operation of the system. The velocity was measured using a Fourier transformation with a Shah function, since the response...... of the fight array was designed to approximate a square profile. Deviations from this response were observed as a result of the multimode nature of the integrated waveguides....

Clifford Fourier transform on vector fields.

Science.gov (United States)

Ebling, Julia; Scheuermann, Gerik

2005-01-01

Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.

Optical bistability without the rotating wave approximation

Energy Technology Data Exchange (ETDEWEB)

Sharaby, Yasser A., E-mail: Yasser_Sharaby@hotmail.co [Physics Department, Faculty of Applied Sciences, Suez Canal University, Suez (Egypt); Joshi, Amitabh, E-mail: ajoshi@eiu.ed [Department of Physics, Eastern Illinois University, Charleston, IL 61920 (United States); Hassan, Shoukry S., E-mail: Shoukryhassan@hotmail.co [Mathematics Department, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain)

2010-04-26

Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.

Optical bistability without the rotating wave approximation

International Nuclear Information System (INIS)

Sharaby, Yasser A.; Joshi, Amitabh; Hassan, Shoukry S.

2010-01-01

Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.

Phase-only SLM Generating Variable Patterns Applied in Optical Connection

International Nuclear Information System (INIS)

Liu, B H; Wu, L Y; Zhang, J

2006-01-01

An adaptive optical communication system is proposed. The system sends spatial information by emitting multiple variable laser beams generated from a programmable diffractive optical element (DOE): phase-only liquid crystal Spatial Light Modulator (SLM). Laser beams carrying signals are programmable by an optimal algorithm based on an iterative Fourier transformation algorithm. The system has the advantage in redundancy of signal by the means of broadcast. It can adaptively seek position and transmit information in parallel

High-resolution and high-throughput multichannel Fourier transform spectrometer with two-dimensional interferogram warping compensation

Science.gov (United States)

Watanabe, A.; Furukawa, H.

2018-04-01

The resolution of multichannel Fourier transform (McFT) spectroscopy is insufficient for many applications despite its extreme advantage of high throughput. We propose an improved configuration to realise both performance using a two-dimensional area sensor. For the spectral resolution, we obtained the interferogram of a larger optical path difference by shifting the area sensor without altering any optical components. The non-linear phase error of the interferometer was successfully corrected using a phase-compensation calculation. Warping compensation was also applied to realise a higher throughput to accumulate the signal between vertical pixels. Our approach significantly improved the resolution and signal-to-noise ratio by factors of 1.7 and 34, respectively. This high-resolution and high-sensitivity McFT spectrometer will be useful for detecting weak light signals such as those in non-invasive diagnosis.

Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

Science.gov (United States)

Hennelly, Bryan M.; Sheridan, John T.

2005-05-01

By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.

Reconstructions in ultrasound modulated optical tomography

KAUST Repository

Allmaras, Moritz; Bangerth, Wolfgang

2011-01-01

We introduce a mathematical model for ultrasound modulated optical tomography and present a simple reconstruction scheme for recovering the spatially varying optical absorption coefficient from scanning measurements with narrowly focused ultrasound signals. Computational results for this model show that the reconstruction of sharp features of the absorption coefficient is possible. A formal linearization of the model leads to an equation with a Fredholm operator, which explains the stability observed in our numerical experiments. © de Gruyter 2011.

Formalized Epistemology, Logic, and Grammar

Science.gov (United States)

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.

Linear ray and wave optics in phase space bridging ray and wave optics via the Wigner phase-space picture

CERN Document Server

Torre, Amalia

2005-01-01

Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner f

SPICA/SAFARI Fourier transform spectrometer mechanism evolutionary design

Science.gov (United States)

van den Dool, Teun C.; Kruizinga, Bob; Braam, Ben C.; Hamelinck, Roger F. M. M.; Loix, Nicolas; Van Loon, Dennis; Dams, Johan

2012-09-01

TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI1 Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme2 in 2022. JAXA3 leads the development of the SPICA satellite and SRON is the prime investigator of the Safari instrument. The FTS scanning mechanism (FTSM) has to meet a 35 mm stroke requirement with an Optical Path Difference resolution of less then 15 nm and must fit in a small volume. It consists of two back-to-back roof-top mirrors mounted on a small carriage, which is moved using a magnetic bearing linear guiding system in combination with a magnetic linear motor serving as the OPD actuator. The FTSM will be used at cryogenic temperatures of 4 Kelvin inducing challenging requirements on the thermal power dissipation and heat leak. The magnetic bearing enables movements over a scanning stroke of 35.5 mm in a small volume. It supports the optics in a free-floating way with no friction, or other non-linearities, with sub-nanometer accuracy. This solution is based on the design of the breadboard ODL (Optical Delay Line) developed for the ESA Darwin mission4 and the MABE mechanism developed by Micromega Dynamics. During the last couple of years the initial design of the SAFARI instrument, as described in an earlier SPIE 2010 paper5, was adapted by the SAFARI team in an evolutionary way to meet the changing requirements of the SPICA payload module. This presentation will focus on the evolution of the FTSM to meet these changing requirements. This work is supported by the Netherlands Space Office (NSO).

Optical theorem, depolarization and vector tomography

International Nuclear Information System (INIS)

Toperverg, B.P.

2003-01-01

A law of the total flux conservation is formulated in the form of the optical theorem. It is employed to explicitly derive equations for the description of the neutron polarization within the range of the direct beam defined by its angular divergence. General considerations are illustrated by calculations using the Born and Eikonal approximations. Results are briefly discussed as applied to Larmor-Fourier tomography

Linear electro-optical properties of tetragonal BaTiO 3

Indian Academy of Sciences (India)

Linear optical susceptibility and clamped linear electro-optical tensor coefficients of tetragonal BaTiO3 are calculated using a formalism based on bond charge theory. Calculated values are in close agreement with experimental data. The covalent Ti–O bonds constituting distorted TiO6 octahedral groups are found to be ...

Indigenous Knowledge and Education from the Quechua Community to School: Beyond the Formal/Non-Formal Dichotomy

Science.gov (United States)

Sumida Huaman, Elizabeth; Valdiviezo, Laura Alicia

2014-01-01

In this article, we propose to approach Indigenous education beyond the formal/non-formal dichotomy. We argue that there is a critical need to conscientiously include Indigenous knowledge in education processes from the school to the community; particularly, when formal systems exclude Indigenous cultures and languages. Based on ethnographic…

New procedure for departure formalities

CERN Multimedia

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...

Harmonic analysis from Fourier to wavelets

CERN Document Server

Pereyra, Maria Cristina

2012-01-01

In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...

Fourier analysis and boundary value problems

CERN Document Server

Gonzalez-Velasco, Enrique A

1996-01-01

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...

Mathematical principles of signal processing Fourier and wavelet analysis

CERN Document Server

Brémaud, Pierre

2002-01-01

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...

Quantum arithmetic with the Quantum Fourier Transform

OpenAIRE

Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos

2014-01-01

The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.

Time-of-flight Fourier spectrometry of UCN

International Nuclear Information System (INIS)

Kulin, G.V.; Frank, A.I.; Goryunov, S.V.; Kustov, D.V.; Geltenbort, P.; Jentshel, M.; Strepetov, A.N.; Bushuev, V.A.

2014-01-01

The results of preliminary experiments on TOF Fourier UCN spectrometry are presented. The description of the new Fourier spectrometer that may be used for the measurement of the UCN spectra arising from diffraction by a moving grating is given. The results of preliminary experiments and Monte Carlo calculations give reason to hope for the success of the planned experiment.

Reducing Approximation Error in the Fourier Flexible Functional Form

Directory of Open Access Journals (Sweden)

Tristan D. Skolrud

2017-12-01

Full Text Available The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.

Concepts of formal concept analysis

Science.gov (United States)

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.

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm

Science.gov (United States)

Zhang, B.; Sang, Jun; Alam, Mohammad S.

2013-03-01

An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.