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.
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
Simple Fourier optics formalism for high-angular-resolution systems and nulling interferometry.
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.
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
Teaching Fourier optics through ray matrices
International Nuclear Information System (INIS)
Moreno, I; Sanchez-Lopez, M M; Ferreira, C; Davis, J A; Mateos, F
2005-01-01
In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics
Fourier-transform optical microsystems
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
Fourier phase in Fourier-domain optical coherence tomography
Uttam, Shikhar; Liu, Yang
2015-01-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
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
New focus on Fourier optics techniques
Calvo, M.L.; Alieva, T.; Bastiaans, M.J.; Rodrigo Martín-Romo, J.A.; Rodríguez Merlo, D.; Vlad, V.I.
2004-01-01
We present a short overview on the application of fractional cyclic and linear canonical transformations to optical signal processing and dedicate some of the discussions to the particular features found in the fractional Fourier transform domain.
An optical Fourier transform coprocessor with direct phase determination.
Macfaden, Alexander J; Gordon, George S D; Wilkinson, Timothy D
2017-10-20
The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Fourier optical cryptosystem using complex spatial modulation
International Nuclear Information System (INIS)
Sarkadi, T; Koppa, P
2014-01-01
Our goal is to enhance the security level of a Fourier optical encryption system. Therefore we propose a Mach–Zehnder interferometer based encryption setup. The input data is organized in a binary array, and it is encoded in the two wave fronts propagated in the arms of the interferometer. Both input wave fronts are independently encrypted by Fourier systems, hence the proposed method has two encryption keys. During decryption, the encrypted wave fronts are propagated through the interferometer setup. The interference pattern of the output shows the reconstructed data in cases where the correct decryption Fourier keys are used. We propose a novel input image modulation method with a user defined phase parameter. We show that the security level of the proposed cryptosystem can be enhanced by an optimally chosen phase parameter. (paper)
Fourier optics treatment of classical relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.
2006-08-15
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)
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...
Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie
2015-10-20
In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.
Extending Single-Molecule Microscopy Using Optical Fourier Processing
2015-01-01
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862
An OTDM-To-WDM Converter Using Optical Fourier Transformation
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...
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)....
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.
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...
Electro-Optical Imaging Fourier-Transform Spectrometer
Chao, Tien-Hsin; Zhou, Hanying
2006-01-01
An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.
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)
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
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
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
DEFF Research Database (Denmark)
Galili, Michael; Guan, Pengyu; Lillieholm, Mads
2017-01-01
In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed.......In the talk, we will review recent work on optical signal processing based on time lenses. Various applications of optical Fourier transformation for optical communications will be discussed....
Energy Technology Data Exchange (ETDEWEB)
Zheng, Y. [Pennsylvania State Univ., University Park, PA (United States)]|[Lawrence Berkeley Lab., CA (United States); Shirley, D.A. [Pennsylvania State Univ., University Park, PA (United States)
1995-02-01
The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.
DEFF Research Database (Denmark)
Guan, Pengyu; Røge, Kasper Meldgaard; Kjøller, Niels-Kristian
2015-01-01
We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time.......We propose a novel all-optical WDM regeneration scheme for DPSK signals based on optical Fourier transformation and phase sensitive amplification. Phase regeneration of a WDM signal consisting of 4x10-Gbit/s phase noise degraded DPSK channels is demonstrated for the first time....
The tomography inside of a Fourier Optics course: some opto-mechanical illustrative arrays
International Nuclear Information System (INIS)
Rodriguez Z, G.; Rodriguez V, R.; Luna C, A.
1999-01-01
The introduction of tomography as an advanced topic to be included in a Fourier optics course at graduated level is proposed. It is shown a possible presentation sequence which features the use of typical Fourier optics techniques, as well as some well known opto-mechanical devices as examples. Finally, a simplified apparatus which illustrates the central Fourier theorem as an experimental project on Fourier optics is described. Corresponding experimental results are also shown. (Author)
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.
DEFF Research Database (Denmark)
Clausen, Anders; Guan, Pengyu; Mulvad, Hans Christian Hansen
2014-01-01
All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented.......All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented....
Universal discrete Fourier optics RF photonic integrated circuit architecture.
Hall, Trevor J; Hasan, Mehedi
2016-04-04
This paper describes a coherent electro-optic circuit architecture that generates a frequency comb consisting of N spatially separated orders using a generalised Mach-Zenhder interferometer (MZI) with its N × 1 combiner replaced by an optical N × N Discrete Fourier Transform (DFT). Advantage may be taken of the tight optical path-length control, component and circuit symmetries and emerging trimming algorithms offered by photonic integration in any platform that offers linear electro-optic phase modulation such as LiNbO3, silicon, III-V or hybrid technology. The circuit architecture subsumes all MZI-based RF photonic circuit architectures in the prior art given an appropriate choice of output port(s) and dimension N although the principal application envisaged is phase correlated subcarrier generation for all optical orthogonal frequency division multiplexing. A transfer matrix approach is used to model the operation of the architecture. The predictions of the model are validated by simulations performed using an industry standard software tool. Implementation is found to be practical.
Selection of unstable patterns and control of optical turbulence by Fourier plane filtering
DEFF Research Database (Denmark)
Mamaev, A.V.; Saffman, M.
1998-01-01
We report on selection and stabilization of transverse optical patterns in a feedback mirror experiment. Amplitude filtering in the Fourier plane is used to select otherwise unstable spatial patterns. Optical turbulence observed for nonlinearities far above the pattern formation threshold...
Time-Domain Optical Fourier Transformation for OTDM-DWDM and DWDM-OTDM Conversion
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael
2011-01-01
Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats.......Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats....
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
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.
Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms.
Volkov, V V; Han, M G; Zhu, Y
2013-11-01
We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. Published by Elsevier B.V.
Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms
International Nuclear Information System (INIS)
Volkov, V.V.; Han, M.G.; Zhu, Y.
2013-01-01
We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. - Highlights: • We propose a fringe-shifting holographic method simple enough for practical implementations. • Our new image-wave-recovery algorithm follows from exact solution of holographic equations. • With autocorrelation band removal from holograms it is possible to achieve double-resolution electron holography data free from several commonly known artifacts. • The new fringe-shifting method can reach an image wave resolution close to single fringe spacing
Double-resolution electron holography with simple Fourier transform of fringe-shifted holograms
Energy Technology Data Exchange (ETDEWEB)
Volkov, V.V., E-mail: volkov@bnl.gov; Han, M.G.; Zhu, Y.
2013-11-15
We propose a fringe-shifting holographic method with an appropriate image wave recovery algorithm leading to exact solution of holographic equations. With this new method the complex object image wave recovered from holograms appears to have much less traditional artifacts caused by the autocorrelation band present practically in all Fourier transformed holograms. The new analytical solutions make possible a double-resolution electron holography free from autocorrelation band artifacts and thus push the limits for phase resolution. The new image wave recovery algorithm uses a popular Fourier solution of the side band-pass filter technique, while the fringe-shifting holographic method is simple to implement in practice. - Highlights: • We propose a fringe-shifting holographic method simple enough for practical implementations. • Our new image-wave-recovery algorithm follows from exact solution of holographic equations. • With autocorrelation band removal from holograms it is possible to achieve double-resolution electron holography data free from several commonly known artifacts. • The new fringe-shifting method can reach an image wave resolution close to single fringe spacing.
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
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....
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....
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.)
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....
Optical Two Dimensional Fourier Transform Spectroscopy of Layered Metal Dichalcogenides
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.
Nonlinear Fourier transform for dual-polarization optical communication system
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...
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
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....
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....
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...
Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs
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.
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....
Raman Spectroscopy with simple optic components
International Nuclear Information System (INIS)
Mendoza, Mario; Cunya, Eduardo; Olivera, Paula
2014-01-01
Raman Spectroscopy is .a high resolution photonics technique that provides chemical and structural information of almost any material, organic or inorganic compound. In this report we describe the implementation of a system based on the principle of Raman scattering, developed to analyze solid samples. The spectrometer integrates an optical bench coupled to an optical fiber and a green laser source of 532 nm. The spectrometer was tested obtaining the Naphthalene and the Yellow 74 Pigment Raman patterns. (authors).
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...
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...
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...
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...
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....
A planar waveguide optical discrete Fourier transformer design for 160 Gb/s all-optical OFDM systems
Li, Wei; Liang, Xiaojun; Ma, Weidong; Zhou, Tianhong; Huang, Benxiong; Liu, Deming
2010-01-01
A cost-effective all-optical discrete Fourier transformer (ODFT) is designed based on a silicon planar lightwave circuit (PLC), which can be applied to all-optical orthogonal frequency division multiplexing (OFDM) transmission systems and can be achieved by current techniques. It consists of 2 × 2 directional couplers, phase shifters and optical delay lines. Metal-film heaters are used as phase shifters, according to the thermooptic effect of SiO 2. Based on the ODFT, a 160 Gb/s OFDM system is set up. Simulation results show excellent bit error rate (BER) and optical signal-to-noise ratio (OSNR) performances after 400 km transmission.
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.
International Nuclear Information System (INIS)
Feit, M.D.; Fleck, J.A. Jr.
1989-01-01
We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage
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...
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.
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.
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.
Propagation of a general-type beam through a truncated fractional Fourier transform optical system.
Zhao, Chengliang; Cai, Yangjian
2010-03-01
Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.
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.
Quantification of DNA in simple eukaryotic cells using Fourier transform infrared spectroscopy.
Whelan, Donna R; Bambery, Keith R; Puskar, Ljiljana; McNaughton, Don; Wood, Bayden R
2013-10-01
A technique capable of detecting and monitoring nucleic acid concentration offers potential in diagnosing cancer and further developing an understanding of the biochemistry of disease. The application of Fourier transform infrared (FTIR) spectroscopy has previously been hindered by the supposed non-Beer-Lambert absorption behavior of DNA in intact cells making elucidation of the DNA bands difficult. We use known composition DNA/hemoglobin standards to successfully estimate the DNA content in avian erythrocyte nuclei (44.2%) and intact erythrocytes (12.8%). Furthermore we demonstrate that the absorption of cellular DNA does follow the Beer-Lambert Law and highlights the role of conformation and hydration in FTIR spectroscopy of biological samples. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.
Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José
2015-12-14
We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.
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....
A simple optical spectral calibration technique for pulsed THz sources
Wijnen, F.J.P.; G. Berden,; Jongma, R.T.
2010-01-01
We have quantified the sensitivity of a simple method to measurethe frequency spectrum of pulsed terahertz (THz) radiation. The THzpulses are upconverted to the optical regime by sideband generation in a zinctelluride (ZnTe) crystal using a continuous wave (cw) narrow-bandwidthnear-infrared laser. A
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.
High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform
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
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.
Hiding objects and creating illusions above a carpet filter using a Fourier optics approach.
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.
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
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....
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
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...
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...
Differences between time domain and Fourier domain optical coherence tomography in imaging tissues.
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.
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.)
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.
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.)
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....
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
Beyond MOS and fibers: Optical Fourier-transform Imaging Unit for Cananea Observatory (OFIUCO)
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.
Metasurface Enabled Wide-Angle Fourier Lens.
Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo
2018-06-01
Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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.
Research on FBG-based longitudinal-acousto-optic modulator with Fourier mode coupling method.
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.
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....
Pulse Propagation Effects in Optical 2D Fourier-Transform Spectroscopy: Theory.
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.
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
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.
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...
Muñoz Morales, Aarón A; Vázquez Y Montiel, Sergio
2012-10-01
The determination of optical parameters of biological tissues is essential for the application of optical techniques in the diagnosis and treatment of diseases. Diffuse Reflection Spectroscopy is a widely used technique to analyze the optical characteristics of biological tissues. In this paper we show that by using diffuse reflectance spectra and a new mathematical model we can retrieve the optical parameters by applying an adjustment of the data with nonlinear least squares. In our model we represent the spectra using a Fourier series expansion finding mathematical relations between the polynomial coefficients and the optical parameters. In this first paper we use spectra generated by the Monte Carlo Multilayered Technique to simulate the propagation of photons in turbid media. Using these spectra we determine the behavior of Fourier series coefficients when varying the optical parameters of the medium under study. With this procedure we find mathematical relations between Fourier series coefficients and optical parameters. Finally, the results show that our method can retrieve the optical parameters of biological tissues with accuracy that is adequate for medical applications.
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.
Glaucoma diagnosis by mapping macula with Fourier domain optical coherence tomography
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.
ADVANTAGES OF DIFFRACTIVE OPTICAL ELEMENTS APPLICATION IN SIMPLE OPTICAL IMAGING SYSTEMS
Directory of Open Access Journals (Sweden)
N. D. Zoric
2015-01-01
Full Text Available The paper deals with the influence of diffractive optical elements on the optical aberrations. The correction of optical aberrations was investigated in the simple optical systems with one and two lenses (singlet and doublet. The advantages of diffractive optical elements are their ability to generate arbitrary complex wave fronts from a piece of optical material that is essentially flat. The optical systems consisting of the standard surfaces were designed and optimized by using the same starting points. Further, the diffractive and aspheric surfaces were introduced into the developed systems. The resulting hybrid systems were optimized. To compare the complicity of the development of narrow field systems and wide field optical systems, the optimization has been done separately for these two types of the instruments. The optical systems were designed by using special Optical Design Software. Тhe characteristics of designed diffractive surfaces were controlled in Software DIFSYS 2.30. Due to the application of diffractive optical elements the longitudinal chromatic aberration was 5 times reduced for the narrow field systems. The absolute value of Seidel coefficient related to the spherical aberration was reduced in the range of 0.03. Considering that diffractive optical elements have the known disadvantages, like possible parasitic diffraction orders and probable decrease of the transmission, we also developed and analyzed the optical systems with combined aspheric and diffractive surfaces. A combination of the aspheric and diffractive surfaces in the optical disk system of the disk reading lens, gave cutting down of the longitudinal color aberrations almost 15 times on-axis, comparing to the lens consisting of the aspherical and standard surfaces. All of the designed diffractive optical elements possess the parameters within the fabrication limits.
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
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.
Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan
2012-02-15
Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.
DEFF Research Database (Denmark)
Hu, Hao; Kong, Deming; Palushani, Evarist
2013-01-01
320 Gb/s Nyquist-OTDM is generated by rectangular filtering with a bandwidth of 320 GHz and received by polarization-insensitive time-domain optical Fourier transformation (TD-OFT) followed by passive filtering. After the time-to-frequency mapping in the TD-OFT, the Nyquist-OTDM is converted into...
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
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
Simple optical readout for ethanol-chlorobenzene dosimetry system
International Nuclear Information System (INIS)
Ilijas, B.; Razem, D.
1999-01-01
Optical readout of the ethanol-chlorobenzene (ECB) or Dvornik dosimetry system is based on the development of the coloured secondary complex of ferric thiocyanate which has a maximum absorption at 485 nm. The applicability of a rugged, hand-held, battery powered filter colorimeter operating at 480 nm has been investigated as a reader for this purpose. This simple reader performs very well within absorbance one displaying an excellent linearity of absorbance with the concentration of Cl - ions. It is shown that by choosing the appropriate dilution factor when preparing the secondary complex solution the entire useful dose range of the dosimeter up to 2 MGy can be covered. The applicability of this reader to some other liquid chemical dosimeters is also discussed. (author)
Simple optical readout for ethanol - chlorobenzene dosimetry system
International Nuclear Information System (INIS)
Ilijas, B.; Razem, D.
1999-01-01
Optical readout of the ethanol-chlorobenzene (ECB or Dvornik dosimetry system) is based on the development of coloured secondary complex of ferric thiocyanate which has a maximum absorption at 485 nm. The applicability of a rugged, hand-held, battery powered filter colorimeter operating at 480 nm has been investigated as a reader for this purpose. This simple reader performs very well within absorbance displaying an excellent linearity of absorbance with the concentration of Cl - ions. It was shown, by choosing the appropriate dilution factor when preparing the secondary complex solution, the entire useful dose range of the dosimeter up to 2 MGy can be covered. The applicability of the same reader to some other liquid chemical dosimeters is also discussed. (author)
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.
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
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
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.
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.
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
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.
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.
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.
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.
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
International Nuclear Information System (INIS)
Britton, D.T.; Bentvelsen, P.; Vries, J. de; Veen, A. van
1988-01-01
A deconvolution scheme for digital lineshapes using fast Fourier transforms and a filter based on background subtraction in Fourier space has been developed. In tests on synthetic data this has been shown to give optimum deconvolution without prior inspection of the Fourier spectrum. Although offering significant improvements on the raw data, deconvolution is shown to be limited. The contribution of the resolution function is substantially reduced but not eliminated completely and unphysical oscillations are introduced into the lineshape. The method is further tested on measurements of the lineshape for positron annihilation in single crystal copper at the relatively poor resolution of 1.7 keV at 512 keV. A two-component fit is possible yielding component widths in agreement with previous measurements. (orig.)
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.
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
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.
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)
Simple method for measuring reflectance of optical coatings
International Nuclear Information System (INIS)
Wen Gui Wang; Yi Sheng Chen
1995-01-01
The quality of optical coatings has an important effect on the performance of optical instrument. The last few years, the requirements for super low loss dielectric mirror coatings used in low gain laser systems such as free electron laser and the ring laser etc., have given an impetus to the development of the technology of precise reflectance measurement of optical coatings. A reliable and workable technique is to measure the light intensity decay time of optical resonant cavity. This paper describes a measuring method which is dependent on direct measurement of the light intensity decay time of a resonant cavity comprised of low loss optical components. According to the evolution of a luminous flux stored inside the cavity, this method guarantees not only a quick and precise reflectance measurements of low loss highly reflecting mirror coatings but also transmittance measurements of low loss antireflection coatings and is especially effective with super los loss highly reflecting mirror. From the round-trip path length of the cavity and the speed of light, the light intensity exponential decay time of an optical cavity is easy to obtain and the cavity losses can be deduced. An optical reflectance of low loss highly mirror coatings and antireflection coatings is precisely measured as well. This is highly significant for the discrimination of the coating surface characteristics, the improvement of the performance of optical instrument and the development of high technology
A simple multipurpose double-beam optical image analyzer
Energy Technology Data Exchange (ETDEWEB)
Popowicz, A., E-mail: adam.popowicz@polsl.pl [Institute of Automatic Control, Silesian University of Technology, Akademicka Str. 16, 44-100 Gliwice (Poland); Blachowicz, T. [Institute of Physics - Center for Science and Education, Silesian University of Technology, S. Konarskiego 22B Str., 44-100 Gliwice (Poland)
2016-07-15
In the paper we present a low cost optical device which splits the light in the focal plane into two separate optical paths and collimates it back into a single image plane, and where a selective information processing can be carried out. The optical system is straightforward and easily implementable as it consists of only three lenses and two mirrors. The system is dedicated for imaging in low-light-level conditions in which widely used optical devices, based on beam splitters or dichroic mirrors, suffer from light loss. We expose examples of applications of our device, using a prototype model. The proposed optical system may be employed for: monitoring the objects located at different distances from observer (1), creating regions of different magnification within a single image plane (2), high dynamic range photometry (3), or imaging in two wavelength bands simultaneously (4).
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...
Energy Technology Data Exchange (ETDEWEB)
Mendoza, Mario; Cunya, Eduardo; Olivera, Paula [Direccion de Investigacion y Desarrollo, Instituto Peruano de Energia Nuclear, Lima (Peru)
2014-07-01
Raman Spectroscopy is .a high resolution photonics technique that provides chemical and structural information of almost any material, organic or inorganic compound. In this report we describe the implementation of a system based on the principle of Raman scattering, developed to analyze solid samples. The spectrometer integrates an optical bench coupled to an optical fiber and a green laser source of 532 nm. The spectrometer was tested obtaining the Naphthalene and the Yellow 74 Pigment Raman patterns. (authors).
Simple Room Temperature Method for Polymer Optical Fibre Cleaving
DEFF Research Database (Denmark)
Saez-Rodriguez, David; Nielsen, Kristian; Bang, Ole
2015-01-01
In this paper, we report on a new method to cleave polymer optical fibre. The most common way to cut a polymer optical fibre is chopping it with a razor blade; however, in this approach both the fibre and the blade must be preheated in order to turn the material ductile, and thus, prevent crazing...... of similar quality to those produced by more complex and expensive heated systems....
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)
Development of Fourier domain optical coherence tomography for applications in developmental biology
Davis, Anjul Maheshwari
Developmental biology is a field in which explorations are made to answer how an organism transforms from a single cell to a complex system made up of trillions of highly organized and highly specified cells. This field, however, is not just for discovery, it is crucial for unlocking factors that lead to diseases, defects, or malformations. The one key ingredient that contributes to the success of studies in developmental biology is the technology that is available for use. Optical coherence tomography (OCT) is one such technology. OCT fills a niche between the high resolution of confocal microscopy and deep imaging penetration of ultrasound. Developmental studies of the chicken embryo heart are of great interest. Studies in mature hearts, zebrafish animal models, and to a more limited degree chicken embryos, indicate a relationship between blood flow and development. It is believed that at the earliest stages, when the heart is still a tube, the purpose of blood flow is not for convective transport of oxygen, nutrients and waster, bur rather to induce shear-related gene expressions to induce further development. Yet, to this date, the simple question of "what makes blood flow?" has not been answered. This is mainly due limited availability to adequate imaging and blood flow measurement tools. Earlier work has demonstrated the potential of OCT for use in studying chicken embryo heart development, however quantitative measurement techniques still needed to be developed. In this dissertation I present technological developments I have made towards building an OCT system to study chick embryo heart development. I will describe: (1) a swept-source OCT with extended imaging depth; (2) a spectral domain OCT system for non-invasive small animal imaging; (3) Doppler flow imaging and techniques for quantitative blood flow measurement in living chicken embryos; and (4) application of the OCT system that was developed in the Specific Aims 2-5 to test hypotheses generated by a
Suspension and simple optical characterization of two-dimensional membranes
Northeast, David B.; Knobel, Robert G.
2018-03-01
We report on a method for suspending two-dimensional crystal materials in an electronic circuit using an only photoresists and solvents. Graphene and NbSe2 are suspended tens of nanometers above metal electrodes with clamping diameters of several microns. The optical cavity formed from the membrane/air/metal structures enables a quick method to measure the number of layers and the gap separation using comparisons between the expected colour and optical microscope images. This characterization technique can be used with just an illuminated microscope with a digital camera which makes it adaptable to environments where other means of characterization are not possible, such as inside nitrogen glove boxes used in handling oxygen-sensitive materials.
Analyzing Fourier Transforms for NASA DFRC's Fiber Optic Strain Sensing System
Fiechtner, Kaitlyn Leann
2010-01-01
This document provides a basic overview of the fiber optic technology used for sensing stress, strain, and temperature. Also, the document summarizes the research concerning speed and accuracy of the possible mathematical algorithms that can be used for NASA DFRC's Fiber Optic Strain Sensing (FOSS) system.
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.
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.
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.
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...
Optical-Path-Difference Linear Mechanism for the Panchromatic Fourier Transform Spectrometer
Blavier, Jean-Francois L.; Heverly, Matthew C.; Key, Richard W.; Sander, Stanley P.
2011-01-01
A document discusses a mechanism that uses flex-pivots in a parallelogram arrangement to provide frictionless motion with an unlimited lifetime. A voicecoil actuator drives the parallelogram over the required 5-cm travel. An optical position sensor provides feedback for a servo loop that keeps the velocity within 1 percent of expected value. Residual tip/tilt error is compensated for by a piezo actuator that drives the interferometer mirror. This mechanism builds on previous work that targeted ground-based measurements. The main novelty aspects include cryogenic and vacuum operation, high reliability for spaceflight, compactness of the design, optical layout compatible with the needs of an imaging FTS (i.e. wide overall field-of-view), and mirror optical coatings to cover very broad wavelength range (i.e., 0.26 to 15 m).
DEFF Research Database (Denmark)
Guan, P.; Mulvad, Hans Christian Hansen; Tomiyama, Y.
2010-01-01
A single-channel 1.28 Tbit/s transmission over 525 km is demonstrated for the first time with a single-polarization DQPSK signal. Ultrafast time-domain optical Fourier transformation is successfully applied to DQPSK signals and results in improved performance and increased system margin.......A single-channel 1.28 Tbit/s transmission over 525 km is demonstrated for the first time with a single-polarization DQPSK signal. Ultrafast time-domain optical Fourier transformation is successfully applied to DQPSK signals and results in improved performance and increased system margin....
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.
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.
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…
A simple system for 160GHz optical terahertz wave generation and data modulation
Li, Yihan; He, Jingsuo; Sun, Xueming; Shi, Zexia; Wang, Ruike; Cui, Hailin; Su, Bo; Zhang, Cunlin
2018-01-01
A simple system based on two cascaded Mach-Zehnder modulators, which can generate 160GHz optical terahertz waves from 40GHz microwave sources, is simulated and tested in this paper. Fiber grating filter is used in the system to filter out optical carrier. By properly adjusting the modulator DC bias voltages and the signal voltages and phases, 4-tupling optical terahertz wave can be generated with fiber grating. This notch fiber grating filter is greatly suitable for terahertz over fiber (TOF) communication system. This scheme greatly reduces the cost of long-distance terahertz communication. Furthermore, 10Gbps digital signal is modulated in the 160GHz optical terahertz wave.
Sato, Kenichi; Seimiya, Masanori; Kodera, Yoshio; Kitamura, Akihide; Nomura, Fumio
2010-02-01
Fourier-transform infrared (FT-IR) spectroscopy is a simple and reagent-free physicochemical analysis method, and is a potential alternative to more time-consuming and labor-intensive procedures. In this study, we aimed to use FT-IR spectroscopy to determine serum concentrations of chylomicron-triglyceride (TG) and very low density lipoprotein (VLDL)-TG. We analyzed a chylomicron fraction and VLDL fraction, which had been obtained by ultracentrifugation, to search for wavelengths to designate to each fraction. Then, partial least square (PLS) calibrations were developed using a training set of samples, for which TG concentrations had been determined by conventional procedures. Validation was conducted with another set of samples using the PLS model to predict serum TG concentrations on the basis of the samples' IR spectra. We analyzed a total of 150 samples. Serum concentrations of chylomicron-TG and VLDL-TG estimated by FT-IR spectroscopy agreed well with those obtained by the reference method (r=0.97 for both lipoprotein fractions). FT-IR spectrometric analysis required 15mul of serum and was completed within 1min. Serum chylomicron-TG and VLDL-TG concentrations can be determined with FT-IR spectroscopy. This rapid and simple test may have a great impact on the management of patients with dyslipidemia. Copyright 2009. Published by Elsevier B.V.
Fourier transform infrared (FTIR) fiber optic monitoring of composites during cure in an autoclave
Druy, Mark A.; Elandjian, Lucy; Stevenson, William A.; Driver, Richard D.; Leskowitz, Garett M.
1990-01-01
Real-time in situ monitoring of the chemical states of epoxy resins was investigated during cure in an autoclave using infrared evanescent spectroscopy. Fiber evanescent sensors were developed which may be sandwiched between the plies of the prepreg sample. A short length of sapphire fiber was used as the sensor cell portion of the fiber probe. Heavy metal fluoride glass optical fiber cables were designed for connecting the FTIR spectrometer to the sensor fiber within the autoclave. The sapphire fibers have outstanding mechanical thermal properties which should permit their use as an embedded link in all thermoset composites. The system is capable of operation at a temperature of 250 C for periods up to 8 hours without major changes to the fiber transmission. A discussion of the selection of suitable sensor fibers, the construction of a fiber-optic interface, and the interpretation of in situ infrared spectra of the curing process is presented.
Quantitative Fourier Domain Optical Coherence Tomography Imaging of the Ocular Anterior Segment
McNabb, Ryan Palmer
Clinical imaging within ophthalmology has had transformative effects on ocular health over the last century. Imaging has guided clinicians in their pharmaceutical and surgical treatments of macular degeneration, glaucoma, cataracts and numerous other pathologies. Many of the imaging techniques currently used are photography based and are limited to imaging the surface of ocular structures. This limitation forces clinicians to make assumptions about the underlying tissue which may reduce the efficacy of their diagnoses. Optical coherence tomography (OCT) is a non-invasive, non-ionizing imaging modality that has been widely adopted within the field of ophthalmology in the last 15 years. As an optical imaging technique, OCT utilizes low-coherence interferometry to produce micron-scale three-dimensional datasets of a tissue's structure. Much of the human body consists of tissues that significantly scatter and attenuate optical signals limiting the imaging depth of OCT in those tissues to only 1-2mm. However, the ocular anterior segment is unique among human tissue in that it is primarily transparent or translucent. This allows for relatively deep imaging of tissue structure with OCT and is no longer limited by the optical scattering properties of the tissue. This goal of this work is to develop methods utilizing OCT that offer the potential to reduce the assumptions made by clinicians in their evaluations of their patients' ocular anterior segments. We achieved this by first developing a method to reduce the effects of patient motion during OCT volume acquisitions allowing for accurate, three dimensional measurements of corneal shape. Having accurate corneal shape measurements then allowed us to determine corneal spherical and astigmatic refractive contribution in a given individual. This was then validated in a clinical study that showed OCT better measured refractive change due to surgery than other clinical devices. Additionally, a method was developed to combine
Singh, G.; McElroy, C. T.; Vaziri, Z.; Barton, D.; Blair, G.; Grandmont, F. J.
2017-12-01
The fifth assessment report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) states that the warming of zonal mean surface temperature at higher latitudes exceeds the global average temperature change. This poses a great problem as the warming leads to the thawing of the permafrost in the Arctic region that acts as an envelope to trap greenhouse gases such as carbon dioxide and methane. Therefore, there is an urgent need to develop scientific instruments that can be flown in space over the Arctic to provide atmospheric information to quantify the evolution and transport of these gases. The Laboratory for Atmospheric Remote Sounding from Space (LARSS) at York University is developing an imaging Fourier transform spectrometer (IFTS) for climate observations by atmospheric sounding. The spectrometer has two individual channels, one centred at 1650 nm to measure the atmospheric column of carbon dioxide and methane, and another centred at 762 nm to measure the temperature-pressure profile by making measurements of the O2A band. A Commercial-Off-The-Shelf (COTS) modulator has been purchased from ABB Inc. of Quebec City. Interferometers are widely used in many scientific laboratories to measure concentrations of different constituents in a given sample. The performance of these instruments is highly dependent on environmental effects and various properties of the input beam such as coherence, polarity, etc. Thus, the use of such instruments to measure atmospheric concentration is complicated and challenging. The immediate goal of this project is to develop an IFTS system which can measure backscattered radiation in a laboratory environment and develop design elements that will make it operable in the space environment. Progress on the project and information concerning some of the issues listed above will be discussed. The developments which flow from this research project will support efforts by Environment and Climate Change Canada, the Canadian Space
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.
A simple optical fiber device for quantitative fluorescence microscopy of single living cells
van Graft, M.; van Graft, Marja; Oosterhuis, B.; Oosterhuis, Bernard; van der Werf, Kees; de Grooth, B.G.; Greve, Jan
1993-01-01
simple and relatively inexpensive system is described for obtaining quantitative fluorescence measurements on single living cells loaded with a fluorescent probe to study cell physiological processes. The light emitted from the fluorescent cells is captured by and transported through an optical fiber. After passage through appropriate filters the light is measured using a photomultiplier tube. The optical fiber is mounted in one of the microscope outlets. Signals derived from the photomultipl...
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.
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.
Perrin, Stephane; Baranski, Maciej; Froehly, Luc; Albero, Jorge; Passilly, Nicolas; Gorecki, Christophe
2015-11-01
We report a simple method, based on intensity measurements, for the characterization of the wavefront and aberrations produced by micro-optical focusing elements. This method employs the setup presented earlier in [Opt. Express 22, 13202 (2014)] for measurements of the 3D point spread function, on which a basic phase-retrieval algorithm is applied. This combination allows for retrieval of the wavefront generated by the micro-optical element and, in addition, quantification of the optical aberrations through the wavefront decomposition with Zernike polynomials. The optical setup requires only an in-motion imaging system. The technique, adapted for the optimization of micro-optical component fabrication, is demonstrated by characterizing a planoconvex microlens.
Liu, Yongliang; Kim, Hee-Jin
2017-06-22
With cotton fiber growth or maturation, cellulose content in cotton fibers markedly increases. Traditional chemical methods have been developed to determine cellulose content, but it is time-consuming and labor-intensive, mostly owing to the slow hydrolysis process of fiber cellulose components. As one approach, the attenuated total reflection Fourier transform infrared (ATR FT-IR) spectroscopy technique has also been utilized to monitor cotton cellulose formation, by implementing various spectral interpretation strategies of both multivariate principal component analysis (PCA) and 1-, 2- or 3-band/-variable intensity or intensity ratios. The main objective of this study was to compare the correlations between cellulose content determined by chemical analysis and ATR FT-IR spectral indices acquired by the reported procedures, among developmental Texas Marker-1 (TM-1) and immature fiber ( im ) mutant cotton fibers. It was observed that the R value, CI IR , and the integrated intensity of the 895 cm -1 band exhibited strong and linear relationships with cellulose content. The results have demonstrated the suitability and utility of ATR FT-IR spectroscopy, combined with a simple algorithm analysis, in assessing cotton fiber cellulose content, maturity, and crystallinity in a manner which is rapid, routine, and non-destructive.
Kim, In-Hye; Son, Jun Sik; Min, Bong Ki; Kim, Young Kyoung; Kim, Kyo-Han; Kwon, Tae-Yub
2016-03-30
Although many techniques are available to assess enamel erosion in vitro, a simple, non-destructive method with sufficient sensitivity for quantifying dental erosion is required. This study characterized the bovine dental enamel erosion induced by various acidic beverages in vitro using attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy. Deionized water (control) and 10 acidic beverages were selected to study erosion, and the pH and neutralizable acidity were measured. Bovine anterior teeth (110) were polished with up to 1 200-grit silicon carbide paper to produce flat enamel surfaces, which were then immersed in 20 mL of the beverages for 30 min at 37 °C. The degree of erosion was evaluated using ATR-FTIR spectroscopy and Vickers' microhardness measurements. The spectra obtained were interpreted in two ways that focused on the ν1, ν3 phosphate contour: the ratio of the height amplitude of ν3 PO4 to that of ν1 PO4 (Method 1) and the shift of the ν3 PO4 peak to a higher wavenumber (Method 2). The percentage changes in microhardness after the erosion treatments were primarily affected by the pH of the immersion media. Regression analyses revealed highly significant correlations between the surface hardness change and the degree of erosion, as detected by ATR-FTIR spectroscopy (Perosion.
A simple optical fiber device for quantitative fluorescence microscopy of single living cells
van Graft, M.; van Graft, Marja; Oosterhuis, B.; Oosterhuis, Bernard; van der Werf, Kees; de Grooth, B.G.; Greve, Jan
1993-01-01
simple and relatively inexpensive system is described for obtaining quantitative fluorescence measurements on single living cells loaded with a fluorescent probe to study cell physiological processes. The light emitted from the fluorescent cells is captured by and transported through an optical
A simple optical fibre-linked remote control system for multiple devices
Indian Academy of Sciences (India)
We report on the development of a simple control system which can handle multiple devices through an optical ﬁbre data link. The devices are controlled using a set of DACs through serial data communication via a serial port of a PC. Serial data from the PC get converted to parallel mode using a homemade “serial in ...
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.
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.
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.
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.
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.
Simple theory of the inverse Faraday effect with relationship to optical constants N and K
International Nuclear Information System (INIS)
Yoshino, Toshihiko
2011-01-01
The inverse Faraday effect in general materials is theoretically investigated based on the classical motion of an electron. It is shown that the inverse Faraday effect is simply and explicitly expressed in terms of optical constants N and K, i.e., the real and imaginary parts of complex refractive index of materials. The derived new formula provides a good physical perspective for the inverse Faraday effect and enables its easy quantitative evaluation from familiar optical constants. - Highlights: → The theory of the inverse Faraday effect in general materials is presented based on the classical motion model of electron. → The simple relationship between optical constants of materials and the inverse Faraday effect is given. → The given new formula enables easy quantitative evaluation of the inverse Faraday effect from known optical constants.
Z-scan: A simple technique for determination of third-order optical nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Singh, Vijender, E-mail: chahal-gju@rediffmail.com [Department of Applied Science, N.C. College of Engineering, Israna, Panipat-132107, Haryana (India); Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.co.in [Department of Physics, Chaudhary Devi Lal University, Sirsa-125055, Haryana (India)
2015-08-28
Z-scan is a simple experimental technique to measure intensity dependent nonlinear susceptibilities of third-order nonlinear optical materials. This technique is used to measure the sign and magnitude of both real and imaginary part of the third order nonlinear susceptibility (χ{sup (3)}) of nonlinear optical materials. In this paper, we investigate third-order nonlinear optical properties of Ag-polymer composite film by using single beam z-scan technique with Q-switched, frequency doubled Nd: YAG laser (λ=532 nm) at 5 ns pulse. The values of nonlinear absorption coefficient (β), nonlinear refractive index (n{sub 2}) and third-order nonlinear optical susceptibility (χ{sup (3)}) of permethylazine were found to be 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.
Directory of Open Access Journals (Sweden)
Ryu Jiheun
2015-01-01
Full Text Available During the research using fluorescence-tagged or auto-fluorescence molecules, meaningful information is often buried deep inside the tissue, not its surface. Therefore, especially in the field of biomedical imaging, acquiring optically sectioned images from deep inside the tissue is very important. As well know already, confocal laser scanning microscopy (the most well-known optical sectioning microscopy gives axially-resolved fluorescence information using the physical background blocking component called pinhole. However, the axial range of imaging is practically limited due to such optical phenomena as the light scattered and absorbed in the tissue. However, nonlinear optical microscopy (e.g. Multiphoton microscopy, harmonic generation microscopy, coherent anti-Stokes Raman spectroscopy realized by the development of ultrafast light sources has been used for visualizing various tissues, especially in vivo, because of their low sensitivity to the limitation caused by the scattering and the absorption of light. Although nonlinear optical microscopy gives deep tissue image, it is not easy for many researcher to build customized nonlinear system. Here, we introduce an easy and simple way designing and developing such nonlinear optical microscope with upright or inverted epi-illumination platform using commercial optical components only.
Simple scattering analysis and simulation of optical components created by additive manufacturing
Rank, M.; Horsak, A.; Heinrich, A.
2017-10-01
Additive manufacturing of optical elements is known but still new to the field of optical fabrication. In 3D printers, the parts are deposited layer-by-layer approximating the shape defined in optics design enabling new shapes, which cannot be manufactured using conventional methods. However, the layered structure also causes surface roughness and subsurface scattering, which decrease the quality of optical elements. Illuminating a flat sample with a laser beam, different light distributions are generated on a screen depending on the printing orientation of the sample. Whereas the laser beam is mainly diffused by the samples, a line shaped light distribution can be achieved for a special case in which the laser light goes parallel to the layer structure. These optical effects of 3D printed parts are analyzed using a goniometric setup and fed back into the optics simulation with the goal to improve the design considering the characteristics of the real sample. For a detailed look on the effect, the total scattering is split up into surface contributions and subsurface scattering using index matching techniques to isolate the effects from each other. For an index matched sample with negligible surface effects the line shaped distribution turns into a diffraction pattern which corresponds to the layer thickness of the printer. Finally, an optic simulation with the scattering data is set up for a simple curved sample. The light distribution measured with a robot-based goniophotometer differs from the simulation, because the curvature is approximated by the layer structure. This makes additional analysis necessary.
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
Hossein-Javaheri, Nima; Molday, Laurie L.; Xu, Jing; Molday, Robert S.; Sarunic, Marinko V.
2009-02-01
Visualization of the internal structures of the retina is critical for clinical diagnosis and monitoring of pathology as well as for medical research investigating the root causes of retinal degeneration. Optical Coherence Tomography (OCT) is emerging as the preferred technique for non-contact sub-surface depth-resolved imaging of the retina. The high resolution cross sectional images acquired in vivo by OCT can be compared to histology to visually delineate the retinal layers. The recent demonstration of the significant sensitivity increase obtained through use of Fourier domain (FD) detection with OCT has been used to facilitate high speed scanning for volumetric reconstruction of the retina in software. The images acquired by OCT are purely structural, relying on refractive index differences in the tissue for contrast, and do not provide information on the molecular content of the sample. We have constructed a FDOCT prototype and combined it with a fluorescent Scanning Laser Ophthalmoscope (fSLO) to permit real time alignment of the field of view on the retina. The alignment of the FDOCT system to the specimen is crucial for the registration of measurements taken throughout longitudinal studies. In addition, fluorescence detection has been integrated with the SLO to enable the en face localization of a molecular contrast signal, which is important for retinal angiography, and also for detection of autofluorescence associated with some forms of retinal degeneration, for example autofluorescence lipofuscin accumulations are associated with Stargardt's Macular Dystrophy. The integrated FD OCT/fSLO system was investigated for imaging the retina of the mice in vivo.
Smith, Allison J.; Telander, David G.; Zawadzki, Robert J.; Choi, Stacey S.; Morse, Lawrence S.; Werner, John S.; Park, Susanna S.
2009-01-01
Objective To evaluate the morphologic changes in the macula of subjects with repaired macula-off retinal detachment (RD) using high-resolution Fourier-domain optical coherence tomography (FD OCT) and to perform functional correlation in a subset of patients using microperimetry (MP-1). Design Prospective observational case series. Participants Seventeen eyes from 17 subjects who had undergone anatomically successful repair for macula-off, rhegmatogenous RD at least 3 months earlier and without visually significant maculopathy on funduscopy. Methods FD OCT with axial and transverse resolution of 4.5 μm and 10 to 15 μm, respectively, was used to obtain rapid serial B-scans of the macula, which were compared with that from Stratus OCT. The FD OCT B-scans were used to create a 3-dimensional volume, from which en face C-scans were created. Among 11 patients, MP-1 was performed to correlate morphologic changes with visual function. Main Outcome Measures Stratus OCT scans, FD OCT scans, and MP-1 data. Results Stratus OCT and FD OCT images of the macula were obtained 3 to 30 months (mean 7 months) postoperatively in all eyes. Although Stratus OCT revealed photoreceptor disruption in 2 eyes (12%), FD OCT showed photoreceptor disruption in 13 eyes (76%). This difference was statistically significant (Pmacula-off RD repair is a common abnormality in the macula that is detected better with FD OCT than Stratus OCT. A good correlation between MP-1 abnormality and presence of photoreceptor disruption or subretinal fluid on FD OCT demonstrates that these anatomic abnormalities contribute to decreased visual function after successful repair. PMID:18672289
A simple optical method for measuring the vibration amplitude of a speaker
UEDA, Masahiro; YAMAGUCHI, Toshihiko; KAKIUCHI, Hiroki; SUGA, Hiroshi
1999-01-01
A simple optical method has been proposed for measuring the vibration amplitude of a speaker vibrating with a frequency of approximately 10 kHz. The method is based on a multiple reflection between a vibrating speaker plane and a mirror parallel to that speaker plane. The multiple reflection can magnify a dispersion of the laser beam caused by the vibration, and easily make a measurement of the amplitude. The measuring sensitivity ranges between sub-microns and 1 mm. A preliminary experim...
A simple model explaining super-resolution in absolute optical instruments
Leonhardt, Ulf; Sahebdivan, Sahar; Kogan, Alex; Tyc, Tomáš
2015-05-01
We develop a simple, one-dimensional model for super-resolution in absolute optical instruments that is able to describe the interplay between sources and detectors. Our model explains the subwavelength sensitivity of a point detector to a point source reported in previous computer simulations and experiments (Miñano 2011 New J. Phys.13 125009; Miñano 2014 New J. Phys.16 033015).
Optical interconnection for a polymeric PLC device using simple positional alignment.
Ryu, Jin Hwa; Kim, Po Jin; Cho, Cheon Soo; Lee, El-Hang; Kim, Chang-Seok; Jeong, Myung Yung
2011-04-25
This study proposes a simple cost-effective method of optical interconnection between a planar lightwave circuit (PLC) device chip and an optical fiber. It was conducted to minimize and overcome the coupling loss caused by lateral offset which is due to the process tolerance and the dimensional limitation existing between PLC device chips and fiber array blocks with groove structures. A PLC device chip and a fiber array block were simultaneously fabricated in a series of polymer replication processes using the original master. The dimensions (i.e., width and thickness) of the under-clad of the PLC device chip were identical to those of the fiber array block. The PLC device chip and optical fiber were aligned by simple positional control for the vertical direction of the PLC device chip under a particular condition. The insertion loss of the proposed 1 x 2 multimode optical splitter device interconnection was 4.0 dB at 850 nm and the coupling loss was below 0.1 dB compared with single-fiber based active alignment.
Directory of Open Access Journals (Sweden)
Baskaran, Prabu
2017-10-01
Full Text Available Aim: Presumed congenital simple retinal pigment epithelium hamartoma is a rare benign lesion of the macula that mimics congenital hypertrophy of the retinal pigment epithelium (RPE and combined hamartoma of the retina and the RPE; newer imaging modalities can help in diagnosis. We report three patients with presumed congenital simple RPE hamartoma, and describe the enhanced-depth imaging optical coherence tomography (EDI-OCT and fundus autofluorescence (FAF findings. Methods: Two patients were asymptomatic; one had an intraocular foreign body in addition to the hamartoma. All had a similar jet black, elevated lesion in the macula, sparing the fovea. EDI-OCT showed a characteristic hyperreflective layer with complete optical shadowing of the deeper layers; FAF showed pronounced hypoautofluorescence of the lesion. Conclusion: Multimodal imaging with FAF and EDI-OCT can help to differentiate simple RPE hamartoma from similar RPE lesions, and may serve as a useful adjunct to clinical diagnosis of this rare tumor. We present the second largest series of presumed congenital simple RPE hamartoma, and – to the best of our knowledge – the first report of FAF findings of this tumor.
Fourier analysis an introduction
Stein, Elias M
2003-01-01
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Dimitrov, Vesselin, E-mail: vesselin@uctm.edu [Department of Silicate Technology, University of Chemical Technology and Metallurgy, 8, Kl. Ohridski Blvd., Sofia 1756 (Bulgaria); Komatsu, Takayuki, E-mail: komatsu@mst.nagaokaut.ac.jp [Department of Materials Science and Technology, Nagaoka University of Technology, 1603-1 Kamitomioka-cho, Nagaoka 940-2188 (Japan)
2012-12-15
A suitable relationship between free-cation polarizability and electronegativity of elements in different valence states and with the most common coordination numbers has been searched on the basis of the similarity in physical nature of both quantities. In general, the cation polarizability increases with decreasing element electronegativity. A systematic periodic change in the polarizability against the electronegativity has been observed in the isoelectronic series. It has been found that generally the optical basicity increases and the single bond strength of simple oxides decreases with decreasing the electronegativity. The observed trends have been discussed on the basis of electron donation ability of the oxide ions and type of chemical bonding in simple oxides. - Graphical abstract: This figure shows the single bond strength of simple oxides as a function of element electronegativity. A remarkable correlation exists between these independently obtained quantities. High values of electronegativity correspond to high values of single bond strength and vice versa. It is obvious that the observed trend in this figure is closely related to the type of chemical bonding in corresponding oxide. Highlights: Black-Right-Pointing-Pointer A suitable relationship between free-cation polarizability and electronegativity of elements was searched. Black-Right-Pointing-Pointer The cation polarizability increases with decreasing element electronegativity. Black-Right-Pointing-Pointer The single bond strength of simple oxides decreases with decreasing the electronegativity. Black-Right-Pointing-Pointer The observed trends were discussed on the basis of type of chemical bonding in simple oxides.
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.
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)
Oubei, Hassan M.
2017-06-16
In this Letter, we use laser beam intensity fluctuation measurements to model and describe the statistical properties of weak temperature-induced turbulence in underwater wireless optical communication (UWOC) channels. UWOC channels with temperature gradients are modeled by the generalized gamma distribution (GGD) with an excellent goodness of fit to the measured data under all channel conditions. Meanwhile, thermally uniform channels are perfectly described by the simple gamma distribution which is a special case of GGD. To the best of our knowledge, this is the first model that comprehensively describes both thermally uniform and gradient-based UWOC channels.
A simple formalism for diffusion coefficient calculations in cells having a small optical thickness
International Nuclear Information System (INIS)
Benoist, Pierre.
1980-04-01
A very simple formalism, using directionnal first flight collision probabilities, is established; it is assigned to the calculation of the diffusion coefficients in cells having a small optical thickness. This formalism can be used, at least as a first approximation, in lattices of sodium-cooled fast reactors or of light water reactors. However, due to the two assumptions -cylindricalization of the cell and restriction to the zeroth order term in B 2 (k)- this formalissm cannot be used for sodium-voided or gas-cooled fast reactor lattices [fr
Directory of Open Access Journals (Sweden)
K. Hedayati
2015-10-01
Full Text Available In this research zinc oxide (ZnO nano-crystalline powders were prepared by sol-gel method using zinc acetate. The ZnO nanoparticles were characterized by X-ray diffraction (XRD, scanning electron microscopy (SEM, ultraviolet-visible (UV-Vis, Fourier transform infra-red (FT-IR and energy dispersive X-ray (EDX spectroscopy. The structure of nanoparticles was studied using XRD pattern. The crystallite size of ZnO nanoparticles was calculated by Debye–Scherrer formula. Morphology of nano-crystals was observed and investigated using the SEM. The grain size of zinc oxide nanoparticles were in suitable agreement with the crystalline size calculated by XRD results. The optical properties of particles were studied with UV-Vis an FTIR absorption spectrum. The Raman spectrum measurements were carried out using a micro-laser Raman spectrometer forms the ZnO nanoparticles. At the end studied the effect of calcined temperature on the photoluminescence (PL emission of ZnO nanoparticles.
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.
Energy Technology Data Exchange (ETDEWEB)
Barrera-Calva, E., E-mail: ebc@xanum.uam.m [Departamento de Ingenieria de Procesos e hidraulica, Universidad Autonoma Metropolitana - Iztapalapa, Av. Purisima Esq. Michoacan, Col. Vicentina, Mexico, D.F., 09340 (Mexico); Ortega-Lopez, M.; Avila-Garcia, A.; Matsumoto-Kwabara, Y. [Departamento de Ingenieria Electrica, Centro de Investigacion y de Estudios Avanzados del IPN, Mexico DF 07360 (Mexico)
2010-01-31
Silver sulphide (Ag{sub 2}S) thin films were grown on the surface of silver films (Ag) deposited on glass substrate by using a simple chemical sulphurization method. According to X-ray diffraction analysis, the Ag{sub 2}S thin films display low intensity peaks at 34.48{sup o}, 36.56{sup o}, and 44.28{sup o}, corresponding to diffraction from (100), (112) and (103) planes of the acanthite phase (monoclinic). A model of the type Ag{sub 2}S/Ag/glass was deduced from spectroscopic ellipsometric measurements. Also, the optical constants (n, k) of the system were determined. Furthermore, the optical properties as solar selective absorber for collector applications were assessed. The optical reflectance of the Ag{sub 2}S/Ag thin film systems exhibits the expected behavior for an ideal selective absorber, showing a low reflectance in the wavelength range below 2 {mu}m and a high reflectance for wavelengths higher than that value. An absorptance about 70% and an emittance about 3% or less were calculated for several samples.
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.
Wang, Xiaogang; Chen, Wen; Chen, Xudong
2014-09-22
We present a novel image hiding method based on phase retrieval algorithm under the framework of nonlinear double random phase encoding in fractional Fourier domain. Two phase-only masks (POMs) are efficiently determined by using the phase retrieval algorithm, in which two cascaded phase-truncated fractional Fourier transforms (FrFTs) are involved. No undesired information disclosure, post-processing of the POMs or digital inverse computation appears in our proposed method. In order to achieve the reduction in key transmission, a modified image hiding method based on the modified phase retrieval algorithm and logistic map is further proposed in this paper, in which the fractional orders and the parameters with respect to the logistic map are regarded as encryption keys. Numerical results have demonstrated the feasibility and effectiveness of the proposed algorithms.
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.
A New Simple Model for Underwater Wireless Optical Channels in the Presence of Air Bubbles
Zedini, Emna
2018-01-15
A novel statistical model is proposed to characterize turbulence-induced fading in underwater wireless optical channels in the presence of air bubbles for fresh and salty waters, based on experimental data. In this model, the channel irradiance fluctuations are characterized by the mixture Exponential-Gamma distribution. We use the expectation maximization (EM) algorithm to obtain the maximum likelihood parameter estimation of the new model. Interestingly, the proposed model is shown to provide a perfect fit with the measured data under all the channel conditions for both types of water. The major advantage of the new model is that it has a simple mathematical form making it attractive from a performance analysis point of view. Indeed, the application of the Exponential-Gamma model leads to closed-form and analytically tractable expressions for key system performance metrics such as the outage probability and the average bit-error rate.
A Simple Metric for Determining Resolution in Optical, Ion, and Electron Microscope Images.
Curtin, Alexandra E; Skinner, Ryan; Sanders, Aric W
2015-06-01
A resolution metric intended for resolution analysis of arbitrary spatially calibrated images is presented. By fitting a simple sigmoidal function to pixel intensities across slices of an image taken perpendicular to light-dark edges, the mean distance over which the light-dark transition occurs can be determined. A fixed multiple of this characteristic distance is then reported as the image resolution. The prefactor is determined by analysis of scanning transmission electron microscope high-angle annular dark field images of Si. This metric has been applied to optical, scanning electron microscope, and helium ion microscope images. This method provides quantitative feedback about image resolution, independent of the tool on which the data were collected. In addition, our analysis provides a nonarbitrary and self-consistent framework that any end user can utilize to evaluate the resolution of multiple microscopes from any vendor using the same metric.
A New Simple Model for Underwater Wireless Optical Channels in the Presence of Air Bubbles
Zedini, Emna; Oubei, Hassan M.; Kammoun, Abla; Hamdi, Mounir; Ooi, Boon S.; Alouini, Mohamed-Slim
2018-01-01
A novel statistical model is proposed to characterize turbulence-induced fading in underwater wireless optical channels in the presence of air bubbles for fresh and salty waters, based on experimental data. In this model, the channel irradiance fluctuations are characterized by the mixture Exponential-Gamma distribution. We use the expectation maximization (EM) algorithm to obtain the maximum likelihood parameter estimation of the new model. Interestingly, the proposed model is shown to provide a perfect fit with the measured data under all the channel conditions for both types of water. The major advantage of the new model is that it has a simple mathematical form making it attractive from a performance analysis point of view. Indeed, the application of the Exponential-Gamma model leads to closed-form and analytically tractable expressions for key system performance metrics such as the outage probability and the average bit-error rate.
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.
Machine learning plus optical flow: a simple and sensitive method to detect cardioactive drugs
Lee, Eugene K.; Kurokawa, Yosuke K.; Tu, Robin; George, Steven C.; Khine, Michelle
2015-07-01
Current preclinical screening methods do not adequately detect cardiotoxicity. Using human induced pluripotent stem cell-derived cardiomyocytes (iPS-CMs), more physiologically relevant preclinical or patient-specific screening to detect potential cardiotoxic effects of drug candidates may be possible. However, one of the persistent challenges for developing a high-throughput drug screening platform using iPS-CMs is the need to develop a simple and reliable method to measure key electrophysiological and contractile parameters. To address this need, we have developed a platform that combines machine learning paired with brightfield optical flow as a simple and robust tool that can automate the detection of cardiomyocyte drug effects. Using three cardioactive drugs of different mechanisms, including those with primarily electrophysiological effects, we demonstrate the general applicability of this screening method to detect subtle changes in cardiomyocyte contraction. Requiring only brightfield images of cardiomyocyte contractions, we detect changes in cardiomyocyte contraction comparable to - and even superior to - fluorescence readouts. This automated method serves as a widely applicable screening tool to characterize the effects of drugs on cardiomyocyte function.
Indian Academy of Sciences (India)
polynomials are dense in the class of continuous functions! The body of literature dealing with Fourier series has reached epic proportions over the last two centuries. We have only given the readers an outline of the topic in this article. For the full length episode we refer the reader to the monumental treatise of. A Zygmund.
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 ...
Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A
2017-08-21
In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.
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.
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.
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.
Optical Characterization of Light-Bending Mechanisms in Photonic Crystals with Simple Cubic Symmetry
Frey, Brian James
For much of Earth's history, light was reputed to be an intangible, intractable, and transient quantity, but our understanding of light has since been revolutionized. The flow of electromagnetic energy through space can today be manipulated with a degree of precision and control once only dreamed of; rapidly developing technologies can create, guide, bend, and detect light to produce useful energy and information. One field where these technologies are most relevant is the field of light trapping, which concerns the harvesting of incident photons within a limited space by scattering, slowing, or otherwise prolonging and enhancing their interaction with matter. Over the past few decades, a class of materials, called photonic crystals (PCs), has emerged that is ideally suited for this task. This is because their wavelength-scale periodicity in one, two, or three dimensions can be designed to alter the dispersion relation and photonic density-of-states in a controllable manner. In this work, a TiO2 simple cubic PC with high dielectric contrast ( > 4:1) is fabricated with a lattice constant of 450 nm, and a newly discovered light-trapping mechanism is demonstrated, which bends light by 90 degrees and enhances optical absorption by one to two orders-of-magnitude over that in a reference film of the same thickness. It is shown that, for wavelengths from 450-950 nm, the achievable enhancement factor for this structure surpasses the theoretical limit of 4n2 derived under the assumption of ergodic system by multiple times. These results derive directly from the symmetry of the simple cubic lattice and are fundamental in nature, not depending on the material used or on the method of fabrication. The light trapping capability of these PCs has straight-forward applications that would be useful in a variety of areas where increased light-matter interaction is desirable, such as white-light generation, thin-film solar cells, photocatalytic pollutant degradation and hydrogen fuel
Ganeshraja, Ayyakannu Sundaram; Clara, Antoni Samy; Rajkumar, Kanniah; Wang, Yanjie; Wang, Yu; Wang, Junhu; Anbalagan, Krishnamoorthy
2015-10-01
The present article is focused on recent developments toward the preparation of room temperature ferromagnetic nanocomposites using better photocatalytic performance. These nanocomposites were successfully prepared by a simple hydrothermal method and their molecular formulas were confirmed as Ti0.90Sn0.10O2 (S1), 0.2CuO-Ti0.73Sn0.06Cu0.21O2-δ (S2), and Ti0.82Sn0.09Fe0.09O2-δ (S3). The ICP, XRD, DRS, FTIR, Raman, XAFS, XPS, EPR, SEM-EDX, HRSEM, HRTEM, photoluminescence and vibrating sample magnetometric measurements were employed to characterize the phase structures, morphologies, optical and magnetic properties of the photocatalysts. The local structures of Sn4+ and Fe3+ were confirmed by 119Sn and 57Fe Mössbauer analysis. The photocatalytic activities of the samples were evaluated by the degradation of methyl orange in water under visible light irradiation. Among the samples, tin doped TiO2 (S1) showed the best photocatalytic performance and stability.
Directory of Open Access Journals (Sweden)
Xiaoli Li
Full Text Available The potential of Fourier transform infrared (FT-IR transmission spectroscopy for determination of lead chrome green in green tea was investigated based on chemometric methods. Firstly, the qualitative analysis of lead chrome green in tea was performed based on partial least squares discriminant analysis (PLS-DA, and the correct rate of classification was 100%. And then, a hybrid method of interval partial least squares (iPLS regression and successive projections algorithm (SPA was proposed to select characteristic wavenumbers for the quantitative analysis of lead chrome green in green tea, and 19 wavenumbers were obtained finally. Among these wavenumbers, 1384 (C = C, 1456, 1438, 1419(C = N, and 1506 (CNH cm-1 were the characteristic wavenumbers of lead chrome green. Then, these 19 wavenumbers were used to build determination models. The best model was achieved by least squares support vector machine (LS-SVMalgorithm with high coefficient of determination and low root-mean square error of prediction set (R2p = 0.864 and RMSEP = 0.291. All these results indicated the feasibility of IR spectra for detecting lead chrome green in green tea.
Habibi, Mohammad Hossein; Mardani, Maryam
2015-02-25
Binary zinc tin oxide nano-composite was synthesized by a facile sol-gel method using simple precursors from the solutions consisting of zinc acetate, tin(IV) chloride and ethanol. Effect of annealing temperature on optical and structural properties was investigated using X-ray diffraction (XRD), diffuse reflectance spectra (DRS), field emission scanning electron microscopy (FESEM) and Fourier transform infrared spectroscopy (FTIR). XRD results revealed the existence of the ZnO and SnO2 phases. FESEM results showed that binary zinc tin oxide nano-composites ranges from 56 to 60 nm in diameter at 400°C and 500°C annealing temperatures respectively. The optical band gap was increased from 2.72 eV to 3.11 eV with the increasing of the annealing temperature. FTIR results confirmed the presence of zinc oxide and tin oxide and the broad absorption peaks at 3426 and 1602 cm(-1) can be ascribed to the vibration of absorptive water, and the absorption peaks at 546, 1038 and 1410 cm(-1) are due to the vibration of Zn-O or Sn-O groups in binary zinc tin oxide. Copyright © 2014 Elsevier B.V. All rights reserved.
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.
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
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)
Leportier, Thibault; Park, Min Chul; Kim, You Seok; Kim, Taegeun
2015-02-09
In this paper, we present a three-dimensional holographic imaging system. The proposed approach records a complex hologram of a real object using optical scanning holography, converts the complex form to binary data, and then reconstructs the recorded hologram using a spatial light modulator (SLM). The conversion from the recorded hologram to a binary hologram is achieved using a direct binary search algorithm. We present experimental results that verify the efficacy of our approach. To the best of our knowledge, this is the first time that a hologram of a real object has been reconstructed using a binary SLM.
Energy Technology Data Exchange (ETDEWEB)
Arikawa, Ryo [Division of Cardiology, Tenyoukai Central Hospital, Izumi-cho, Kagoshima City, Kagoshima (Japan); Yamaguchi, Hiroshi, E-mail: hyamaguchi@tsm.bbiq.jp [Division of Cardiology, Tenyoukai Central Hospital, Izumi-cho, Kagoshima City, Kagoshima (Japan); Takaoka, Junichiro; Miyamura, Akihiro; Atsuchi, Nobuhiko; Ninomiya, Toshiko; Atsuchi, Yoshihiko [Division of Cardiology, Tenyoukai Central Hospital, Izumi-cho, Kagoshima City, Kagoshima (Japan); Ohishi, Mitsuru [Department of Cardiovascular Medicine and Hypertension, Graduate School of Medical and Dental Science, Kagoshima University, Kagoshima (Japan); Terashima, Mitsuyasu [Department of Cardiology, Toyohashi Heart Center, Toyohashi (Japan); Kaneda, Hideaki [Okinaka Memorial Institute for Medical Research, Tokyo (Japan)
2015-01-15
Background: Although drug-eluting stent (DES) has significantly reduced restenosis, the treatment of DES-in-stent restenosis (ISR) remains a challenge with high restenosis rate. Methods: We examined whether morphologic appearance of restenosis tissue by optical coherent tomography (OCT) had an impact on outcomes after balloon angioplasty for DES-ISR. The morphologic appearance of restenosis tissue was qualitatively assessed for tissue structures such as homogeneous, layered, and heterogeneous patterns. Results: Using OCT, 50 patients with DES-ISR were divided into 2 groups: 25 lesions with homogeneous or layered patterns (homo/layered group) and 25 lesions with heterogeneous patterns (hetero group). Acute gain was larger in the hetero group (1.33 ± 0.41 mm vs. 1.06 ± 0.32 mm in the homo/layered group, P = 0.03). On intravascular ultrasound analysis, post-procedural percent neointimal area was smaller in the hetero group (27.4 ± 9.2% vs. 34.0 ± 11.2% in the homo/layered group, P = 0.05). Angiographic follow-up was performed in 37 lesions (74%). Follow-up minimal lumen diameter was larger in the hetero group (1.75 ± 0.89 mm vs. 1.01 ± 0.81 mm in the homo/layered group, P = 0.04). Target lesion revascularization rates tended to be lower in the hetero group (20% vs. 43% in the homo/layered group, P = 0.12). Conclusions: Balloon angioplasty was more effective for DES-ISR with heterogeneous tissue appearance than DES-ISR with homogeneous/layered tissue appearance. OCT assessment of DES-ISR morphology may be a useful adjunct in determining clinical strategies. Simple balloon dilatation is a possible treatment strategy for DES-ISR lesions with a heterogeneous appearance on OCT images.
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.
A Novel Low-Power-Consumption All-Fiber-Optic Anemometer with Simple System Design.
Zhang, Yang; Wang, Fang; Duan, Zhihui; Liu, Zexu; Liu, Zigeng; Wu, Zhenlin; Gu, Yiying; Sun, Changsen; Peng, Wei
2017-09-14
A compact and low-power consuming fiber-optic anemometer based on single-walled carbon nanotubes (SWCNTs) coated tilted fiber Bragg grating (TFBG) is presented. TFBG as a near infrared in-fiber sensing element is able to excite a number of cladding modes and radiation modes in the fiber and effectively couple light in the core to interact with the fiber surrounding mediums. It is an ideal in-fiber device used in a fiber hot-wire anemometer (HWA) as both coupling and sensing elements to simplify the sensing head structure. The fabricated TFBG was immobilized with an SWCNT film on the fiber surface. SWCNTs, a kind of innovative nanomaterial, were utilized as light-heat conversion medium instead of traditional metallic materials, due to its excellent infrared light absorption ability and competitive thermal conductivity. When the SWCNT film strongly absorbs the light in the fiber, the sensor head can be heated and form a "hot wire". As the sensor is put into wind field, the wind will take away the heat on the sensor resulting in a temperature variation that is then accurately measured by the TFBG. Benefited from the high coupling and absorption efficiency, the heating and sensing light source was shared with only one broadband light source (BBS) without any extra pumping laser complicating the system. This not only significantly reduces power consumption, but also simplifies the whole sensing system with lower cost. In experiments, the key parameters of the sensor, such as the film thickness and the inherent angle of the TFBG, were fully investigated. It was demonstrated that, under a very low BBS input power of 9.87 mW, a 0.100 nm wavelength response can still be detected as the wind speed changed from 0 to 2 m/s. In addition, the sensitivity was found to be -0.0346 nm/(m/s) under the wind speed of 1 m/s. The proposed simple and low-power-consumption wind speed sensing system exhibits promising potential for future long-term remote monitoring and on-chip sensing in
Directory of Open Access Journals (Sweden)
Li-Qin Zhou
2014-10-01
Full Text Available AIM: To dynamically observe the feeling change of the photorecrptor layer in the eyes with acute central serous chorioretinopathy(CSCRkrypton laser treatment by fourier-domain optical coherence tomography(FD-OCT, and to study their correlation with the chang of vision.METHODS: This is a retrospective case series study. The clinical diagnosis of 52 patients with monocular initial onset of central serous chorioretinopathy, krypton laser photocoagulation before treatment, after 1, 2, 4, 6, 8wk, 6mo, FD-OCT were performed to observe the morphological changes characteristic of photoreceptor layer and changes in vision. RESULTS: After 1wk treatment, all cases were improved; 2wk, 6 cases were cured; 4wk, 38 cases were cured; 6wk, 41 cases were cured; 8wk, 45 cases were cured, the OCT showed macular retinal neuroepithelial layer(RNLfrom fully absorbed; 6mo with the same 8wk. Before and after treatment in patients with best corrected visual acuity and from the height difference between the macular region of RNL was statistically significant(PPPCONCLUSION: FD-OCT can dynamicaly observed acute central serous chorioretinopathy krypton laser treatment of photoreceptor ultrastruture changes. Photoreceptor layer of complete and incomplete best corrected visual acuity difference was statistically significant(P<0.01.
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.
A simple enantioconvergent and chemoenzymatic synthesis of optically active α-substituted amides
Szymanski, Wiktor; Westerbeek, Alja; Janssen, Dick B.; Feringa, Ben L.
2011-01-01
Simple and efficient: The combination of an enzymatic, enantioinverting reaction with simple follow-up processes allows the transformation of readily available racemic compounds into versatile chiral α-substituted amides. These important building blocks are prepared in high overall yield and
Application of simple all-sky imagers for the estimation of aerosol optical depth
Kazantzidis, Andreas; Tzoumanikas, Panagiotis; Nikitidou, Efterpi; Salamalikis, Vasileios; Wilbert, Stefan; Prahl, Christoph
2017-06-01
Aerosol optical depth is a key atmospheric constituent for direct normal irradiance calculations at concentrating solar power plants. However, aerosol optical depth is typically not measured at the solar plants for financial reasons. With the recent introduction of all-sky imagers for the nowcasting of direct normal irradiance at the plants a new instrument is available which can be used for the determination of aerosol optical depth at different wavelengths. In this study, we are based on Red, Green and Blue intensities/radiances and calculations of the saturated area around the Sun, both derived from all-sky images taken with a low-cost surveillance camera at the Plataforma Solar de Almeria, Spain. The aerosol optical depth at 440, 500 and 675nm is calculated. The results are compared with collocated aerosol optical measurements and the mean/median difference and standard deviation are less than 0.01 and 0.03 respectively at all wavelengths.
Fourier transforms in spectroscopy
Kauppinen, Jyrki
2000-01-01
This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi
Patterning via optical-saturable transformations: A review and simple simulation model
Energy Technology Data Exchange (ETDEWEB)
Cantu, Precious; Menon, Rajesh, E-mail: cantu@eng.utah.edu [Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, Utah 84112 (United States); Andrew, Trisha L. [Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)
2014-11-10
Most of the nanoscale fabrication in the semiconductor industry is based on patterning with scanning-electron beam lithography (SEBL). Although this approach is very versatile and has very high resolution, it is intrinsically a serial writing process, and therefore, relatively slow. Our group has been investigating alternative nano-fabrication techniques, adapted from ideas of saturating optical transitions such as those used in stimulated emission-depletion microscopy and related methods, and optical interference lithography. Linewidths and resolutions on the scale of a few tens of nanometers and below are highly desirable for various applications in nanotechnology. However, the spatial resolution of optical lithography is restricted by diffraction. In the past, we developed absorbance modulation to overcome this limit. This approach utilizes photochromic molecules that can be optically switched between two thermally stable states, one opaque and the other transparent. However, absorbance modulation is limited to surface (2-D) patterning. Here, we report on an alternative approach that exploits unique combinations of spectrally selective reversible and irreversible photochemical transitions to achieve deep subwavelength resolution with potential extension to 3-dimensions. This approach, which we refer to as patterning via optical-saturable transformations have the potential for massive parallelism, enabling the creation of nanostructures and devices at a speed far surpassing what is possible with SEBL. The aim of our research is to translate the success in circumventing Abbe's diffraction limit in optical microscopy to optical lithography.
Patterning via optical-saturable transformations: A review and simple simulation model
International Nuclear Information System (INIS)
Cantu, Precious; Menon, Rajesh; Andrew, Trisha L.
2014-01-01
Most of the nanoscale fabrication in the semiconductor industry is based on patterning with scanning-electron beam lithography (SEBL). Although this approach is very versatile and has very high resolution, it is intrinsically a serial writing process, and therefore, relatively slow. Our group has been investigating alternative nano-fabrication techniques, adapted from ideas of saturating optical transitions such as those used in stimulated emission-depletion microscopy and related methods, and optical interference lithography. Linewidths and resolutions on the scale of a few tens of nanometers and below are highly desirable for various applications in nanotechnology. However, the spatial resolution of optical lithography is restricted by diffraction. In the past, we developed absorbance modulation to overcome this limit. This approach utilizes photochromic molecules that can be optically switched between two thermally stable states, one opaque and the other transparent. However, absorbance modulation is limited to surface (2-D) patterning. Here, we report on an alternative approach that exploits unique combinations of spectrally selective reversible and irreversible photochemical transitions to achieve deep subwavelength resolution with potential extension to 3-dimensions. This approach, which we refer to as patterning via optical-saturable transformations have the potential for massive parallelism, enabling the creation of nanostructures and devices at a speed far surpassing what is possible with SEBL. The aim of our research is to translate the success in circumventing Abbe's diffraction limit in optical microscopy to optical lithography
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
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)
Ryu Jiheun; Kim Jayul; Kim Hyunjun; Yoo Hongki; Gweon Daegab
2015-01-01
During the research using fluorescence-tagged or auto-fluorescence molecules, meaningful information is often buried deep inside the tissue, not its surface. Therefore, especially in the field of biomedical imaging, acquiring optically sectioned images from deep inside the tissue is very important. As well know already, confocal laser scanning microscopy (the most well-known optical sectioning microscopy) gives axially-resolved fluorescence information using the physical background blocking c...
Jun, An Won
2006-01-01
We implement a first practical holographic security system using electrical biometrics that combines optical encryption and digital holographic memory technologies. Optical information for identification includes a picture of face, a name, and a fingerprint, which has been spatially multiplexed by random phase mask used for a decryption key. For decryption in our biometric security system, a bit-error-detection method that compares the digital bit of live fingerprint with of fingerprint information extracted from hologram is used.
Implementation of quantum and classical discrete fractional Fourier transforms
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-01-01
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.
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.
Fraisier, V; Clouvel, G; Jasaitis, A; Dimitrov, A; Piolot, T; Salamero, J
2015-09-01
Multiconfocal microscopy gives a good compromise between fast imaging and reasonable resolution. However, the low intensity of live fluorescent emitters is a major limitation to this technique. Aberrations induced by the optical setup, especially the mismatch of the refractive index and the biological sample itself, distort the point spread function and further reduce the amount of detected photons. Altogether, this leads to impaired image quality, preventing accurate analysis of molecular processes in biological samples and imaging deep in the sample. The amount of detected fluorescence can be improved with adaptive optics. Here, we used a compact adaptive optics module (adaptive optics box for sectioning optical microscopy), which was specifically designed for spinning disk confocal microscopy. The module overcomes undesired anomalies by correcting for most of the aberrations in confocal imaging. Existing aberration detection methods require prior illumination, which bleaches the sample. To avoid multiple exposures of the sample, we established an experimental model describing the depth dependence of major aberrations. This model allows us to correct for those aberrations when performing a z-stack, gradually increasing the amplitude of the correction with depth. It does not require illumination of the sample for aberration detection, thus minimizing photobleaching and phototoxicity. With this model, we improved both signal-to-background ratio and image contrast. Here, we present comparative studies on a variety of biological samples. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.
A Simple Approach to Dynamic Optimisation of Flexible Optical Networks with Practical Application
Directory of Open Access Journals (Sweden)
Vic Grout
2017-05-01
Full Text Available This paper provides an initial introduction to, and definition of, the ‘Dynamically Powered Relays for a Flexible Optical Network’ (DPR-FON problem for opto-electro-optical (OEO regenerators used in optical networks. In such networks, optical transmission parameters can be varied dynamically as traffic patterns change. This will provide different bandwidths, but also change the regeneration limits as a result. To support this flexibility, OEOs (‘relays’ may be switched on and off as required, thus saving power. DPR-FON is shown to be NP-complete; consequently, solving such a dynamic problem in real-time requires a fast heuristic capable of delivering an acceptable approximation to the optimal configuration with low complexity. In this paper, just such an algorithm is developed, implemented, and evaluated against more computationally-demanding alternatives for two known cases. A number of real-world extensions are considered as the paper develops, combining to produce the ‘Generalised Dynamically Powered Relays for a Flexible Optical Network’ (GDPR-FON problem. This, too, is analysed and an associated fast heuristic proposed, along with an exploration of the further research that is required.
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Simple and versatile long range swept source for optical coherence tomography applications
International Nuclear Information System (INIS)
Bräuer, Bastian; Lippok, Norman; Murdoch, Stuart G; Vanholsbeeck, Frédérique
2015-01-01
We present a versatile long coherence length swept-source laser design for optical coherence tomography applications. This design consists of a polygonal spinning mirror and an optical gain chip in a modified Littman–Metcalf cavity. A narrowband intra-cavity filter is implemented through multiple passes off a diffraction grating set at grazing incidence. The key advantage of this design is that it can be readily adapted to any wavelength regions for which broadband gain chips are available. We demonstrate this by implementing sources at 1650 nm, 1550 nm, 1310 nm and 1050 nm. In particular, we present a 1310 nm swept source laser with 24 mm coherence length, 95 nm optical bandwidth, 2 kHz maximum sweep frequency and 7.5 mW average output power. These parameters make it a suitable source for the imaging of biological samples. (paper)
A Simple Technique to Facilitate Treatment of Urethral Strictures with Optical Internal Urethrotomy
Stamatiou, Konstantinos; Papadatou, Aggeliki; Moschouris, Hippocrates; Kornezos, Ioannis; Pavlis, Anargiros; Christopoulos, Georgios
2014-01-01
Urethral stricture is a common condition that can lead to serious complications such as urinary infections and renal insufficiency secondary to urinary retention. Treatment options include catheterization, urethroplasty, endoscopic internal urethrotomy, and dilation. Optical internal urethrotomy offers faster recovery, minimal scarring, and less risk of infection, although recurrence is possible. However, technical difficulties associated with poor visualization of the stenosis or of the uret...
Simple method of modelling of digital holograms registering and their optical reconstruction
International Nuclear Information System (INIS)
Evtikhiev, N N; Cheremkhin, P A; Krasnov, V V; Kurbatova, E A; Molodtsov, D Yu; Porshneva, L A; Rodin, V G
2016-01-01
The technique of modeling of digital hologram recording and image optical reconstruction from these holograms is described. The method takes into account characteristics of the object, digital camera's photosensor and spatial light modulator used for digital holograms displaying. Using the technique, equipment can be chosen for experiments for obtaining good reconstruction quality and/or holograms diffraction efficiency. Numerical experiments were conducted. (paper)
A simple pendulum borehole tiltmeter based on a triaxial optical-fibre displacement sensor
Chawah , P; Chéry , J; Boudin , F; Cattoen , Michel; Seat , Han Cheng; Plantier , Guy; Lizion , Françoise; Sourice , A; Bernard , Patrick; Brunet , C; Boyer , D; Gaffet , S
2015-01-01
International audience; Sensitive instruments like strainmeters and tiltmeters are necessary for measuring slowly varying low amplitude Earth deformations. Nonetheless, laser and fibre interferometers are particularly suitable for interrogating such instruments due to their extreme precision and accuracy. In this paper, a practical design of a simple pendulum borehole tiltmeter based on laser fibre interferometric displacement sensors is presented. A prototype instrument has been constructed ...
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....
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
A simple model for fibre optics: planar dielectric waveguides in rotation
International Nuclear Information System (INIS)
Perez-Ocon, F; Pena, A; Jimenez, J R; Diaz, J A
2006-01-01
In planar dielectric waveguides, there is only one type of propagated ray: the one that crosses the waveguide axis after each total internal reflection. According to the model of geometrical optics, there are two types of guided ray in fibre optics: meridional and skew. Each one is formulated by a suitable mathematical treatment. In this work, we demonstrate that the complex mathematical treatment for the skew rays can be avoided by considering a planar waveguide (with the same refractive index profile as the fibre and thickness equal to its diameter) that rotates around the direction of the axis with angular velocity ω. A section of this fibre is inscribed in the hypothetical slab. This model has been successfully introduced to students of engineering and physics
Localization and Imaging of Integrated Circuit Defect Using Simple Optical Feedback Detection
Directory of Open Access Journals (Sweden)
Vernon Julius Cemine
2004-12-01
Full Text Available High-contrast microscopy of semiconductor and metal edifices in integrated circuits is demonstrated by combining laser-scanning confocal reflectance microscopy, one-photon optical-beam-induced current (1P-OBIC imaging, and optical feedback detection via a commercially available semiconductor laser that also serves as the excitation source. The confocal microscope has a compact in-line arrangement with no external photodetector. Confocal and 1P-OBIC images are obtained simultaneously from the same focused beam that is scanned across the sample plane. Image pairs are processed to generate exclusive high-contrast distributions of the semiconductor, metal, and dielectric sites in a GaAs photodiode array sample. The method is then utilized to demonstrate defect localization and imaging in an integrated circuit.
International Nuclear Information System (INIS)
Cheng Chuanwei; Xu Guoyue; Zhang Haiqian; Li Yingying; Luo Yan; Zhang Peigen
2008-01-01
Multiform structures of SnO 2 nanobelts including of zigzag, branching and straight structures have been synthesized by a simple molten-salt assisted route. The obtained samples were characterized by X-ray diffraction (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM) and high resolution transmission electron microscope (HRTEM). The growth mechanism of zigzag nanobelts was proposed. A strong blue emission band centered in 425 nm was observed in the photoluminescence spectrum
Simple and practical approach for computing the ray Hessian matrix in geometrical optics.
Lin, Psang Dain
2018-02-01
A method is proposed for simplifying the computation of the ray Hessian matrix in geometrical optics by replacing the angular variables in the system variable vector with their equivalent cosine and sine functions. The variable vector of a boundary surface is similarly defined in such a way as to exclude any angular variables. It is shown that the proposed formulations reduce the computation time of the Hessian matrix by around 10 times compared to the previous method reported by the current group in Advanced Geometrical Optics (2016). Notably, the method proposed in this study involves only polynomial differentiation, i.e., trigonometric function calls are not required. As a consequence, the computation complexity is significantly reduced. Five illustrative examples are given. The first three examples show that the proposed method is applicable to the determination of the Hessian matrix for any pose matrix, irrespective of the order in which the rotation and translation motions are specified. The last two examples demonstrate the use of the proposed Hessian matrix in determining the axial and lateral chromatic aberrations of a typical optical system.
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...
A simple technique to facilitate treatment of urethral strictures with optical internal urethrotomy.
Stamatiou, Konstantinos; Papadatou, Aggeliki; Moschouris, Hippocrates; Kornezos, Ioannis; Pavlis, Anargiros; Christopoulos, Georgios
2014-01-01
Urethral stricture is a common condition that can lead to serious complications such as urinary infections and renal insufficiency secondary to urinary retention. Treatment options include catheterization, urethroplasty, endoscopic internal urethrotomy, and dilation. Optical internal urethrotomy offers faster recovery, minimal scarring, and less risk of infection, although recurrence is possible. However, technical difficulties associated with poor visualization of the stenosis or of the urethral lumen may increase procedural time and substantially increase the failure rates of internal urethrotomy. In this report we describe a technique for urethral catheterization via a suprapubic, percutaneous approach through the urinary bladder in order to facilitate endoscopic internal urethrotomy.
A Simple Technique to Facilitate Treatment of Urethral Strictures with Optical Internal Urethrotomy
Directory of Open Access Journals (Sweden)
Konstantinos Stamatiou
2014-01-01
Full Text Available Urethral stricture is a common condition that can lead to serious complications such as urinary infections and renal insufficiency secondary to urinary retention. Treatment options include catheterization, urethroplasty, endoscopic internal urethrotomy, and dilation. Optical internal urethrotomy offers faster recovery, minimal scarring, and less risk of infection, although recurrence is possible. However, technical difficulties associated with poor visualization of the stenosis or of the urethral lumen may increase procedural time and substantially increase the failure rates of internal urethrotomy. In this report we describe a technique for urethral catheterization via a suprapubic, percutaneous approach through the urinary bladder in order to facilitate endoscopic internal urethrotomy.
de Oliveira, N; Joyeux, D; Phalippou, D; Rodier, J C; Polack, F; Vervloet, M; Nahon, L
2009-04-01
We describe a Fourier transform (FT) spectrometer designed to operate down to 60 nm (20 eV) on a synchrotron radiation beamline for high resolution absorption spectrometry. As far as we know, such an instrument is not available below 140 nm mainly because manufacturing accurate and efficient beam splitters remains a major problem at these wavelengths, especially if a wide bandwidth operation is desired. In order to overcome this difficulty, we developed an interferometer based on wave front division instead of amplitude division. It relies on a modified Fresnel bimirror configuration that requires only flat mirrors. The instrument provides path difference scanning through the translation of one reflector. During the scanning, the moving reflector is controlled by an optical system that keeps its direction constant within a tolerable value and provides an accurate interferometric measurement of the path difference variation. Therefore, a regular interferogram sampling is obtained, producing a nominal spectral impulse response and an accurate spectral calibration. The first results presented in this paper show a measured spectral resolution of delta(sigma)=0.33 cm-1 (interval between spectral samples). This was obtained with a sampling interval of 29 nm (path difference) and 512 K samples from a one-sided interferogram using a cosine FT. Such a sampling interval should allow the recording of large bandwidth spectra down to lambda=58 nm with an ultimate resolving power of 500,000 at this wavelength. In order to check the instrument performances, we first recorded an interferogram from a He-Ne stabilized laser. This provided the actual spectral impulse function, which was found to be fully satisfactory. The determination of the impulse response distortion and of the noise on the vacuum ultraviolet (VUV) spectral range provided accurate information in the sampling error profile over a typical scan. Finally, the instrument has been moved to the SU5 undulator
Suratwala, Tayyab; Steele, Rusty; Feit, Michael; Dylla-Spears, Rebecca; Desjardin, Richard; Mason, Dan; Wong, Lana; Geraghty, Paul; Miller, Phil; Shen, Nan
2014-01-01
Convergent Polishing is a novel polishing system and method for finishing flat and spherical glass optics in which a workpiece, independent of its initial shape (i.e., surface figure), will converge to final surface figure with excellent surface quality under a fixed, unchanging set of polishing parameters in a single polishing iteration. In contrast, conventional full aperture polishing methods require multiple, often long, iterative cycles involving polishing, metrology and process changes to achieve the desired surface figure. The Convergent Polishing process is based on the concept of workpiece-lap height mismatch resulting in pressure differential that decreases with removal and results in the workpiece converging to the shape of the lap. The successful implementation of the Convergent Polishing process is a result of the combination of a number of technologies to remove all sources of non-uniform spatial material removal (except for workpiece-lap mismatch) for surface figure convergence and to reduce the number of rogue particles in the system for low scratch densities and low roughness. The Convergent Polishing process has been demonstrated for the fabrication of both flats and spheres of various shapes, sizes, and aspect ratios on various glass materials. The practical impact is that high quality optical components can be fabricated more rapidly, more repeatedly, with less metrology, and with less labor, resulting in lower unit costs. In this study, the Convergent Polishing protocol is specifically described for fabricating 26.5 cm square fused silica flats from a fine ground surface to a polished ~λ/2 surface figure after polishing 4 hr per surface on a 81 cm diameter polisher. PMID:25489745
A simple pendulum borehole tiltmeter based on a triaxial optical-fibre displacement sensor
Chawah, P.; Chéry, J.; Boudin, F.; Cattoen, M.; Seat, H. C.; Plantier, G.; Lizion, F.; Sourice, A.; Bernard, P.; Brunet, C.; Boyer, D.; Gaffet, S.
2015-11-01
Sensitive instruments like strainmeters and tiltmeters are necessary for measuring slowly varying low amplitude Earth deformations. Nonetheless, laser and fibre interferometers are particularly suitable for interrogating such instruments due to their extreme precision and accuracy. In this paper, a practical design of a simple pendulum borehole tiltmeter based on laser fibre interferometric displacement sensors is presented. A prototype instrument has been constructed using welded borosilicate with a pendulum length of 0.85 m resulting in a main resonance frequency of 0.6 Hz. By implementing three coplanar extrinsic fibre Fabry-Perot interferometric probes and appropriate signal filtering, our instrument provides tilt measurements that are insensitive to parasitic deformations caused by temperature and pressure variations. This prototype has been installed in an underground facility (Rustrel, France) where results show accurate measurements of Earth strains derived from Earth and ocean tides, local hydrologic effects, as well as local and remote earthquakes. The large dynamic range and the high sensitivity of this tiltmeter render it an invaluable tool for numerous geophysical applications such as transient fault motion, volcanic strain and reservoir monitoring.
Using McStas for modelling complex optics, using simple building bricks
International Nuclear Information System (INIS)
Willendrup, Peter K.; Udby, Linda; Knudsen, Erik; Farhi, Emmanuel; Lefmann, Kim
2011-01-01
The McStas neutron ray-tracing simulation package is a versatile tool for producing accurate neutron simulations, extensively used for design and optimization of instruments, virtual experiments, data analysis and user training. In McStas, component organization and simulation flow is intrinsically linear: the neutron interacts with the beamline components in a sequential order, one by one. Historically, a beamline component with several parts had to be implemented with a complete, internal description of all these parts, e.g. a guide component including all four mirror plates and required logic to allow scattering between the mirrors. For quite a while, users have requested the ability to allow 'components inside components' or meta-components, allowing to combine functionality of several simple components to achieve more complex behaviour, i.e. four single mirror plates together defining a guide. We will here show that it is now possible to define meta-components in McStas, and present a set of detailed, validated examples including a guide with an embedded, wedged, polarizing mirror system of the Helmholtz-Zentrum Berlin type.
Loranger, Sébastien; Parent, François; Lambin-Iezzi, Victor; Kashyap, Raman
2016-02-01
Rayleigh scatter in optical fiber communication systems has long been considered a nuisance as a loss mechanism, although applications have used such scatter to probe the fiber for faults and propagation loss using time domain reflectometry (OTDR). It is however only with the development of Frequency domain reflectometry (OFDR) and coherent-phase OTDR that Rayleigh scatter has been probed to its deepest and can now be used to measure strain and temperature along a fiber, leading to the first distributed sensing applications. However, Rayleigh scatter remains very weak giving rise to very small signals which limits the technique for sensing. We show here a new technique to significantly enhance the Rayleigh scatter signal by at least two orders of magnitude, in a standard optical fiber with simple UV exposure of the core. A study of various exposures with different types of fibers has been conducted and a phenomenological description developed. We demonstrate that such an increase in signal can enhance the temperature and strain sensitivity by an order of magnitude for distributed sensing with an OFDR technique. Such improved performance can lead to temperature/strain RMS noise levels of 6 mK and 50 nɛ for 1 cm spatial resolution in UV exposed SMF-28, compared to the typical noise level of 100 mK for the same spatial resolution in the similar unexposed fiber.
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
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.
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
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
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
Trägårdh, J; Macrae, K; Travis, C; Amor, R; Norris, G; Wilson, S H; Oppo, G-L; McConnell, G
2015-07-01
We report a method for characterizing the focussing laser beam exiting the objective in a laser scanning microscope. This method provides the size of the optical focus, the divergence of the beam, the ellipticity and the astigmatism. We use a microscopic-scale knife edge in the form of a simple transmission electron microscopy grid attached to a glass microscope slide, and a light-collecting optical fibre and photodiode underneath the specimen. By scanning the laser spot from a reflective to a transmitting part of the grid, a beam profile in the form of an error function can be obtained and by repeating this with the knife edge at different axial positions relative to the beam waist, the divergence and astigmatism of the postobjective laser beam can be obtained. The measured divergence can be used to quantify how much of the full numerical aperture of the lens is used in practice. We present data of the beam radius, beam divergence, ellipticity and astigmatism obtained with low (0.15, 0.7) and high (1.3) numerical aperture lenses and lasers commonly used in confocal and multiphoton laser scanning microscopy. Our knife-edge method has several advantages over alternative knife-edge methods used in microscopy including that the knife edge is easy to prepare, that the beam can be characterized also directly under a cover slip, as necessary to reduce spherical aberrations for objectives designed to be used with a cover slip, and it is suitable for use with commercial laser scanning microscopes where access to the laser beam can be limited. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.
Replica Fourier Transform: Properties and applications
International Nuclear Information System (INIS)
Crisanti, A.; De Dominicis, C.
2015-01-01
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically
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.
Energy Technology Data Exchange (ETDEWEB)
Shi, Wei [Oil & Gas Field Applied Chemistry Key Laboratory of Sichuan Province, School of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610500 (China); Key Laboratory of Oil & Gas Fine Chemicals, Ministry of Education, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi 83004 (China); Chen, Yabin [Key Laboratory of Oil & Gas Fine Chemicals, Ministry of Education, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi 83004 (China); Chen, Xin [Oil & Gas Field Applied Chemistry Key Laboratory of Sichuan Province, School of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610500 (China); Xie, Zhengfeng, E-mail: xiezhf@swpu.edu.cn [Oil & Gas Field Applied Chemistry Key Laboratory of Sichuan Province, School of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610500 (China); Key Laboratory of Oil & Gas Fine Chemicals, Ministry of Education, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi 83004 (China); Hui, Yonghai [Key Laboratory of Oil & Gas Fine Chemicals, Ministry of Education, College of Chemistry and Chemical Engineering, Xinjiang University, Urumqi 83004 (China)
2016-06-15
A type of simple-structured, hydrazinecarbothioamide-containing Schiff-base derivative, 2-(4-(diphenylamino)benzylidene)hydrazinecarbothioamide (M1), was synthesized through condensation reaction between 4-(diphenylamino)benzaldehyde and thiosemicarbazide. In the mixture of DMSO/H{sub 2}O (DMSO/H{sub 2}O=9:1(v:v), pH=4.5), distinct “turn-off” fluorescence alterations of M1 were observed upon the addition of Hg{sup 2+}, and the addition of Ag{sup +} induced fluorescence bathochromic shift. The detection limits of Hg{sup 2+} and Ag{sup +} reach~0.19 μM and ~0.59 μM, respectively, as evaluated by the detailed fluorescence response of M1 toward incremental target ions. The different extent of photo-induced electron transfer (PET) between M1 and these two ions might be the plausible reason for such different optical response behaviors. - Highlights: • Hydrazinecarbothioamide-containing Schiff-base derivative (M1) was synthesized. • “Turn-off” fluorescence alterations of M1 were observed upon the addition of Hg{sup 2+}. • The addition of Ag{sup +} induced fluorescence bathochromic shift of M1. • Detection limits of Hg{sup 2+} and Ag{sup +} reaches ~0.19 μM and ~0.59 μM, respectively. • Hg{sup 2+} and Ag{sup +} can be detected in independent channels by M1 thus.
International Nuclear Information System (INIS)
Takeuchi, Takashi; Ohnuki, Shinichiro; Sako, Tokuei
2017-01-01
A simple formula for predicting the ratio between the field strengths of the incident laser pulse and of the near-field created in the vicinity of the target electron system has been proposed, in the context of optically controlling confined electron systems. The formula is easy to use and does not involve elaborate computation, thus enabling one to judge whether to use the time-consuming Maxwell–Schrödinger hybrid simulation or to stay with the conventional time-dependent Schrödinger equation approach that takes no near-field effect into account. As a demonstration we have examined in detail the system of an electron confined in a quasi-one-dimensional nanoscale potential well. The highly accurate Maxwell–Schrödinger hybrid simulation has been employed to demonstrate the usefulness of the proposed formula in predicting the significance of the near-field effect. The near-field effect has shown to depend sensitively on the characteristics of the laser pulse and of the geometry of the confined electron system, which can be predicted well by the proposed formula. (paper)
Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
Fractional finite Fourier transform.
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.
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.
Tutorial on Fourier space coverage for scattering experiments, with application to SAR
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.
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Kolb, Jan Philip; Pfeiffer, Tom; Eibl, Matthias; Hakert, Hubertus; Huber, Robert
2018-01-01
We present a new 1060 nm Fourier domain mode locked laser (FDML laser) with a record 143 nm sweep bandwidth at 2∙ 417 kHz = 834 kHz and 120 nm at 1.67 MHz, respectively. We show that not only the bandwidth alone, but also the shape of the spectrum is critical for the resulting axial resolution, because of the specific wavelength-dependent absorption of the vitreous. The theoretical limit of our setup lies at 5.9 µm axial resolution. In vivo MHz-OCT imaging of human retina is performed and the image quality is compared to the previous results acquired with 70 nm sweep range, as well as to existing spectral domain OCT data with 2.1 µm axial resolution from literature. We identify benefits of the higher resolution, for example the improved visualization of small blood vessels in the retina besides several others.
Directory of Open Access Journals (Sweden)
Anton Bourdine
2015-01-01
Full Text Available This work presents fast and simple method for evaluation of polarization correction to scalar propagation constant of arbitrary order guided modes propagating over weakly guiding optical fibers. Proposed solution is based on earlier on developed modified Gaussian approximation extended for analysis of weakly guiding optical fibers with arbitrary refractive index profile in the core region bounded by single solid outer cladding. Some results are presented that illustrate the decreasing of computational error during the estimation of propagation constant when polarization corrections are taken into account. Analytical expressions for the first and second derivatives of polarization correction are derived and presented.
Weinstock, B André; Guiney, Linda M; Loose, Christopher
2012-11-01
We have developed a rapid, nondestructive analytical method that estimates the thickness of a surface polymer layer with high precision but unknown accuracy using a single attenuated total reflection Fourier transform infrared (ATR FT-IR) measurement. Because the method is rapid, nondestructive, and requires no sample preparation, it is ideal as a process analytical technique. Prior to implementation, the ATR FT-IR spectrum of the substrate layer pure component and the ATR FT-IR and real refractive index spectra of the surface layer pure component must be known. From these three input spectra a synthetic mid-infrared spectral matrix of surface layers 0 nm to 10,000 nm thick on substrate is created de novo. A minimum statistical distance match between a process sample's ATR FT-IR spectrum and the synthetic spectral matrix provides the thickness of that sample. We show that this method can be used to successfully estimate the thickness of polysulfobetaine surface modification, a hydrated polymeric surface layer covalently bonded onto a polyetherurethane substrate. A database of 1850 sample spectra was examined. Spectrochemical matrix-effect unknowns, such as the nonuniform and molecularly novel polysulfobetaine-polyetherurethane interface, were found to be minimal. A partial least squares regression analysis of the database spectra versus their thicknesses as calculated by the method described yielded an estimate of precision of ±52 nm.
Fourier transform infrared spectrometery: an undergraduate experiment
International Nuclear Information System (INIS)
Lerner, L
2016-01-01
Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory. (paper)
Geometric Representations for Discrete Fourier Transforms
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
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…
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
Fourier Transform Mass Spectrometry
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-01-01
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
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....
Directory of Open Access Journals (Sweden)
Nabanita Barua
2016-01-01
Full Text Available Context: Analysis of diagnostic ability of macular ganglionic cell complex and retinal nerve fiber layer (RNFL in glaucoma. Aim: To correlate functional and structural parameters and comparing predictive value of each of the structural parameters using Fourier-domain (FD optical coherence tomography (OCT among primary open angle glaucoma (POAG and ocular hypertension (OHT versus normal population. Setting and Design: Single centric, cross-sectional study done in 234 eyes. Materials and Methods: Patients were enrolled in three groups: POAG, ocular hypertensive and normal (40 patients in each group. After comprehensive ophthalmological examination, patients underwent standard automated perimetry and FD-OCT scan in optic nerve head and ganglion cell mode. The relationship was assessed by correlating ganglion cell complex (GCC parameters with mean deviation. Results were compared with RNFL parameters. Statistical Analysis: Data were analyzed with SPSS, analysis of variance, t-test, Pearson′s coefficient, and receiver operating curve. Results: All parameters showed strong correlation with visual field (P 0.5 when compared with other parameters. None of the parameters showed significant diagnostic capability to detect OHT from normal population. In diagnosing early glaucoma from OHT and normal population, only inferior GCC had statistically significant AUC value (0.715. Conclusion: In this study, GCC and RNFL parameters showed equal predictive capability in perimetric versus normal group. In early stage, inferior GCC was the best parameter. In OHT population, single day cross-sectional imaging was not valuable.
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)
Multichannel Dynamic Fourier-Transform IR Spectrometer
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.
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.
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.
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
Huo, Yanfeng; Duan, Minzheng; Tian, Wenshou; Min, Qilong
2015-08-01
A differential optical absorption spectroscopy (DOAS)-like algorithm is developed to retrieve the column-averaged dryair mole fraction of carbon dioxide from ground-based hyper-spectral measurements of the direct solar beam. Different to the spectral fitting method, which minimizes the difference between the observed and simulated spectra, the ratios of multiple channel-pairs—one weak and one strong absorption channel—are used to retrieve from measurements of the shortwave infrared (SWIR) band. Based on sensitivity tests, a super channel-pair is carefully selected to reduce the effects of solar lines, water vapor, air temperature, pressure, instrument noise, and frequency shift on retrieval errors. The new algorithm reduces computational cost and the retrievals are less sensitive to temperature and H2O uncertainty than the spectral fitting method. Multi-day Total Carbon Column Observing Network (TCCON) measurements under clear-sky conditions at two sites (Tsukuba and Bremen) are used to derive xxxx for the algorithm evaluation and validation. The DOAS-like results agree very well with those of the TCCON algorithm after correction of an airmass-dependent bias.
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.
Fourier Transform Mass Spectrometry.
Gross, Michael L.; Rempel, Don L.
1984-01-01
Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)
Goldovsky, David; Jouravsky, Valery; Pe'er, Avi
2016-12-12
We present an approach to locking of optical cavities with piezoelectric actuated mirrors based on a simple and effective mechanical decoupling of the mirror and actuator from the surrounding mount. Using simple elastic materials (e.g. rubber or soft silicone gel pads) as mechanical dampers between the piezo-mirror compound and the surrounding mount, a firm and stable mounting of a relatively large mirror (8mm diameter) can be maintained that is isolated from external mechanical resonances, and is limited only by the internal piezo-mirror resonance of > 330 KHz. Our piezo lock showed positive servo gain up to 208 KHz, and a temporal response to a step interference within < 3 μs.
Novel, compact, and simple ND:YVO4 laser with 12 W of CW optical output power and good beam quality
Zimer, H.; Langer, B.; Wittrock, U.; Heine, F.; Hildebrandt, U.; Seel, S.; Lange, R.
2017-11-01
We present first, promising experiments with a novel, compact and simple Nd:YVO4 slab laser with 12 W of 1.06 μm optical output power and a beam quality factor M2 2.5. The laser is made of a diffusion-bonded YVO4/Nd:YVO4 composite crystal that exhibits two unique features. First, it ensures a one-dimensional heat removal from the laser crystal, which leads to a temperature profile without detrimental influence on the laser beam. Thus, the induced thermo-optical aberrations to the laser field are low, allowing power scaling with good beam quality. Second, the composite crystal itself acts as a waveguide for the 809 nm pump-light that is supplied from a diode laser bar. Pump-light shaping optics, e.g. fast- or slow-axis collimators can be omitted, reducing the complexity of the system. Pump-light redundancy can be easily achieved. Eventually, the investigated slab laser might be suitable for distortion-free high gain amplification of weak optical signals.
Energy Technology Data Exchange (ETDEWEB)
Hassan, Moinuddin, E-mail: moinuddin.hassan@fda.hhs.gov; Ilev, Ilko [Optical Therapeutics and Medical Nanophotonics Laboratory, Division of Biomedical Physics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, Maryland 20993 (United States)
2014-10-15
Contamination of medical devices has become a critical and prevalent public health safety concern since medical devices are being increasingly used in clinical practices for diagnostics, therapeutics and medical implants. The development of effective sensing methods for real-time detection of pathogenic contamination is needed to prevent and reduce the spread of infections to patients and the healthcare community. In this study, a hollow-core fiber-optic Fourier transform infrared spectroscopy methodology employing a grazing incidence angle based sensing approach (FO-FTIR-GIA) was developed for detection of various biochemical contaminants on medical device surfaces. We demonstrated the sensitivity of FO-FTIR-GIA sensing approach for non-contact and label-free detection of contaminants such as lipopolysaccharide from various surface materials relevant to medical device. The proposed sensing system can detect at a minimum loading concentration of approximately 0.7 μg/cm{sup 2}. The FO-FTIR-GIA has the potential for the detection of unwanted pathogen in real time.
Czech Academy of Sciences Publication Activity Database
Lacina, K.; Žák, J.; Sopoušek, J.; Szabó, Z.; Václavek, Tomáš; Žeravík, J.; Fiala, P.; Skládal, P.
2016-01-01
Roč. 216, OCT (2016), s. 147-151 ISSN 0013-4686 R&D Projects: GA ČR GA13-09086S; GA ČR(CZ) GBP206/12/G014 Institutional support: RVO:68081715 Keywords : electrochemical transducer transistor * operational amplifier * optical read-out * ( bio )sensing Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 4.798, year: 2016
Czech Academy of Sciences Publication Activity Database
Lacina, K.; Žák, J.; Sopoušek, J.; Szabó, Z.; Václavek, Tomáš; Žeravík, J.; Fiala, P.; Skládal, P.
2016-01-01
Roč. 216, OCT (2016), s. 147-151 ISSN 0013-4686 R&D Projects: GA ČR GA13-09086S; GA ČR(CZ) GBP206/12/G014 Institutional support: RVO:68081715 Keywords : electrochemical transducer transistor * operational amplifier * optical read-out * (bio)sensing Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 4.798, year: 2016
Nguyen, Minh-Hang; Nguyen, Hai-Binh; Nguyen, Tuan-Hung; Vu, Xuan-Manh; Lai, Jain-Ren; Tseng, Fan-Gang; Chen, Te-Chang; Lee, Ming-Chang
2016-05-01
This paper presents two facile methods to fabricate off-plane lenses made of SU-8, an epoxy-based negative photoresist from MicroChem, on glass for optical interconnection. The methods allow the fabrication of lenses with flexible spot size and focal length depending on SU-8 well size and SU-8 drop volume and viscosity. In the first method, SU-8 drops were applied directly into patterned SU-8 wells with Teflon-coated micropipettes, and were baked to become (a)-spherical lenses. The lens shape and size were mainly determined by SU-8 viscosity, ratio of drop volume to well volume, and baking temperature and time. In the second method, a glass substrate with SU-8 patterned wells was emerged in diluted SU-8, then drawn up and baked to form lenses. The lens shapes and sizes were mainly determined by SU-8 viscosity and well volume. By the two methods, SU-8 lenses were successfully fabricated with spot sizes varying in range from micrometers to hundred micrometers, and focal lengths varying in range of several millimeters, depending on the lens rim diameters and aspheric sag height. Besides, on-plane SU-8 lenses were fabricated by photolithography to work in conjunction with the off-plane SU-8 lenses. The cascaded lenses produced light spots reduced to several micrometers, and they can be applied as a coupler for light coupling from fiber/Light-emitting diode (LED) to microstructures and nanostructures. The results open up the path for fabricating novel optical microsystems for optical communication and optical sensing applications.
Simple approach to three-color two-photon microscopy by a fiber-optic wavelength convertor.
Li, Kuen-Che; Huang, Lynn L H; Liang, Jhih-Hao; Chan, Ming-Che
2016-11-01
A simple approach to multi-color two-photon microscopy of the red, green, and blue fluorescent indicators was reported based on an ultra-compact 1.03-μm femtosecond laser and a nonlinear fiber. Inside the nonlinear fiber, the 1.03-μm laser pulses were simultaneously blue-shifted to 0.6~0.8 μm and red-shifted to 1.2~1.4 μm region by the Cherenkov radiation and fiber Raman gain effects. The wavelength-shifted 0.6~0.8 μm and 1.2~1.4 μm radiations were co-propagated with the residual non-converted 1.03-μm pulses inside the same nonlinear fiber to form a fiber-output three-color femtosecond source. The application of the multi-wavelength sources on multi-color two-photon fluorescence microscopy were also demonstrated. Overall, due to simple system configuration, convenient wavelength conversion, easy wavelength tunability within the entire 0.7~1.35 μm bio-penetration window and less requirement for high power and bulky light sources, the simple approach to multi-color two-photon microscopy could be widely applicable as an easily implemented and excellent research tool for future biomedical and possibly even clinical applications.
Fourier analysis: from cloaking to imaging
Wu, Kedi; Cheng, Qiluan; Wang, Guo Ping
2016-04-01
Regarding invisibility cloaks as an optical imaging system, we present a Fourier approach to analytically unify both Pendry cloaks and complementary media-based invisibility cloaks into one kind of cloak. By synthesizing different transfer functions, we can construct different devices to realize a series of interesting functions such as hiding objects (events), creating illusions, and performing perfect imaging. In this article, we give a brief review on recent works of applying Fourier approach to analysis invisibility cloaks and optical imaging through scattering layers. We show that, to construct devices to conceal an object, no constructive materials with extreme properties are required, making most, if not all, of the above functions realizable by using naturally occurring materials. As instances, we experimentally verify a method of directionally hiding distant objects and create illusions by using all-dielectric materials, and further demonstrate a non-invasive method of imaging objects completely hidden by scattering layers.
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)
Approximating the Analytic Fourier Transform with the Discrete Fourier Transform
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.
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...
Energy Technology Data Exchange (ETDEWEB)
Filho, Fausto M. Faria [Instituto de Física, Universidade Federal de Goiás-UFG, Campus II, Caixa Postal 131, CEP 74001-970 Goiânia, GO (Brazil); Gonçalves, Rogéria R. [Departamento de Química, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo-USP, Av. Bandeirantes, 3900, CEP 14040-901 Ribeirão Preto, SP (Brazil); Ribeiro, Sidney J.L. [Institute of Chemistry, São Paulo State University-UNESP, Rua Professor Francisco Degni, 55, CEP 14801-970 Araraquara, SP (Brazil); Maia, Lauro J.Q., E-mail: lauro@ufg.br [Instituto de Física, Universidade Federal de Goiás-UFG, Campus II, Caixa Postal 131, CEP 74001-970 Goiânia, GO (Brazil)
2015-04-15
Highlights: • We developed a simple route to obtain gels and powders using GeO{sub 2}, TEOS and TMAH solution. • Al{sub 6}Ge{sub 2}O{sub 13} crystalline nanoparticles embedded in amorphous matrix were obtained. • The Al{sub 2}O{sub 3} enhance Er{sup 3+} dispersion in GeO{sub 2}–SiO{sub 2} increasing its emission and the full width at half maximum from 41 to 56 nm. • The {sup 4}I{sub 13/2} Er{sup 3+} level lifetime varies between 4.8 and 5.6 ms (1533 nm emission). - Abstract: Samples of (1 − x)[0.70SiO{sub 2} + 0.30Al{sub 2}O{sub 3}] + xGeO{sub 2} compositions, containing x = 0.05, 0.10, 0.20, 0.30, 0.40 and 0.50, and doped with 1 mol% of Er{sup 3+}, were prepared by a mixed route (sol–gel process and Pechini method). Transparent gels were synthesized and homogeneous powders were obtained by heat treatments from 800 °C to 1050 °C. The final powders were characterized by X-ray diffraction, Fourier transform infrared spectroscopy and high-resolution transmission electron microscopy. The optical properties were studied by photoluminescence measurements in the infrared region, and the average lifetime of the metastable state {sup 4}I{sub 13/2} of Er{sup 3+} ions and the full-width at half maximum (FWHM) were determined. A silica-rich amorphous phase and nanocrystallites with orthorhombic structure of Al{sub 6}Ge{sub 2}O{sub 13} phase were obtained. The samples present a broad emission centered at around 1532 nm under excitation at 977 nm, with a FWHM of 53 nm and a lifetime of 5.6 ms. The synthesized compounds by an easy chemical procedure are potentially applicable in integrated optical systems.
Fourier transforms principles and applications
Hansen, Eric W
2014-01-01
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.
On the Fourier integral theorem
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
All-optical spin switching: A new frontier in femtomagnetism — A short review and a simple theory
Zhang, G. P.; Latta, T.; Babyak, Z.; Bai, Y. H.; George, Thomas F.
2016-08-01
Using an ultrafast laser pulse to manipulate the spin degree of freedom has broad technological appeal. It allows one to control the spin dynamics on a femtosecond time scale. The discipline, commonly called femtomagnetism, started with the pioneering experiment by Beaurepaire and coworkers in 1996, who showed subpicosecond demagnetization occurs in magnetic Ni thin films. This finding has motivated extensive research worldwide. All-optical helicity-dependent spin switching (AO-HDS) represents a new frontier in femtomagnetism, where a single ultrafast laser pulse can permanently switch spin without any assistance from a magnetic field. This review summarizes some of the crucial aspects of this new discipline: key experimental findings, leading mechanisms, controversial issues, and possible future directions. The emphasis is on our latest investigation. We first develop the all-optical spin switching (AOS) rule that determines how the switchability depends on the light helicity. This rule allows one to understand microscopically how the spin is reversed and why the circularly polarized light appears more powerful than the linearly polarized light. Then we invoke our latest spin-orbit coupled harmonic oscillator model to simulate single spin reversal. We consider both continuous wave (cw) excitation and pulsed laser excitation. The results are in a good agreement with the experimental result (a MatLab code is available upon request from the author). We then extend the code to include the exchange interaction among different spin sites. We show where the “inverse-Faraday field” comes from and how the laser affects the spin reversal nonlinearly. Our hope is that this review will motivate new experimental and theoretical investigations and discussions.
Mo, Yangzhi; Li, Jun; Jiang, Bin; Su, Tao; Geng, Xiaofei; Liu, Junwen; Jiang, Haoyu; Shen, Chengde; Ding, Ping; Zhong, Guangcai; Cheng, Zhineng; Liao, Yuhong; Tian, Chongguo; Chen, Yingjun; Zhang, Gan
2018-08-01
Humic-like substances (HULIS) are a class of high molecular weight, light-absorbing compounds that are highly related to brown carbon (BrC). In this study, the sources and compositions of HULIS isolated from fine particles collected in Beijing, China during the 2014 Asia-Pacific Economic Cooperation (APEC) summit were characterized based on carbon isotope ( 13 C and 14 C) and Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR MS) analyses, respectively. HULIS were the main light-absorbing components of water-soluble organic carbon (WSOC), accounting for 80.2 ± 6.1% of the WSOC absorption capacity at 365 nm. The carbon isotope data showed that HULIS had a lower non-fossil contribution (53 ± 4%) and were less enriched with 13 C (-24.2 ± 0.6‰) relative to non-HULIS (62 ± 8% and -20.8 ± 0.3‰, respectively). The higher relative intensity fraction of sulfur-containing compounds in HULIS before and after APEC was attributed to higher sulfur dioxide levels emitted from fossil fuel combustion, whereas the higher fraction of nitrogen-containing compounds during APEC may have been due to the relatively greater contribution of non-fossil compounds or the influence of nitrate radical chemistry. The results of investigating the relationships among the sources, elemental compositions, and optical properties of HULIS demonstrated that the light absorption of HULIS appeared to increase with increasing unsaturation degree, but decrease with increasing oxidation level. The unsaturation of HULIS was affected by both sources and aging level. Copyright © 2018 Elsevier Ltd. All rights reserved.
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
The relationship between shock response spectrum and fast Fourier transform
International Nuclear Information System (INIS)
Zola, Maurizio
2001-01-01
In this paper the basic relationship between response spectrum and fast Fourier transform is laid down. Since a long time the response spectrum has been used by structural engineers in the seismic domain and nowadays it is going to be used to define transient motions. This way to define the excitation is more general and more real than the use of classical shape pulses for the reproduction of real environment. Nevertheless the response spectrum of a real excitation represents a loss of some information with respect to the Fourier transform. A useful discussion could arise from these observations. Appendix A gives the relationship between the mathematic Fourier transform and the digital Fourier transform given by computers, while Appendix B gives some examples of response spectra and Fourier transforms of simple functions. (author)
International Nuclear Information System (INIS)
Granitza, B.; Salvietti, M.; Torello, E.; Mattera, L.; Sasso, A.
1995-01-01
Diode laser optical pumping to produce a highly spin-polarized metastable He beam to be used in a spin-polarized metastable atom deexcitation spectroscopy experiment on magnetized surfaces is described. Efficient pumping of the beam is performed by means of an SDL-6702 distributed Bragg reflector diode laser which yields 50 mW of output power in a single longitudinal mode at 1083 nm, the resonance wavelength for the 2 3 S→2 3 P 0,1,2 (D 0 , D 1 , and D 2 ) transitions of He*. The light is circularly polarized by a quarter-wave plate, allowing easy change of the sense of atomic polarization. The laser frequency can be locked to the atomic transition for several hours by phase-sensitive detection of the saturated absorption signal in a He discharge cell. Any of the three transitions of the triplet system can be pumped with the laser but the maximum level of atomic polarization of 98.5% is found pumping the D 2 line. copyright 1995 American Institute of Physics
Fast Fourier transform telescope
International Nuclear Information System (INIS)
Tegmark, Max; Zaldarriaga, Matias
2009-01-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog 2 N rather than N 2 ) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Directory of Open Access Journals (Sweden)
Singh A.
2015-12-01
Full Text Available In this work, zinc oxide (ZnO nanorods were obtained by a simple chemical precipitation method in the presence of capping agent: polyvinyl pyrrolidone (PVP at room temperature. X-ray diffraction (XRD result indicates that the synthesized undoped ZnO nanorods have hexagonal wurtzite structure without any impurities. It has been observed that the growth direction of the prepared ZnO nanorods is [1 0 1]. XRD analysis revealed that the nanorods have the crystallite size of 49 nm. Crystallite size is calculated by Debye-Scherrer formula and lattice strain is calculated by Williomson-Hall equation. Cell volume, Lorentz factor, Lorentz polarization factor, bond length, texture coefficient, lattice constants and dislocation density have also been studied. We also compared the interplanar spacings and relative peak intensities with their standard values at different angles. The scanning electron microscope (SEM images confirmed the size and shape of these nanorods. It has been found that the diameter of the nanorods ranges from 1.52 μm to 1.61 μm and the length is about 4.89 μm. It has also been observed that at room temperature ultraviolet visible (UV-Vis absorption band is around 355 nm (blue shifted as compared to the bulk. The average particle size has also been calculated by mathematical model of effective mass approximation equation, using UV-Vis absorption peak. Finally, the bandgap has been calculated using UV-absorption peak. Electroluminescence (EL studies show that emission of light is possible at very small threshold voltage and it increases rapidly with increasing applied voltage. It is seen that smaller ZnO nanoparticles give higher electroluminescence brightness starting at lower threshold voltage. The brightness is also affected by increasing the frequency of AC signal.
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
Energy Technology Data Exchange (ETDEWEB)
Al-Gaashani, R., E-mail: Rashad_jashani@yahoo.com [School of Applied Physics, Faculty Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia); Department of Physics, Thamar University, Dhamar, Republic of Yemen (Yemen); Radiman, S. [School of Applied Physics, Faculty Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia); Tabet, N. [Department of Physics and Center of Research Excellence in Renewable Energy, King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia); Daud, A.R. [School of Applied Physics, Faculty Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia)
2013-02-15
Highlights: Black-Right-Pointing-Pointer A novel method for the synthesis of hematite nanopowder is reported. Black-Right-Pointing-Pointer The morphology of {alpha}-Fe{sub 2}O{sub 3} changed with altering the preparation temperature. Black-Right-Pointing-Pointer The coral like nano {alpha}-Fe{sub 2}O{sub 3} prepared at 500 and 600 Degree-Sign C showed novel optical behavior. Black-Right-Pointing-Pointer The coral like nano {alpha}-Fe{sub 2}O{sub 3} could be used to enhance efficiency of the solar cells. - Abstract: Hematite nanostructures were prepared by a simple technique using the thermal decomposition of iron (III) nitrate 9-hydrate at different temperatures under air atmosphere. Observations using field emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM) showed that the morphology of the nanostructures changed as the temperature was varied while their size increased with increasing preparation time. Samples prepared at 300, 400, and 500 Degree-Sign C were made of particles with a quantum dots (QDs) size. X-ray photoelectron spectroscopy (XPS), energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD) confirmed that the as-synthesized powders are pure {alpha}-Fe{sub 2}O{sub 3}. The optical energy gap of the samples varied from 3.2 eV to 2.7 eV as the preparation temperature increased from 300 Degree-Sign C to 600 Degree-Sign C.
Mathieu, Jean Paul
1975-01-01
Optics, Parts 1 and 2 covers electromagnetic optics and quantum optics. The first part of the book examines the various of the important properties common to all electromagnetic radiation. This part also studies electromagnetic waves; electromagnetic optics of transparent isotropic and anisotropic media; diffraction; and two-wave and multi-wave interference. The polarization states of light, the velocity of light, and the special theory of relativity are also examined in this part. The second part is devoted to quantum optics, specifically discussing the classical molecular theory of optical p
van Schie, C H; Abbott, C A; Vileikyte, L; Shaw, J E; Hollis, S; Boulton, A J
1999-02-01
To test the Podotrack, a simple inexpensive semiquantitative footprint mat, for potential use as a screening tool for high plantar pressures, against the optical pedobarograph (a computerized device). The Podotrack was superimposed on the pedobarograph for simultaneous measurement of pressures from both systems. Three independent observers quantified the pressures of Podotrack footprints from healthy controls and diabetic patients, both before (n=164) and after (n=183) training. The sensitivity of the Podotrack to identify high pressure areas measured by the pedobarograph (> 12.3 kg/cm2) was 78.7%, 45.8% and 44.3% (observer A, B and C) before training, but improved to 96.2%, 92.4% and 91.1% after training (P<0.01). Specificity for all three observers was more than 90% before and after training. Inter-observer agreement improved significantly after training (P<0.001). After a simple training of the observers, the Podotrack identified approximately all high pressure areas, suggesting that the Podotrack could be a useful screening tool to identify areas at risk of ulceration in diabetic patients. We recommend a standard training package for new Podotrack users, to optimize identification of diabetic patients at risk of foot ulceration.
Fourier Transform Spectrometer System
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
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.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Fincham, W H A
2013-01-01
Optics: Ninth Edition Optics: Ninth Edition covers the work necessary for the specialization in such subjects as ophthalmic optics, optical instruments and lens design. The text includes topics such as the propagation and behavior of light; reflection and refraction - their laws and how different media affect them; lenses - thick and thin, cylindrical and subcylindrical; photometry; dispersion and color; interference; and polarization. Also included are topics such as diffraction and holography; the limitation of beams in optical systems and its effects; and lens systems. The book is recommen
Fourier-Hermite communications; where Fourier meets Hermite
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
On fractional Fourier transform moments
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
Grafakos, Loukas
2014-01-01
This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews fr...
Fourier transform infrared spectroscopy of peptides.
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.
Functional Fourier transforms and the loop equation
International Nuclear Information System (INIS)
Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.
1986-01-01
The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables
Fincham, W H A
2013-01-01
Optics: Eighth Edition covers the work necessary for the specialization in such subjects as ophthalmic optics, optical instruments and lens design. The text includes topics such as the propagation and behavior of light; reflection and refraction - their laws and how different media affect them; lenses - thick and thin, cylindrical and subcylindrical; photometry; dispersion and color; interference; and polarization. Also included are topics such as diffraction and holography; the limitation of beams in optical systems and its effects; and lens systems. The book is recommended for engineering st
Fourier transform wavefront control with adaptive prediction of the atmosphere.
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.
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Nikoleli, Georgia-Paraskevi; Nikolelis, Dimitrios P; Methenitis, Constantinos
2010-08-18
This work describes the construction of a simple optical sensor for the rapid, selective and sensitive detection of urea in milk using air stable lipid films with incorporated urease. The lipid film is stabilized on a glass filter by polymerization using UV (ultra-violet) radiation prior its use. Methacrylic acid was the functional monomer, ethylene glycol dimethacrylate was the crosslinker and 2,2'-azobis-(2-methylpropionitrile) was the initiator. Urease is incorporated within this mixture prior to the polymerization. The presence of the enzyme in these films quenched this fluorescence and the colour became similar to that of the filters without the lipid films. A drop of aqueous solution of urea provided a "switching on" of the fluorescence which allows the rapid detection of this compound at the levels of 10(-8) M concentrations. The investigation of the effect of potent interferences included a wide range of compounds usually found in foods and also of proteins and lipids. These lipid membranes were used for the rapid detection of urea in milk. Copyright 2010 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Kandula, Syam; Jeevanandam, P.
2014-01-01
Highlights: • SiO x @CdS nanoparticles have been synthesized by a novel thermal decomposition approach. • The method is easy and there is no need for surface functionalization of silica core. • SiO x @CdS nanoparticles show different optical properties compared to pure CdS. - Abstract: SiO x @CdS core–shell nanoparticles have been synthesized by a simple thermal decomposition approach. The synthesis involves two steps. In the first step, SiO x spheres were synthesized using StÖber’s process. Then, cadmium sulfide nanoparticles were deposited on the SiO x spheres by the thermal decomposition of cadmium acetate and thiourea in ethylene glycol at 180 °C. Electron microscopy results show uniform deposition of cadmium sulfide nanoparticles on the surface of SiO x spheres. Electron diffraction patterns confirm crystalline nature of the cadmium sulfide nanoparticles on silica and high resolution transmission electron microscopy images clearly show the lattice fringes due to cubic cadmium sulfide. Diffuse reflectance spectroscopy results show blue shift of band gap absorption of SiO x @CdS core–shell nanoparticles with respect to bulk cadmium sulfide and this is attributed to quantum size effect. Photoluminescence results show enhancement in intensity of band edge emission and weaker emission due to surface defects in SiO x @CdS core–shell nanoparticles compared to pure cadmium sulfide nanoparticles
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.
Fourier analysis of the parametric resonance in neutrino oscillations
International Nuclear Information System (INIS)
Koike, Masafumi; Ota, Toshihiko; Saito, Masako; Sato, Joe
2009-01-01
Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.
Fieldable Fourier transform spectrometer
Hatchell, Brian K.; Harper, Warren W.; Schultz, John F.
2004-10-01
The infrared sensors group at the Pacific Northwest National Laboratory (PNNL) is focused on the science and technology of remote and in-situ chemical sensors for detecting proliferation and countering terrorism. To support these vital missions, PNNL is developing frequency-modulation techniques for remote probing over long optical paths by means of differential-absorption light detecting and ranging (LIDAR). This technique can easily monitor large areas, or volumes, that could only be accomplished with a large network of point sensors. Recently, PNNL began development of a rugged frequency-modulation differential-abosrption LIDAR (FM-DIAL) system to conduct field experiments. To provide environmentla protection for the system and facilitate field deployments and operations, a large, well insulated, temperature controlled trailer was specified and acquired. The trailer was outfitted with a shock-mounted optical bench, an electronics rack, a liquid nitrogen Dewar, and a power generator. A computer-controlled gimbal-mounted mirror was added to allow the telescope beam to be accurately pointed in both the vertical and horizontal plane. This turned out to be the most complicated addition, and is described in detail. This paper provides an overview of the FM-DIAL system and illustrates innovative solutions developed to overcome several alignment and stability issues encountered in the field.
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)
Grid-Independent Compressive Imaging and Fourier Phase Retrieval
Liao, Wenjing
2013-01-01
This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem. Many situations in optics, medical imaging and signal processing call…
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.
Dual beam encoded extended fractional Fourier transform security ...
Indian Academy of Sciences (India)
This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit ...
Fourier transform distribution function of relaxation times; application and limitations
Boukamp, Bernard A.
2015-01-01
A simple Fourier transform (FT) method is presented for obtaining a Distribution Function of Relaxation Times (DFRT) for electrochemical impedance spectroscopy (EIS) data. By using a special data extension procedure the FT is performed over the range from -∞ ≤ lnω ≤ + ∞. The integration procedure is
Graybill, George
2007-01-01
Just how simple are simple machines? With our ready-to-use resource, they are simple to teach and easy to learn! Chocked full of information and activities, we begin with a look at force, motion and work, and examples of simple machines in daily life are given. With this background, we move on to different kinds of simple machines including: Levers, Inclined Planes, Wedges, Screws, Pulleys, and Wheels and Axles. An exploration of some compound machines follows, such as the can opener. Our resource is a real time-saver as all the reading passages, student activities are provided. Presented in s
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
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.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Quadrature formulas for Fourier coefficients
Bojanov, Borislav; Petrova, Guergana
2009-01-01
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
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
On integral and finite Fourier transforms of continuous q-Hermite polynomials
International Nuclear Information System (INIS)
Atakishiyeva, M. K.; Atakishiyev, N. M.
2009-01-01
We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H n (x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.
Lee, Young Han; Park, Eun Hae; Suh, Jin-Suck
2015-01-01
The objectives are: 1) to introduce a simple and efficient method for extracting region of interest (ROI) values from a Picture Archiving and Communication System (PACS) viewer using optical character recognition (OCR) software and a macro program, and 2) to evaluate the accuracy of this method with a PACS workstation. This module was designed to extract the ROI values on the images of the PACS, and created as a development tool by using open-source OCR software and an open-source macro program. The principal processes are as follows: (1) capture a region of the ROI values as a graphic file for OCR, (2) recognize the text from the captured image by OCR software, (3) perform error-correction, (4) extract the values including area, average, standard deviation, max, and min values from the text, (5) reformat the values into temporary strings with tabs, and (6) paste the temporary strings into the spreadsheet. This principal process was repeated for the number of ROIs. The accuracy of this module was evaluated on 1040 recognitions from 280 randomly selected ROIs of the magnetic resonance images. The input times of ROIs were compared between conventional manual method and this extraction module-assisted input method. The module for extracting ROI values operated successfully using the OCR and macro programs. The values of the area, average, standard deviation, maximum, and minimum could be recognized and error-corrected with AutoHotkey-coded module. The average input times using the conventional method and the proposed module-assisted method were 34.97 seconds and 7.87 seconds, respectively. A simple and efficient method for ROI value extraction was developed with open-source OCR and a macro program. Accurate inputs of various numbers from ROIs can be extracted with this module. The proposed module could be applied to the next generation of PACS or existing PACS that have not yet been upgraded. Copyright © 2015 AUR. Published by Elsevier Inc. All rights reserved.
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)
Directory of Open Access Journals (Sweden)
Lizeth Torres
2018-05-01
Full Text Available The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier transform (FT of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1 the reconstruction of a simple periodical signal, (2 the approximation of both a square and a triangular signal, (3 the edge detection in signals by using the Fourier coefficients, (4 the fitting of the historical Bitcoin market data from 1 December 2014 to 8 January 2018 and (5 the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT, which is a well-known method for time-frequency analysis.
Directory of Open Access Journals (Sweden)
Pietro Emanuele Napoli
Full Text Available To compare a novel spectral-domain optical coherence tomography (SD-OCT technique with traditional lid transillumination for evaluation of meibomian glands (MGs and to assess the relation of MG morphologic changes to the glandular atrophy.Evaluation of diagnostic technology.Sixty-one patients with obstructive MGD (30 men, 31 women; age [mean ± standard deviation] 45.1 ± 12.1 years, and 75 control subjects (32 men, 43 women; 44.1 ± 12.5 years were recruited in order to have a balanced distribution of glandular features.Agreement between SD-OCT and lid transillumination examination for the detection of drop-out (partial or complete loss of MGs and microscopic changes (i.e. shortening, distortion, segmentation and entanglement, as well as the relationship between morphological features and MG atrophy were evaluated.Agreement between the two meibographic techniques, bias in symmetry of classification, and association analysis between microscopic changes and MG dropout.Overall agreement for all morphological features was substantial (Cohen kappa coefficient = 0.77; p<0.001, even if, the majority of disagreement occurred for cases with segmentation, where agreement was present in only 108 (81.82% of 132 eyes with adequate images for interpretation, and where SD-OCT tended to diagnose more cases not detected by traditional lid transillumination (McNemar test, p<0.001. Moreover, segmentation and distortion pattern negatively correlated with the degree of drop-out, whereas shortening and entanglement pattern demonstrated only a weak correlation (Spearman's ρ was -0.691, -0.491, -0.359, -0.385, respectively.Each method has its advantages but in general there was close agreement between these meibographic techniques, particularly for MG dropout, which supports the reliability of our novel, simple and patient-friendly SD-OCT approach.
Comparative analysis of imaging configurations and objectives for Fourier microscopy.
Kurvits, Jonathan A; Jiang, Mingming; Zia, Rashid
2015-11-01
Fourier microscopy is becoming an increasingly important tool for the analysis of optical nanostructures and quantum emitters. However, achieving quantitative Fourier space measurements requires a thorough understanding of the impact of aberrations introduced by optical microscopes that have been optimized for conventional real-space imaging. Here we present a detailed framework for analyzing the performance of microscope objectives for several common Fourier imaging configurations. To this end, we model objectives from Nikon, Olympus, and Zeiss using parameters that were inferred from patent literature and confirmed, where possible, by physical disassembly. We then examine the aberrations most relevant to Fourier microscopy, including the alignment tolerances of apodization factors for different objective classes, the effect of magnification on the modulation transfer function, and vignetting-induced reductions of the effective numerical aperture for wide-field measurements. Based on this analysis, we identify an optimal objective class and imaging configuration for Fourier microscopy. In addition, the Zemax files for the objectives and setups used in this analysis have been made publicly available as a resource for future studies.
Application of Fourier analysis to multispectral/spatial recognition
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.
General Correlation Theorem for Trinion Fourier Transform
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...
Products of multiple Fourier series with application to the multiblade transformation
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.
Fourier series, Fourier transform and their applications to mathematical physics
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...
Fourier series and orthogonal polynomials
Jackson, Dunham
2004-01-01
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe
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.
Fourier transform zero field NMR and NQR
International Nuclear Information System (INIS)
Zax, D.B.
1985-01-01
In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low λ nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI
Levene, Michael John
In all attempts to emulate the considerable powers of the brain, one is struck by both its immense size, parallelism, and complexity. While the fields of neural networks, artificial intelligence, and neuromorphic engineering have all attempted oversimplifications on the considerable complexity, all three can benefit from the inherent scalability and parallelism of optics. This thesis looks at specific aspects of three modes in which optics, and particularly volume holography, can play a part in neural computation. First, holography serves as the basis of highly-parallel correlators, which are the foundation of optical neural networks. The huge input capability of optical neural networks make them most useful for image processing and image recognition and tracking. These tasks benefit from the shift invariance of optical correlators. In this thesis, I analyze the capacity of correlators, and then present several techniques for controlling the amount of shift invariance. Of particular interest is the Fresnel correlator, in which the hologram is displaced from the Fourier plane. In this case, the amount of shift invariance is limited not just by the thickness of the hologram, but by the distance of the hologram from the Fourier plane. Second, volume holography can provide the huge storage capacity and high speed, parallel read-out necessary to support large artificial intelligence systems. However, previous methods for storing data in volume holograms have relied on awkward beam-steering or on as-yet non- existent cheap, wide-bandwidth, tunable laser sources. This thesis presents a new technique, shift multiplexing, which is capable of very high densities, but which has the advantage of a very simple implementation. In shift multiplexing, the reference wave consists of a focused spot a few millimeters in front of the hologram. Multiplexing is achieved by simply translating the hologram a few tens of microns or less. This thesis describes the theory for how shift
Rotational Fourier tracking of diffusing polygons.
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.
... Han M, Partin AW. Simple prostatectomy: open and robot-assisted laparoscopic approaches. In: Wein AJ, Kavoussi LR, ... M. is also a founding member of Hi-Ethics and subscribes to the principles of the Health ...
Multicomplementary operators via finite Fourier transform
International Nuclear Information System (INIS)
Klimov, Andrei B; Sanchez-Soto, Luis L; Guise, Hubert de
2005-01-01
A complete set of d + 1 mutually unbiased bases exists in a Hilbert space of dimension d, whenever d is a power of a prime. We discuss a simple construction of d + 1 disjoint classes (each one having d - 1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
International Nuclear Information System (INIS)
Ponce, W.A.; Zepeda, A.
1987-08-01
We present the results obtained from our systematic search of a simple Lie group that unifies weak and electromagnetic interactions in a single truly unified theory. We work with fractionally charged quarks, and allow for particles and antiparticles to belong to the same irreducible representation. We found that models based on SU(6), SU(7), SU(8) and SU(10) are viable candidates for simple unification. (author). 23 refs
FOURIER SERIES MODELS THROUGH TRANSFORMATION
African Journals Online (AJOL)
DEPT
monthly temperature data (1996 – 2005) collected from the National Root ... KEY WORDS: Fourier series, square transformation, multiplicative model, ... fluctuations or movements are often periodic(Ekpeyong,2005). .... significant trend or not, if the trend is not significant, the grand mean may be used as an estimate of trend.
Optical spatial differentiator based on subwavelength high-contrast gratings
Dong, Zhewei; Si, Jiangnan; Yu, Xuanyi; Deng, Xiaoxu
2018-04-01
An optical spatial differentiator based on subwavelength high-contrast gratings (HCGs) is proposed experimentally. The spatial differentiation property of the subwavelength HCG is analyzed by calculating its spatial spectral transfer function based on the periodic waveguide theory. By employing the FDTD solutions, the performance of the subwavelength HCG spatial differentiator was investigated numerically. The subwavelength HCG differentiator with the thickness at the nanoscale was fabricated on the quartz substrate by electron beam lithography and Bosch deep silicon etching. Observed under an optical microscope with a CCD camera, the spatial differentiation of the incident field profile was obtained by the subwavelength HCG differentiator in transmission without Fourier lens. By projecting the images of slits, letter "X," and a cross on the subwavelength HCG differentiator, edge detections of images were obtained in transmission. With the nanoscale HCG structure and simple optical implementation, the proposed optical spatial differentiator provides the prospects for applications in optical computing systems and parallel data processing.
Iterative wave-front reconstruction in the Fourier domain.
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.
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
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
Directory of Open Access Journals (Sweden)
André Luiz Galo
2009-01-01
Full Text Available We describe the design and tests of a set-up mounted in a conventional double beam spectrophotometer, which allows the determination of optical density of samples confined in a long liquid core waveguide (LCW capillary. Very long optical path length can be achieved with capillary cell, allowing measurements of samples with very low optical densities. The device uses a custom optical concentrator optically coupled to LCW (TEFLON® AF. Optical density measurements, carried out using a LCW of ~ 45 cm, were in accordance with the Beer-Lambert Law. Thus, it was possible to analyze quantitatively samples at concentrations 45 fold lower than that regularly used in spectrophotometric measurements.
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
An algorithm for the basis of the finite Fourier transform
Santhanam, Thalanayar S.
1995-01-01
The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.
Uncertainty Principles and Fourier Analysis
Indian Academy of Sciences (India)
analysis on the part of the reader. Those who are not fa- miliar with Fourier analysis are encouraged to look up Box. 1 along with [3]. (A) Heisenberg's inequality: Let us measure concentration in terms of standard deviation i.e. for a square integrable func-. 00 tion defined on 1R and normalized so that J If(x)12d,x = 1,. -00. 00.
An introduction to Fourier series and integrals
Seeley, Robert T
2006-01-01
This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Damin, Craig A; Sommer, André J
2013-11-01
Advances in fiber optic materials have allowed for the construction of fibers and waveguides capable of transmitting infrared radiation. An investigation of the transmission characteristics associated with two commonly used types of infrared-transmitting fibers/waveguides for prospective use in a fiber/waveguide-coupled attenuated total internal reflection (ATR) probe was performed. Characterization of silver halide polycrystalline fiber optics and hollow silica waveguides was done on the basis of the transmission of infrared light using a conventional fiber optic coupling accessory and an infrared microscope. Using the fiber optic coupling accessory, the average percent transmission for three silver halide fibers was 18.1 ± 6.1% relative to a benchtop reflection accessory. The average transmission for two hollow waveguides (HWGs) using the coupling accessory was 8.0 ± 0.3%. (Uncertainties in the relative percent transmission represent the standard deviations.) Reduced transmission observed for the HWGs was attributed to the high numerical aperture of the coupling accessory. Characterization of the fibers/waveguides using a zinc selenide lens objective on an infrared microscope indicated 24.1 ± 7.2% of the initial light input into the silver halide fibers was transmitted. Percent transmission obtained for the HWGs was 98.7 ± 0.1%. Increased transmission using the HWGs resulted from the absence or minimization of insertion and scattering losses due to the hollow air core and a better-matched numerical aperture. The effect of bending on the transmission characteristics of the fibers/waveguides was also investigated. Significant deviations in the transmission of infrared light by the solid-core silver halide fibers were observed for various bending angles. Percent transmission greater than 98% was consistently observed for the HWGs at the bending angles. The combined benefits of high percent transmission, reproducible instrument responses, and increased bending
Properties of the distributional finite Fourier transform
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.
Fourier techniques in X-ray timing
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
Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.
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.
Comparison of delay-interferometer and time-lens-based all-optical OFDM demultiplexers
DEFF Research Database (Denmark)
Lillieholm, Mads; Mulvad, Hans Christian Hansen; Galili, Michael
2015-01-01
) based on time lenses. In the former scheme, cascaded delay-interferometers (DIs) are used to perform the O-DFT, with subsequent active optical gating to remove the intercarrier interference (ICI). Here a reduced-complexity partial O-DFT, realized by replacing a number of DIs with optical bandpass......In this paper we present the first detailed numerical comparison of two promising all-optical schemes to demultiplex orthogonal frequency-division multiplexing (OFDM) signals. The investigated schemes are the optical discrete Fourier transformation (O-DFT) and the optical spectral magnification (SM...... filters, is investigated. In the latter scheme the OFDM spectrum is magnified, allowing for simple optical bandpass filtering of the individual subcarriers with reduced ICI. Ideally only a single unit consisting of two time lenses is needed, reducing the complexity and potentially the energy consumption...
Comparison of Delay-Interferometer and Time- Lens-Based All-Optical OFDM Demultiplexers
DEFF Research Database (Denmark)
Lillieholm, Mads; Mulvad, Hans Christian Hansen; Galili, Michael
2015-01-01
(SM) based on time lenses. In the former scheme, cascaded delay-interferometers (DIs) are used to perform the O-DFT, with subsequent active optical gating to remove the intercarrier interference (ICI). Here, a reduced-complexity partial O-DFT, realized by replacing a number of DIs with optical......In this letter, we present the first detailed numerical comparison of two promising all-optical schemes to demultiplex orthogonal frequency-division multiplexing (OFDM) signals. The investigated schemes are the optical discrete Fourier transformation (O-DFT) and the optical spectral magnification...... bandpass filters, is investigated. In the latter scheme, the OFDM spectrum is magnified, allowing for simple optical bandpass filtering of the individual subcarriers with reduced ICI. Ideally, only a single unit consisting of two time lenses is needed, reducing the complexity and potentially the energy...
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
Fourier Transform Methods. Chapter 4
Kaplan, Simon G.; Quijada, Manuel A.
2015-01-01
This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..
Simple Analysis of Historical Lime Mortars
Pires, Joa~o
2015-01-01
A laboratory experiment is described in which a simple characterization of a historical lime mortar is made by the determination of its approximate composition by a gravimetric method. Fourier transform infrared (FTIR) spectroscopy and X-ray diffraction (XRD) are also used for the qualitative characterization of the lime mortar components. These…
On a q-extension of Mehta's eigenvectors of the finite Fourier transform for q a root of unity
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.
2008-01-01
It is shown that the continuous q-Hermite polynomials for q a root of unity have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.
q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity
Atakishiyeva, M.K.; Atakishiyev, N.M.; Koornwinder, T.H.
2009-01-01
It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.
Closed contour fractal dimension estimation by the Fourier transform
International Nuclear Information System (INIS)
Florindo, J.B.; Bruno, O.M.
2011-01-01
Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.
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.
Pointwise convergence of Fourier series
Arias de Reyna, Juan
2002-01-01
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
Is Fourier analysis performed by the visual system or by the visual investigator.
Ochs, A L
1979-01-01
A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.
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)
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...
Cryogenic Scan Mechanism for Fourier Transform Spectrometer
Brasunas, John C.; Francis, John L.
2011-01-01
A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear
First order deformations of the Fourier matrix
Energy Technology Data Exchange (ETDEWEB)
Banica, Teodor, E-mail: teo.banica@gmail.com [Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise (France)
2014-01-15
The N × N complex Hadamard matrices form a real algebraic manifold C{sub N}. The singularity at a point H ∈ C{sub N} is described by a filtration of cones T{sub H}{sup ×}C{sub N}⊂T{sub H}{sup ∘}C{sub N}⊂T{sub H}C{sub N}⊂T{sup ~}{sub H}C{sub N}, coming from the trivial, affine, smooth, and first order deformations. We study here these cones in the case where H = F{sub N} is the Fourier matrix, (w{sup ij}) with w = e{sup 2πi/N}, our main result being a simple description of T{sup ~}{sub H}C{sub N}. As a consequence, the rationality conjecture dim{sub R}(T{sup ~}{sub H}C{sub N})=dim{sub Q}(T{sup ~}{sub H}C{sub N}∩M{sub N}(Q)) holds at H = F{sub N}.
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.
High resolution integral holography using Fourier ptychographic approach.
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.
Applications of Fourier transforms to generalized functions
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...
Whitesides, George M.; Tang, Sindy K. Y.
2006-09-01
Fluidic optics is a new class of optical system with real-time tunability and reconfigurability enabled by the introduction of fluidic components into the optical path. We describe the design, fabrication, operation of a number of fluidic optical systems, and focus on three devices, liquid-core/liquid-cladding (L2) waveguides, microfluidic dye lasers, and diffraction gratings based on flowing, crystalline lattices of bubbles, to demonstrate the integration of microfluidics and optics. We fabricate these devices in poly(dimethylsiloxane) (PDMS) with soft-lithographic techniques. They are simple to construct, and readily integrable with microanalytical or lab-on-a-chip systems.
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.
Energy Technology Data Exchange (ETDEWEB)
Kato, Y; Miyamoto, M [Yamaguchi University, Yamaguchi (Japan). Faculty of Engineering; Chimura, T [Toyota Motor Co. Ltd., Tokyo (Japan); Idei, Y [Ube Industries, Ltd., Tokyo (Japan)
1991-09-25
In order to clarify the relationship between the heat transfer rate and the expansion bed in a group of horizontal pipes in a freeboard region (an area of the heat-transfer pipe exposed above the height of static particle bed from the beginning) in a cold model of the fluidized bed, particle behavior was measured using an optical measuring method. The light axis position was set higher than the heat-transfer as X {sub p} in a direction perpendicular from the distributor, and the static bed height was set to L {sub c}. The frequency of particles and particle lumps coming to presence between the light axes is termed V {prime}{sub p}(time-averaged dimensionless amount of the optical probe output). The V {prime}{sub p} decreases with an increase in the flow velocity, and, when the difference between the probe tip and the static bed height, X {sub p}{minus} L {sub c} is small, it shows the minimum value at a certain flow velocity and then rises again. The root mean square value of the probe output, V {prime}{sub f} increased with an increase in the flow velocity, reached its maximum, then decreased to the minimum, and rose again. The flow velocity that takes the maximum heat transfer rate can be identified from the relationship among the dimensionless amount of the maximum expansion bed height and the average expansion bed height, the dimensionless height of X {sub p} when V {prime}{sub p} and V {prime}{sub f} obtained at each X {sub p} show the extreme values, and the dimensionless height of the heat-transfer pipes when the average transfer rate takes the maximum value. 6 refs., 5 figs.
Applied optics and optical design
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
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.
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.
Quantum arithmetic with the Quantum Fourier Transform
Ruiz-Perez, Lidia; Garcia-Escartin, Juan Carlos
2014-01-01
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their capabilities. Among the new circuits, we propose a quantum method to compute the weighted average of a series of inputs in the transform domain.
On the inverse windowed Fourier transform
Rebollo Neira, Laura; Fernández Rubio, Juan Antonio
1999-01-01
The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion. Peer Reviewed
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.; Boashash, B.
2003-01-01
We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept
Manikandan, A.; Sridhar, R.; Arul Antony, S.; Ramakrishna, Seeram
2014-11-01
Nanocrystalline magnetic spinel CoFe2O4 was synthesized by a simple microwave combustion method (MCM) using ferric nitrate, cobalt nitrate and Aloe vera plant extracted solution. For the comparative study, it was also prepared by a conventional combustion method (CCM). Powder X-ray diffraction, energy dispersive X-ray and selected-area electron diffraction results indicate that the as-synthesized samples have only single-phase spinel structure with high crystallinity and without the presence of other phase impurities. The crystal structure and morphology of the powders were revealed by high resolution scanning electron microscopy and transmission electron microscopy, show that the MCM products of CoFe2O4 samples contain sphere-like nanoparticles (SNPs), whereas the CCM method of samples consist of flake-like nanoplatelets (FNPs). The band gap of the samples was determined by UV-Visible diffuse reflectance and photoluminescence spectroscopy. The magnetization (Ms) results showed a ferromagnetic behavior of the CoFe2O4 nanostructures. The Ms value of CoFe2O4-SNPs is higher i.e. 77.62 emu/g than CoFe2O4-FNPs (25.46 emu/g). The higher Ms value of the sample suggest that the MCM technique is suitable for preparing high quality nanostructures for magnetic applications. Both the samples were successfully tested as catalysts for the conversion of benzyl alcohol. The resulting spinel ferrites were highly selective for the oxidation of benzyl alcohol and exhibit important difference among their activities. It was found that CoFe2O4-SNPs catalyst show the best performance, whereby 99.5% selectivity of benzaldehyde was achieved at close to 93.2% conversion.
Magneto-sensor circuit efficiency incremented by Fourier-transformation
Talukdar, Abdul Hafiz Ibne; Useinov, Arthur; Hussain, Muhammad Mustafa
2011-01-01
In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.
Magneto-sensor circuit efficiency incremented by Fourier-transformation
Talukdar, Abdul Hafiz Ibne
2011-10-01
In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.
The fractional Fourier transform and applications
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.
Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.
Caple, Jodi; Byrd, John; Stephan, Carl N
2017-11-01
The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.
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.
Fourier transform based scalable image quality measure.
Narwaria, Manish; Lin, Weisi; McLoughlin, Ian; Emmanuel, Sabu; Chia, Liang-Tien
2012-08-01
We present a new image quality assessment (IQA) algorithm based on the phase and magnitude of the 2D (twodimensional) Discrete Fourier Transform (DFT). The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the Human Visual Systems (HVSs) sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of nonuniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Lastly, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is therefore further scalable for RR scenarios. We report extensive experimental results using a total of 9 publicly available databases: 7 image (with a total of 3832 distorted images with diverse distortions) and 2 video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing fullreference (FR) algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar.
International Nuclear Information System (INIS)
Giavazzi, Fabio; Cerbino, Roberto; Haro-Pérez, Catalina
2016-01-01
We probe the roto-translational Brownian motion of optically anisotropic particles suspended in water with a simple and straightforward optical microscopy experiment that does not require positional or rotational particle tracking. We acquire a movie of the suspension placed between two polarizing elements and we extract the translational diffusion coefficient D T and the rotational diffusion coefficient D R from the analysis of the temporal correlation properties of the spatial Fourier modes of the intensity fluctuations in the movie. Our method is successfully tested with a dilute suspension of birefringent spherical colloidal particles obtained by polymerizing an emulsion of droplets of liquid crystal in a nematic phase, whose roto-translational dynamics is found to be well described by theory. The simplicity of our approach makes our method a viable alternative to particle tracking and depolarized dynamic light scattering. (paper)
Realization of an optical interferometer based on holographic optics ...
Indian Academy of Sciences (India)
The paper describes a simple and cost effective method for the realization of an optical interferometer based on holographic optics, which use minimal bulk optical components. The optical arrangement in the proposed method involves a very simple alignment procedure and inexpensive holographic recording material is ...
Goodman, J. W.
This book is based on the thesis that some training in the area of statistical optics should be included as a standard part of any advanced optics curriculum. Random variables are discussed, taking into account definitions of probability and random variables, distribution functions and density functions, an extension to two or more random variables, statistical averages, transformations of random variables, sums of real random variables, Gaussian random variables, complex-valued random variables, and random phasor sums. Other subjects examined are related to random processes, some first-order properties of light waves, the coherence of optical waves, some problems involving high-order coherence, effects of partial coherence on imaging systems, imaging in the presence of randomly inhomogeneous media, and fundamental limits in photoelectric detection of light. Attention is given to deterministic versus statistical phenomena and models, the Fourier transform, and the fourth-order moment of the spectrum of a detected speckle image.
Fourier transforms in radar and signal processing
Brandwood, David
2011-01-01
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit
The Wigner distribution function and Hamilton's characteristics of a geometric-optical system
Bastiaans, M.J.
1979-01-01
Four system functions have been defined for an optical system; each of these functions describes the system completely in terms of Fourier optics. From the system functions the Wigner distribution function of an optical system has been defined; although derived from Fourier optics, this Wigner
Progress report of a static Fourier transform spectrometer breadboard
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.
Gas Measurement Using Static Fourier Transform Infrared Spectrometers.
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.
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...
Power filtering of n-th order in the fractional Fourier domain
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
Orthonormal mode sets for the two-dimensional fractional Fourier transformation
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
Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding
Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.
1977-01-01
An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.
The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.
Suslick, Kenneth S.; And Others
1987-01-01
Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)
Wink, Alle Meije; Hoogduin, Hans; Roerdink, Jos B.T.M.
2008-01-01
Background: We present a simple, data-driven method to extract haemodynamic response functions (HRF) from functional magnetic resonance imaging (fMRI) time series, based on the Fourier-wavelet regularised deconvolution (ForWaRD) technique. HRF data are required for many fMRI applications, such as
Wink, Alle Meije; Hoogduin, Hans; Roerdink, Jos B.T.M.
2010-01-01
Background: We present a simple, data-driven method to extract haemodynamic response functions (HRF) from functional magnetic resonance imaging (fMRI) time series, based on the Fourier-wavelet regularised deconvolution (ForWaRD) technique. HRF data are required for many fMRI applications, such as
Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules
International Nuclear Information System (INIS)
Dong Ping; Yang Ming; Cao Zhuoliang
2008-01-01
In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system
Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method
Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.
2013-01-01
Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…
Microcomputer Simulation of a Fourier Approach to Optical Wave Propagation
1992-06-01
and transformed input in transform domain). 44 Figure 21. SHFTOUTPUT1 ( inverse transform of product of Bessel filter and transformed input). . . . 44...Figure 22. SHFT OUTPUT2 ( inverse transform of product of ,derivative filter and transformed input).. 45 Figure 23. •tIFT OUTPUT (sum of SHFTOUTPUT1...52 Figure 33. SHFT OUTPUT1 at time slice 1 ( inverse transform of product of Bessel filter and transformed input) .... ............. ... 53
Optical fiber interferometer array for scanless Fourier-transform spectroscopy
Czech Academy of Sciences Publication Activity Database
Velasco, A. V.; Cheben, P.; Florjańczyk, M.; Schmid, J. H.; Bock, P. J.; Lapointe, J.; Delage, A.; Janz, S.; Vachon, M.; Calvo, M. L.; Xu, D.-X.; Civiš, Svatopluk
2013-01-01
Roč. 38, č. 13 (2013), s. 2262-2264 ISSN 0146-9592 Institutional support: RVO:61388955 Keywords : SPATIAL HETERODYNE SPECTROMETER * WAVE-GUIDE Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.179, year: 2013
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.
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 finite Fourier transform of classical polynomials
Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe
2014-01-01
The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.
Mountain Wave Analysis Using Fourier Methods
National Research Council Canada - National Science Library
Roadcap, John R
2007-01-01
...) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms...
A new twist to fourier transforms
Meikle, Hamish D
2004-01-01
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs
Mapped Fourier Methods for stiff problems in toroidal geometry
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...
Fourier transform spectroscopy of semiconductor materials
International Nuclear Information System (INIS)
Jonak-Auer, I.
1996-11-01
In order to determine the type of charge carriers, i.e. electrons or holes, participating in optical transitions, cyclotron resonance experiments using circularly polarized radiation were performed on strained-layer [111]-oriented InGaAs/(Al)GaAs multiple quantum wells and on a [100]-oriented InAs/GaSb double-heterostructure. Because of the rather complicated band-structures of these samples it is a priori unknown which carriers take part in transitions. The measurements yield the surprising result, that for the InGaAs/GaAs multiple quantum well the experimentally observed cyclotron resonance appears in the electron-active polarization in the frequency-regime of the Far Infrared (FIR), but in the hole-active polarization in the range of millimeter waves, whereas for the InGaAs/AlGaAs sample the resonance is caused by holes also in the FIR. Since by theoretical considerations the possibility of electrons causing the FIR cyclotron resonance could be excluded, the measurements are interpreted as being caused by holes due to broken selection rules. In the InAs/GaSb sample hole cyclotron resonance could for the first time be measured on a double-heterostructure. As for the application oriented measurements, they comprised a study of the hydrogen content of amorphous silicon nitride layers, and were performed in collaboration with Austria Mikro Systeme International AG. Fourier spectroscopy is a fast and non-destructive means for determining impurity concentrations. Radiation in the Mid Infrared regime stimulates N-H and Si-H stretching vibrations which lead to absorption peaks and can directly be attributed to the hydrogen concentration via calibration factors taken from the literature. In comparison with recommended procedures in the literature, a much higher accuracy in determining the areas of the absorption peaks could be gained in the course of this thesis by a proper polynomial fit of the background spectrum outside the absorption lines. The hydrogen content of
Matong, Joseph M; Nyaba, Luthando; Nomngongo, Philiswa N
2017-01-01
A rapid, simple and green ultrasound-assisted extraction method using deep eutectic solvents (DES) for extraction of As, Cr, Mo, Sb, Se and V in soil samples, has been developed. Choline chloride-oxalic acid based DES was used as a solvent. The target analytes were subsequently quantified using inductively coupled plasma optical emission spectrometer (ICP OES). The parameters that affect the extraction of the target analytes was optimized using standard reference material of San Joaquin soil (SRM 2709a). In the optimization step, a two-level full factorial experimental design was used. The factors under investigation include extraction time, sample mass and acid concentration. Under optimized conditions, limits of detection (LOD) and limits of quantification (LOQ) ranged from 0.009 to 0.1 and 0.03-0.3µgg -1 , respectively. The repeatability (n=20) estimated in terms of relative standard deviation (%RSD) ranged from 0.9% to 3.7%. The accuracy of the proposed method was carried out using SRM 2709a. The obtained and certified/ indicative values were statistically in good agreement at 95% confidence level. The proposed method applied for quantification of As, Cr, Mo, Sb, Se and V in real soil samples. For comparison, the analytes of interest were also determined using a conventional acid digestion method. According to the paired t-test, the analytical results were not significant differences at 95% confidence level. The method was found to be accurate, precise and environmentally friendly. Copyright © 2016 Elsevier Inc. All rights reserved.
Simple lock-in detection technique utilizing multiple harmonics for digital PGC demodulators.
Duan, Fajie; Huang, Tingting; Jiang, Jiajia; Fu, Xiao; Ma, Ling
2017-06-01
A simple lock-in detection technique especially suited for digital phase-generated carrier (PGC) demodulators is proposed in this paper. It mixes the interference signal with rectangular waves whose Fourier expansions contain multiple odd or multiple even harmonics of the carrier to recover the quadrature components needed for interference phase demodulation. In this way, the use of a multiplier is avoided and the efficiency of the algorithm is improved. Noise performance with regard to light intensity variation and circuit noise is analyzed theoretically for both the proposed technique and the traditional lock-in technique, and results show that the former provides a better signal-to-noise ratio than the latter with proper modulation depth and average interference phase. Detailed simulations were conducted and the theoretical analysis was verified. A fiber-optic Michelson interferometer was constructed and the feasibility of the proposed technique is demonstrated.
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.
Holographic memory system based on projection recording of computer-generated 1D Fourier holograms.
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.
Suppression law of quantum states in a 3D photonic fast Fourier transform chip
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
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)
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...
Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.
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.
Fourier phasing with phase-uncertain mask
International Nuclear Information System (INIS)
Fannjiang, Albert; Liao, Wenjing
2013-01-01
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to stagnate and produce wrong or inaccurate solutions. In this paper Fourier phase retrieval is carried out with the introduction of a randomly fabricated mask in measurement and reconstruction. Highly probable uniqueness of solution, up to a global phase, was previously proved with exact knowledge of the mask. Here the uniqueness result is extended to the case where only rough information about the mask’s phases is assumed. The exponential probability bound for uniqueness is given in terms of the uncertainty-to-diversity ratio of the unknown mask. New phasing algorithms alternating between the object update and the mask update are systematically tested and demonstrated to have the capability of recovering both the object and the mask (within the object support) simultaneously, consistent with the uniqueness result. Phasing with a phase-uncertain mask is shown to be robust with respect to the correlation in the mask as well as the Gaussian and Poisson noises. (paper)
Simplified equations for transient heat transfer problems at low Fourier numbers
DEFF Research Database (Denmark)
Christensen, Martin Gram; Adler-Nissen, Jens
2015-01-01
and validated for infinite slabs, infinite cylinders and spheres and by an industrial application example, covering the center temperature and the volume average temperature. The approach takes ground in the residual difference between a 1 term series solution and a 100 term solution to the Fourier equation...... of the thermal response for solids subjected to convective heat transfer. By representing the residual thermal response as a function of the Biot number and the first eigenvalue, the new approach enables the description of the thermal response in the whole Fourier regime. The presented equation is simple...
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)
DEFF Research Database (Denmark)
Hanson, Steen Grüner; Jakobsen, Michael Linde; Pedersen, Henrik Chresten
2012-01-01
A simple optical implementation of a touch screen is made possible by disrupting the total internal reflection in a 2D waveguide.......A simple optical implementation of a touch screen is made possible by disrupting the total internal reflection in a 2D waveguide....
... Solitary Kidney Your Kidneys & How They Work Simple Kidney Cysts What are simple kidney cysts? Simple kidney cysts are abnormal, fluid-filled ... that form in the kidneys. What are the kidneys and what do they do? The kidneys are ...
Harmonic analysis from Fourier to wavelets
Pereyra, Maria Cristina
2012-01-01
In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introd...
Projective Fourier duality and Weyl quantization
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs
Fourier duality as a quantization principle
International Nuclear Information System (INIS)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Group-invariant finite Fourier transforms
International Nuclear Information System (INIS)
Shenefelt, M.H.
1988-01-01
The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved in 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are organized into a family using the group structure of the crystallographic groups to make iterative procedures possible
Institute of Scientific and Technical Information of China (English)
周丽琴; 王毅; 王晟; 孔琛柯
2014-01-01
AIM:To dynamically observe the feeling change of the photorecrptor layer in the eyes with acute central serous chorioretinopathy ( CSCR ) krypton laser treatment by fourier- domain optical coherence tomography ( FD -OCT ), and to study their correlation with the chang of vision. METHODS: This is a retrospective case series study. The clinical diagnosis of 52 patients with monocular initial onset of central serous chorioretinopathy, krypton laser photocoagulation before treatment, after 1,2,4,6,8wk,6mo, FD - OCT were performed to observe the morphological changes characteristic of photoreceptor layer and changes in vision. RESULTS: After 1wk treatment, all cases were improved;2wk,6 cases were cured;4wk,38 cases were cured;6wk,41 cases were cured;8wk,45 cases were cured, the OCT showed macular retinal neuroepithelial layer ( RNL ) from fully absorbed;6mo with the same 8wk. Before and after treatment in patients with best corrected visual acuity and from the height difference between the macular region of RNL was statistically significant (P CONCLUSION:FD-OCT can dynamicaly observed acute central serous chorioretinopathy krypton laser treatment of photoreceptor ultrastruture changes. Photoreceptor layer of complete and incomplete best corrected visual acuity difference was statistically significant (P METHODS: This is a retrospective case series study. The clinical diagnosis of 52 patients with monocular initial onset of central serous chorioretinopathy, krypton laser photocoagulation before treatment, after 1, 2, 4, 6, 8wk, 6mo, FD - OCT were performed to observe the morphological changes characteristic of photoreceptor layer and changes in vision. RESULTS: After 1wk treatment, all cases were improved; 2wk, 6 cases were cured; 4wk, 38 cases were cured; 6wk, 41 cases were cured; 8wk, 45 cases were cured, the OCT showed macular retinal neuroepithelial layer ( RNL ) from fully absorbed; 6mo with the same 8wk. Before and after treatment in patients with best corrected
Fourier analysis in several complex variables
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 and convolutions for the experimentalist
Jennison, RC
1961-01-01
Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t
Influences of overlap index on Fourier ptychography imaging
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.
Fourier-based automatic alignment for improved Visual Cryptography schemes.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net [NASA Ames Research Center, Astrobiology and Space Science Division, Moffett Field, CA 94035 (United States)
2017-04-10
We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.
International Nuclear Information System (INIS)
Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.
2017-01-01
We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.
Simple Lie groups without the approximation property
DEFF Research Database (Denmark)
Haagerup, Uffe; de Laat, Tim
2013-01-01
For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...... on the space M0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely, SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center...
The periodogram at the Fourier frequencies
Kokoszka, P; Mikosch, T
In the time series literature one can often find the claim that the periodogram ordinates of an lid sequence at the Fourier frequencies behave like an lid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,
Pi, Fourier Transform and Ludolph van Ceulen
Vajta, Miklos
2000-01-01
The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of p (first by hand and then from the mid-20th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as
Wigner distribution and fractional Fourier transform
Alieva, T.; Bastiaans, M.J.
2001-01-01
The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution
The Fourier transform of tubular densities
Prior, C B; Goriely, A
2012-01-01
molecules. We consider tubes of both finite radii and unrestricted radius. When there is overlap of the tube structure the net density is calculated using the super-position principle. The Fourier transform of this density is composed of two expressions, one
Fourier analysis in combinatorial number theory
International Nuclear Information System (INIS)
Shkredov, Il'ya D
2010-01-01
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
Fourier analysis in combinatorial number theory
Energy Technology Data Exchange (ETDEWEB)
Shkredov, Il' ya D [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2010-09-16
In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory. Bibliography: 162 titles.
A Fourier analysis of extremal events
DEFF Research Database (Denmark)
Zhao, Yuwei
is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...
The Fourier modal method for aperiodic structures
Pisarenco, M.; Maubach, J.M.L.; Setija, I.D.; Mattheij, R.M.M.
2010-01-01
This paper extends the area of application of the Fourier modal method from periodic structures to non-periodic ones illuminated under arbitrary angles. This is achieved by placing perfectly matched layers at the lateral boundaries and reformulating the problem in terms of a contrast field.
Discrete Fourier analysis of multigrid algorithms
van der Vegt, Jacobus J.W.; Rhebergen, Sander
2011-01-01
The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Fourier inversion on a reductive symmetric space
Ban, E.P. van den
1999-01-01
Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we
Fractional-Fourier-domain weighted Wigner distribution
Stankovic, L.; Alieva, T.; Bastiaans, M.J.
2001-01-01
A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the
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.
Clifford Fourier transform on vector fields.
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.
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Schlichtkrull, H.
1994-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
Fourier transforms on a semisimple symmetric space
Ban, E.P. van den; Carmona, J.; Delorme, P.
1997-01-01
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose of this paper is to study an explicit Fourier transform on G=H. In terms of general representation
Simple synthesis of ZnSe nanoparticles by thermal treatment and their characterization
Directory of Open Access Journals (Sweden)
Aeshah Salem
Full Text Available A simple thermal treatment was used to synthesize ZnSe nanoparticles at different calcination temperatures in a nitrogen flowing. The samples of ZnSe nanoparticles were prepared by reacting zinc nitrate (source of zinc and selenium powder with Polyvinylpyrrolidone (capping agent. Analysis of their X-ray diffraction patterns suggested the formation of an amorphous phase of the unheated material before calcination, which then transformed into a cubic crystalline structure of ZnSe nanoparticles after calcination. The phase analyses using energy-dispersive X-ray spectroscopy and Fourier-transform infrared spectroscopy confirmed the presence of Zn and Se as the original compounds of prepared ZnSe nanoparticle samples. The average particle size of the samples increased from 7 ± 5 to 18 ± 3 nm as the calcination temperature was increased from 450 to 700 °C, which is also supported by the transmission electron microscopy results. Diffuse UV–visible reflectance spectra were used to determine the optical band gap through the Kubelka–Munk equation; the energy band gap was found to decrease from 4.24 to 3.95 eV with increasing calcination temperature. Keywords: Metals, Calcination, Differential thermal analysis (DTA, Fourier transform infrared spectroscopy (FTIR
International Nuclear Information System (INIS)
Du, Qiang; Yang, Jiang
2017-01-01
This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2007-01-01
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found
A simple and facile synthesis of MPA capped CdSe and CdSe/CdS core/shell nanoparticles
Sukanya, D.; Sagayaraj, P.
2015-06-01
II-VI semiconductor nanostructures, in particular, CdSe quantum dots have drawn a lot of attention because of their promising potential applications in biological tagging, photovoltaic, display devices etc. due to their excellent optical properties, high emission quantum yield, size dependent emission wavelength and high photostability. In this paper, we describe the synthesis and properties of mercaptopropionic acid capped CdSe and CdSe/CdS nanoparticles through a simple and efficient co-precipitation method followed by hydrothermal treatment. The growth process, characterization and the optical absorption as a function of wavelength for the synthesized MPA capped CdSe and CdSe/CdS nanoparticles have been determined using X-ray diffraction study (XRD), Ultraviolet-Visible spectroscopy (UV-Vis), Fourier transform infrared spectroscopy (FT-IR) and High Resolution Transmission Electron Microscopy (HRTEM).
A simple and facile synthesis of MPA capped CdSe and CdSe/CdS core/shell nanoparticles
International Nuclear Information System (INIS)
Sukanya, D.; Sagayaraj, P.
2015-01-01
II-VI semiconductor nanostructures, in particular, CdSe quantum dots have drawn a lot of attention because of their promising potential applications in biological tagging, photovoltaic, display devices etc. due to their excellent optical properties, high emission quantum yield, size dependent emission wavelength and high photostability. In this paper, we describe the synthesis and properties of mercaptopropionic acid capped CdSe and CdSe/CdS nanoparticles through a simple and efficient co-precipitation method followed by hydrothermal treatment. The growth process, characterization and the optical absorption as a function of wavelength for the synthesized MPA capped CdSe and CdSe/CdS nanoparticles have been determined using X-ray diffraction study (XRD), Ultraviolet-Visible spectroscopy (UV-Vis), Fourier transform infrared spectroscopy (FT-IR) and High Resolution Transmission Electron Microscopy (HRTEM)
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.
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
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.
Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy*
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...
Discrete Fourier transform in nanostructures using scattering
International Nuclear Information System (INIS)
Leuenberger, Michael N.; Flatte, Michael E.; Loss, Daniel; Awschalom, D.D.
2004-01-01
In this article, we show that the discrete Fourier transform (DFT) can be performed by scattering a coherent particle or laser beam off an electrically controllable two-dimensional (2D) potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential by means of electric gates, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant. Since the time to perform the DFT is much smaller than the clock cycle of today's computers, our proposed device performs DFTs at the frequency of the computer clock speed
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
Fourier transform of momentum distribution in vanadium
International Nuclear Information System (INIS)
Singh, A.K.; Manuel, A.A.; Peter, M.; Singru, R.M.
1985-01-01
Experimental Compton profile and 2D-angular correlation of positron annihilation radiation data from vanadium are analyzed by the mean of their Fourier transform. They are compared with the functions calculated with the help of both the linear muffin-tin orbital and the Hubbard-Mijnarends band structure methods. The results show that the functions are influenced by the positron wave function, by the e + -e - many-body correlations and by the differences in the electron wave functions used for the band structure calculations. It is concluded that Fourier analysis is a sensitive approach to investigate the momentum distributions in transition metals and to understnad the effects of the positron. (Auth.)
Correcting sample drift using Fourier harmonics.
Bárcena-González, G; Guerrero-Lebrero, M P; Guerrero, E; Reyes, D F; Braza, V; Yañez, A; Nuñez-Moraleda, B; González, D; Galindo, P L
2018-07-01
During image acquisition of crystalline materials by high-resolution scanning transmission electron microscopy, the sample drift could lead to distortions and shears that hinder their quantitative analysis and characterization. In order to measure and correct this effect, several authors have proposed different methodologies making use of series of images. In this work, we introduce a methodology to determine the drift angle via Fourier analysis by using a single image based on the measurements between the angles of the second Fourier harmonics in different quadrants. Two different approaches, that are independent of the angle of acquisition of the image, are evaluated. In addition, our results demonstrate that the determination of the drift angle is more accurate by using the measurements of non-consecutive quadrants when the angle of acquisition is an odd multiple of 45°. Copyright © 2018 Elsevier Ltd. All rights reserved.
Spectroscopie de Fourier par peignes de fréquences femtosecondes
Mandon , Julien
2009-01-01
This work presents results towards the development of a novel frequency-comb based Fourier transform spectroscopy (FTS). Since 1970, due to its exceptional qualities, FTS has offered a simple way for spectral analysis and has assumed a position of dominance for the measurement of broadband well-resolved accurate spectra. However, FTS doesn't satisfy the new requirements in molecular physics. Acquisition time at the limit, extreme resolution, broad spectral extension, high sensitivity, and acc...
Analytical calculation of the average scattering cross sections using fourier series
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da
2009-01-01
The precise determination of the Doppler broadening functions is very important in different applications of reactors physics, mainly in the processing of nuclear data. Analytical approximations are obtained in this paper for average scattering cross section using expansions in Fourier series, generating an approximation that is simple and precise. The results have shown to be satisfactory from the point-of-view of accuracy and do not depend on the type of resonance considered. (author)
Directory of Open Access Journals (Sweden)
Pavel Zaskalicky
2008-01-01
Full Text Available Reluctance stepper motors are becoming to be very attractive transducer to conversion of electric signal to the mechanical position. Due to its simple construction is reluctance machine considered a very reliable machine which not requiring any maintenance. Present paper proposes a mathematical method of an analytical calculus of a phase current and electromagnetic torque of the motor via Fourier series. Saturation effect and winding reluctance are neglected.
Solution of the Doppler broadening function based on the fourier cosine transform
Energy Technology Data Exchange (ETDEWEB)
Goncalves, Alessandro da C [COPPE/UFRJ - Programa de Engenharia Nuclear, Universidade Federal do Rio de Janeiro, P.O. Box 68509, 21941-914 Rio de Janeiro, RJ (Brazil)], E-mail: agoncalves@con.ufrj.br; Martinez, Aquilino S.; Silva, Fernando C. da [COPPE/UFRJ - Programa de Engenharia Nuclear, Universidade Federal do Rio de Janeiro, P.O. Box 68509, 21941-914 Rio de Janeiro, RJ (Brazil)
2008-10-15
This paper provides a new integral representation for the Doppler broadening function {psi}({xi}, x), which is interpreted as being a Fourier cosine transform. This integral form allows the obtaining of an analytical solution in a simple and accurate functional manner as regards the elementary functions. The solution obtained through the new integral representation can be widely used in several applications such as the calculation of self-shielding factors and measurement corrections for the microscopic cross section through the activation technique.
Solution of the Doppler broadening function based on the fourier cosine transform
International Nuclear Information System (INIS)
Goncalves, Alessandro da C; Martinez, Aquilino S.; Silva, Fernando C. da
2008-01-01
This paper provides a new integral representation for the Doppler broadening function ψ(ξ, x), which is interpreted as being a Fourier cosine transform. This integral form allows the obtaining of an analytical solution in a simple and accurate functional manner as regards the elementary functions. The solution obtained through the new integral representation can be widely used in several applications such as the calculation of self-shielding factors and measurement corrections for the microscopic cross section through the activation technique
Analytical calculation of the average scattering cross sections using fourier series
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P. [Instituto Federal do Rio de Janeiro, Nilopolis, RJ (Brazil)], e-mail: dpalmaster@gmail.com; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da [Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear], e-mail: asilva@con.ufrj.br, e-mail: agoncalves@con.ufrj.br, e-mail: aquilino@lmp.ufrj.br, e-mail: fernando@con.ufrj.br
2009-07-01
The precise determination of the Doppler broadening functions is very important in different applications of reactors physics, mainly in the processing of nuclear data. Analytical approximations are obtained in this paper for average scattering cross section using expansions in Fourier series, generating an approximation that is simple and precise. The results have shown to be satisfactory from the point-of-view of accuracy and do not depend on the type of resonance considered. (author)
International Nuclear Information System (INIS)
Takeshi, Y.; Keisuke, K.
1983-01-01
The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method
International Nuclear Information System (INIS)
Mori, N.; Kobayashi, K.
1996-01-01
A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-01-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples for amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Fourier evaluation of broad Moessbauer spectra
International Nuclear Information System (INIS)
Vincze, I.
1981-09-01
It is shown by the Fourier analysis of broad Moessbauer spectra that the even part of the distribution of the dominant hyperfine interaction (hyperfine field or quadrupole splitting) can be obtained directly without using least-square fitting procedures. Also the odd part of this distribution correlated with other hyperfine parameters (e.g. isomer shift) can be directly determined. Examples covering the case of amorphous magnetic and paramagnetic iron-based alloys are presented. (author)
Quantum Fourier Transform Over Galois Rings
Zhang, Yong
2009-01-01
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorit...
Fourier Transform Spectrometer Controller for Partitioned Architectures
DEFF Research Database (Denmark)
Tamas-Selicean, Domitian; Keymeulen, D.; Berisford, D.
2013-01-01
The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Resear......, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture....
A Fourier analysis of extreme events
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
International Nuclear Information System (INIS)
Collins, T.
1985-08-01
A simple criterion governs the beam distortion and/or loss of protons on a fast resonance crossing. Results from numerical integrations are illustrated for simple sextupole, octupole, and 10-pole resonances
Energy Technology Data Exchange (ETDEWEB)
Collins, T.
1985-08-01
A simple criterion governs the beam distortion and/or loss of protons on a fast resonance crossing. Results from numerical integrations are illustrated for simple sextupole, octupole, and 10-pole resonances.
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)
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)