Time Lens based Optical Fourier Transformation for All-Optical Signal Processing of Spectrally-Efficient Data

DEFF Research Database (Denmark)

Guan, Pengyu; Røge, Kasper Meldgaard; Lillieholm, Mads

2017-01-01

We review recent progress in the use of time lens based optical Fourier transformation for advanced all-optical signal processing. A novel time lens based complete optical Fourier transformation (OFT) technique is introduced. This complete OFT is based on two quadratic phase-modulation stages using...... four-wave mixing (FWM), separated by a dispersive medium, which enables time-to-frequency and frequency-to-time conversions simultaneously, thus performing an exchange between the temporal and spectral profiles of the input signal. Using the proposed complete OFT, several advanced all-optical signal......, such as orthogonal frequency division multiplexing (OFDM), Nyquist wavelength-division multiplexing (Nyquist-WDM) and Nyquist optical time division multiplexing (Nyquist-OTDM) signals....

A Fourier Optical Model for the Laser Doppler Velocimeter

DEFF Research Database (Denmark)

Lading, Lars

1972-01-01

The treatment is based on a fourier optical model. It is shown how the various configurations (i.e. ldquodifferential moderdquo and reference beam mode with both one and two incident beams) are incorporated in the model, and how it can be extended to three dimensions. The particles are represented...... filtering ability vanishes as the aperture size converges towards zero. The results based on fourier optics are compared with the rough estimates obtainable by using the "antenna formular" for heterodyning (ArΩr≈λ2)....

Fourier convergence analysis applied to neutron diffusion Eigenvalue problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2004-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge

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....

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.

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.

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)

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

Applied Fourier analysis from signal processing to medical imaging

CERN Document Server

Olson, Tim

2017-01-01

The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medical i maging, and heat and wave equations. Fo...

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

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.

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.

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.

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.

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...

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...

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...

Applied optics

International Nuclear Information System (INIS)

Orszag, A.; Antonetti, A.

1988-01-01

The 1988 progress report, of the Applied Optics laboratory, of the (Polytechnic School, France), is presented. The optical fiber activities are focused on the development of an optical gyrometer, containing a resonance cavity. The following domains are included, in the research program: the infrared laser physics, the laser sources, the semiconductor physics, the multiple-photon ionization and the nonlinear optics. Investigations on the biomedical, the biological and biophysical domains are carried out. The published papers and the congress communications are listed [fr

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

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.

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...

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.

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.

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...

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)

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.

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...

Simple Fourier optics formalism for high-angular-resolution systems and nulling interferometry.

Science.gov (United States)

Hénault, François

2010-03-01

Reviewed are various designs of advanced, multiaperture optical systems dedicated to high-angular-resolution imaging or to the detection of exoplanets by nulling interferometry. A simple Fourier optics formalism applicable to both imaging arrays and nulling interferometers is presented, allowing their basic theoretical relationships to be derived as convolution or cross-correlation products suitable for fast and accurate computation. Several unusual designs, such as a "superresolving telescope" utilizing a mosaicking observation procedure or a free-flying, axially recombined interferometer are examined, and their performance in terms of imaging and nulling capacity are assessed. In all considered cases, it is found that the limiting parameter is the diameter of the individual telescopes. A final section devoted to nulling interferometry shows an apparent superiority of axial versus multiaxial recombining schemes. The entire study is valid only in the framework of first-order geometrical optics and scalar diffraction theory. Furthermore, it is assumed that all entrance subapertures are optically conjugated with their associated exit pupils.

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

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

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.

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.

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

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.

Applied Optics Golden Anniversary commemorative reviews: introduction.

Science.gov (United States)

Mait, Joseph N; Mendez, Eugenio; Peyghambarian, Nasser; Poon, T-C

2013-01-01

Applied Optics presents three special issues to end its retrospective of Applied Optics' 50 years. The special issues are interference, interferometry, and phase; imaging, optical processing, and telecommunications; and polarization and scattering. The issues, which contain 19 commemorative reviews from some of the journal's luminaries, are summarized.

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.

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

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.

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

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.

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

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.)

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.

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.

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.

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.

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

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

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.

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)

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.

Applied Optics growth: 1991-1999.

Science.gov (United States)

Murray, John R

2012-07-20

A commemorative editorial for the 50th anniversary of Applied Optics describes the journal's growth during the 1990s including internationalization of authors and editors as well as the rise of the Internet.

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.

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 ...

Applied photometry, radiometry, and measurements of optical losses

CERN Document Server

Bukshtab, Michael

2012-01-01

Applied Photometry, Radiometry, and Measurements of Optical Losses reviews and analyzes physical concepts of radiation transfer, providing quantitative foundation for the means of measurements of optical losses, which affect propagation and distribution of light waves in various media and in diverse optical systems and components. The comprehensive analysis of advanced methodologies for low-loss detection is outlined in comparison with the classic photometric and radiometric observations, having a broad range of techniques examined and summarized: from interferometric and calorimetric, resonator and polarization, phase-shift and ring-down decay, wavelength and frequency modulation to pulse separation and resonant, acousto-optic and emissive - subsequently compared to direct and balancing methods for studying free-space and polarization optics, fibers and waveguides. The material is focused on applying optical methods and procedures for evaluation of transparent, reflecting, scattering, absorbing, and aggregat...

The 1989 progress report: applied optics

International Nuclear Information System (INIS)

Antonetti, A.

1989-01-01

The 1989 progress report of the laboratory of Applied Optics of the Polytechnic School (France) is presented. The research programs are carried out in the following fields: Ultrafast Physics, including the development of femtoseconds laser sources and their utilization in Physics, Biology and Physical Chemistry; physics of infrared lasers and their applications in space and industries; Guided Optics, including investigations and construction of fiber optics couplers; biomedical studies on muscle mechanics and laser applications. The published papers, the conferences and the Laboratory staff are listed [fr

Optical high-performance computing: introduction to the JOSA A and Applied Optics feature.

Science.gov (United States)

Caulfield, H John; Dolev, Shlomi; Green, William M J

2009-08-01

The feature issues in both Applied Optics and the Journal of the Optical Society of America A focus on topics of immediate relevance to the community working in the area of optical high-performance computing.

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 Transform Infrared Radiation Spectroscopy Applied for Wood Rot Decay and Mould Fungi Growth Detection

OpenAIRE

Jelle, Bjørn Petter; Hovde, Per Jostein

2012-01-01

Material characterization may be carried out by the attenuated total reflectance (ATR) Fourier transform infrared (FTIR) radiation spectroscopical technique, which represents a powerful experimental tool. The ATR technique may be applied on both solid state materials, liquids, and gases with none or only minor sample preparations, also including materials which are nontransparent to IR radiation. This facilitation is made possible by pressing the sample directly onto various crystals, for exa...

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

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.

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

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.

Characterization of Campylobacter jejuni applying flaA short variable region sequencing, multilocus sequencing and Fourier transform infrared spectroscopy

DEFF Research Database (Denmark)

Josefsen, Mathilde Hartmann; Bonnichsen, Lise; Larsson, Jonas

flaA short variable region sequencing and phenetic Fourier transform infrared (FTIR) spectroscopy was applied on a collection of 102 Campylobacter jejuni isolated from continuous sampling of organic, free range geese and chickens. FTIR has been shown to serve as a valuable tool in typing...

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.

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.

Optical fiber-applied radiation detection system

International Nuclear Information System (INIS)

Nishiura, Ryuichi; Uranaka, Yasuo; Izumi, Nobuyuki

2001-01-01

A technique to measure radiation by using plastic scintillation fibers doped radiation fluorescent (scintillator) to plastic optical fiber for a radiation sensor, was developed. The technique contains some superiority such as high flexibility due to using fibers, relatively easy large area due to detecting portion of whole of fibers, and no electromagnetic noise effect due to optical radiation detection and signal transmission. Measurable to wide range of and continuous radiation distribution along optical fiber cable at a testing portion using scintillation fiber and flight time method, the optical fiber-applied radiation sensing system can effectively monitor space radiation dose or apparatus operation condition monitoring. And, a portable type scintillation optical fiber body surface pollution monitor can measure pollution concentration of radioactive materials attached onto body surface by arranging scintillation fiber processed to a plate with small size and flexibility around a man to be tested. Here were described on outline and fundamental properties of various application products using these plastic scintillation fiber. (G.K.)

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.

Relative-coordinate determination for visual double stars by applying Fourier transforms

Directory of Open Access Journals (Sweden)

Radović Viktor

2013-01-01

Full Text Available We discuss the software developed for the purpose of determining the relative coordinates (position angle θ and separation ρ for visual double or multiple stars. It is based on application of Fourier transforms in treating CCD frames of these systems. The objective was to determine the relative coordinates automatically to an extent as large as possible. In this way the time needed for the reduction of many CCD frames becomes shorter. The capabilities and limitations of the software are examined. Besides, the possibility of improving is also considered. The software has been tested and checked on a sample consisting of CCD frames of 165 double or multiple stars obtained with the 2m telescope at NAO Rozhen in Bulgaria in October 2011. The results have been compared with the corresponding results obtained by applying different software and the agreement is found to be very good.

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.

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)

Validation and qualification of surface-applied fibre optic strain sensors using application-independent optical techniques

International Nuclear Information System (INIS)

Schukar, Vivien G; Kadoke, Daniel; Kusche, Nadine; Münzenberger, Sven; Gründer, Klaus-Peter; Habel, Wolfgang R

2012-01-01

Surface-applied fibre optic strain sensors were investigated using a unique validation facility equipped with application-independent optical reference systems. First, different adhesives for the sensor's application were analysed regarding their material properties. Measurements resulting from conventional measurement techniques, such as thermo-mechanical analysis and dynamic mechanical analysis, were compared with measurements resulting from digital image correlation, which has the advantage of being a non-contact technique. Second, fibre optic strain sensors were applied to test specimens with the selected adhesives. Their strain-transfer mechanism was analysed in comparison with conventional strain gauges. Relative movements between the applied sensor and the test specimen were visualized easily using optical reference methods, digital image correlation and electronic speckle pattern interferometry. Conventional strain gauges showed limited opportunities for an objective strain-transfer analysis because they are also affected by application conditions. (paper)

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

Applied optics and optical design

CERN Document Server

Conrady, Alexander Eugen

1957-01-01

""For the optical engineer it is an indispensable work."" - Journal, Optical Society of America""As a practical guide this book has no rival."" - Transactions, Optical Society""A noteworthy contribution,"" - Nature (London)Part I covers all ordinary ray-tracing methods, together with the complete theory of primary aberrations and as much of higher aberration as is needed for the design of telescopes, low-power microscopes and simple optical systems. Chapters: Fundamental Equations, Spherical Aberration, Physical Aspect of Optical Images, Chromatic Aberration, Design of Achromatic Object-Glass

Joint Applied Optics and Chinese Optics Letters feature introduction: digital holography and three-dimensional imaging

OpenAIRE

Poon, Ting-Chung

2011-01-01

This feature issue serves as a pilot issue promoting the joint issue of Applied Optics and Chinese Optics Letters. It focuses upon topics of current relevance to the community working in the area of digital holography and 3-D imaging. (C) 2011 Optical Society of America

Joint Applied Optics and Chinese Optics Letters feature introduction: digital holography and three-dimensional imaging.

Science.gov (United States)

Poon, Ting-Chung

2011-12-01

This feature issue serves as a pilot issue promoting the joint issue of Applied Optics and Chinese Optics Letters. It focuses upon topics of current relevance to the community working in the area of digital holography and 3-D imaging. © 2011 Optical Society of America

Imaging and applied optics: introduction to the feature issue.

Science.gov (United States)

Zalevsky, Zeev; Arnison, Matthew R; Javidi, Bahram; Testorf, Markus

2018-03-01

This special issue of Applied Optics contains selected papers from OSA's Imaging Congress with particular emphasis on work from mathematics in imaging, computational optical sensing and imaging, imaging systems and applications, and 3D image acquisition and display.

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.

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.

Integrated design course of applied optics focusing on operating and maintaining abilities

Science.gov (United States)

Xu, Zhongjie; Ning, Yu; Jiang, Tian; Cheng, Xiangai

2017-08-01

The abilities of operating and maintaining optical instruments are crucial in modern society. Besides the basic knowledge in optics, the optics courses in the National University of Defense Technology also focus on the training on handling typical optical equipment. As the link between classroom courses on applied optics and the field trips, the integrated design course of applied optics aims to give the students a better understanding on several instantly used optical equipment, such as hand-held telescope and periscope, etc. The basic concepts of optical system design are also emphasized as well. The course is arranged rightly after the classroom course of applied optics and composed of experimental and design tasks. The experimental tasks include the measurements of aberrations and major parameters of a primitive telescope, while in the design parts, the students are asked to design a Keplerian telescope. The whole course gives a deepened understandings on the concepts, assembling, and operating of telescopes. The students are also encouraged to extend their interests on other typical optical instruments.

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

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.

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

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

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.

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.

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%.

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)

Applied optics fundamentals and device applications nano, MOEMS, and biotechnology

CERN Document Server

Mentzer, Mark

2011-01-01

How does the field of optical engineering impact biotechnology? Perhaps for the first time, Applied Optics Fundamentals and Device Applications: Nano, MOEMS, and Biotechnology answers that question directly by integrating coverage of the many disciplines and applications involved in optical engineering, and then examining their applications in nanobiotechnology. Written by a senior U.S. Army research scientist and pioneer in the field of optical engineering, this book addresses the exponential growth in materials, applications, and cross-functional relevance of the many convergent disciplines

Wavelength modulation spectroscopy--digital detection of gas absorption harmonics based on Fourier analysis.

Science.gov (United States)

Mei, Liang; Svanberg, Sune

2015-03-20

This work presents a detailed study of the theoretical aspects of the Fourier analysis method, which has been utilized for gas absorption harmonic detection in wavelength modulation spectroscopy (WMS). The lock-in detection of the harmonic signal is accomplished by studying the phase term of the inverse Fourier transform of the Fourier spectrum that corresponds to the harmonic signal. The mathematics and the corresponding simulation results are given for each procedure when applying the Fourier analysis method. The present work provides a detailed view of the WMS technique when applying the Fourier analysis method.

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...

Efficient formalism for treating tapered structures using the Fourier modal method

DEFF Research Database (Denmark)

Østerkryger, Andreas Dyhl; Gregersen, Niels

2016-01-01

We investigate the development of the mode occupations in tapered structures using the Fourier modal method. In order to use the Fourier modal method, tapered structures are divided into layers of uniform refractive index in the propagation direction and the optical modes are found within each...... layer. This is not very efficient and in this proceeding we take the first steps towards a more efficient formalism for treating tapered structures using the Fourier modal method. We show that the coupling coefficients through the structure are slowly varying and that only the first few modes...

Fourier-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.)

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 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

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.

Fourier Series Formalization in ACL2(r

Directory of Open Access Journals (Sweden)

Cuong K. Chau

2015-09-01

Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.

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.

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.

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…

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.

Intense laser effects on nonlinear optical absorption and optical rectification in single quantum wells under applied electric and magnetic field

International Nuclear Information System (INIS)

Duque, C.A.; Kasapoglu, E.; Sakiroglu, S.; Sari, H.; Soekmen, I.

2011-01-01

In this work the effects of intense laser on the electron-related nonlinear optical absorption and nonlinear optical rectification in GaAs-Ga 1-x Al x As quantum wells are studied under, applied electric and magnetic field. The electric field is applied along the growth direction of the quantum well whereas the magnetic field has been considered to be in-plane. The calculations were performed within the density matrix formalism with the use of the effective mass and parabolic band approximations. The intense laser effects are included through the Floquet method, by modifying the confining potential associated to the heterostructure. Results are presented for the nonlinear optical absorption, the nonlinear optical rectification and the resonant peak of these two optical processes. Several configurations of the dimensions of the quantum well, the applied electric and magnetic fields, and the incident intense laser radiation have been considered. The outcome of the calculation suggests that the nonlinear optical absorption and optical rectification are non-monotonic functions of the dimensions of the heterostructure and of the external perturbations considered in this work.

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.

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 analysis in several complex variables

CERN Document Server

Ehrenpreis, Leon

2006-01-01

Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations.The three-part treatment begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis. Topics include the geometric structure of ideals and modules, quantitative estimates, and examples in which the theory can be applied. The second part focuses on applications to partial differential equations and covers the solution of homogeneous and inh

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....

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.

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.

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.

Applying simulation to optimize plastic molded optical parts

Science.gov (United States)

Jaworski, Matthew; Bakharev, Alexander; Costa, Franco; Friedl, Chris

2012-10-01

Optical injection molded parts are used in many different industries including electronics, consumer, medical and automotive due to their cost and performance advantages compared to alternative materials such as glass. The injection molding process, however, induces elastic (residual stress) and viscoelastic (flow orientation stress) deformation into the molded article which alters the material's refractive index to be anisotropic in different directions. Being able to predict and correct optical performance issues associated with birefringence early in the design phase is a huge competitive advantage. This paper reviews how to apply simulation analysis of the entire molding process to optimize manufacturability and part performance.

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.

Evaluation of Geometrical Modulation Transfer Function in Optical Lens System

Directory of Open Access Journals (Sweden)

Cheng-Mu Tsai

2015-01-01

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

Fast Fourier and discrete wavelet transforms applied to sensorless vector control induction motor for rotor bar faults diagnosis.

Science.gov (United States)

Talhaoui, Hicham; Menacer, Arezki; Kessal, Abdelhalim; Kechida, Ridha

2014-09-01

This paper presents new techniques to evaluate faults in case of broken rotor bars of induction motors. Procedures are applied with closed-loop control. Electrical and mechanical variables are treated using fast Fourier transform (FFT), and discrete wavelet transform (DWT) at start-up and steady state. The wavelet transform has proven to be an excellent mathematical tool for the detection of the faults particularly broken rotor bars type. As a performance, DWT can provide a local representation of the non-stationary current signals for the healthy machine and with fault. For sensorless control, a Luenberger observer is applied; the estimation rotor speed is analyzed; the effect of the faults in the speed pulsation is compensated; a quadratic current appears and used for fault detection. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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.

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.)

Application of velocity filtering to optical-flow passive ranging

Science.gov (United States)

Barniv, Yair

1992-01-01

The performance of the velocity filtering method as applied to optical-flow passive ranging under real-world conditions is evaluated. The theory of the 3-D Fourier transform as applied to constant-speed moving points is reviewed, and the space-domain shift-and-add algorithm is derived from the general 3-D matched filtering formulation. The constant-speed algorithm is then modified to fit the actual speed encountered in the optical flow application, and the passband of that filter is found in terms of depth (sensor/object distance) so as to cover any given range of depths. Two algorithmic solutions for the problems associated with pixel interpolation and object expansion are developed, and experimental results are presented.

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…

Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations

NARCIS (Netherlands)

Bhowmik, S.K.; Stolk, C.C.

2011-01-01

We investigate the application of windowed Fourier frames to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given

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.

Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots

Energy Technology Data Exchange (ETDEWEB)

Cundiff, Steven T. [Univ. of Colorado, Boulder, CO (United States)

2016-05-03

This final report describes the activities undertaken under grant "Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots". The goal of this program was to implement optical 2-dimensional Fourier transform spectroscopy and apply it to electronic excitations, including excitons, in semiconductors. Specifically of interest are quantum wells that exhibit disorder due to well width fluctuations and quantum dots. In both cases, 2-D spectroscopy will provide information regarding coupling among excitonic localization sites.

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.

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.

Fourier diffraction theorem for diffusion-based thermal tomography

International Nuclear Information System (INIS)

Baddour, Natalie

2006-01-01

There has been much recent interest in thermal imaging as a method of non-destructive testing and for non-invasive medical imaging. The basic idea of applying heat or cold to an area and observing the resulting temperature change with an infrared camera has led to the development of rapid and relatively inexpensive inspection systems. However, the main drawback to date has been that such an approach provides mainly qualitative results. In order to advance the quantitative results that are possible via thermal imaging, there is interest in applying techniques and algorithms from conventional tomography. Many tomography algorithms are based on the Fourier diffraction theorem, which is inapplicable to thermal imaging without suitable modification to account for the attenuative nature of thermal waves. In this paper, the Fourier diffraction theorem for thermal tomography is derived and discussed. The intent is for this thermal-diffusion based Fourier diffraction theorem to form the basis of tomographic reconstruction algorithms for quantitative thermal imaging

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.

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

Reflections on 35 years with Applied Optics: outgoing editorial.

Science.gov (United States)

Mait, Joseph N

2014-10-20

Applied Optics' Editor-in-Chief, Joseph N. Mait reflects on his experience as a reader, author, reviewer and eventual editor of the journal. Dr. Mait also introduces the incoming Editor-in-Chief, Ronald G. Driggers and acknowledges outgoing Division Editor, T.-C. Poon.

Improving optical properties of silicon nitride films to be applied in the middle infrared optics by a combined high-power impulse/unbalanced magnetron sputtering deposition technique.

Science.gov (United States)

Liao, Bo-Huei; Hsiao, Chien-Nan

2014-02-01

Silicon nitride films are prepared by a combined high-power impulse/unbalanced magnetron sputtering (HIPIMS/UBMS) deposition technique. Different unbalance coefficients and pulse on/off ratios are applied to improve the optical properties of the silicon nitride films. The refractive indices of the Si3N4 films vary from 2.17 to 2.02 in the wavelength ranges of 400-700 nm, and all the extinction coefficients are smaller than 1×10(-4). The Fourier transform infrared spectroscopy and x-ray diffractometry measurements reveal the amorphous structure of the Si3N4 films with extremely low hydrogen content and very low absorption between the near IR and middle IR ranges. Compared to other deposition techniques, Si3N4 films deposited by the combined HIPIMS/UBMS deposition technique possess the highest refractive index, the lowest extinction coefficient, and excellent structural properties. Finally a four-layer coating is deposited on both sides of a silicon substrate. The average transmittance from 3200 to 4800 nm is 99.0%, and the highest transmittance is 99.97% around 4200 nm.

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.

Fourier-based integration of quasi-periodic gait accelerations for drift-free displacement estimation using inertial sensors.

Science.gov (United States)

Sabatini, Angelo Maria; Ligorio, Gabriele; Mannini, Andrea

2015-11-23

In biomechanical studies Optical Motion Capture Systems (OMCS) are considered the gold standard for determining the orientation and the position (pose) of an object in a global reference frame. However, the use of OMCS can be difficult, which has prompted research on alternative sensing technologies, such as body-worn inertial sensors. We developed a drift-free method to estimate the three-dimensional (3D) displacement of a body part during cyclical motions using body-worn inertial sensors. We performed the Fourier analysis of the stride-by-stride estimates of the linear acceleration, which were obtained by transposing the specific forces measured by the tri-axial accelerometer into the global frame using a quaternion-based orientation estimation algorithm and detecting when each stride began using a gait-segmentation algorithm. The time integration was performed analytically using the Fourier series coefficients; the inverse Fourier series was then taken for reconstructing the displacement over each single stride. The displacement traces were concatenated and spline-interpolated to obtain the entire trace. The method was applied to estimate the motion of the lower trunk of healthy subjects that walked on a treadmill and it was validated using OMCS reference 3D displacement data; different approaches were tested for transposing the measured specific force into the global frame, segmenting the gait and performing time integration (numerically and analytically). The width of the limits of agreements were computed between each tested method and the OMCS reference method for each anatomical direction: Medio-Lateral (ML), VerTical (VT) and Antero-Posterior (AP); using the proposed method, it was observed that the vertical component of displacement (VT) was within ±4 mm (±1.96 standard deviation) of OMCS data and each component of horizontal displacement (ML and AP) was within ±9 mm of OMCS data. Fourier harmonic analysis was applied to model stride-by-stride linear

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

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.

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...

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.

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

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.

Comparative study on γ energy spectrum denoise by fourier and wavelet transforms

International Nuclear Information System (INIS)

Shi Dongsheng; Di Yuming; Zhou Chunlin

2007-01-01

This paper introduces the basic principle of wavelet and Fourier transforms, applies wavelet transform method to denoise γ energy spectrum of 60 Co and compares it with Fourier transform method. The result of simulation with MATLAB software tool showed that as compared with traditional Fourier transform, wavelet transform has comparatively higher accuracy for γ energy spectrum denoising and is more feasible to γ energy spectrum denoising. (authors)

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

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.

Teaching pattern diversification for optics course: motivate interest, open minds and apply flexibly

Science.gov (United States)

Wang, Yunxin; Wang, Dayong; Rong, Lu; Zhao, Jie

2015-10-01

Optics is one of the most important basic courses for college students majoring in Applied Physics in university, which can supply the essential theoretical foundation for the subsequent courses such as Information Optics and Electrodynamics etc.. So Optics course plays a supporting effect in the knowledge frame of the college students. Optics course has its own feature, for one thing, many optical contents cannot be understood directly and easily, for another the optical phenomenon or experiments are interesting and can be displayed intuitively. Considering the above feature, the diversiform teaching patterns are developed to improve the teaching effect. To motivate their interest, students have the chance to visit optical laboratory for both teaching demonstration and science research, and voluntary demonstration of teaching apparatus in class are another approach. Furthermore, digital simulation and experimental design according to the classical knowledge are introduced to the optics course, so students can comprehend and verify the optical principle. Students are encouraged to propose new ideas, and these ideas can be achieved with the help of teachers and the funds support from our university. Besides, some talent students will be invited to join a research group composing by graduate students and teachers. In this group, the students have the chance to touch frontier topics in optics. The diversification of teaching patterns can supply a developing space with the rising gradient for students, which can inspire the interest, open their minds and make them apply flexibly by the participatory and inquiry.

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.

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.

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.

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

Residual Stress Studies Using the Cairo Fourier Diffractometer Facility

International Nuclear Information System (INIS)

Maayouf, R.M.A.; El-Shaer, Y.H.

2002-01-01

The present paper deals with residual stress studies using the Cairo Fourier diffractometer facility CFDF. The CFDF is a reverse - time of -flight (RTOF) diffractometer; applies a Fourier chopper. The measurements were performed for copper samples in order to study the residual stress after welding. The maximum modulation of the Fourier chopper during the measurements was 136 khz; leading to a time resolution half-width of about 7 μ s. It has been found from the present measurements that, the resulting diffraction spectra could be successfully used for studying the residual stress; in the wavelength range between 0.7-2.9 A degree at ∼ 0.45 % relative resolution

Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2005-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique

The fiber optics router apply to the control system of HIRFL-CSR

International Nuclear Information System (INIS)

Zhang Shuocheng; Wang Dan; Jing Lan; Qiao Weimin; Ma Yunhai

2006-01-01

The authors introduced a kind of Fiber Optic Router that we had designed specially applies to the engineering HIRFL-CSR (Heavy Ion Research Facility in Lanzhou). Including design principle, operational principle, and hardware construction, field of application. The router has standard communication interface such as RS232, RS485, Ethernet and Optics; setup of an optical communication network is simplified. It solved problems such as communication disturb. The requirements of control in the national great science engineering HIRFL-CSR are fulfilled. (authors)

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 analysis of temporal NDVI in the Southern African and American continents

NARCIS (Netherlands)

Azzali, S.; Menenti, M.

1996-01-01

Results of applying Fourier analysis of temporal NDVI in southern Africa and southern America are summarized. The decomposition of complex time series of images in simpler periodic components by Fourier analysis allowed the factors that affect the vegetation cover to be analysed much easier. The

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.

SU-E-QI-08: Fourier Properties of Cone Beam CT Projection

International Nuclear Information System (INIS)

Bai, T; Yan, H; Jia, X; Jiang, Steve B.; Mou, X

2014-01-01

Purpose: To explore the Fourier properties of cone beam CT (CBCT) projections and apply the property to directly estimate noise level of CBCT projections without any prior information. Methods: By utilizing the property of Bessel function, we derivate the Fourier properties of the CBCT projections for an arbitrary point object. It is found that there exists a double-wedge shaped region in the Fourier space where the intensity is approximately zero. We further derivate the Fourier properties of independent noise added to CBCT projections. The expectation of the square of the module in any point of the Fourier space is constant and the value approximately equals to noise energy. We further validate the theory in numerical simulations for both a delta function object and a NCAT phantom with different levels of noise added. Results: Our simulation confirmed the existence of the double-wedge shaped region in Fourier domain for the x-ray projection image. The boundary locations of this region agree well with theoretical predictions. In the experiments of estimating noise level, the mean relative error between the theory estimation and the ground truth values is 2.697%. Conclusion: A novel theory on the Fourier properties of CBCT projections has been discovered. Accurate noise level estimation can be achieved by applying this theory directly to the measured CBCT projections. This work was supported in part by NIH(1R01CA154747-01), NSFC((No. 61172163), Research Fund for the Doctoral Program of Higher Education of China (No. 20110201110011) and China Scholarship Council

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

Sets of Fourier coefficients using numerical quadrature

International Nuclear Information System (INIS)

Lyness, J. N.

2001-01-01

One approach to the calculation of Fourier trigonometric coefficients f(r) of a given function f(x) is to apply the trapezoidal quadrature rule to the integral representation f(r)=(line i ntegral)(sub 0)(sup 1) f(x)e(sup -2(pi)irx)dx. Some of the difficulties in this approach are discussed. A possible way of overcoming many of these is by means of a subtraction function. Thus, one sets f(x)= h(sub p-1)(x)+ g(sub p)(x), where h(sub -1)(x) is an algebraic polynomial of degree p-1, specified in such a way that the Fourier series of g(sub p)(x) converges more rapidly than that of f(x). To obtain the Fourier coefficients of f(x), one uses an analytic expression for those of h(sub p-1)(x) and numerical quadrature to approximately those of g(sub p)(x)

Solution of 3-dimensional diffusion equation by finite Fourier transformation

International Nuclear Information System (INIS)

Krishnani, P.D.

1978-01-01

Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)

Optical Fiber-Tip Sensors Based on In-Situ µ-Printed Polymer Suspended-Microbeams.

Science.gov (United States)

Yao, Mian; Ouyang, Xia; Wu, Jushuai; Zhang, A Ping; Tam, Hwa-Yaw; Wai, P K A

2018-06-05

Miniature optical fiber-tip sensors based on directly µ-printed polymer suspended-microbeams are presented. With an in-house optical 3D μ-printing technology, SU-8 suspended-microbeams are fabricated in situ to form Fabry⁻Pérot (FP) micro-interferometers on the end face of standard single-mode optical fiber. Optical reflection spectra of the fabricated FP micro-interferometers are measured and fast Fourier transform is applied to analyze the cavity of micro-interferometers. The applications of the optical fiber-tip sensors for refractive index (RI) sensing and pressure sensing, which showed 917.3 nm/RIU to RI change and 4.29 nm/MPa to pressure change, respectively, are demonstrated in the experiments. The sensors and their optical µ-printing method unveil a new strategy to integrate complicated microcomponents on optical fibers toward 'lab-on-fiber' devices and applications.

Cognition and thinking on Applied Optics course's reformation and innovation

Science.gov (United States)

Chen, Jingjing; Ji, Feng; Liu, Zhijian; Xia, Haojie; Shu, Shuangbao

2017-08-01

The course of "Applied Optics" is professional and foundational for the specialty of photo-electric information and engineering. According to the characteristics of the specialty, the teaching contents, teaching means, innovations and appraisal methods are mainly discussed in this paper. Firstly, one of the most difficult part to comprehend, the Fermat principle is taken as an example in the teaching content. By using the development history of optics and interesting natural phenomenon, students' understanding of the optical knowledge can be enhanced. Secondly, in various means of teaching art, ZEMAX provides students with a platform of training innovative consciousness and engineering capacity, and it make high cohesion in teaching and scientific research. Thirdly, in the teaching innovation, photoelectric contest can stimulate students' innovative thinking, innovation awareness, and cultivate undergraduate students' optics, mechanics, electricity, numerology integrated design capabilities. Lastly, the reform in the appraisal methods guide students from focusing on the examination results to pay attention to the learning process. Eventually, students' study interest has improved, demand of the engineering practice has adapted, and the well teaching effect has realized.

Fourier-based magnetic induction tomography for mapping resistivity

International Nuclear Information System (INIS)

Puwal, Steffan; Roth, Bradley J.

2011-01-01

Magnetic induction tomography is used as an experimental tool for mapping the passive electromagnetic properties of conductors, with the potential for imaging biological tissues. Our numerical approach to solving the inverse problem is to obtain a Fourier expansion of the resistivity and the stream functions of the magnetic fields and eddy current density. Thus, we are able to solve the inverse problem of determining the resistivity from the applied and measured magnetic fields for a two-dimensional conducting plane. When we add noise to the measured magnetic field, we find the fidelity of the measured to the true resistivity is quite robust for increasing levels of noise and increasing distances of the applied and measured field coils from the conducting plane, when properly filtered. We conclude that Fourier methods provide a reliable alternative for solving the inverse problem.

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.

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.

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.

[Apply fourier transform infrared spectra coupled with two-dimensional correlation analysis to study the evolution of humic acids during composting].

Science.gov (United States)

Bu, Gui-jun; Yu, Jing; Di, Hui-hui; Luo, Shi-jia; Zhou, Da-zhai; Xiao, Qiang

2015-02-01

The composition and structure of humic acids formed during composting play an important influence on the quality and mature of compost. In order to explore the composition and evolution mechanism, municipal solid wastes were collected to compost and humic and fulvic acids were obtained from these composted municipal solid wastes. Furthermore, fourier transform infrared spectra and two-dimensional correlation analysis were applied to study the composition and transformation of humic and fulvic acids during composting. The results from fourier transform infrared spectra showed that, the composition of humic acids was complex, and several absorbance peaks were observed at 2917-2924, 2844-2852, 2549, 1662, 1622, 1566, 1454, 1398, 1351, 990-1063, 839 and 711 cm(-1). Compared to humic acids, the composition of fulvci acids was simple, and only three peaks were detected at 1725, 1637 and 990 cm(-1). The appearance of these peaks showed that both humic and fulvic acids comprised the benzene originated from lignin and the polysaccharide. In addition, humic acids comprised a large number of aliphatic and protein which were hardly detected in fulvic acids. Aliphatic, polysaccharide, protein and lignin all were degraded during composting, however, the order of degradation was different between humic and fulvci acids. The result from two-dimensional correlation analysis showed that, organic compounds in humic acids were degraded in the following sequence: aliphatic> protein> polysaccharide and lignin, while that in fulvic acids was as following: protein> polysaccharide and aliphatic. A large number of carboxyl, alcohols and ethers were formed during the degradation process, and the carboxyl was transformed into carbonates. It can be concluded that, fourier transform infrared spectra coupled with two-dimensional correlation analysis not only can analyze the function group composition of humic substances, but also can characterize effectively the degradation sequence of these

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

Measurement of surface temperature and emissivity by a multitemperature method for Fourier-transform infrared spectrometers

DEFF Research Database (Denmark)

Clausen, Sønnik; Morgenstjerne, Axel; Rathmann, Ole

1996-01-01

Surface temperatures are estimated with high precision based on a multitemperature method for Fourier-transform spectrometers. The method is based on Planck's radiation law and a nonlinear least-squares fitting algorithm applied to two or more spectra at different sample temperatures and a single...... of blackbody sources are estimated with an uncertainty of 0.2-2 K. The method is demonstrated for measuring the spectral emissivity of a brass specimen and an oxidized nickel specimen. (C) 1996 Optical Society of America...... measurement at a known sample temperature, for example, at ambient temperature. The temperature of the sample surface can be measured rather easily at ambient temperature. The spectrum at ambient temperature is used to eliminate background effects from spectra as measured at other surface temperatures...

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

Practical protocols for fast histopathology by Fourier transform infrared spectroscopic imaging

Science.gov (United States)

Keith, Frances N.; Reddy, Rohith K.; Bhargava, Rohit

2008-02-01

Fourier transform infrared (FT-IR) spectroscopic imaging is an emerging technique that combines the molecular selectivity of spectroscopy with the spatial specificity of optical microscopy. We demonstrate a new concept in obtaining high fidelity data using commercial array detectors coupled to a microscope and Michelson interferometer. Next, we apply the developed technique to rapidly provide automated histopathologic information for breast cancer. Traditionally, disease diagnoses are based on optical examinations of stained tissue and involve a skilled recognition of morphological patterns of specific cell types (histopathology). Consequently, histopathologic determinations are a time consuming, subjective process with innate intra- and inter-operator variability. Utilizing endogenous molecular contrast inherent in vibrational spectra, specially designed tissue microarrays and pattern recognition of specific biochemical features, we report an integrated algorithm for automated classifications. The developed protocol is objective, statistically significant and, being compatible with current tissue processing procedures, holds potential for routine clinical diagnoses. We first demonstrate that the classification of tissue type (histology) can be accomplished in a manner that is robust and rigorous. Since data quality and classifier performance are linked, we quantify the relationship through our analysis model. Last, we demonstrate the application of the minimum noise fraction (MNF) transform to improve tissue segmentation.

Fourier-based reconstruction via alternating direction total variation minimization in linear scan CT

International Nuclear Information System (INIS)

Cai, Ailong; Wang, Linyuan; Yan, Bin; Zhang, Hanming; Li, Lei; Xi, Xiaoqi; Li, Jianxin

2015-01-01

In this study, we consider a novel form of computed tomography (CT), that is, linear scan CT (LCT), which applies a straight line trajectory. Furthermore, an iterative algorithm is proposed for pseudo-polar Fourier reconstruction through total variation minimization (PPF-TVM). Considering that the sampled Fourier data are distributed in pseudo-polar coordinates, the reconstruction model minimizes the TV of the image subject to the constraint that the estimated 2D Fourier data for the image are consistent with the 1D Fourier transform of the projection data. PPF-TVM employs the alternating direction method (ADM) to develop a robust and efficient iteration scheme, which ensures stable convergence provided that appropriate parameter values are given. In the ADM scheme, PPF-TVM applies the pseudo-polar fast Fourier transform and its adjoint to iterate back and forth between the image and frequency domains. Thus, there is no interpolation in the Fourier domain, which makes the algorithm both fast and accurate. PPF-TVM is particularly useful for limited angle reconstruction in LCT and it appears to be robust against artifacts. The PPF-TVM algorithm was tested with the FORBILD head phantom and real data in comparisons with state-of-the-art algorithms. Simulation studies and real data verification suggest that PPF-TVM can reconstruct higher accuracy images with lower time consumption

A study of optical design and optimization applied to lens module of laser beam shaping of advanced modern optical device

Science.gov (United States)

Tsai, Cheng-Mu; Fang, Yi-Chin; Chen, Zhen Hsiang

2011-10-01

This study used the aspheric lens to realize the laser flat-top optimization, and applied the genetic algorithm (GA) to find the optimal results. Using the characteristics of aspheric lens to obtain the optimized high quality Nd: YAG 355 waveband laser flat-top optical system, this study employed the Light tools LDS (least damped square) and the GA of artificial intelligence optimization method to determine the optimal aspheric coefficient and obtain the optimal solution. This study applied the aspheric lens with GA for the flattening of laser beams using two aspheric lenses in the aspheric surface optical system to complete 80% spot narrowing under standard deviation of 0.6142.

The Fourier analysis applied to the relationship between (7)Be activity in the Serbian atmosphere and meteorological parameters.

Science.gov (United States)

Rajačić, M M; Todorović, D J; Krneta Nikolić, J D; Janković, M M; Djurdjević, V S

2016-09-01

Air sample monitoring in Serbia, Belgrade started in the 1960s, while (7)Be activity in air and total (dry and wet) deposition has been monitored for the last 22 years by the Environment and Radiation Protection Department of the Institute for Nuclear Sciences, Vinca. Using this data collection, the changes of the (7)Be activity in the air and the total (wet and dry) deposition samples, as well as their correlation with meteorological parameters (temperature, pressure, cloudiness, sunshine duration, precipitation and humidity) that affect (7)Be concentration in the atmosphere, were mathematically described using the Fourier analysis. Fourier analysis confirmed the expected; the frequency with the largest intensity in the harmonic spectra of the (7)Be activity corresponds to a period of 1 year, the same as the largest intensity frequency in Fourier series of meteorological parameters. To analyze the quality of the results produced by the Fourier analysis, we compared the measured values of the parameters with the values calculated according to the Fourier series. Absolute deviations between measured and predicted mean monthly values are in range from 0.02 mBq/m(3) to 0.7 mBq/m(3) for (7)Be activity in air, and 0.01 Bq/m(2) and 0.6 Bq/m(2) for (7)Be activity in deposition samples. Relatively good agreement of measured and predicted results offers the possibility of prediction of the (7)Be activity. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modeling and forecasting monthly movement of annual average solar insolation based on the least-squares Fourier-model

International Nuclear Information System (INIS)

Yang, Zong-Chang

2014-01-01

Highlights: • Introduce a finite Fourier-series model for evaluating monthly movement of annual average solar insolation. • Present a forecast method for predicting its movement based on the extended Fourier-series model in the least-squares. • Shown its movement is well described by a low numbers of harmonics with approximately 6-term Fourier series. • Predict its movement most fitting with less than 6-term Fourier series. - Abstract: Solar insolation is one of the most important measurement parameters in many fields. Modeling and forecasting monthly movement of annual average solar insolation is of increasingly importance in areas of engineering, science and economics. In this study, Fourier-analysis employing finite Fourier-series is proposed for evaluating monthly movement of annual average solar insolation and extended in the least-squares for forecasting. The conventional Fourier analysis, which is the most common analysis method in the frequency domain, cannot be directly applied for prediction. Incorporated with the least-square method, the introduced Fourier-series model is extended to predict its movement. The extended Fourier-series forecasting model obtains its optimums Fourier coefficients in the least-square sense based on its previous monthly movements. The proposed method is applied to experiments and yields satisfying results in the different cities (states). It is indicated that monthly movement of annual average solar insolation is well described by a low numbers of harmonics with approximately 6-term Fourier series. The extended Fourier forecasting model predicts the monthly movement of annual average solar insolation most fitting with less than 6-term Fourier series

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...

On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation

International Nuclear Information System (INIS)

Bürger, Steven; Flemming, Jens; Hofmann, Bernd

2016-01-01

Convergence rates results for the Tikhonov regularization of nonlinear ill-posed operator equations are missing, even for a Hilbert space setting, if a range type source condition fails and if moreover nonlinearity conditions of tangential cone type cannot be shown. This situation applies for a deautoconvolution problem in complex-valued L 2 -spaces over finite real intervals, occurring in a slightly generalized version in laser optics. For this problem we show that the lack of applicable convergence rates results can be overcome under the assumption that the solution of the operator equation has a sparse Fourier representation. Precisely, we derive a variational source condition for that case, which implies a convergence rate immediately. The surprising observation is that a sparsity assumption imposed on the solution leads to success, although the used norm square is not known to be a sparsity promoting penalty in the Tikhonov functional. (paper)

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)

Acousto-optic replication of ultrashort laser pulses

Science.gov (United States)

Yushkov, Konstantin B.; Molchanov, Vladimir Ya.; Ovchinnikov, Andrey V.; Chefonov, Oleg V.

2017-10-01

Precisely controlled sequences of ultrashort laser pulses are required in various scientific and engineering applications. We developed a phase-only acousto-optic pulse shaping method for replication of ultrashort laser pulses in a TW laser system. A sequence of several Fourier-transform-limited pulses is generated from a single femtosecond laser pulse by means of applying a piecewise linear phase modulation over the whole emission spectrum. Analysis demonstrates that the main factor which limits maximum delay between the pulse replicas is spectral resolution of the acousto-optic dispersive delay line used for pulse shaping. In experiments with a Cr:forsterite laser system, we obtained delays from 0.3 to 3.5 ps between two replicas of 190 fs transform-limited pulses at the central wavelength of laser emission, 1230 nm.

Fourier analysis in dynamic non periodic phenomena in nuclear medicine

International Nuclear Information System (INIS)

Constantinesco, A.; Lallot, C.

1984-01-01

The success of Fourier analysis in assessing cardiac function has led us to investigate other possible uses of this technique. We show that phase analysis applied to dynamic non periodic activity changes gives useful parametric functional images. The phase image is comparable to a transit time image, the amplitude image is comparable to the maximum variations of activity and the mean image corresponds to a normalized sum of images. Exemples of this powerful application of Fourier analysis are discussed [fr

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.

Solution of two-dimensional diffusion equation for hexagonal cells by the finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

Science.gov (United States)

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Error Analysis for Fourier Methods for Option Pricing

KAUST Repository

Häppölä, Juho

2016-01-06

We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential Levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the Levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.

Application of Fractional Fourier Transform to Moving Target Indication via Along-Track Interferometry

Directory of Open Access Journals (Sweden)

Chiu Shen

2005-01-01

Full Text Available A relatively unknown yet powerful technique, the so-called fractional Fourier transform (FrFT, is applied to SAR along-track interferometry (SAR-ATI in order to estimate moving target parameters. By mapping a target's signal onto a fractional Fourier axis, the FrFT permits a constant-velocity target to be focused in the fractional Fourier domain thereby affording orders of magnitude improvement in SCR. Moving target velocity and position parameters are derived and expressed in terms of an optimum fractional angle and a measured fractional Fourier position , allowing a target to be accurately repositioned and its velocity components computed without actually forming an SAR image. The new estimation algorithm is compared with the matched filter bank approach, showing some of the advantages of the FrFT method. The proposed technique is applied to the data acquired by the two-aperture CV580 airborne radar system configured in its along-track mode. Results show that the method is effective in estimating target velocity and position parameters.

The short time Fourier transform and local signals

Science.gov (United States)

Okumura, Shuhei

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

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...

Fourier-Based Fast Multipole Method for the Helmholtz Equation

KAUST Repository

Cecka, Cris

2013-01-01

The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.

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.

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....

Understanding and applying open-path optical sensing data

Science.gov (United States)

Virag, Peter; Kricks, Robert J.

1999-02-01

During the last 10 years, open-path air monitors have evolved to yield reliable and effective measurements of single and multiple compounds on a real-time basis. To many individuals within the optical remote sensing community, the attributes of open-path and its the potential uses seem unlimited. Then why has the market has been stagnant for the last few years? The reason may center on how open-path information is applied and how well the end user understands that information. We constantly try to compare open-path data to risk/health or safety levels that are based for use at a single point and for a specific averaging period often far longer than a typical open-path data point. Often this approach is perceived as putting a square peg in a round hole. This perception may be well founded, as open-path data at times may need to go through extensive data manipulation and assumptions before it can be applied. This paper will review pervious open-path monitoring programs and their success in applying the data collected. We will also look at how open-path data is being currently used, some previous pitfalls in data use, alternate methods of data interpretation, and how open-path data can be best practically applied to fit current needs.

Multi-Stress Monitoring System with Fiber-Optic Mandrels and Fiber Bragg Grating Sensors in a Sagnac Loop.

Science.gov (United States)

Kim, Hyunjin; Sampath, Umesh; Song, Minho

2015-07-29

Fiber Bragg grating sensors are placed in a fiber-optic Sagnac loop to combine the grating temperature sensors and the fiber-optic mandrel acoustic emission sensors in single optical circuit. A wavelength-scanning fiber-optic laser is used as a common light source for both sensors. A fiber-optic attenuator is placed at a specific position in the Sagnac loop in order to separate buried Bragg wavelengths from the Sagnac interferometer output. The Bragg wavelength shifts are measured with scanning band-pass filter demodulation and the mandrel output is analyzed by applying a fast Fourier transform to the interference signal. This hybrid-scheme could greatly reduce the size and the complexity of optical circuitry and signal processing unit, making it suitable for low cost multi-stress monitoring of large scale power systems.

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.

Binary zone-plate array for a parallel joint transform correlator applied to face recognition.

Science.gov (United States)

Kodate, K; Hashimoto, A; Thapliya, R

1999-05-10

Taking advantage of small aberrations, high efficiency, and compactness, we developed a new, to our knowledge, design procedure for a binary zone-plate array (BZPA) and applied it to a parallel joint transform correlator for the recognition of the human face. Pairs of reference and unknown images of faces are displayed on a liquid-crystal spatial light modulator (SLM), Fourier transformed by the BZPA, intensity recorded on an optically addressable SLM, and inversely Fourier transformed to obtain correlation signals. Consideration of the bandwidth allows the relations among the channel number, the numerical aperture of the zone plates, and the pattern size to be determined. Experimentally a five-channel parallel correlator was implemented and tested successfully with a 100-person database. The design and the fabrication of a 20-channel BZPA for phonetic character recognition are also included.

On sharp estimates of the convergence of double Fourier-Bessel series

Science.gov (United States)

Abilov, V. A.; Abilova, F. V.; Kerimov, M. K.

2017-11-01

The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier-Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier-Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented.

Products of multiple Fourier series with application to the multiblade transformation

Science.gov (United States)

Kunz, D. L.

1981-01-01

A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.

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...

Fourier Transform Infrared Radiation Spectroscopy Applied for Wood Rot Decay and Mould Fungi Growth Detection

Directory of Open Access Journals (Sweden)

Bjørn Petter Jelle

2012-01-01

Full Text Available Material characterization may be carried out by the attenuated total reflectance (ATR Fourier transform infrared (FTIR radiation spectroscopical technique, which represents a powerful experimental tool. The ATR technique may be applied on both solid state materials, liquids, and gases with none or only minor sample preparations, also including materials which are nontransparent to IR radiation. This facilitation is made possible by pressing the sample directly onto various crystals, for example, diamond, with high refractive indices, in a special reflectance setup. Thus ATR saves time and enables the study of materials in a pristine condition, that is, the comprehensive sample preparation by pressing thin KBr pellets in traditional FTIR transmittance spectroscopy is hence avoided. Materials and their ageing processes, both ageing by natural and accelerated climate exposure, decomposition and formation of chemical bonds and products, may be studied in an ATR-FTIR analysis. In this work, the ATR-FTIR technique is utilized to detect wood rot decay and mould fungi growth on various building material substrates. An experimental challenge and aim is to be able to detect the wood rot decay and mould fungi growth at early stages when it is barely visible to the naked eye. Another goal is to be able to distinguish between various species of fungi and wood rot.

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....

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

Accelerated radial Fourier-velocity encoding using compressed sensing

Energy Technology Data Exchange (ETDEWEB)

Hilbert, Fabian; Han, Dietbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wech, Tobias; Koestler, Herbert [Wuerzburg Univ. (Germany). Inst. of Radiology; Wuerzburg Univ. (Germany). Comprehensive Heart Failure Center (CHFC)

2014-10-01

Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity

Accelerated radial Fourier-velocity encoding using compressed sensing

International Nuclear Information System (INIS)

Hilbert, Fabian; Han, Dietbert

2014-01-01

Purpose:Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. Materials and Methods:We imaged the femoral artery of healthy volunteers with ECG - triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Results:Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6 - fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Conclusion: Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity

Accelerated radial Fourier-velocity encoding using compressed sensing.

Science.gov (United States)

Hilbert, Fabian; Wech, Tobias; Hahn, Dietbert; Köstler, Herbert

2014-09-01

Phase Contrast Magnetic Resonance Imaging (MRI) is a tool for non-invasive determination of flow velocities inside blood vessels. Because Phase Contrast MRI only measures a single mean velocity per voxel, it is only applicable to vessels significantly larger than the voxel size. In contrast, Fourier Velocity Encoding measures the entire velocity distribution inside a voxel, but requires a much longer acquisition time. For accurate diagnosis of stenosis in vessels on the scale of spatial resolution, it is important to know the velocity distribution of a voxel. Our aim was to determine velocity distributions with accelerated Fourier Velocity Encoding in an acquisition time required for a conventional Phase Contrast image. We imaged the femoral artery of healthy volunteers with ECG-triggered, radial CINE acquisition. Data acquisition was accelerated by undersampling, while missing data were reconstructed by Compressed Sensing. Velocity spectra of the vessel were evaluated by high resolution Phase Contrast images and compared to spectra from fully sampled and undersampled Fourier Velocity Encoding. By means of undersampling, it was possible to reduce the scan time for Fourier Velocity Encoding to the duration required for a conventional Phase Contrast image. Acquisition time for a fully sampled data set with 12 different Velocity Encodings was 40 min. By applying a 12.6-fold retrospective undersampling, a data set was generated equal to 3:10 min acquisition time, which is similar to a conventional Phase Contrast measurement. Velocity spectra from fully sampled and undersampled Fourier Velocity Encoded images are in good agreement and show the same maximum velocities as compared to velocity maps from Phase Contrast measurements. Compressed Sensing proved to reliably reconstruct Fourier Velocity Encoded data. Our results indicate that Fourier Velocity Encoding allows an accurate determination of the velocity distribution in vessels in the order of the voxel size. Thus

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.

Applied Electronics and Optical Laboratory: an optimized practical course for comprehensive training on optics and electronics

Science.gov (United States)

Wang, Kaiwei; Wang, Xiaoping

2017-08-01

In order to enhance the practical education and hands-on experience of optoelectronics and eliminate the overlapping contents that previously existed in the experiments section adhering to several different courses, a lab course of "Applied Optoelectronics Laboratory" has been established in the College of Optical Science and Engineering, Zhejiang University. The course consists of two sections, i.e., basic experiments and project design. In section 1, basic experiments provide hands-on experience with most of the fundamental concept taught in the corresponding courses. These basic experiments including the study of common light sources such as He-Ne laser, semiconductor laser and solid laser and LED; the testing and analysis of optical detectors based on effects of photovoltaic effect, photoconduction effect, photo emissive effect and array detectors. In section 2, the course encourages students to build a team and establish a stand-alone optical system to realize specific function by taking advantage of the basic knowledge learned from section 1. Through these measures, students acquired both basic knowledge and the practical application skills. Moreover, interest in science has been developed among students.

Fourier transformation methods in the field of gamma spectrometry

Indian Academy of Sciences (India)

The basic principles of a new version of Fourier transformation is presented. This new version was applied to solve some main problems such as smoothing, and denoising in gamma spectroscopy. The mathematical procedures were first tested by simulated data and then by actual experimental data.

Prototypes and matrix relevance learning in complex fourier space

NARCIS (Netherlands)

Straat, M.; Kaden, M.; Gay, M.; Villmann, T.; Lampe, Alexander; Seiffert, U.; Biehl, M.; Melchert, F.

2017-01-01

In this contribution, we consider the classification of time-series and similar functional data which can be represented in complex Fourier coefficient space. We apply versions of Learning Vector Quantization (LVQ) which are suitable for complex-valued data, based on the so-called Wirtinger

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.

Multiconjugate adaptive optics applied to an anatomically accurate human eye model

Science.gov (United States)

Bedggood, P. A.; Ashman, R.; Smith, G.; Metha, A. B.

2006-09-01

Aberrations of both astronomical telescopes and the human eye can be successfully corrected with conventional adaptive optics. This produces diffraction-limited imagery over a limited field of view called the isoplanatic patch. A new technique, known as multiconjugate adaptive optics, has been developed recently in astronomy to increase the size of this patch. The key is to model atmospheric turbulence as several flat, discrete layers. A human eye, however, has several curved, aspheric surfaces and a gradient index lens, complicating the task of correcting aberrations over a wide field of view. Here we utilize a computer model to determine the degree to which this technology may be applied to generate high resolution, wide-field retinal images, and discuss the considerations necessary for optimal use with the eye. The Liou and Brennan schematic eye simulates the aspheric surfaces and gradient index lens of real human eyes. We show that the size of the isoplanatic patch of the human eye is significantly increased through multiconjugate adaptive optics.

Multiconjugate adaptive optics applied to an anatomically accurate human eye model.

Science.gov (United States)

Bedggood, P A; Ashman, R; Smith, G; Metha, A B

2006-09-04

Aberrations of both astronomical telescopes and the human eye can be successfully corrected with conventional adaptive optics. This produces diffraction-limited imagery over a limited field of view called the isoplanatic patch. A new technique, known as multiconjugate adaptive optics, has been developed recently in astronomy to increase the size of this patch. The key is to model atmospheric turbulence as several flat, discrete layers. A human eye, however, has several curved, aspheric surfaces and a gradient index lens, complicating the task of correcting aberrations over a wide field of view. Here we utilize a computer model to determine the degree to which this technology may be applied to generate high resolution, wide-field retinal images, and discuss the considerations necessary for optimal use with the eye. The Liou and Brennan schematic eye simulates the aspheric surfaces and gradient index lens of real human eyes. We show that the size of the isoplanatic patch of the human eye is significantly increased through multiconjugate adaptive optics.

Non-Fourier heat conduction and phase transition in laser ablation of polytetrafluoroethylene (PTFE)

Science.gov (United States)

Zhang, Yu; Zhang, Daixian; Wu, Jianjun; Li, Jian; He, Zhaofu

2017-11-01

The phase transition in heat conduction of polytetrafluoroethylene-like polymers was investigated and applied in many fields of science and engineering. Considering more details including internal absorption of laser radiation, reflectivity of material and non-Fourier effect etc., the combined heat conduction and phase transition in laser ablation of polytetrafluoroethylene were modeled and investigated numerically. The thermal and mechanic issues in laser ablation were illustrated and analyzed. Especially, the phenomenon of temperature discontinuity formed in the combined phase transition and non-Fourier heat conduction was discussed. Comparisons of target temperature profiles between Fourier and non-Fourier heat conduction in melting process were implemented. It was indicated that the effect of non-Fourier plays an important role in the temperature evolvement. The effect of laser fluence was proven to be significant and the thermal wave propagation was independent on the laser intensity for the non-Fourier heat conduction. Besides, the effect of absorption coefficients on temperature evolvements was studied. For different ranges of absorption coefficients, different temperature evolvements can be achieved. The above numerical simulation provided insight into physical processes of combined non-Fourier heat conduction and phase transition in laser ablation.

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

New significance test methods for Fourier analysis of geophysical time series

Directory of Open Access Journals (Sweden)

Z. Zhang

2011-09-01

Full Text Available When one applies the discrete Fourier transform to analyze finite-length time series, discontinuities at the data boundaries will distort its Fourier power spectrum. In this paper, based on a rigid statistics framework, we present a new significance test method which can extract the intrinsic feature of a geophysical time series very well. We show the difference in significance level compared with traditional Fourier tests by analyzing the Arctic Oscillation (AO and the Nino3.4 time series. In the AO, we find significant peaks at about 2.8, 4.3, and 5.7 yr periods and in Nino3.4 at about 12 yr period in tests against red noise. These peaks are not significant in traditional tests.

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.

Effects of illumination on image reconstruction via Fourier ptychography

Science.gov (United States)

Cao, Xinrui; Sinzinger, Stefan

2017-12-01

The Fourier ptychographic microscopy (FPM) technique provides high-resolution images by combining a traditional imaging system, e.g. a microscope or a 4f-imaging system, with a multiplexing illumination system, e.g. an LED array and numerical image processing for enhanced image reconstruction. In order to numerically combine images that are captured under varying illumination angles, an iterative phase-retrieval algorithm is often applied. However, in practice, the performance of the FPM algorithm degrades due to the imperfections of the optical system, the image noise caused by the camera, etc. To eliminate the influence of the aberrations of the imaging system, an embedded pupil function recovery (EPRY)-FPM algorithm has been proposed [Opt. Express 22, 4960-4972 (2014)]. In this paper, we study how the performance of FPM and EPRY-FPM algorithms are affected by imperfections of the illumination system using both numerical simulations and experiments. The investigated imperfections include varying and non-uniform intensities, and wavefront aberrations. Our study shows that the aberrations of the illumination system significantly affect the performance of both FPM and EPRY-FPM algorithms. Hence, in practice, aberrations in the illumination system gain significant influence on the resulting image quality.

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.

The PROSAIC Laplace and Fourier Transform

International Nuclear Information System (INIS)

Smith, G.A.

1994-01-01

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting

Deconvolution of H-alpha profiles measured by Thompson scattering collecting optics

International Nuclear Information System (INIS)

LeBlanc, B.; Grek, B.

1986-01-01

This paper discusses that optically fast multichannel Thomson scattering optics that can be used for H-alpha emission profile measurement. A technique based on the fact that a particular volume element of the overall field of view can be seen by many channels, depending on its location, is discussed. It is applied to measurement made on PDX with the vertically viewing TVTS collecting optics (56 channels). The authors found that for this case, about 28 Fourier modes are optimum to represent the spatial behavior of the plasma emissivity. The coefficients for these modes are obtained by doing a least-square-fit to the data subjet to certain constraints. The important constraints are non-negative emissivity, the assumed up and down symmetry and zero emissivity beyond the liners. H-alpha deconvolutions are presented for diverted and circular discharges

Fourier acceleration of iterative processes in disordered systems

International Nuclear Information System (INIS)

Batrouni, G.G.; Hansen, A.

1988-01-01

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria

Fourier transform resampling: Theory and application

International Nuclear Information System (INIS)

Hawkins, W.G.

1996-01-01

One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF's were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF's were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm)

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.

Nonlinear optical rectification in semiparabolic quantum wells with an applied electric field

International Nuclear Information System (INIS)

Karabulut, ibrahim; Safak, Haluk

2005-01-01

The optical rectification (OR) in a semiparabolic quantum well with an applied electric field has been theoretically investigated. The electronic states in a semiparabolic quantum well with an applied electric field are calculated exactly, within the envelope function and the displaced harmonic oscillator approach. Numerical results are presented for the typical Al x Ga 1- x As/GaAs quantum well. These results show that the applied electric field and the confining potential frequency of the semiparabolic quantum well have a great influence on the OR coefficient. Moreover, the OR coefficient also depends sensitively on the relaxation rate of the semiparabolic quantum well system

Study on time-varying velocity measurement with self-mixing laser diode based on Discrete Chirp-Fourier Transform

International Nuclear Information System (INIS)

Zhang Zhaoyun; Gao Yang; Zhao Xinghai; Zhao Xiang

2011-01-01

Laser's optical output power and frequency are modulated when the optical beam is back-scattered into the active cavity of the laser. By signal processing, the Doppler frequency can be acquired, and the target's velocity can be calculated. Based on these properties, an interferometry velocity sensor can be designed. When target move in time-varying velocity mode, it is difficult to extract the target's velocity. Time-varying velocity measurement by self-mixing laser diode is explored. A mathematics model was proposed for the time-varying velocity (invariable acceleration) measurement by self-mixing laser diode. Based on this model, a Discrete Chirp-Fourier Transform (DCFT) method was applied, DCFT is analogous to DFT. We show that when the signal length N is prime, the magnitudes of all the side lobes are 1, whereas the magnitudes of the main lobe is √N, And the coordinates of the main lobe shows the target's velocity and acceleration information. The simulation results prove the validity of the algorithm even in the situation of low SNR when N is prime.

Fringe pattern analysis for optical metrology theory, algorithms, and applications

CERN Document Server

Servin, Manuel; Padilla, Moises

2014-01-01

The main objective of this book is to present the basic theoretical principles and practical applications for the classical interferometric techniques and the most advanced methods in the field of modern fringe pattern analysis applied to optical metrology. A major novelty of this work is the presentation of a unified theoretical framework based on the Fourier description of phase shifting interferometry using the Frequency Transfer Function (FTF) along with the theory of Stochastic Process for the straightforward analysis and synthesis of phase shifting algorithms with desired properties such

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.

Conception and development of an optical methodology applied to long-distance measurement of suspension bridges dynamic displacement

International Nuclear Information System (INIS)

Martins, L Lages; Ribeiro, A Silva; Rebordão, J M

2013-01-01

This paper describes the conception and development of an optical system applied to suspension bridge structural monitoring, aiming real-time and long-distance measurement of dynamical three-dimensional displacement, namely, in the central section of the main span. The main innovative issues related to this optical approach are described and a comparison with other optical and non-optical measurement systems is performed. Moreover, a computational simulator tool developed for the optical system design and validation of the implemented image processing and calculation algorithms is also presented

1st International Conference on Opto-Electronics and Applied Optics

CERN Document Server

Bhattacharya, Indrani

2015-01-01

The Proceedings of First International Conference on Opto-Electronics and Applied Optics 2014, IEM OPTRONIX 2014 presents the research contributions presented in the conference by researchers from both India and abroad. Contributions from established scientists as well as students are included. The book is organized to enable easy access to various topics of interest.   The first part includes the Keynote addresses by Phillip Russell, Max Planck Institute of the Light Sciences, Erlangen, Germany and Lorenzo Pavesi, University of Trento, Italy.   The second part focuses on the Plenary Talks given by eminent scientists, namely, Azizur Rahman, City University London, London; Bishnu Pal, President, The Optical Society of India; Kamakhya Ghatak, National Institute of Technology, Agartala; Kehar Singh, Former Professor, India Institute of Technology Delhi; Mourad Zghal, SUPCOM, University of Carthage, Tunisia; Partha Roy Chaudhuri, IIT Kharagpur; S K. Bhadra, CSIR-Central Glass and Ceramic Research Institute, Kol...

Optical diffraction tomography in an inhomogeneous background medium

International Nuclear Information System (INIS)

Devaney, A; Cheng, J

2008-01-01

The filtered back-propagation algorithm (FBP algorithm) is a computationally fast and efficient inversion algorithm for reconstructing the 3D index of refraction distribution of weak scattering samples in free space from scattered field data collected in a set of coherent optical scattering experiments. This algorithm is readily derived using classical Fourier analysis applied to the Born or Rytov weak scattering models appropriate to scatterers embedded in a non-attenuating uniform background. In this paper, the inverse scattering problem for optical diffraction tomography (ODT) is formulated using the so-called distorted wave Born and Rytov approximations and a generalized version of the FBP algorithm is derived that applies to weakly scattering samples that are embedded in realistic, multiple scattering ODT experimental configurations. The new algorithms are based on the generalized linear inverse of the linear transformation relating the scattered field data to the complex index of refraction distribution of the scattering samples and are in the form of a superposition of filtered data, computationally back propagated into the ODT experimental configuration. The paper includes a computer simulation comparing the generalized Born and Rytov based FBP inversion algorithms as well as reconstructions generated using the generalized Born based FBP algorithm of a step index optical fiber from experimental ODT data

Fourier descriptors analysis of anisotropy and preferred Orientation in geological samples

International Nuclear Information System (INIS)

Santiago Buey, C. de

2011-01-01

This study focuses on the use of Fourier descriptors to evaluate and quantify two specific fabric characteristics of geological materials: anisotropy of particles or voids morphologies and particle orientation. To this end, a theoretical section of a rock was created, made of ellipses and rectangles of different axes ratios and different orientations. The Fourier descriptors method was applied to calculate the anisotropy and orientation of each particle and, finally, a rose diagram was constructed to represent the particles orientations distribution and to observe the presence or not of any preferred orientation. (Author) 15 refs.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

Science.gov (United States)

Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.

2012-01-01

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

Digital Holography and 3D Imaging: introduction to the joint feature issue in Applied Optics and Journal of the Optical Society of America A.

Science.gov (United States)

Kang, Hoonjong; Lee, Byoungho; Kozacki, Tomasz; Picart, Pascal; Situ, Guohai

2018-01-01

The OSA Topical Meeting on Digital Holography and 3D Imaging (DH) was held 29 May to 1 June 2017 in Jeju Island, South Korea. Feature issues based on the DH meeting series have been released by Applied Optics (AO) since 2007. This year, AO and the Journal of the Optical Society of America A (JOSA A) jointly decided to have one such feature issue in each journal. This feature issue includes 33 papers in AO and 9 in JOSA A and covers a large range of topics, reflecting the rapidly expanding techniques and applications of digital holography and 3D imaging. The upcoming DH meeting (DH 2018) will be held 25-28 June 2018 in Orlando, Florida, USA, as part of the OSA Imaging and Applied Optics Congress.

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.

Photoacoustic spectroscopy applied to the optical characterization of calcium phosphates for biomedical use

Energy Technology Data Exchange (ETDEWEB)

Mendez G, M. [ESFM-IPN, 07738 Mexico D.F. (Mexico); Cruz O, A. [CINVESTAV, Dept. of Physics, 07360 Mexico D.F. (Mexico)

2007-07-01

Full text: Photoacoustic Spectroscopy (PAS), based on the Rosencwaig and Gersho model, has been used for thermal and optical characterization of diverse materials. The use of PAS has become an important tool because is a nondestructive and no contact analytical technique. Furthermore its use to measure optical absorption spectra has advantages over the usual transmission measurements due to important features as the fact that scattered light does not disturb the measurements significantly and also the sample don't need to be prepared to have good quality surfaces. Then the optical properties of biological samples can be easily investigated with this technique. In the present study PAS is applied to obtain the optical absorption spectra of hydroxyapatite (HAp) [Ca{sub 10} (PO{sub 4} ){sub 6} (OH ){sub 2}] and bioactive calcium phosphates. The spectra of these samples ranged from 300 to 800 nm. All samples were prepared in a power form with particle size < 741m. Complementary studies X-ray diffraction and EDC were performed. (Author)

Optical tweezers with 2.5 kHz bandwidth video detection for single-colloid electrophoresis

Science.gov (United States)

Otto, Oliver; Gutsche, Christof; Kremer, Friedrich; Keyser, Ulrich F.

2008-02-01

We developed an optical tweezers setup to study the electrophoretic motion of colloids in an external electric field. The setup is based on standard components for illumination and video detection. Our video based optical tracking of the colloid motion has a time resolution of 0.2ms, resulting in a bandwidth of 2.5kHz. This enables calibration of the optical tweezers by Brownian motion without applying a quadrant photodetector. We demonstrate that our system has a spatial resolution of 0.5nm and a force sensitivity of 20fN using a Fourier algorithm to detect periodic oscillations of the trapped colloid caused by an external ac field. The electrophoretic mobility and zeta potential of a single colloid can be extracted in aqueous solution avoiding screening effects common for usual bulk measurements.

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

Maximum-entropy data restoration using both real- and Fourier-space analysis

International Nuclear Information System (INIS)

Anderson, D.M.; Martin, D.C.; Thomas, E.L.

1989-01-01

An extension of the maximum-entropy (ME) data-restoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-noise ratio for periodic information in Fourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier filtering. This procedure incorporates concepts underlying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introduced that speeds convergence of the ME computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases improvement can be obtained from two to four stages of iteration. It is shown that in traditional Fourier filtering spurious features can be induced by selection or elimination of Fourier components without regard to their statistical significance. With the present approach there is no such freedom for the user to exert personal bias, so that features present in the final image and power spectrum are those which have survived the tests of statistical significance in both real and Fourier space. However, it is still possible for periodicities to 'bleed' across sharp boundaries. An 'uncertainty' relation is derived describing the inverse relationship between the resolution of these boundaries and the level of noise that can be eliminated. (orig./BHO)

The Fractional Fourier Transform and Its Application to Energy Localization Problems

Directory of Open Access Journals (Sweden)

ter Morsche Hennie G

2003-01-01

Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.

MULTI-CORE AND OPTICAL PROCESSOR RELATED APPLICATIONS RESEARCH AT OAK RIDGE NATIONAL LABORATORY

Energy Technology Data Exchange (ETDEWEB)

Barhen, Jacob [ORNL; Kerekes, Ryan A [ORNL; ST Charles, Jesse Lee [ORNL; Buckner, Mark A [ORNL

2008-01-01

High-speed parallelization of common tasks holds great promise as a low-risk approach to achieving the significant increases in signal processing and computational performance required for next generation innovations in reconfigurable radio systems. Researchers at the Oak Ridge National Laboratory have been working on exploiting the parallelization offered by this emerging technology and applying it to a variety of problems. This paper will highlight recent experience with four different parallel processors applied to signal processing tasks that are directly relevant to signal processing required for SDR/CR waveforms. The first is the EnLight Optical Core Processor applied to matched filter (MF) correlation processing via fast Fourier transform (FFT) of broadband Dopplersensitive waveforms (DSW) using active sonar arrays for target tracking. The second is the IBM CELL Broadband Engine applied to 2-D discrete Fourier transform (DFT) kernel for image processing and frequency domain processing. And the third is the NVIDIA graphical processor applied to document feature clustering. EnLight Optical Core Processor. Optical processing is inherently capable of high-parallelism that can be translated to very high performance, low power dissipation computing. The EnLight 256 is a small form factor signal processing chip (5x5 cm2) with a digital optical core that is being developed by an Israeli startup company. As part of its evaluation of foreign technology, ORNL's Center for Engineering Science Advanced Research (CESAR) had access to a precursor EnLight 64 Alpha hardware for a preliminary assessment of capabilities in terms of large Fourier transforms for matched filter banks and on applications related to Doppler-sensitive waveforms. This processor is optimized for array operations, which it performs in fixed-point arithmetic at the rate of 16 TeraOPS at 8-bit precision. This is approximately 1000 times faster than the fastest DSP available today. The optical core

MULTI-CORE AND OPTICAL PROCESSOR RELATED APPLICATIONS RESEARCH AT OAK RIDGE NATIONAL LABORATORY

International Nuclear Information System (INIS)

Barhen, Jacob; Kerekes, Ryan A.; St Charles, Jesse Lee; Buckner, Mark A.

2008-01-01

High-speed parallelization of common tasks holds great promise as a low-risk approach to achieving the significant increases in signal processing and computational performance required for next generation innovations in reconfigurable radio systems. Researchers at the Oak Ridge National Laboratory have been working on exploiting the parallelization offered by this emerging technology and applying it to a variety of problems. This paper will highlight recent experience with four different parallel processors applied to signal processing tasks that are directly relevant to signal processing required for SDR/CR waveforms. The first is the EnLight Optical Core Processor applied to matched filter (MF) correlation processing via fast Fourier transform (FFT) of broadband Dopplersensitive waveforms (DSW) using active sonar arrays for target tracking. The second is the IBM CELL Broadband Engine applied to 2-D discrete Fourier transform (DFT) kernel for image processing and frequency domain processing. And the third is the NVIDIA graphical processor applied to document feature clustering. EnLight Optical Core Processor. Optical processing is inherently capable of high-parallelism that can be translated to very high performance, low power dissipation computing. The EnLight 256 is a small form factor signal processing chip (5x5 cm2) with a digital optical core that is being developed by an Israeli startup company. As part of its evaluation of foreign technology, ORNL's Center for Engineering Science Advanced Research (CESAR) had access to a precursor EnLight 64 Alpha hardware for a preliminary assessment of capabilities in terms of large Fourier transforms for matched filter banks and on applications related to Doppler-sensitive waveforms. This processor is optimized for array operations, which it performs in fixed-point arithmetic at the rate of 16 TeraOPS at 8-bit precision. This is approximately 1000 times faster than the fastest DSP available today. The optical core

Optimization of the segmented method for optical compression and multiplexing system

Science.gov (United States)

Al Falou, Ayman

2002-05-01

Because of the constant increasing demands of images exchange, and despite the ever increasing bandwidth of the networks, compression and multiplexing of images is becoming inseparable from their generation and display. For high resolution real time motion pictures, electronic performing of compression requires complex and time-consuming processing units. On the contrary, by its inherent bi-dimensional character, coherent optics is well fitted to perform such processes that are basically bi-dimensional data handling in the Fourier domain. Additionally, the main limiting factor that was the maximum frame rate is vanishing because of the recent improvement of spatial light modulator technology. The purpose of this communication is to benefit from recent optical correlation algorithms. The segmented filtering used to store multi-references in a given space bandwidth product optical filter can be applied to networks to compress and multiplex images in a given bandwidth channel.

3rd International Conference on Opto-Electronics and Applied Optics

CERN Document Server

Chakrabarti, Satyajit; Reehal, Haricharan; Lakshminarayanan, Vasudevan

2017-01-01

The Proceedings of 3rd International Conference on Opto-Electronics and Applied Optics, OPTRONIX 2016 is an effort to promote and present the research works by scientists and researchers including students in India and abroad in the area of Green Photonics and other related areas as well as to raise awareness about the recent trends of research and development in the area of the related fields. The book has been organized in such a way that it will be easier for the readers to go through and find out the topic of their interests. The first part includes the Keynote addresses by Rajesh Gupta, Department of Energy Science and Engineering, Indian Institute of Technology, Bombay; P.T. Ajith Kumar, President and Leading Scientist Light Logics Holography and Optics, Crescent Hill, Trivandrum, Kerala; and K.K. Ghosh, Institute of Engineering & Management, Kolkata, India.  The second part focuses on the Plenary and Invited Talks given by eminent scientists namely, Vasudevan Lakshminarayanan, University of Wate...

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)

Horn–Schunck optical flow applied to deformation measurement of a birdlike airfoil

Directory of Open Access Journals (Sweden)

Gong Xiaoliang

2015-10-01

Full Text Available Current deformation measurement techniques suffer from limited spatial resolution. In this work, a highly accurate and high-resolution Horn–Schunck optical flow method is developed and then applied to measuring the static deformation of a birdlike flexible airfoil at a series of angles of attack at Reynolds number 100,000 in a low speed, low noise wind tunnel. To allow relatively large displacements, a nonlinear Horn–Schunck model and a coarse-to-fine warping process are adopted. To preserve optical flow discontinuities, a nonquadratic penalization function, a multi-cue driven bilateral filtering and a principle component analysis of local image patterns are used. First, the accuracy and convergence of this Horn–Schunck technique are verified on a benchmark. Then, the maximum displacement that can be reliably calculated by this technique is studied on synthetic images. Both studies are compared with the performance of a Lucas–Kanade optical flow method. Finally, the Horn–Schunck technique is used to estimate the 3-D deformation of the birdlike airfoil through a stereoscopic camera setup. The results are compared with those computed by Lucas–Kanade optical flow, image correlation and numerical simulation.

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.

Fourier acceleration in lattice gauge theories. I. Landau gauge fixing

International Nuclear Information System (INIS)

Davies, C.T.H.; Batrouni, G.G.; Katz, G.R.; Kronfeld, A.S.; Lepage, G.P.; Wilson, K.G.; Rossi, P.; Svetitsky, B.

1988-01-01

Fourier acceleration is a useful technique which can be applied to many different numerical algorithms in order to alleviate the problem of critical slowing down. Here we describe its application to an optimization problem in the simulation of lattice gauge theories, that of gauge fixing a configuration of link fields to the Landau gauge (partial/sub μ/A/sup μ/ = 0). We find that a steepest-descents method of gauge fixing link fields at β = 5.8 on an 8 4 lattice can be made 5 times faster using Fourier acceleration. This factor will grow as the volume of the lattice is increased. We also discuss other gauges that are useful to lattice-gauge-theory simulations, among them one that is a combination of the axial and Landau gauges. This seems to be the optimal gauge to impose for the Fourier acceleration of two other important algorithms, the inversion of the fermion matrix and the updating of gauge field configurations

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)

The prosaic Laplace and Fourier transform

International Nuclear Information System (INIS)

Smith, G.A.

1995-01-01

Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics

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

Swept source optical coherence tomography of objects with arbitrary reflectivity profiles

Science.gov (United States)

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

2018-03-01

Swept Source optical coherence tomography (SS-OCT) has become a well established 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 interferogram measured in the frequency domain (k-space). Fourier inversion of the obtained interferogram typically produces a potentially overlapping conjugate mirror image, whose overlap could be avoided by restricting the object to have its highest reflectivity at its surface. However, this restriction may not be fulfilled when imaging a very thin object that is placed on a highly reflective surface, or imaging an object containing a contrast agent with high reflectivity. In this paper, we show that oversampling of the SS-OCT signal in k-space would overcome the need for such restriction on the object. Our result is demonstrated using SS-OCT images of Axolotl salamander eggs.

Effects of applied electromagnetic fields on the linear and nonlinear optical properties in an inverse parabolic quantum well

International Nuclear Information System (INIS)

Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sökmen, I.

2012-01-01

In this present work, we have investigated theoretically the effects of applied electric and magnetic fields on the linear and nonlinear optical properties in a GaAs/Al x Ga 1−x As inverse parabolic quantum well for different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The energy levels and wave functions are calculated within the effective mass approximation and the envelope function approach. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The linear, third-order nonlinear and total absorption and refractive index changes depending on the Al concentration at the well center are investigated as a function of the incident photon energy for the different values of the applied electric and magnetic fields. The results show that the applied electric and magnetic fields have a great effect on these optical quantities. - Highlights: ► The x c concentration has a great effect on the optical characteristics of these structures. ► The EM fields have a great effect on the optical properties of these structures. ► The total absorption coefficients increased as the electric and magnetic field increases. ► The RICs reduced as the electric and magnetic field increases.

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.

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.

Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

Science.gov (United States)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

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)

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.

Reduction and coding of synthetic aperture radar data with Fourier transforms

Science.gov (United States)

Tilley, David G.

1995-01-01

Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.

Fourier Analysis: Graphical Animation and Analysis of Experimental Data with Excel

Directory of Open Access Journals (Sweden)

Margarida Oliveira

2012-05-01

Full Text Available According to Fourier formulation, any function that can be represented in a graph may be approximated by the “sum” of infinite sinusoidal functions (Fourier series, termed as “waves”.The adopted approach is accessible to students of the first years of university studies, in which the emphasis is put on the understanding of mathematical concepts through illustrative graphic representations, the students being encouraged to prepare animated Excel-based computational modules (VBA-Visual Basic for Applications.Reference is made to the part played by both trigonometric and complex representations of Fourier series in the concept of discrete Fourier transform. Its connection with the continuous Fourier transform is demonstrated and a brief mention is made of the generalization leading to Laplace transform.As application, the example presented refers to the analysis of vibrations measured on engineering structures: horizontal accelerations of a one-storey building deriving from environment noise. This example is integrated in the curriculum of the discipline “Matemática Aplicada à Engenharia Civil” (Mathematics Applied to Civil Engineering, lectured at ISEL (Instituto Superior de Engenharia de Lisboa. In this discipline, the students have the possibility of performing measurements using an accelerometer and a data acquisition system, which, when connected to a PC, make it possible to record the accelerations measured in a file format recognizable by Excel.

Automatic analysis of ciliary beat frequency using optical flow

Science.gov (United States)

Figl, Michael; Lechner, Manuel; Werther, Tobias; Horak, Fritz; Hummel, Johann; Birkfellner, Wolfgang

2012-02-01

Ciliary beat frequency (CBF) can be a useful parameter for diagnosis of several diseases, as e.g. primary ciliary dyskinesia. (PCD). CBF computation is usually done using manual evaluation of high speed video sequences, a tedious, observer dependent, and not very accurate procedure. We used the OpenCV's pyramidal implementation of the Lukas-Kanade algorithm for optical flow computation and applied this to certain objects to follow the movements. The objects were chosen by their contrast applying the corner detection by Shi and Tomasi. Discrimination between background/noise and cilia by a frequency histogram allowed to compute the CBF. Frequency analysis was done using the Fourier transform in matlab. The correct number of Fourier summands was found by the slope in an approximation curve. The method showed to be usable to distinguish between healthy and diseased samples. However there remain difficulties in automatically identifying the cilia, and also in finding enough high contrast cilia in the image. Furthermore the some of the higher contrast cilia are lost (and sometimes found) by the method, an easy way to distinguish the correct sub-path of a point's path have yet to be found in the case where the slope methods doesn't work.

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.

Monitoring of interaction of low-frequency electric field with biological tissues upon optical clearing with optical coherence tomography.

Science.gov (United States)

Peña, Adrián F; Doronin, Alexander; Tuchin, Valery V; Meglinski, Igor

2014-08-01

The influence of a low-frequency electric field applied to soft biological tissues ex vivo at normal conditions and upon the topical application of optical clearing agents has been studied by optical coherence tomography (OCT). The electro-kinetic response of tissues has been observed and quantitatively evaluated by the double correlation OCT approach, utilizing consistent application of an adaptive Wiener filtering and Fourier domain correlation algorithm. The results show that fluctuations, induced by the electric field within the biological tissues are exponentially increased in time. We demonstrate that in comparison to impedance measurements and the mapping of the temperature profile at the surface of the tissue samples, the double correlation OCT approach is much more sensitive to the changes associated with the tissues' electro-kinetic response. We also found that topical application of the optical clearing agent reduces the tissues' electro-kinetic response and is cooling the tissue, thus reducing the temperature induced by the electric current by a few degrees. We anticipate that dcOCT approach can find a new application in bioelectrical impedance analysis and monitoring of the electric properties of biological tissues, including the resistivity of high water content tissues and its variations.

Fourier Spectroscopy: A Bayesian Way

Directory of Open Access Journals (Sweden)

Stefan Schmuck

2017-01-01

Full Text Available The concepts of standard analysis techniques applied in the field of Fourier spectroscopy treat fundamental aspects insufficiently. For example, the spectra to be inferred are influenced by the noise contribution to the interferometric data, by nonprobed spatial domains which are linked to Fourier coefficients above a certain order, by the spectral limits which are in general not given by the Nyquist assumptions, and by additional parameters of the problem at hand like the zero-path difference. To consider these fundamentals, a probabilistic approach based on Bayes’ theorem is introduced which exploits multivariate normal distributions. For the example application, we model the spectra by the Gaussian process of a Brownian bridge stated by a prior covariance. The spectra themselves are represented by a number of parameters which map linearly to the data domain. The posterior for these linear parameters is analytically obtained, and the marginalisation over these parameters is trivial. This allows the straightforward investigation of the posterior for the involved nonlinear parameters, like the zero-path difference location and the spectral limits, and hyperparameters, like the scaling of the Gaussian process. With respect to the linear problem, this can be interpreted as an implementation of Ockham’s razor principle.

Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1975-01-01

The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)

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...

Methods of applied mathematics with a software overview

CERN Document Server

Davis, Jon H

2016-01-01

This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and si...

APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission.

Science.gov (United States)

Temprana, E; Myslivets, E; Kuo, B P-P; Liu, L; Ataie, V; Alic, N; Radic, S

2015-06-26

Nonlinear optical response of silica imposes a fundamental limit on the information transfer capacity in optical fibers. Communication beyond this limit requires higher signal power and suppression of nonlinear distortions to prevent irreversible information loss. The nonlinear interaction in silica is a deterministic phenomenon that can, in principle, be completely reversed. However, attempts to remove the effects of nonlinear propagation have led to only modest improvements, and the precise physical mechanism preventing nonlinear cancellation remains unknown. We demonstrate that optical carrier stability plays a critical role in canceling Kerr-induced distortions and that nonlinear wave interaction in silica can be substantially reverted if optical carriers possess a sufficient degree of mutual coherence. These measurements indicate that fiber information capacity can be notably increased over previous estimates. Copyright © 2015, American Association for the Advancement of Science.

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 fiber applied to radiation detection

Energy Technology Data Exchange (ETDEWEB)

Junior, Francisco A.B.; Costa, Antonella L.; Oliveira, Arno H. de; Vasconcelos, Danilo C., E-mail: fanbra@yahoo.com.br, E-mail: antonella@nuclear.ufmg.br, E-mail: heeren@nuclear.ufmg.br, E-mail: danilochagas@yahoo.com.br [Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG (Brazil). Escola de Engenharia. Departamento de Engenharia Nuclear

2015-07-01

In the last years, the production of optical fibers cables has make possible the development of a range of spectroscopic probes for in situ analysis performing beyond nondestructive tests, environmental monitoring, security investigation, application in radiotherapy for dose monitoring, verification and validation. In this work, a system using an optical fiber cable to light signal transmission from a NaI(Tl) radiation detector is presented. The innovative device takes advantage mainly of the optical fibers small signal attenuation and immunity to electromagnetic interference to application for radiation detection systems. The main aim was to simplify the detection system making it to reach areas where the conventional device cannot access due to its lack of mobility and external dimensions. Some tests with this innovative system are presented and the results stimulate the continuity of the researches. (author)

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).

An introduction to Laplace transforms and Fourier series

CERN Document Server

Dyke, Phil

2014-01-01

Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...

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

Quantitative comparison of tympanic membrane displacements using two optical methods to recover the optical phase

Science.gov (United States)

Santiago-Lona, Cynthia V.; Hernández-Montes, María del Socorro; Mendoza-Santoyo, Fernando; Esquivel-Tejeda, Jesús

2018-02-01

The study and quantification of the tympanic membrane (TM) displacements add important information to advance the knowledge about the hearing process. A comparative statistical analysis between two commonly used demodulation methods employed to recover the optical phase in digital holographic interferometry, namely the fast Fourier transform and phase-shifting interferometry, is presented as applied to study thin tissues such as the TM. The resulting experimental TM surface displacement data are used to contrast both methods through the analysis of variance and F tests. Data are gathered when the TMs are excited with continuous sound stimuli at levels 86, 89 and 93 dB SPL for the frequencies of 800, 1300 and 2500 Hz under the same experimental conditions. The statistical analysis shows repeatability in z-direction displacements with a standard deviation of 0.086, 0.098 and 0.080 μm using the Fourier method, and 0.080, 0.104 and 0.055 μm with the phase-shifting method at a 95% confidence level for all frequencies. The precision and accuracy are evaluated by means of the coefficient of variation; the results with the Fourier method are 0.06143, 0.06125, 0.06154 and 0.06154, 0.06118, 0.06111 with phase-shifting. The relative error between both methods is 7.143, 6.250 and 30.769%. On comparing the measured displacements, the results indicate that there is no statistically significant difference between both methods for frequencies at 800 and 1300 Hz; however, errors and other statistics increase at 2500 Hz.

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...

Photographic-Based Optical Evaluation of Tissues and Biomaterials Used for Corneal Surface Repair: A New Easy-Applied Method.

Directory of Open Access Journals (Sweden)

Miguel Gonzalez-Andrades

Full Text Available Tissues and biomaterials used for corneal surface repair require fulfilling specific optical standards prior to implantation in the patient. However, there is not a feasible evaluation method to be applied in clinical or Good Manufacturing Practice settings. In this study, we describe and assess an innovative easy-applied photographic-based method (PBM for measuring functional optical blurring and transparency in corneal surface grafts.Plastic compressed collagen scaffolds (PCCS and multilayered amniotic membranes (AM samples were optically and histologically evaluated. Transparency and image blurring measures were obtained by PBM, analyzing photographic images of a standardized band pattern taken through the samples. These measures were compared and correlated to those obtained applying the Inverse Adding-Doubling (IAD technique, which is the gold standard method.All the samples used for optical evaluation by PBM or IAD were histological suitable. PCCS samples presented transmittance values higher than 60%, values that increased with increasing wavelength as determined by IAD. The PBM indicated that PCCS had a transparency ratio (TR value of 80.3 ± 2.8%, with a blurring index (BI of 50.6 ± 4.2%. TR and BI obtained from the PBM showed a high correlation (ρ>|0.6| with the diffuse transmittance and the diffuse reflectance, both determined using the IAD (p<0.005. The AM optical properties showed that there was a largely linear relationship between the blurring and the number of amnion layers, with more layers producing greater blurring.This innovative proposed method represents an easy-applied technique for evaluating transparency and blurriness of tissues and biomaterials used for corneal surface repair.

A new analytical solution to the diffusion problem: Fourier series ...

African Journals Online (AJOL)

This paper reviews briefly the origin of Fourier Series Method. The paper then gives a vivid description of how the method can be applied to solve a diffusion problem, subject to some boundary conditions. The result obtained is quite appealing as it can be used to solve similar examples of diffusion equations. JONAMP Vol.

Donor impurity states and related optical response in a lateral coupled dot-ring system under applied electric field

Energy Technology Data Exchange (ETDEWEB)

Correa, J.D. [Departamento de Ciencias Básicas, Universidad de Medellín, Medellín (Colombia); Mora-Ramos, M.E. [Centro de Investigación en Ciencias, Instituto de Ciencias Básicas y Aplicadas, Universidad Autonoma del Estado de Morelos, Av. Universidad 1001, CP 62209 Cuernavaca, Morelos (Mexico); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia)

2015-09-01

A study on the effects of an externally applied electric field on the linear optical absorption and relative refractive index change associated with transitions between off-center donor impurity states in laterally coupled quantum dot-ring system is reported. Electron states are calculated within the effective mass and parabolic band approximations by means of an exact diagonalization procedure. The states and the optical response in each case show significant sensitivity to the geometrical distribution of confining energies as well as to the strength of the applied field.

Donor impurity states and related optical response in a lateral coupled dot-ring system under applied electric field

International Nuclear Information System (INIS)

Correa, J.D.; Mora-Ramos, M.E.; Duque, C.A.

2015-01-01

A study on the effects of an externally applied electric field on the linear optical absorption and relative refractive index change associated with transitions between off-center donor impurity states in laterally coupled quantum dot-ring system is reported. Electron states are calculated within the effective mass and parabolic band approximations by means of an exact diagonalization procedure. The states and the optical response in each case show significant sensitivity to the geometrical distribution of confining energies as well as to the strength of the applied field

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...

Spectrums Transform Operators in Bases of Fourier and Walsh Functions

Directory of Open Access Journals (Sweden)

V. V. Syuzev

2017-01-01

Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel

Simplification of gamma-ray spectral data by using Fourier transform

International Nuclear Information System (INIS)

Tominaga, Shoji; Nagata, Shojiro; Nayatani, Yoshinobu; Ueda, Isamu; Sasaki, Satoshi.

1977-01-01

A method is proposed to represent γ-ray response spectra by Fourier series for the purpose of compressing spectral data. The usefulness of the method was confirmed by applying it to a spectral library of a NaI detector. In the method, a response spectrum as a wave is described by superposition of sine (cosine) waves with low frequencies, whose coefficient parameters can be obtained by a Fast Fourier Transform program. The relation between the number of parameters and the fitting error is discussed, and as the result, it is shown that the number of parameters can be reduced to about a half. The merits and features are presented in practical application of the method to the analysis of γ-ray spectra. (auth.)

Research on fabrication of aspheres at the Center of Optics Technology (University of Applied Science in Aalen); Techical Digest

Science.gov (United States)

Boerret, Rainer; Burger, Jochen; Bich, Andreas; Gall, Christoph; Hellmuth, Thomas

2005-05-01

The Center of Optics Technology at the University of Applied Science, founded in 2003, is part of the School of Optics and Mechatronics. It completes the existing optical engineering department with a full optical fabrication and metrology chain and serves in parallel as a technology transfer center, to provide area industries with the most up-to-date technology in optical fabrication and engineering. Two examples of research work will be presented. The first example is the optimizing of the grinding process for high precision aspheres, the other is generating and polishing of a freeform optical element which is used as a phase plate.

The reform of the teaching mode of Applied Optics curriculum and analysis of teaching effect

Science.gov (United States)

Ning, Yu; Xu, Zhongjie; Li, Dun; Chen, Zilun; Cheng, Xiangai; Zhong, Hairong

2017-08-01

Military academies have two distinctive characteristics on talent training: Firstly, we must teach facing actual combat and connecting with academic frontier. Secondly, the bachelor's degree education and the military education should be balanced. The teaching mode of basic curriculum in military academies must be reformed and optimized on the basis of the traditional teaching mode, so as to ensure the high quality of teaching and provide enough guidance and help for students to support their academic burden. In this paper, our main work on "Applied Optics" teaching mode reform is introduced: First of all, we research extensively and learn fully from advanced teaching modes of the well-known universities at home and abroad, a whole design is made for the teaching mode of the core curriculum of optical engineering in our school "Applied Optics", building a new teaching mode which takes the methods of teaching basic parts as details, teaching application parts as emphases, teaching frontier parts as topics and teaching actual combat parts on site. Then combining with the questionnaire survey of students and opinions proposed by relevant experts in the teaching seminar, teaching effect and generalizability of the new teaching mode are analyzed and evaluated.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction.

Science.gov (United States)

Fahimian, Benjamin P; Zhao, Yunzhe; Huang, Zhifeng; Fung, Russell; Mao, Yu; Zhu, Chun; Khatonabadi, Maryam; DeMarco, John J; Osher, Stanley J; McNitt-Gray, Michael F; Miao, Jianwei

2013-03-01

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 m

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction

International Nuclear Information System (INIS)

Fahimian, Benjamin P.; Zhao Yunzhe; Huang Zhifeng; Fung, Russell; Zhu Chun; Miao Jianwei; Mao Yu; Khatonabadi, Maryam; DeMarco, John J.; McNitt-Gray, Michael F.; Osher, Stanley J.

2013-01-01

Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Results: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest

Vectorial magnetometry with the magneto-optic Kerr effect applied to Co/Cu/Co trilayer structures

Science.gov (United States)

Daboo, C.; Bland, J. A. C.; Hicken, R. J.; Ives, A. J. R.; Baird, M. J.; Walker, M. J.

1993-05-01

We describe an arrangement in which the magnetization components parallel and perpendicular to the applied field are both determined from longitudinal magneto-optic Kerr effect measurements. This arrangement differs from the usual procedures in that the same optical geometry is used but the magnet geometry altered. This leads to two magneto-optic signals which are directly comparable in magnitude thereby giving the in-plane magnetization vector directly. We show that it is of great value to study both in-plane magnetization vector components when studying coupled structures where significant anisotropies are also present. We discuss simulations which show that it is possible to accurately determine the coupling strength in such structures by examining the behavior of the component of magnetization perpendicular to the applied field in the vicinity of the hard in-plane anisotropy axis. We illustrate this technique by examining the magnetization and magnetic anisotropy behavior of ultrathin Co/Cu(111)/Co (dCu=20 Å and 27 Å) trilayer structures prepared by molecular beam epitaxy, in which coherent rotation of the magnetization vector is observed when the magnetic field B is applied along the hard in-plane anisotropy axis, with the magnitude of the magnetization vector constant and close to its bulk value. Results of micromagnetic calculations closely reproduce the observed parallel and perpendicular magnetization loops, and yield strong uniaxial magnetic anisotropies in both layers, while the interlayer coupling appears to be absent or negligible in comparison with the anisotropy strengths.

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.

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...

Matrix-Vector Based Fast Fourier Transformations on SDR Architectures

Directory of Open Access Journals (Sweden)

Y. He

2008-05-01

Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.

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)

Ultrafast and versatile spectroscopy by temporal Fourier transform

Science.gov (United States)

Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.

2014-06-01

One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.

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.

Applied electro-optics educational and training program with multiple entrance and exit pathways

Science.gov (United States)

Scott, Patricia; Zhou, Feng; Zilic, Dorothy

2007-06-01

This paper presents an innovative hands-on training program designed to create a pipeline of highly-skilled technical workers for today's workforce economy. The 2+2+2 Pennsylvania Integrated Workforce Leadership Program in Electro-Optics prepares students for a career in this new high-tech field. With seamless transition from high school into college, the program offers the versatility of multiple entrance and exit pathways. After completion of each educational level, students can exit the program with various skill levels, including certificates, an associate's degree, or a bachelor's degree. Launched by Indiana University of Pennsylvania (IUP) in partnership with Lenape Vocational School (Lenape), the 2+2+2 educational pathway program was implemented to promote early training of high-school students. During the first level, students in their junior and/or senior year enroll in four Electro-Optics courses at Lenape. Upon completion of these courses and an Advanced Placement Equivalency course with an appropriate exam score, students can earn a certificate from Lenape for the 15+ credits, which also can be articulated into IUP's associate degree program in Electro-Optics. During the second level, students can earn an associate's degree in Electro-Optics, offered only at the IUP Northpointe Campus. After completion of the Associate in Applied Science (A.A.S.), students are prepared to enter the workforce as senior technicians. During the third level, students who have completed the Associate of Science (A.S.) in Electro-Optics have the opportunity to matriculate at IUP's Indiana Campus to earn a Bachelor of Science (B.S.) degree in Applied Physics with a track in Electro-Optics. Hence, the name 2+2+2 refers to getting started in high school, continuing the educational experience with an associate's degree program, and optionally moving on to a bachelor's degree. Consequently, students move from one educational level to the next with advanced credits toward the next

Left ventricular wall motion abnormalities evaluated by factor analysis as compared with Fourier analysis

International Nuclear Information System (INIS)

Hirota, Kazuyoshi; Ikuno, Yoshiyasu; Nishikimi, Toshio

1986-01-01

Factor analysis was applied to multigated cardiac pool scintigraphy to evaluate its ability to detect left ventricular wall motion abnormalities in 35 patients with old myocardial infarction (MI), and in 12 control cases with normal left ventriculography. All cases were also evaluated by conventional Fourier analysis. In most cases with normal left ventriculography, the ventricular and atrial factors were extracted by factor analysis. In cases with MI, the third factor was obtained in the left ventricle corresponding to wall motion abnormality. Each case was scored according to the coincidence of findings of ventriculography and those of factor analysis or Fourier analysis. Scores were recorded for three items; the existence, location, and degree of asynergy. In cases of MI, the detection rate of asynergy was 94 % by factor analysis, 83 % by Fourier analysis, and the agreement in respect to location was 71 % and 66 %, respectively. Factor analysis had higher scores than Fourier analysis, but this was not significant. The interobserver error of factor analysis was less than that of Fourier analysis. Factor analysis can display locations and dynamic motion curves of asynergy, and it is regarded as a useful method for detecting and evaluating left ventricular wall motion abnormalities. (author)

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.

Application of the Fourier descriptors method to the morphological classification of particles in geological materials

International Nuclear Information System (INIS)

Manzanas Lopez, J.; Santiago Buey, C.

2010-01-01

This study focuses on the use of Fourier descriptors to quantitatively describe the morphology of particles aggregates or pores in geological materials. Firstly, the mathematical fundaments of the method are explained. Then, the Fourier descriptors method is applied to the Krumbein Scale, a system of measuring roundness and sphericity of particles. the analysis of the comparison shows that there is good correlation between the Sphericity parameter at the Krumbein classifications and the value of the modulus of the Fourier descriptor No-1. This good correlation, along with the mathematical precision which allows to prevent subjective valorisations in the morphological description, corroborates the validity of the method to quantify the sphericity elongation of particles in geological materials. (Author) 12 refs.

On the Application of the Fourier Series Solution to the Hydromagnetic Buoyant Two-Dimensional Laminar Vertical Jet

Directory of Open Access Journals (Sweden)

Marco Rosales-Vera

2012-01-01

Full Text Available The problem of a hydromagnetic hot two-dimensional laminar jet issuing vertically into an otherwise quiescent fluid of a lower temperature is studied. We propose solutions to the boundary layer equations using the classical Fourier series. The method is essentiall to transform the boundary layer equations to a coupled set of nonlinear first-order ordinary differential equations through the Fourier series. The accuracy of the results has been tested by the comparison of the velocity distributions obtained by the Fourier series with those calculated by finite difference method. The results show that the present method, based on the Fourier series, is an efficient method, suitable to solve boundary layer equations applied to plane jet flows with high accuracy.

Multifocus microscopy with precise color multi-phase diffractive optics applied in functional neuronal imaging.

Science.gov (United States)

Abrahamsson, Sara; Ilic, Rob; Wisniewski, Jan; Mehl, Brian; Yu, Liya; Chen, Lei; Davanco, Marcelo; Oudjedi, Laura; Fiche, Jean-Bernard; Hajj, Bassam; Jin, Xin; Pulupa, Joan; Cho, Christine; Mir, Mustafa; El Beheiry, Mohamed; Darzacq, Xavier; Nollmann, Marcelo; Dahan, Maxime; Wu, Carl; Lionnet, Timothée; Liddle, J Alexander; Bargmann, Cornelia I

2016-03-01

Multifocus microscopy (MFM) allows high-resolution instantaneous three-dimensional (3D) imaging and has been applied to study biological specimens ranging from single molecules inside cells nuclei to entire embryos. We here describe pattern designs and nanofabrication methods for diffractive optics that optimize the light-efficiency of the central optical component of MFM: the diffractive multifocus grating (MFG). We also implement a "precise color" MFM layout with MFGs tailored to individual fluorophores in separate optical arms. The reported advancements enable faster and brighter volumetric time-lapse imaging of biological samples. In live microscopy applications, photon budget is a critical parameter and light-efficiency must be optimized to obtain the fastest possible frame rate while minimizing photodamage. We provide comprehensive descriptions and code for designing diffractive optical devices, and a detailed methods description for nanofabrication of devices. Theoretical efficiencies of reported designs is ≈90% and we have obtained efficiencies of > 80% in MFGs of our own manufacture. We demonstrate the performance of a multi-phase MFG in 3D functional neuronal imaging in living C. elegans.

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

The application of network teaching in applied optics teaching

Science.gov (United States)

Zhao, Huifu; Piao, Mingxu; Li, Lin; Liu, Dongmei

2017-08-01

Network technology has become a creative tool of changing human productivity, the rapid development of it has brought profound changes to our learning, working and life. Network technology has many advantages such as rich contents, various forms, convenient retrieval, timely communication and efficient combination of resources. Network information resources have become the new education resources, get more and more application in the education, has now become the teaching and learning tools. Network teaching enriches the teaching contents, changes teaching process from the traditional knowledge explanation into the new teaching process by establishing situation, independence and cooperation in the network technology platform. The teacher's role has shifted from teaching in classroom to how to guide students to learn better. Network environment only provides a good platform for the teaching, we can get a better teaching effect only by constantly improve the teaching content. Changchun university of science and technology introduced a BB teaching platform, on the platform, the whole optical classroom teaching and the classroom teaching can be improved. Teachers make assignments online, students learn independently offline or the group learned cooperatively, this expands the time and space of teaching. Teachers use hypertext form related knowledge of applied optics, rich cases and learning resources, set up the network interactive platform, homework submission system, message board, etc. The teaching platform simulated the learning interest of students and strengthens the interaction in the teaching.

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

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.

On the computation of molecular surface correlations for protein docking using fourier techniques.

Science.gov (United States)

Sakk, Eric

2007-08-01

The computation of surface correlations using a variety of molecular models has been applied to the unbound protein docking problem. Because of the computational complexity involved in examining all possible molecular orientations, the fast Fourier transform (FFT) (a fast numerical implementation of the discrete Fourier transform (DFT)) is generally applied to minimize the number of calculations. This approach is rooted in the convolution theorem which allows one to inverse transform the product of two DFTs in order to perform the correlation calculation. However, such a DFT calculation results in a cyclic or "circular" correlation which, in general, does not lead to the same result as the linear correlation desired for the docking problem. In this work, we provide computational bounds for constructing molecular models used in the molecular surface correlation problem. The derived bounds are then shown to be consistent with various intuitive guidelines previously reported in the protein docking literature. Finally, these bounds are applied to different molecular models in order to investigate their effect on the correlation calculation.

High-resolution wave-theory-based ultrasound reflection imaging using the split-step fourier and globally optimized fourier finite-difference methods

Science.gov (United States)

Huang, Lianjie

2013-10-29

Methods for enhancing ultrasonic reflection imaging are taught utilizing a split-step Fourier propagator in which the reconstruction is based on recursive inward continuation of ultrasonic wavefields in the frequency-space and frequency-wave number domains. The inward continuation within each extrapolation interval consists of two steps. In the first step, a phase-shift term is applied to the data in the frequency-wave number domain for propagation in a reference medium. The second step consists of applying another phase-shift term to data in the frequency-space domain to approximately compensate for ultrasonic scattering effects of heterogeneities within the tissue being imaged (e.g., breast tissue). Results from various data input to the method indicate significant improvements are provided in both image quality and resolution.

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.

Cross-talk free selective reconstruction of individual objects from multiplexed optical field data

Science.gov (United States)

Zea, Alejandro Velez; Barrera, John Fredy; Torroba, Roberto

2018-01-01

In this paper we present a data multiplexing method for simultaneous storage in a single package composed by several optical fields of tridimensional (3D) objects, and their individual cross-talk free retrieval. Optical field data are extracted from off axis Fourier holograms, and then sampled by multiplying them with random binary masks. The resulting sampled optical fields can be used to reconstruct the original objects. Sampling causes a loss of quality that can be controlled by the number of white pixels in the binary masks and by applying a padding procedure on the optical field data. This process can be performed using a different binary mask for each optical field, and then added to form a multiplexed package. With the adequate choice of sampling and padding, we can achieve a volume reduction in the multiplexed package over the addition of all individual optical fields. Moreover, the package can be multiplied by a binary mask to select a specific optical field, and after the reconstruction procedure, the corresponding 3D object is recovered without any cross-talk. We demonstrate the effectiveness of our proposal for data compression with a comparison with discrete cosine transform filtering. Experimental results confirm the validity of our proposal.

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....

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.

Increasing signal-to-noise ratio of swept-source optical coherence tomography by oversampling in k-space

Science.gov (United States)

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

2018-03-01

Optical coherence tomography systems suffer from noise that could reduce ability to interpret reconstructed images correctly. We describe a method to increase the signal-to-noise ratio of swept-source optical coherence tomography (SSOCT) using oversampling in k-space. Due to this oversampling, information redundancy would be introduced in the measured interferogram that could be used to reduce white noise in the reconstructed A-scan. We applied our novel scaled nonuniform discrete Fourier transform to oversampled SS-OCT interferograms to reconstruct images of a salamander egg. The peak-signal-to-noise (PSNR) between the reconstructed images using interferograms sampled at 250MS/s andz50MS/s demonstrate that this oversampling increased the signal-to-noise ratio by 25.22 dB.

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.

Optical waveguiding and applied photonics technological aspects, experimental issue approaches and measurements

CERN Document Server

Massaro, Alessandro

2012-01-01

Optoelectronics--technology based on applications light such as micro/nano quantum electronics, photonic devices, laser for measurements and detection--has become an important field of research. Many applications and physical problems concerning optoelectronics are analyzed in Optical Waveguiding and Applied Photonics.The book is organized in order to explain how to implement innovative sensors starting from basic physical principles. Applications such as cavity resonance, filtering, tactile sensors, robotic sensor, oil spill detection, small antennas and experimental setups using lasers are a

Annual report of the Applied Optics Laboratory, 1985

International Nuclear Information System (INIS)

1986-01-01

Research on optical fiber coupling by evanescent fields; fiber optics resonators; infrared lasers; remote measurement by laser; dephasing time in GaAs; heat transfer in thin silicon films; quantum wells; a picosecond electron source; modeling of III-V semiconductors; nonlinear optics properties of materials; femtosecond spectroscopy of the internal dynamics of proteins; computer simulation of protein dynamics; electron solvation; reactions of radicals in micella phase; sarcoma; and medical applications of pulsed lasers is presented [fr

Annual report of the Applied Optics Laboratory, 1986

International Nuclear Information System (INIS)

1987-01-01

Research on optical fiber coupling by evanescent fields; fiber optics resonators; infrared lasers; remote measurement by laser; dephasing time in GaAs; heat transfer in thin silicon films; quantum wells; a picosecond electron source; modeling of III-V semiconductors; nonlinear optics properties of materials; femtosecond spectroscopy of the internal dynamics of proteins; computer simulation of protein dynamics; electron solvation; reactions of radicals in micella phase; sarcoma; and medical applications of pulsed lasers is presented [fr

Application of Fourier analysis to the study of roughness profiles of eroded samples

International Nuclear Information System (INIS)

Bethencourt, M.; Botana, F.J.; Calvino, J.J.; Marcos, M.; Rodriguez-Chacon, M.A.

1998-01-01

Fourier transforms are applied to analyse surface roughness profiles recorded on samples coming from erosion-corrosion essays. The information retrieved using this method clearly complements that revealed by the more classical roughness amplitude parameters. The analysis procedure here proposed can be applied not only to characterise the surface of corroded samples but, in general, to evaluate the quality of any surface after application of finishing treatments. (Author) 7 refs

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.

Correction for Eddy Current-Induced Echo-Shifting Effect in Partial-Fourier Diffusion Tensor Imaging.

Science.gov (United States)

Truong, Trong-Kha; Song, Allen W; Chen, Nan-Kuei

2015-01-01

In most diffusion tensor imaging (DTI) studies, images are acquired with either a partial-Fourier or a parallel partial-Fourier echo-planar imaging (EPI) sequence, in order to shorten the echo time and increase the signal-to-noise ratio (SNR). However, eddy currents induced by the diffusion-sensitizing gradients can often lead to a shift of the echo in k-space, resulting in three distinct types of artifacts in partial-Fourier DTI. Here, we present an improved DTI acquisition and reconstruction scheme, capable of generating high-quality and high-SNR DTI data without eddy current-induced artifacts. This new scheme consists of three components, respectively, addressing the three distinct types of artifacts. First, a k-space energy-anchored DTI sequence is designed to recover eddy current-induced signal loss (i.e., Type 1 artifact). Second, a multischeme partial-Fourier reconstruction is used to eliminate artificial signal elevation (i.e., Type 2 artifact) associated with the conventional partial-Fourier reconstruction. Third, a signal intensity correction is applied to remove artificial signal modulations due to eddy current-induced erroneous T2(∗) -weighting (i.e., Type 3 artifact). These systematic improvements will greatly increase the consistency and accuracy of DTI measurements, expanding the utility of DTI in translational applications where quantitative robustness is much needed.

Evaluation of the response of a round hole scintillation camera collimator by the Fourier analysis method

International Nuclear Information System (INIS)

Hernandez, A.; Millan, S.; Yzuel, M.J.

1986-01-01

The Fourier analysis method was used to investigate the response of scintillation camera collimators with parallel holes. This method which takes into account the septal penetration was applied to the case of round hole collimators having a hexagonal distribution. Modulation transfer functions, MTF have been determined to verify the accuracy of the computed Fourier coefficients of the collimator function. Comparisons between the geometric and the penetrating plus geometric transfer function are shown for round and hexagonal holes. (author)

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.

Complex regression Doppler optical coherence tomography

Science.gov (United States)

Elahi, Sahar; Gu, Shi; Thrane, Lars; Rollins, Andrew M.; Jenkins, Michael W.

2018-04-01

We introduce a new method to measure Doppler shifts more accurately and extend the dynamic range of Doppler optical coherence tomography (OCT). The two-point estimate of the conventional Doppler method is replaced with a regression that is applied to high-density B-scans in polar coordinates. We built a high-speed OCT system using a 1.68-MHz Fourier domain mode locked laser to acquire high-density B-scans (16,000 A-lines) at high enough frame rates (˜100 fps) to accurately capture the dynamics of the beating embryonic heart. Flow phantom experiments confirm that the complex regression lowers the minimum detectable velocity from 12.25 mm / s to 374 μm / s, whereas the maximum velocity of 400 mm / s is measured without phase wrapping. Complex regression Doppler OCT also demonstrates higher accuracy and precision compared with the conventional method, particularly when signal-to-noise ratio is low. The extended dynamic range allows monitoring of blood flow over several stages of development in embryos without adjusting the imaging parameters. In addition, applying complex averaging recovers hidden features in structural images.

Displacement sensing based on modal interference in polymer optical fibers with partially applied strain

Science.gov (United States)

Mizuno, Yosuke; Hagiwara, Sonoko; Kawa, Tomohito; Lee, Heeyoung; Nakamura, Kentaro

2018-05-01

Strain sensing based on modal interference in multimode fibers (MMFs) has been extensively studied, but no experimental or theoretical reports have been given as to how the system works when strain is applied not to the whole MMF but only to part of the MMF. Here, using a perfluorinated graded-index polymer optical fiber as the MMF, we investigate the strain sensing characteristics of this type of sensor when strain is partially applied to fiber sections with different lengths. The strain sensitivity dependence on the length of the strained section reveals that this strain sensor actually behaves as a displacement sensor.

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.

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....

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)

Suppression of Brillouin scattering in fibre-optical parametric amplifier by applying temperature control and phase modulation

DEFF Research Database (Denmark)

Lorenzen, Michael Rodas; Noordegraaf, Danny; Nielsen, Carsten Vandel

2009-01-01

An increased gain in a fibre-optical parametric amplifier through suppression of stimulated Brillouin scattering is demonstrated by applying a temperature distribution along the fibre for a fixed phase modulation of the pump. The temperature distribution slightly impacts the gain spectrum....

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.

Fourier expansions and multivariable Bessel functions concerning radiation programmes

International Nuclear Information System (INIS)

Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.

1996-01-01

The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)

Fast Fourier transformation results from gamma-ray burst profiles

Science.gov (United States)

Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.

1992-01-01

Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.

OSA Imaging and Applied Optics Congress Support

Science.gov (United States)

2017-02-16

Digest (online) (Optical Society of America, 20 16), paper JT3A .41. V. Katkovnik, "Sparse phase retrieval from noisy data: variational formulation and...A. Wojdyla, G. Gunjala, J. Dong, M. Benk, A. Neureuther, K. Goldberg , and L. Waller, "Off-axis Aberration Estimation in an EUV Microscope Using...2016, (Optical Society of America, 20 16), paper JT3A.41. V. Katkovnik, "Sparse phase retrieval from noisy data: variational formulation and algorithms

Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach

Directory of Open Access Journals (Sweden)

Ludwig Kohaupt

2015-12-01

Full Text Available The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating images in computer tomography. In order to achieve this, appropriate algorithms are necessary. In this context, the fast Fourier transform (FFT plays a key role which is an algorithm for calculating the discrete Fourier transform (DFT; this, in turn, is tightly connected with the discrete Fourier series. The last one itself is the discrete analog of the common (continuous-time Fourier series and is usually learned by mathematics students from a theoretical point of view. The aim of this expository/pedagogical paper is to give an introduction to the discrete Fourier series for both mathematics and engineering students. It is intended to expand the purely mathematical view; the engineering aspect is taken into account by applying the FFT to an example from signal processing that is small enough to be used in class-room teaching and elementary enough to be understood also by mathematics students. The MATLAB program is employed to do the computations.

Optical modeling based on mean free path calculations for quantum dot phosphors applied to optoelectronic devices.

Science.gov (United States)

Shin, Min-Ho; Kim, Hyo-Jun; Kim, Young-Joo

2017-02-20

We proposed an optical simulation model for the quantum dot (QD) nanophosphor based on the mean free path concept to understand precisely the optical performance of optoelectronic devices. A measurement methodology was also developed to get the desired optical characteristics such as the mean free path and absorption spectra for QD nanophosphors which are to be incorporated into the simulation. The simulation results for QD-based white LED and OLED displays show good agreement with the experimental values from the fabricated devices in terms of spectral power distribution, chromaticity coordinate, CCT, and CRI. The proposed simulation model and measurement methodology can be applied easily to the design of lots of optoelectronics devices using QD nanophosphors to obtain high efficiency and the desired color characteristics.

Experience at Los Alamos with use of the optical model for applied nuclear data calculations

International Nuclear Information System (INIS)

Young, P.G.

1994-01-01

While many nuclear models are important in calculations of nuclear data, the optical model usually provides the basic underpinning of analyses directed at data for applications. An overview is given here of experience in the Nuclear Theory and Applications Group at Los Alamos National Laboratory in the use of the optical model for calculations of nuclear cross section data for applied purposes. We consider the direct utilization of total, elastic, and reaction cross sections for neutrons, protons, deuterons, tritons, 3 He and alpha particles in files of evaluated nuclear data covering the energy range of 0 to 200 MeV, as well as transmission coefficients for reaction theory calculations and neutron and proton wave functions direct-reaction and Feshbach-Kerman-Koonin analyses. Optical model codes such as SCAT and ECIS and the reaction theory codes COMNUC, GNASH FKK-GNASH, and DWUCK have primarily been used in our analyses. A summary of optical model parameterizations from past analyses at Los Alamos will be given, including detailed tabulations of the parameters for a selection of nuclei