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.
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.
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...
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.
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...
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.
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
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)
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....
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....
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.
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....
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....
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.
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 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
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
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....
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....
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.
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....
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...
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.
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...
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
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...
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....
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.
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.
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....
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
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
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.
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
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.
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....
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.
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...
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.
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.
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.
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
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.)
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)
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....
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.
Tang, Chen; Wang, Zhifang; Wang, Linlin; Wu, Jian; Gao, Tao; Yan, Si
2010-02-01
Fringe orientation represents an important property of fringes. The estimation of orientation from a poor quality fringe image is still a challenging problem faced in this area. This paper introduces a new approach for estimating optical fringe orientation with a poor quality image. This approach is based on the power spectrum analysis of the Fourier transform. We evaluate the performance of this algorithm via application to a variety of test cases and comparison with the widely used gradient-based method and accumulate-differences method. The experimental results show that our method is capable of calculating fringe orientation robustly even when the quality of fringe images is considerably low because of high or low density, high noise, and low contrast. Under the same conditions, our accuracy is even better than that obtained with the gradient-based and accumulate-differences methods, especially for fringe images with poor quality.
Fourier 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)
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
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)
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...
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...
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.
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.
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
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)
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....
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
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
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).
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...
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.
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.
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
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.
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.
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.
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.
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
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
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
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.
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)
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.
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....
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.
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.
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...
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.
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.
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.
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).
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.
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.
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…
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.
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 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..
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...
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.
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
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....
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.
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.
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
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
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.
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
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.
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.
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.
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
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.
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.
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
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.
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
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...
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
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.
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.
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.
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
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
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.
Complex nonlinear Fourier transform and its inverse
International Nuclear Information System (INIS)
Saksida, Pavle
2015-01-01
We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (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.)
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.
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
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)
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 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
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.
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
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
Generalized Fourier transforms Fk,a
DEFF Research Database (Denmark)
Salem, Ben Said; Kobayashi, Toshiyuki; Ørsted, Bent
2009-01-01
We construct a two-parameter family of actions ωk,a of the Lie algebra by differential-difference operators on . Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation and the minimal unitary representation of the conformal gro...... of our semigroup Ωk,a provides us with (k,a) -generalized Fourier transforms , which includes the Dunkl transform ( a=2 ) and a new unitary operator ( a=1 ) as a Dunkl-type generalization of the classical Hankel transform....
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.
Realization of quantum Fourier transform over ZN
International Nuclear Information System (INIS)
Fu Xiang-Qun; Bao Wan-Su; Li Fa-Da; Zhang Yu-Chao
2014-01-01
Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z N . According to probability amplitude, we prove that the transform can be used to realize QFT over Z N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z N . (general)
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
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....
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)
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.
(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
Limitations on continuous variable quantum algorithms with Fourier transforms
International Nuclear Information System (INIS)
Adcock, Mark R A; Hoeyer, Peter; Sanders, Barry C
2009-01-01
We study quantum algorithms implemented within a single harmonic oscillator, or equivalently within a single mode of the electromagnetic field. Logical states correspond to functions of the canonical position, and the Fourier transform to canonical momentum serves as the analogue of the Hadamard transform for this implementation. This continuous variable version of quantum information processing has widespread appeal because of advanced quantum optics technology that can create, manipulate and read Gaussian states of light. We show that, contrary to a previous claim, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform, analogous to the famous time-bandwidth theorem of signal processing.
Fourier 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.)
The prosaic Laplace and Fourier transform
International Nuclear Information System (INIS)
Smith, G.A.
1995-01-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today's emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. copyright 1995 American Institute of Physics
Alternating multivariate trigonometric functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2008-01-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A n , which is a subgroup of the permutation (symmetric) group S n . These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel
Fourier transforms in the complex domain
Wiener, N
1934-01-01
With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of MÃ¼nz and SzÃ¡sz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,
Analog fourier transform channelizer and OFDM receiver
2007-01-01
An OFDM receiver having an analog multiplier based I-Q channelizing filter, samples and holds consecutive analog I-Q samples of an I-Q baseband, the I-Q basebands having OFDM sub-channels. A lattice of analog I-Q multipliers and analog I-Q summers concurrently receives the held analog I-Q samples, performs analog I-Q multiplications and analog I-Q additions to concurrently generate a plurality of analog I-Q output signals, representing an N-point discrete Fourier transform of the held analog ...
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
Fourier transform spectroscopy of six stars
Energy Technology Data Exchange (ETDEWEB)
Mendoza V, E E [Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Astronomia
1981-01-01
This paper outlines results from a digital analysis of the Fourier transform spectroscopy of six stars: ..sigma.. Aur, rho Ori, ..cap alpha.. Lyr, zeta Aql and ..cap alpha.. Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ..cap alpha.. Lyr and ..cap alpha.. Cyg show spectral line and profile variations easily seen in their spectra.
Fourier-transforming with quantum annealers
Directory of Open Access Journals (Sweden)
Itay eHen
2014-07-01
Full Text Available We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.
Adaption of optical Fresnel transform to optical Wigner transform
International Nuclear Information System (INIS)
Lv Cuihong; Fan Hongyi
2010-01-01
Enlightened by the algorithmic isomorphism between the rotation of the Wigner distribution function (WDF) and the αth fractional Fourier transform, we show that the optical Fresnel transform performed on the input through an ABCD system makes the output naturally adapting to the associated Wigner transform, i.e. there exists algorithmic isomorphism between ABCD transformation of the WDF and the optical Fresnel transform. We prove this adaption in the context of operator language. Both the single-mode and the two-mode Fresnel operators as the image of classical Fresnel transform are introduced in our discussions, while the two-mode Wigner operator in the entangled state representation is introduced for fitting the two-mode Fresnel operator.
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.
The Fourier transform of tubular densities
Prior, C B
2012-05-18
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer 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 for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. © 2012 IOP Publishing Ltd.
Fourier transform ion cyclotron resonance mass spectrometry
Marshall, Alan G.
1998-06-01
As for Fourier transform infrared (FT-IR) interferometry and nuclear magnetic resonance (NMR) spectroscopy, the introduction of pulsed Fourier transform techniques revolutionized ion cyclotron resonance mass spectrometry: increased speed (factor of 10,000), increased sensitivity (factor of 100), increased mass resolution (factor of 10,000-an improvement not shared by the introduction of FT techniques to IR or NMR spectroscopy), increased mass range (factor of 500), and automated operation. FT-ICR mass spectrometry is the most versatile technique for unscrambling and quantifying ion-molecule reaction kinetics and equilibria in the absence of solvent (i.e., the gas phase). In addition, FT-ICR MS has the following analytically important features: speed (~1 second per spectrum); ultrahigh mass resolution and ultrahigh mass accuracy for analysis of mixtures and polymers; attomole sensitivity; MSn with one spectrometer, including two-dimensional FT/FT-ICR/MS; positive and/or negative ions; multiple ion sources (especially MALDI and electrospray); biomolecular molecular weight and sequencing; LC/MS; and single-molecule detection up to 108 Dalton. Here, some basic features and recent developments of FT-ICR mass spectrometry are reviewed, with applications ranging from crude oil to molecular biology.
The Fourier transform of tubular densities
International Nuclear Information System (INIS)
Prior, C B; Goriely, A
2012-01-01
We consider the Fourier transform of tubular volume densities, with arbitrary axial geometry and (possibly) twisted internal structure. This density can be used to represent, among others, magnetic flux or the electron density of biopolymer 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 for which the radius of the tube is less than the curvature of the axis and one for which the radius is greater (which must have density overlap). This expression can accommodate an asymmetric density distribution and a tube structure which has non-uniform twisting. In addition we give several simpler expressions for isotropic densities, densities of finite radius, densities which decay at a rate sufficient to minimize local overlap and finally individual surfaces of the tube manifold. These simplified cases can often be expressed as arclength integrals and can be evaluated using a system of first-order ODEs. (paper)
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
Fourier transform spectra of quantum dots
Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.
2010-05-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…
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.
Fourier transform inequalities for phylogenetic trees.
Matsen, Frederick A
2009-01-01
Phylogenetic invariants are not the only constraints on site-pattern frequency vectors for phylogenetic trees. A mutation matrix, by its definition, is the exponential of a matrix with non-negative off-diagonal entries; this positivity requirement implies non-trivial constraints on the site-pattern frequency vectors. We call these additional constraints "edge-parameter inequalities". In this paper, we first motivate the edge-parameter inequalities by considering a pathological site-pattern frequency vector corresponding to a quartet tree with a negative internal edge. This site-pattern frequency vector nevertheless satisfies all of the constraints described up to now in the literature. We next describe two complete sets of edge-parameter inequalities for the group-based models; these constraints are square-free monomial inequalities in the Fourier transformed coordinates. These inequalities, along with the phylogenetic invariants, form a complete description of the set of site-pattern frequency vectors corresponding to bona fide trees. Said in mathematical language, this paper explicitly presents two finite lists of inequalities in Fourier coordinates of the form "monomial < or = 1", each list characterizing the phylogenetically relevant semialgebraic subsets of the phylogenetic varieties.
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
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
Fourier transform and its application to 1D and 2D NMR
International Nuclear Information System (INIS)
Canet, D.
1988-01-01
In this review article, the following points are developed: Pulsed NMR and Fourier transform; Fourier transform and two-dimensional spectroscopy; Mathematical properties of Fourier transform; Fourier transform of a sine function- one dimensional NMR; Fourier transform of a product of sine functions - two-dimensional NMR; Data manipulations in the time domain; Numerical Fourier transform [fr
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 transformations for difference analogs of the harmonic oscillator
International Nuclear Information System (INIS)
Askey, R.; Atakishiyev, N.M.
1995-01-01
The relation between the Mehler bilinear generating function for the Hermite polynomials and the kernel of the Fourier transformation that connect the spaces of coordinate and momentum is discussed. On the base of the relation the discrete analogs of the Fourier transformation for the Kravchuk and Charlier functions are considered. 6 refs
The Fourier Transform for Certain HyperKähler Fourfolds
Shen, M.; Vial, C.
2016-01-01
Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle
Fourier transform in multimode systems in the Bargmann representation
International Nuclear Information System (INIS)
Lei, C; Vourdas, A
2007-01-01
A Fourier transform in a multimode system is studied, using the Bargmann representation. The growth of a Bargmann function is shown to be related to the second-order correlation of the corresponding state. Both the total growth and the total second-order correlation remain unchanged under the Fourier transform. Examples with coherent states, squeezed states and Mittag-Leffler states are discussed
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.
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)
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)
On the windowed Fourier transform as an interpolation of the Gabor transform
Bastiaans, M.J.; Prochßzka, A.; Uhlør, J.; Sovka, P.
1997-01-01
The windowed Fourier transform and its sampled version - the Gabor transform - are introduced. With the help of Gabor's signal expansion, an interpolation function is derived with which the windowed Fourier transform can be constructed from the Gabor transform. Using the Zak transform, it is shown
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.
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
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses
Lim, Lucy; Yan, Fangzhi; Bach, Stephen; Pihakari, Katianna; Klein, David
2016-01-01
Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS) has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices. PMID:26784175
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses
Directory of Open Access Journals (Sweden)
Lucy Lim
2016-01-01
Full Text Available Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices.
A discrete Fourier transform for virtual memory machines
Galant, David C.
1992-01-01
An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.
From Fourier Transforms to Singular Eigenfunctions for Multigroup Transport
International Nuclear Information System (INIS)
Ganapol, B.D.
2001-01-01
A new Fourier transform approach to the solution of the multigroup transport equation with anisotropic scattering and isotropic source is presented. Through routine analytical continuation, the inversion contour is shifted from the real line to produce contributions from the poles and cuts in the complex plane. The integrand along the branch cut is then recast in terms of matrix continuum singular eigenfunctions, demonstrating equivalence of Fourier transform inversion and the singular eigenfunction expansion. The significance of this paper is that it represents the initial step in revealing the intimate connection between the Fourier transform and singular eigenfunction approaches as well as serves as a basis for a numerical algorithm
The application and improvement of Fourier transform spectrometer experiment
Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning
2017-08-01
According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.
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)
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
Solution of 3-dimensional diffusion equation by finite Fourier transformation
International Nuclear Information System (INIS)
Krishnani, P.D.
1978-01-01
Three dimensional diffusion equation in Cartesian co-ordinates is solved by using the finite Fourier transformation. This method is different from the usual Fourier transformation method in the sense that the solutions are obtained without performing the inverse Fourier transformation. The advantage has been taken of the fact that the flux is finite and integrable in the finite region. By applying this condition, a two-dimensional integral equation, involving flux and its normal derivative at the boundary, is obtained. By solving this equation with given boundary conditions, all of the boundary values are determined. In order to calculate the flux inside the region, flux is expanded into three-dimensional Fourier series. The Fourier coefficients of the flux in the region are calculated from the boundary values. The advantage of this method is that the integrated flux is obtained without knowing the fluxes inside the region as in the case of finite difference method. (author)
The morphing of geographical features by Fourier transformation.
Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang
2018-01-01
This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.
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.
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.
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.
Revisiting the quantum harmonic oscillator via unilateral Fourier transforms
International Nuclear Information System (INIS)
Nogueira, Pedro H F; Castro, Antonio S de
2016-01-01
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)
q-Generalization of the inverse Fourier transform
International Nuclear Information System (INIS)
Jauregui, M.; Tsallis, C.
2011-01-01
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a q-generalized Central Limit Theorem, where a q-generalized Fourier transform plays an important role. We introduce here a method which determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized representation of the Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems. - Highlights: → We present a method to invert the q-Fourier transform of a distribution. → We illustrate when Dirac delta can be represented using q-exponentials. → We describe a family of functions for which this new representation works.
On the physical relevance of the discrete Fourier transform
CSIR Research Space (South Africa)
Greben, JM
1991-11-01
Full Text Available This paper originated from the author's dissatisfaction with the way the discrete Fourier transform is usually presented in the literature. Although mathematically correct, the physical meaning of the common representation is unsatisfactory...
A fourier transform quality measure for iris images
CSIR Research Space (South Africa)
Makinana, S
2014-08-01
Full Text Available to ensure that good quality images are selected for feature extraction, in order to improve iris recognition system. In addition, this research proposes a measure of iris image quality using a Fourier Transform. The experimental results demonstrate...
Surface Fourier-transform lens using a metasurface
International Nuclear Information System (INIS)
Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun
2015-01-01
We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency. (paper)
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.
Roadmap on transformation optics
McCall, Martin; Pendry, John B.; Galdi, Vincenzo; Lai, Yun; Horsley, S. A. R.; Li, Jensen; Zhu, Jian; Mitchell-Thomas, Rhiannon C.; Quevedo-Teruel, Oscar; Tassin, Philippe; Ginis, Vincent; Martini, Enrica; Minatti, Gabriele; Maci, Stefano; Ebrahimpouri, Mahsa; Hao, Yang; Kinsler, Paul; Gratus, Jonathan; Lukens, Joseph M.; Weiner, Andrew M.; Leonhardt, Ulf; Smolyaninov, Igor I.; Smolyaninova, Vera N.; Thompson, Robert T.; Wegener, Martin; Kadic, Muamer; Cummer, Steven A.
2018-06-01
Transformation optics asks, using Maxwell’s equations, what kind of electromagnetic medium recreates some smooth deformation of space? The guiding principle is Einstein’s principle of covariance: that any physical theory must take the same form in any coordinate system. This requirement fixes very precisely the required electromagnetic medium. The impact of this insight cannot be overestimated. Many practitioners were used to thinking that only a few analytic solutions to Maxwell’s equations existed, such as the monochromatic plane wave in a homogeneous, isotropic medium. At a stroke, transformation optics increases that landscape from ‘few’ to ‘infinity’, and to each of the infinitude of analytic solutions dreamt up by the researcher, there corresponds an electromagnetic medium capable of reproducing that solution precisely. The most striking example is the electromagnetic cloak, thought to be an unreachable dream of science fiction writers, but realised in the laboratory a few months after the papers proposing the possibility were published. But the practical challenges are considerable, requiring meta-media that are at once electrically and magnetically inhomogeneous and anisotropic. How far have we come since the first demonstrations over a decade ago? And what does the future hold? If the wizardry of perfect macroscopic optical invisibility still eludes us in practice, then what compromises still enable us to create interesting, useful, devices? While three-dimensional (3D) cloaking remains a significant technical challenge, much progress has been made in two dimensions. Carpet cloaking, wherein an object is hidden under a surface that appears optically flat, relaxes the constraints of extreme electromagnetic parameters. Surface wave cloaking guides sub-wavelength surface waves, making uneven surfaces appear flat. Two dimensions is also the setting in which conformal and complex coordinate transformations are realisable, and the possibilities in
Fourier series models through transformation | Omekara | Global ...
African Journals Online (AJOL)
As a result, the square transformation which outperforms the others is adopted. Consequently, each of the multiplicative and additive FSA models fitted to the transformed data are then subjected to a test for white noise based on spectral analysis. The result of this test shows that only the multiplicative model is adequate.
The Fastest Fourier Transform in the West
National Research Council Canada - National Science Library
Frigo, Matteo; Johnson, Steven G
1997-01-01
.... Three main ideas are the keys to FFTW's performance. First, the computation of the transform is performed by an executor consisting of highly-optimized, composable blocks of C code called codelets...
Properties of the Simpson discrete fourier transform | Singh ...
African Journals Online (AJOL)
The Simpson discrete Fourier transform (SDFT) and its inverse are transformations relating the time and frequency domains. In this paper we state and prove the important properties of shift, circular convolution, conjugation, time reversal and Plancherel's theorem. In addition, we provide an alternative representation of the ...
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...
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
Efficient Computer Implementations of Fast Fourier Transforms.
1980-12-01
fit in computer? Yes, continue (9) Determine fastest algorithm between WFTA and PFA from Table 4.6. For N=420, WFTA PFA Mult 1296 2528 Add 11352 10956...real adds = 24tN/4 + 2(3tN/4) = 15tN/2 (G.8) 260 All odd prime C<ictors ciual to or (,rater than 5 iso the general transform section. Based on the
Energy Technology Data Exchange (ETDEWEB)
Rodriguez G, A.; Bowtell, R.; Mansfield, P. [Area de Procesamiento Digital de Senales e Imagenes Biomedicas. Universidad Autonoma Metropolitana Iztapalapa. Mexico D.F. 09340 Mexico (Mexico)
1998-12-31
Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)
International Nuclear Information System (INIS)
Rodriguez G, A.; Bowtell, R.; Mansfield, P.
1998-01-01
Velocity maps were studied combining Doyle and Mansfield method (1986) with each of the following transforms: Fourier, window Fourier and wavelet (Mexican hat). Continuous wavelet transform was compared against the two Fourier transform to determine which technique is best suited to study blood maps generated by Half Fourier Echo-Planar Imaging. Coefficient images were calculated and plots of the pixel intensity variation are presented. Finally, contour maps are shown to visualize the behavior of the blood flow in the cardiac chambers for the wavelet technique. (Author)
International Nuclear Information System (INIS)
Fan Hongyi; Hao Ren; Lu Hailiang
2008-01-01
Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible
Vaibhav, V.K.
2017-01-01
This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU(2) nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the
The Scope Of Fourier Transform Infrared (FTIR)
Hirschfeld, T.
1981-10-01
Three auarters of a century after its inception, a generation after its advantages were recognized, and a decade after its first commercialization, FT-IR dominates the growth of the IR market, and reigns alone over its high performance end. What lies ahead for FT-IR now? On one hand, the boundary between it and the classical scanning spectrometers is becoming fuzzy, as gratings attempt to use as much of FT-IR's computer technology as they can handle, and smaller FT systems invade the medium cost instrument range. On the other hand, technology advances in IR detectors, non-Fourier interference devices, and the often announced tunable laser are at long last getting set to make serious inroads in the field (although not necessarily in the manner most of us expected). However, the dominance of FT-IR as the leading edge of IR spectroscopy seems assured for a good many years. The evolution of FT-IR will be dominated by demands not yet fully satisfied such as rapid sample turnover, better quantitation, automated interpretation, higher GC-IR sensitivity, improved LC-IR, and, above all else, reliability and ease of use. These developments will be based on multiple small advances in hardware, large advances in the way systems are put together, and the traditional yearly revolutionary advances of the computer industry. The big question in the field will, however, still be whether our ambition and our skill can continue to keep up with the advances of our tools. It will be fun.
Fourier transform infrared spectra applications to chemical systems
Ferraro, John R
1985-01-01
The final and largest volume to complete this four-volume treatise is published in response to the intense commercial and research interest in Fourier Transform Interferometry.Presenting current information from leading experts in the field, Volume 4 introduces new information on, for example, applications of Diffuse Reflectance Spectroscopy in the Far-Infrared Region. The editors place emphasis on surface studies and address advances in Capillary Gas Chromatography - Fourier Transform Interferometry.Volume 4 especially benefits spectroscopists and physicists, as well as researchers
Fourier transform infrared spectra applications to chemical systems
Ferraro, John R
1978-01-01
Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems presents the chemical applications of the Fourier transform interferometry (FT-IR).The book contains discussions on the applications of FT-IR in the fields of chromatography FT-IR, polymers and biological macromolecules, emission spectroscopy, matrix isolation, high-pressure interferometry, and far infrared interferometry. The final chapter is devoted to the presentation of the use of FT-IR in solving national technical problems such as air pollution, space exploration, and energy related subjects.Researc
Decay of the Fourier transform analytic and geometric aspects
Iosevich, Alex
2014-01-01
The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
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.
SPICA/SAFARI Fourier transform spectrometer mechanism evolutionary design
van den Dool, Teun C.; Kruizinga, Bob; Braam, Ben C.; Hamelinck, Roger F. M. M.; Loix, Nicolas; Van Loon, Dennis; Dams, Johan
2012-09-01
TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI1 Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme2 in 2022. JAXA3 leads the development of the SPICA satellite and SRON is the prime investigator of the Safari instrument. The FTS scanning mechanism (FTSM) has to meet a 35 mm stroke requirement with an Optical Path Difference resolution of less then 15 nm and must fit in a small volume. It consists of two back-to-back roof-top mirrors mounted on a small carriage, which is moved using a magnetic bearing linear guiding system in combination with a magnetic linear motor serving as the OPD actuator. The FTSM will be used at cryogenic temperatures of 4 Kelvin inducing challenging requirements on the thermal power dissipation and heat leak. The magnetic bearing enables movements over a scanning stroke of 35.5 mm in a small volume. It supports the optics in a free-floating way with no friction, or other non-linearities, with sub-nanometer accuracy. This solution is based on the design of the breadboard ODL (Optical Delay Line) developed for the ESA Darwin mission4 and the MABE mechanism developed by Micromega Dynamics. During the last couple of years the initial design of the SAFARI instrument, as described in an earlier SPIE 2010 paper5, was adapted by the SAFARI team in an evolutionary way to meet the changing requirements of the SPICA payload module. This presentation will focus on the evolution of the FTSM to meet these changing requirements. This work is supported by the Netherlands Space Office (NSO).
Discrete Fourier Transform in a Complex Vector Space
Dean, Bruce H. (Inventor)
2015-01-01
An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.
Discrete Fourier Transform Analysis in a Complex Vector Space
Dean, Bruce H.
2009-01-01
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
X-ray Fourier-transform holographic microscope
International Nuclear Information System (INIS)
Haddad, W.S.; Cullen, D.; Solem, J.C.; Boyer, K.; Rhodes, C.K.
1988-01-01
The properties of an x-ray Fourier-transform holographic instrument suitable for imaging hydrated biological samples are described. Recent advances in coherent x-ray source technology are making diffraction-limited holograms of microscopic structures, with corresponding high spatial resolution, a reality. A high priority application of snapshot x-ray holography is the study of microscopic biological structures in the hydrated living state. X-rays offer both high resolution and high contrast for important structures within living organisms, thereby rendering unnecessary the staining of specimens, essential for optical and electron microscopy. If the wavelength is properly chosen. Furthermore, the snapshot feature, arising from picosecond or subpicosecond exposure times, eliminates blurring occurring from either thermal heating or normal biological activity of the sample. Finally, with sufficiently high photon fluxes, such as those available from x-ray lasers, the x-ray snapshot can be accomplished with a single pulse, thereby yielding complete three-dimensional information on a sample having normal biological integrity at the moment of exposure. 10 refs., 6 figs
Fourier transform nuclear magnetic resonance studies of 199Hg
International Nuclear Information System (INIS)
Krueger, H.; Lutz, O.; Nolle, A.; Schwenk, A.
1975-01-01
199 Hg Fourier Transform NMR studies of various solutions of diverse mercury salts in H 2 O and D 2 O or in the appropriate protonated and deuterated acids are reported for both Hg 2 ++ and Hg ++ . In the different solutions investigated the 199 Hg line positions depend on the concentration of the solution, on the solvents and their isotopic composition and on the temperature of the sample. A ratio of the Larmor frequency of 199 Hg and of 2 H in a Hg(NO 3 ) 2 solution in dilute DNO 3 is given. Using this ratio and the measured chemical shifts, a ratio of the Larmor frequencies of 199 Hg for infinite dilution relative to 2 H in pure D 2 O is given. From this a g 1 -factor for 199 Hg is derived and compared with the g 1 -factor of an optical pumping experiment. The resulting shielding constant is sigma (hydrated 199 Hg ++ versus 199 Hg atom) = -24.32(5) x 10 -4 . This yields an atomic reference scale for all measured NMR line shifts of mercury. (orig.) [de
Symmetrized neutron transport equation and the fast Fourier transform method
International Nuclear Information System (INIS)
Sinh, N.Q.; Kisynski, J.; Mika, J.
1978-01-01
The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations
Transformation of a Free-Wilson matrix into Fourier coefficients
Czech Academy of Sciences Publication Activity Database
Holík, M.; Halámek, Josef
2002-01-01
Roč. 20, - (2002), s. 422 - 428 ISSN 0931-8771 Institutional research plan: CEZ:AV0Z2065902 Keywords : Free-Wilson matrix * Fourier transform * multivariate regression Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.558, year: 2002
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 ...
Application of Migration Velocity Using Fourier Transform Approach ...
African Journals Online (AJOL)
Application of velocity by Fourier transform to process 3-D unmigrated seismic sections has been carried out in Fabi Field, Niger Delta – Nigeria. Usually, all seismic events (sections) are characterized by spikes or noise (random or coherent), multiples and shear waves so that when a seismic bed is dipping, the apparent ...
Fourier transformation methods in the field of gamma spectrometry
Indian Academy of Sciences (India)
The basic principles of a new version of Fourier transformation is presented. This new version was applied to solve some main problems such as smoothing, and denoising in gamma spectroscopy. The mathematical procedures were first tested by simulated data and then by actual experimental data.
Fourier transform infrared spectrophotometry and X-ray powder ...
African Journals Online (AJOL)
This study aimed at demonstrating complementary roles offered by both Fourier transform infrared (FTIR) spectrophotometry and x-ray powder diffraction (XRPD) techniques in characterizing clay size fraction of kaolins. The clay size fraction of kaolin samples obtained from Kgwakgwe, Makoro, Lobatse and Serule kaolin ...
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
SPICA/SAFARI fourier transform spectrometer mechanism evolutionary design
Dool, T.C. van den; Kruizinga, B.; Braam, B.C.; Hamelinck, R.F.M.M.; Loix, N.; Loon, D. van; Dams, J.
2012-01-01
TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme in 2022. JAXA leads the development
Quaternion Fourier transforms for signal and image processing
Ell, Todd A; Sangwine, Stephen J
2014-01-01
Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book's attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.
The RC Circuit: An Approach with Fourier Transforms
Indian Academy of Sciences (India)
The RC Circuit: An Approach with Fourier Transforms. Classroom Volume 21 Issue 11 November 2016 pp 1029-1042 ... But a lot of things, (including the complex impedanceitself, and some insight into complex analysis) can be understoodbetter if we use the FT approach to solve the differentialequations that come up in ...
Fourier transform infrared (FTIR) spectroscopy for identification of ...
African Journals Online (AJOL)
Fourier transform infrared (FTIR) spectroscopy was used in this study to identify and determine spectral features of Chlorella vulgaris Beijerinck 1890 and Scenedesmus obliquus (Turpin) Kützing 1833. Two cultures were grown in a chemically-defined media under photoautotrophic culture conditions isolated from eutrophic ...
HEART ABNORMALITY CLASSIFICATIONS USING FOURIER TRANSFORMS METHOD AND NEURAL NETWORKS
Directory of Open Access Journals (Sweden)
Endah Purwanti
2014-05-01
Full Text Available Health problems with cardiovascular system disorder are still ranked high globally. One way to detect abnormalities in the cardiovascular system especially in the heart is through the electrocardiogram (ECG reading. However, reading ECG recording needs experience and expertise, software-based neural networks has designed to help identify any abnormalities ofthe heart through electrocardiogram digital image. This image is processed using image processing methods to obtain ordinate chart which representing the heart’s electrical potential. Feature extraction using Fourier transforms which are divided into several numbers of coefficients. As the software input, Fourier transforms coefficient have been normalized. Output of this software is divided into three classes, namely heart with atrial fibrillation, coronary heart disease and normal. Maximum accuracy rate ofthis software is 95.45%, with the distribution of the Fourier transform coefficients 1/8 and number of nodes 5, while minimum accuracy rate of this software at least 68.18% by distribution of the Fourier transform coefficients 1/32 and the number of nodes 32. Overall result accuracy rate of this software has an average of86.05% and standard deviation of7.82.
Spectrums Transform Operators in Bases of Fourier and Walsh Functions
Directory of Open Access Journals (Sweden)
V. V. Syuzev
2017-01-01
Full Text Available The problems of synthesis of the efficient algorithms for digital processing of discrete signals require transforming the signal spectra from one basis system into other. The rational solution to this problem is to construct the Fourier kernel, which is a spectrum of some basis functions, according to the system of functions of the other basis. However, Fourier kernel properties are not equally studied and described for all basis systems of practical importance. The article sets a task and presents an original way to solve the problem of mutual transformation of trigonometric Fourier spectrum into Walsh spectrum of different basis systems.The relevance of this theoretical and applied problem is stipulated, on the one hand, by the prevalence of trigonometric Fourier basis for harmonic representation of digital signals, and, on the other hand, by the fact that Walsh basis systems allow us to have efficient algorithms to simulate signals. The problem solution is achieved through building the Fourier kernel of a special structure that allows us to establish independent groups of Fourier and Walsh spectrum coefficients for further reducing the computational complexity of the transform algorithms.The article analyzes the properties of the system of trigonometric Fourier functions and shows its completeness. Considers the Walsh function basis systems in three versions, namely those of Hadamard, Paley, and Hartmut giving different ordering and analytical descriptions of the functions that make up the basis. Proves a completeness of these systems.Sequentially, for each of the three Walsh systems the analytical curves for the Fourier kernel components are obtained, and Fourier kernel themselves are built with binary rational number of samples of basis functions. The kernels are presented in matrix form and, as an example, recorded for a particular value of the discrete interval of N, equal to 8. The analysis spectral coefficients of the Fourier kernel
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
Nonlocal transformation optics.
Castaldi, Giuseppe; Galdi, Vincenzo; Alù, Andrea; Engheta, Nader
2012-02-10
We show that the powerful framework of transformation optics may be exploited for engineering the nonlocal response of artificial electromagnetic materials. Relying on the form-invariant properties of coordinate-transformed Maxwell's equations in the spectral domain, we derive the general constitutive "blueprints" of transformation media yielding prescribed nonlocal field-manipulation effects and provide a physically incisive and powerful geometrical interpretation in terms of deformation of the equifrequency contours. In order to illustrate the potentials of our approach, we present an example of application to a wave-splitting refraction scenario, which may be implemented via a simple class of artificial materials. Our results provide a systematic and versatile framework which may open intriguing venues in dispersion engineering of artificial materials.
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.
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
On the finite Fourier transforms of functions with infinite discontinuities
Directory of Open Access Journals (Sweden)
Branko Saric
2002-01-01
Full Text Available The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.
An introduction to Laplace transforms and Fourier series
Dyke, Phil
2014-01-01
Laplace transforms continue to be a very important tool for the engineer, physicist and applied mathematician. They are also now useful to financial, economic and biological modellers as these disciplines become more quantitative. Any problem that has underlying linearity and with solution based on initial values can be expressed as an appropriate differential equation and hence be solved using Laplace transforms. In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and ...
The short time Fourier transform and local signals
Okumura, Shuhei
In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.
Radon-Wigner transform for optical field analysis
Alieva, T.; Bastiaans, M.J.; Nijhawan, O.P.; Gupta, A.K.; Musla, A.K.; Singh, Kehar
1998-01-01
The Radon-Wigner transform, associated with the intensity distribution in the fractional Fourier transform system, is used for the analysis of complex structures of coherent as well as partially coherent optical fields. The application of the Radon-Wigner transform to the analysis of fractal fields
Optimal Padding for the Two-Dimensional Fast Fourier Transform
Dean, Bruce H.; Aronstein, David L.; Smith, Jeffrey S.
2011-01-01
One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that
Metasurface transformation optics
International Nuclear Information System (INIS)
Mencagli, M jr; Martini, E; González-Ovejero, D; Maci, S
2014-01-01
Transformation optics has been recently proposed as a powerful method to manipulate electromagnetic fields by using anisotropic inhomogeneous volumetric media. This method can be extended to design anisotropic modulated metasurfaces (MTSs) able to control the propagation path of surface waves. In this paper, this extension is formalized by defining a systematic procedure that can be applied to design a large number of planar devices, with a significant technological simplification with respect to the realization based on volumetric media. Practical MTS designs are also presented. (paper)
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.
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...
Application of Fourier transforms for microwave radiometric inversions
Holmes, J. J.; Balanis, C. A.; Truman, W. M.
1975-01-01
Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.
Matrix-Vector Based Fast Fourier Transformations on SDR Architectures
Directory of Open Access Journals (Sweden)
Y. He
2008-05-01
Full Text Available Today Discrete Fourier Transforms (DFTs are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex. It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT engines. However, in face of the Software Defined Radio (SDR development, more general (parallel processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.
The Fourier transform for certain hyperkähler fourfolds
Shen, Mingmin
2016-01-01
Using a codimension-1 algebraic cycle obtained from the PoincarÃ© line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring \\mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe"Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of HyperkÃ¤hler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.
10th International Conference on Progress in Fourier Transform Spectroscopy
Keresztury, Gábor; Kellner, Robert
1997-01-01
19 plenary lectures and 203 poster papers presented at the 10th International Conference of Fourier Transform Spectroscopy in Budapest 1995 give an overview on the state-of-the art of this technology and its wide range of applications. The reader will get information on any aspects of FTS including the latest instrumental developments, e.g. in diode array detection, time resolution FTS, microscopy and spectral mapping, double modulation and two-dimensional FTS.
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.
Fast Fourier transformation results from gamma-ray burst profiles
Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.
1992-01-01
Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.
Calibration of the Herschel SPIRE Fourier Transform Spectrometer
Swinyard, Bruce; Polehampton, E. T.; Hopwood, R.; Valtchanov, I.; Lu, N.; Fulton, T.; Benielli, D.; Imhof, P.; Marchili, N.; Baluteau, J.- P.; Bendo, G. J.; Ferlet, M.; Griffin, Matthew Jason; Lim, T. L.; Makiwa, G.
2014-01-01
The Herschel Spectral and Photometric REceiver (SPIRE) instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of ∼450–1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a sp...
Solving singular convolution equations using the inverse fast Fourier transform
Czech Academy of Sciences Publication Activity Database
Krajník, E.; Montesinos, V.; Zizler, P.; Zizler, Václav
2012-01-01
Roč. 57, č. 5 (2012), s. 543-550 ISSN 0862-7940 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular convolution equations * fast Fourier transform * tempered distribution Subject RIV: BA - General Mathematics Impact factor: 0.222, year: 2012 http://www.springerlink.com/content/m8437t3563214048/
Random sampling of evolution time space and Fourier transform processing
International Nuclear Information System (INIS)
Kazimierczuk, Krzysztof; Zawadzka, Anna; Kozminski, Wiktor; Zhukov, Igor
2006-01-01
Application of Fourier Transform for processing 3D NMR spectra with random sampling of evolution time space is presented. The 2D FT is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Signal to noise ratios and linewidths for different random distributions were investigated by simulations and experiments. The experimental examples include 3D HNCA, HNCACB and 15 N-edited NOESY-HSQC spectra of 13 C 15 N labeled ubiquitin sample. Obtained results revealed general applicability of proposed method and the significant improvement of resolution in comparison with conventional spectra recorded in the same time
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.
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.
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.
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...
International Nuclear Information System (INIS)
Tam, K.C.; Perez-Mendez, V.
1981-01-01
The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero has been calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms has been analyzed in detail. it was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect which tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time
Limited-angle 3-D reconstructions using Fourier transform iterations and Radon transform iterations
International Nuclear Information System (INIS)
Tam, K.C.; Perez-Mendez, V.
1979-12-01
The principles of limited-angle reconstruction of space-limited objects using the concepts of allowed cone and missing cone in Fourier space are discussed. The distortion of a point source resulting from setting the Fourier components in the missing cone to zero was calculated mathematically, and its bearing on the convergence of an iteration scheme involving Fourier transforms was analyzed in detail. It was found that the convergence rate is fairly insensitive to the position of the point source within the boundary of the object, apart from an edge effect that tends to enhance some parts of the boundary in reconstructing the object. Another iteration scheme involving Radon transforms was introduced and compared to the Fourier transform method in such areas as root mean square error, stability with respect to noise, and computer reconstruction time. 8 figures, 2 tables
Analysis of the physical simulation on Fourier transform infrared spectrometer
Yue, Peng-yuan; Wan, Yu-xi; Zhao, Zhen
2017-10-01
A kind of oscillating arm type Fourier Transform Infrared Spectrometer (FTS) which based on the corner cube retroreflector is presented, and its principle and properties are studied. It consists of a pair of corner cube retroreflector, beam splitter and compensator. The optical path difference(OPD) is created by oscillating reciprocating motion of the moving corner cube pair, and the OPD value is four times the physical shift value of the moving corner cube pair. Due to the basic property of corner cube retroreflector, the oscillating arm type FTS has no tilt problems. It is almost ideal for very high resolution infrared spectrometer. However, there are some factors to reduce the FTS capability. First, wavefront aberration due to the figures of these surfaces will reduce modulation of FTS system; second, corner cube retroreflector consist of three plane mirror, and orthogonal to each other. When there is a deviation from right angle, it will reduced the modulation of system; third, the apexes of corner cube retroreflector are symmetric about the surface of beam splitter, if one or both of the corner cube retroreflector is displaced laterally from its nominal position, phase of off-axis rays returning from the two arms were difference, this also contributes to loss of modulation of system. In order to solve these problems, this paper sets up a non-sequential interference model, and a small amount of oscillating arm rotation is set to realize the dynamic simulation process, the dynamic interference energy data were acquired at different times, and calculated the modulation of the FTS system. In the simulation, the influence of wedge error of beam splitter, compensator or between them were discussed; effects of oscillating arm shaft deviation from the coplanar of beam splitter was analyzed; and compensation effect of corner cube retroreflector alignment on beam splitter, oscillating arm rotary shaft alignment error is analyzed. In addition, the adjustment procedure
[Continuum based fast Fourier transform processing of infrared spectrum].
Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai
2009-12-01
To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.
Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects
International Nuclear Information System (INIS)
Miao, J.; Sayre, D.; Chapman, H.N.
1998-01-01
It is suggested that, given the magnitude of Fourier transforms sampled at the Bragg density, the phase problem is underdetermined by a factor of 2 for 1D, 2D, and 3D objects. It is therefore unnecessary to oversample the magnitude of Fourier transforms by 2x in each dimension (i.e., oversampling by 4x for 2D and 8x for 3D) in retrieving the phase of 2D and 3D objects. Our computer phasing experiments accurately retrieved the phase from the magnitude of the Fourier transforms of 2D and 3D complex-valued objects by using positivity constraints on the imaginary part of the objects and loose supports, with the oversampling factor much less than 4 for 2D and 8 for 3D objects. Under the same conditions we also obtained reasonably good reconstructions of 2D and 3D complex-valued objects from the magnitude of their Fourier transforms with added noise and a central stop. copyright 1998 Optical Society of America
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.
A transformada de Fourier em basic The Fourier transform (FFT in basic
Directory of Open Access Journals (Sweden)
Mauricio Gomes Constantino
2000-06-01
Full Text Available In this paper we describe three computer programs in Basic language about the Fourier transform (FFT which are available in the Internet site http://artemis.ffclrp.usp.br/SoftwareE.htm (in English or http://artemis.ffclrp.usp.br/softwareP.htm (in Portuguese since October 1998. Those are addresses to the Web Page of our Laboratory of Organic Synthesis. The programs can be downloaded and used by anyone who is interested on the subject. The texts, menus and captions in the programs are written in English.
The gridding method for image reconstruction by Fourier transformation
International Nuclear Information System (INIS)
Schomberg, H.; Timmer, J.
1995-01-01
This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform f. The method involves a window function w and proceeds in three steps. First, the convolution g = w * f is computed numerically on a Cartesian grid, using the available samples of f. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating w * f is much less error prone than merely interpolating f. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform
Liu, Zhengjun; Chen, Hang; Blondel, Walter; Shen, Zhenmin; Liu, Shutian
2018-06-01
A novel image encryption method is proposed by using the expanded fractional Fourier transform, which is implemented with a pair of lenses. Here the centers of two lenses are separated at the cross section of axis in optical system. The encryption system is addressed with Fresnel diffraction and phase modulation for the calculation of information transmission. The iterative process with the transform unit is utilized for hiding secret image. The structure parameters of a battery of lenses can be used for additional keys. The performance of encryption method is analyzed theoretically and digitally. The results show that the security of this algorithm is enhanced markedly by the added keys.
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.
Comparative study on γ energy spectrum denoise by fourier and wavelet transforms
International Nuclear Information System (INIS)
Shi Dongsheng; Di Yuming; Zhou Chunlin
2007-01-01
This paper introduces the basic principle of wavelet and Fourier transforms, applies wavelet transform method to denoise γ energy spectrum of 60 Co and compares it with Fourier transform method. The result of simulation with MATLAB software tool showed that as compared with traditional Fourier transform, wavelet transform has comparatively higher accuracy for γ energy spectrum denoising and is more feasible to γ energy spectrum denoising. (authors)
Hochauflösende Fourier-Transform-Emissionsspektroskopie
Uibel, Christian
2000-01-01
Mittels hochauflösender Fourier-Transform-Infrarot-Emissionsspektroskopie wurden tiefliegende elektronische Anregungszustände der mittelschweren zweiatomigen Radikale As2, Sb2 und TeF untersucht. Dabei lag das Interesse vor allem bei den Emissionen nicht voll erlaubter Übergänge wie beispielsweise der 3Σ +u → 1Σ +g- bzw. (1u) → (0+g)-Übergänge bei den Stickstoff-Homologen. Dieses besondere Interesse an der genauen Analyse der 3Σ +u-Zustände liegt in ihrem metastab...
Multi-band Image Registration Method Based on Fourier Transform
Institute of Scientific and Technical Information of China (English)
庹红娅; 刘允才
2004-01-01
This paper presented a registration method based on Fourier transform for multi-band images which is involved in translation and small rotation. Although different band images differ a lot in the intensity and features,they contain certain common information which we can exploit. A model was given that the multi-band images have linear correlations under the least-square sense. It is proved that the coefficients have no effect on the registration progress if two images have linear correlations. Finally, the steps of the registration method were proposed. The experiments show that the model is reasonable and the results are satisfying.
Directional short-time Fourier transform of distributions
Directory of Open Access Journals (Sweden)
Katerina Hadzi-Velkova Saneva
2016-04-01
Full Text Available Abstract In this paper we consider the directional short-time Fourier transform (DSTFT that was introduced and investigated in (Giv in J. Math. Anal. Appl. 399:100-107, 2013. We analyze the DSTFT and its transpose on test function spaces S ( R n $\\mathcal {S}(\\mathbb {R}^{n}$ and S ( Y 2 n $\\mathcal {S}(\\mathbb {Y}^{2n}$ , respectively, and prove the continuity theorems on these spaces. Then the obtained results are used to extend the DSTFT to spaces of distributions.
Hyperspectral imaging using the single-pixel Fourier transform technique
Jin, Senlin; Hui, Wangwei; Wang, Yunlong; Huang, Kaicheng; Shi, Qiushuai; Ying, Cuifeng; Liu, Dongqi; Ye, Qing; Zhou, Wenyuan; Tian, Jianguo
2017-03-01
Hyperspectral imaging technology is playing an increasingly important role in the fields of food analysis, medicine and biotechnology. To improve the speed of operation and increase the light throughput in a compact equipment structure, a Fourier transform hyperspectral imaging system based on a single-pixel technique is proposed in this study. Compared with current imaging spectrometry approaches, the proposed system has a wider spectral range (400-1100 nm), a better spectral resolution (1 nm) and requires fewer measurement data (a sample rate of 6.25%). The performance of this system was verified by its application to the non-destructive testing of potatoes.
Fourier transform infrared studies in solid egg white lysozyme
International Nuclear Information System (INIS)
Rivzi, T.Z.
1994-12-01
Fourier Transform Infrared (FTIR) Spectroscopy is the most recent addition to the arsenal of bioanalytical techniques capable of providing information about the secondary structure of proteins in a variety of environments. FTIR spectra have been obtained in solid egg white lysozyme. The spectra display the usual amide I, II and III bands. Secondary structural information obtained from the spectra after applying resolution enhancement techniques to the amide I band has been found consistent with the x-ray crystallographic data of the protein and also to the spectroscopic data of the protein in aqueous solution. (author). 17 refs, 6 figs, 2 tabs
Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions
Morelli, Eugene A.
2013-01-01
A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.
The discrete Fourier transform theory, algorithms and applications
Sundaraajan, D
2001-01-01
This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and
Capillary supercritical fluid chromatography - Fourier transform infrared spectrometry
International Nuclear Information System (INIS)
Olesik, S.V.; French, S.B.; Movotny, M.
1984-01-01
One of the most demanding tasks asked of an analytical chemist today is to separate and identify the components of a nonvolatile complex mixture. An efficient separation technique combined with a universal detector that provides structural information, therefore, would be a great asset to analytical chemists. Capillary supercritical fluid chromatography (SFC) - Fourier transform infrared spectrometry (FTIR) shows great potential for being such a technique. SFC-FTIR shows great potential as a very powerful technique for separation and identification of thermally labile and nonvolatile compounds. Research is continuing in these labs to further optimize the technique. 2 refs
Principle and analysis of a rotational motion Fourier transform infrared spectrometer
Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning
2017-09-01
Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.
Diffractive optical elements for transformation of modes in lasers
Sridharan, Arun K.; Pax, Paul H.; Heebner, John E.; Drachenberg, Derrek R.; Armstrong, James P.; Dawson, Jay W.
2015-09-01
Spatial mode conversion modules are described, with the capability of efficiently transforming a given optical beam profile, at one plane in space into another well-defined optical beam profile at a different plane in space, whose detailed spatial features and symmetry properties can, in general, differ significantly. The modules are comprised of passive, high-efficiency, low-loss diffractive optical elements, combined with Fourier transform optics. Design rules are described that employ phase retrieval techniques and associated algorithms to determine the necessary profiles of the diffractive optical components. System augmentations are described that utilize real-time adaptive optical techniques for enhanced performance as well as power scaling.
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
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.
Advances in hyperspectral remote sensing I: The visible Fourier transform hyperspectral imager
Directory of Open Access Journals (Sweden)
J. Bruce Rafert
2015-05-01
Full Text Available We discuss early hyperspectral research and development activities during the 1990s that led to the deployment of aircraft and satellite payloads whose heritage was based on the use of visible, spatially modulated, imaging Fourier transform spectrometers, beginning with early experiments at the Florida Institute of Technology, through successful launch and deployment of the Visible Fourier Transform Hyperspectral Imager on MightySat II.1 on 19 July 2000. In addition to a brief chronological overview, we also discuss several of the most interesting optical engineering challenges that were addressed over this timeframe, present some as-yet un-exploited features of field-widened (slit-less SMIFTS instruments, and present some images from ground-based, aircraft-based and satellite-based instruments that helped provide the impetus for the proliferation and development of entire new families of instruments and countless new applications for hyperspectral imaging.
Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer
Energy Technology Data Exchange (ETDEWEB)
Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.
1993-10-01
We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.
A high-resolution Fourier Transform Spectrometer for planetary spectroscopy
Cruikshank, D. P.; Sinton, W. M.
1973-01-01
The employment of a high-resolution Fourier Transform Spectrometer (FTS) is described for planetary and other astronomical spectroscopy in conjunction with the 88-inch telescope at Mauna Kea Observatory. The FTS system is designed for a broad range of uses, including double-beam laboratory spectroscopy, infrared gas chromatography, and nuclear magnetic resonance spectroscopy. The data system is well-suited to astronomical applications because of its great speed in acquiring and transforming data, and because of the enormous storage capability of the magnetic tape unit supplied with the system. The basic instrument is outlined 2nd some of the initial results from the first attempted use on the Mauna Kea 88-inch telescope are reported.
Quantum Fourier transform, Heisenberg groups and quasi-probability distributions
International Nuclear Information System (INIS)
Patra, Manas K; Braunstein, Samuel L
2011-01-01
This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl-Gabor-Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.
Inverse problem in transformation optics
DEFF Research Database (Denmark)
Novitsky, Andrey
2011-01-01
The straightforward method of transformation optics implies that one starts from the coordinate transformation and determines the Jacobian matrix, the fields and material parameters of the cloak. However, the coordinate transformation appears as an optional function: it is not necessary to know it...
Valuation of European Call Option via Inverse Fourier Transform
Directory of Open Access Journals (Sweden)
Rubenis Oskars
2017-12-01
Full Text Available Very few models allow expressing European call option price in closed form. Out of them, the famous Black- Scholes approach sets strong constraints - innovations should be normally distributed and independent. Availability of a corresponding characteristic function of log returns of underlying asset in analytical form allows pricing European call option by application of inverse Fourier transform. Characteristic function corresponds to Normal Inverse Gaussian (NIG probability density function. NIG distribution is obtained based on assumption that time series of log returns follows APARCH process. Thus, volatility clustering and leptokurtic nature of log returns are taken into account. The Fast Fourier transform based on trapezoidal quadrature is numerically unstable if a standard cumulative probability function is used. To solve the problem, a dampened cumulative probability is introduced. As a computation tool Matlab framework is chosen because it contains many effective vectorization tools that greatly enhance code readability and maintenance. The characteristic function of Normal Inverse Gaussian distribution is taken and exercised with the chosen set of parameters. Finally, the call price dependence on strike price is obtained and rendered in XY plot. Valuation of European call option with analytical form of characteristic function allows further developing models with higher accuracy, as well as developing models for some exotic options.
Vector Radix 2 × 2 Sliding Fast Fourier Transform
Directory of Open Access Journals (Sweden)
Keun-Yung Byun
2016-01-01
Full Text Available The two-dimensional (2D discrete Fourier transform (DFT in the sliding window scenario has been successfully used for numerous applications requiring consecutive spectrum analysis of input signals. However, the results of conventional sliding DFT algorithms are potentially unstable because of the accumulated numerical errors caused by recursive strategy. In this letter, a stable 2D sliding fast Fourier transform (FFT algorithm based on the vector radix (VR 2 × 2 FFT is presented. In the VR-2 × 2 FFT algorithm, each 2D DFT bin is hierarchically decomposed into four sub-DFT bins until the size of the sub-DFT bins is reduced to 2 × 2; the output DFT bins are calculated using the linear combination of the sub-DFT bins. Because the sub-DFT bins for the overlapped input signals between the previous and current window are the same, the proposed algorithm reduces the computational complexity of the VR-2 × 2 FFT algorithm by reusing previously calculated sub-DFT bins in the sliding window scenario. Moreover, because the resultant DFT bins are identical to those of the VR-2 × 2 FFT algorithm, numerical errors do not arise; therefore, unconditional stability is guaranteed. Theoretical analysis shows that the proposed algorithm has the lowest computational requirements among the existing stable sliding DFT algorithms.
Ultrafast and versatile spectroscopy by temporal Fourier transform
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.
2014-06-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.
Soft x-ray microscope using Fourier transform holography
International Nuclear Information System (INIS)
McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H.
1989-01-01
A Fourier transform holographic microscope with an anticipated resolution of better than 100 nm has been built. Extensive testing of the apparatus has begun. Preliminary results include the recording of interference fringes using 3.6 nm x-rays. The microscope employs a charge-coupled device (CCD) detector array of 576 x 384 elements. The system is illuminated by soft x-rays from a high brightness undulator. The reference point source is formed by a Fresnel zone plate with a finest outer zone width of 50 nm. Sufficient temporal coherence for hologram formation is obtained by a spherical grating monochromator. The x-ray hologram intensities at the recording plane are to be collected, digitized and reconstructed by computer. Data acquisition is under CAMAC control, while image display and off-line processing takes place on a VAX graphics workstation. Computational models of Fourier transform hologram synthesis, and reconstruction in the presence of noise, have demonstrated the feasibility of numerical methods in two dimensions, and that three-dimensional information is potentially recoverable. 13 refs., 3 figs
The Fourier transform method for infinite medium resonance absorption problems
International Nuclear Information System (INIS)
Menon, S.V.G.; Sahni, D.C.
1978-01-01
A new method, using Fourier transforms, is developed for solving the integral equation of slowing down of neutrons in the resonance region. The transformations replace the slowing down equation with a discontinuous kernel by an integral equation with a continuous kernel over the interval (-infinity, infinity). Further the Doppler broadened line shape functions have simple analytical representations in the transform variable. In the limit of zero temperature, the integral equation reduces to a second order differential equation. Accurate expressions for the zero temperature resonance integrals are derived, using the WKB method. In general, the integral equation is seen to be amenable to solution by Ganss-Hermite quadrature formule. Doppler coefficients of 238 U resonances are given and compared with Monte Carlo calculations. The method is extended to include the effect of interference between neighbouring resonances of an absorber. For the case of two interfering resonances the slowing down equation is transformed to the coupled integral equations that are amenable to solution by methods indicated earlier. Numerical results presented for the low lying thorium-232 doublet show that the Doppler coefficients of the resonances are reduced considerably because of the overlap between them. (author)
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)....
Kumar, Sanjay
2018-01-01
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also derived and it is shown mathematically that when the rotation angle of Reduced Order Fractional Fourier Transform approaches 90 degrees, the propos...
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.
Energy Technology Data Exchange (ETDEWEB)
Bartosch, T. [Erlanger-Nuernberg Univ., Erlanger (Germany). Lehrstul fuer Nachrichtentechnik I; Seidl, D. [Seismologisches Zentralobservatorium Graefenberg, Erlanegen (Greece). Bundesanstalt fuer Geiwissenschaften und Rohstoffe
1999-06-01
Among a variety of spectrogram methods short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were selected to analyse transients in non-stationary signals. Depending on the properties of the tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli (Italy).
A Fourier transform with speed improvements for microprocessor applications
Lokerson, D. C.; Rochelle, R.
1980-01-01
A fast Fourier transform algorithm for the RCA 1802microprocessor was developed for spacecraft instrument applications. The computations were tailored for the restrictions an eight bit machine imposes. The algorithm incorporates some aspects of Walsh function sequency to improve operational speed. This method uses a register to add a value proportional to the period of the band being processed before each computation is to be considered. If the result overflows into the DF register, the data sample is used in computation; otherwise computation is skipped. This operation is repeated for each of the 64 data samples. This technique is used for both sine and cosine portions of the computation. The processing uses eight bit data, but because of the many computations that can increase the size of the coefficient, floating point form is used. A method to reduce the alias problem in the lower bands is also described.
Using the fast fourier transform in binding free energy calculations.
Nguyen, Trung Hai; Zhou, Huan-Xiang; Minh, David D L
2018-04-30
According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Collision-induced dissociation with Fourier transform mass spectrometry
International Nuclear Information System (INIS)
Cody, R.B.; Burnier, R.C.; Freiser, B.S.
1982-01-01
Collision-induced dissociations (CID) is demonstrated on a number of primary and secondary ions using a Nicolet prototype Fourier transform mass spectrometer (FT-MS). Like the triple quadrupole technique, CID using FT-MS is a relatively low energy and efficient process. The ability to study a wide range of ion-molecule reaction products is exemplified by results on proton-bound dimers and transition metal containing ionic species. Variation of collision energy by varying the RF irradiation level can provide information about product distributions as a function of energy as well as yield ion structural information. Like the triple quadrupole technique, no slits are employed and virtually all of the fragment ions formed by the CID process may be detected. Unlike all previous mass spectrometric techniques for studying CID, a tandem instrument is not required, and different experiments are performed by making software modifications rather than hardware modifications
Seismic Shear Energy Reflection By Radon-Fourier Transform
Directory of Open Access Journals (Sweden)
Malik Umairia
2016-01-01
Full Text Available Seismic waves split in an anisotropic medium, instead of rotating horizontal component to principal direction, Radon-Fourier is derived to observe the signature of shear wave reflection. Synthetic model with fracture is built and discretized using finite difference scheme for spatial and time domain. Common depth point (CDP with single shot gives traces and automatic gain is preprocessed before Radon Transform (RT, a filtering technique gives radon domain. It makes easier to observe fractures at specific incidence and improves its quality in some way by removing the noise. A comparison of synthetic data and BF-data is performed on the basis of root means square error (RMS values. The RMS error is minimum at the 10th trace in radon domain.
A rheumatoid arthritis study by Fourier transform infrared spectroscopy
Carvalho, Carolina S.; Silva, Ana Carla A.; Santos, Tatiano J. P. S.; Martin, Airton A.; dos Santos Fernandes, Ana Célia; Andrade, Luís E.; Raniero, Leandro
2012-01-01
Rheumatoid arthritis is a systemic inflammatory disease of unknown causes and a new methods to identify it in early stages are needed. The main purpose of this work is the biochemical differentiation of sera between normal and RA patients, through the establishment of a statistical method that can be appropriately used for serological analysis. The human sera from 39 healthy donors and 39 rheumatics donors were collected and analyzed by Fourier Transform Infrared Spectroscopy. The results show significant spectral variations with p<0.05 in regions corresponding to protein, lipids and immunoglobulins. The technique of latex particles, coated with human IgG and monoclonal anti-CRP by indirect agglutination known as FR and CRP, was performed to confirm possible false-negative results within the groups, facilitating the statistical interpretation and validation of the technique.
Analysis of cigarette smoke by Fourier transform infrared spectrometry
Energy Technology Data Exchange (ETDEWEB)
Maddox, W.L. (Oak Ridge National Lab., TN); Mamantov, G.
1977-02-01
The application of Fourier transform infrared spectrometry (FT-IR) to the quantitative determination of several components in the gas phase of whole, dilute tobacco smoke was demonstrated. The 18-cm absorption cell was part of a cigarette smoking system similar to the intermittent inhalation exposure devices used in smoking and health research with rodents. Concentrations were measured for carbon monoxide, carbon dioxide, methane, ethylene, and methanol in 7 to 22% smoke. The precision of a measurement in 22% smoke ranged from 3% for carbon dioxide to 34% for ethylene. Absorbances measured for isoprene and hydrogen cyanide followed expected concentrations in different cigarette smokes. It was shown that the concentrations of these components remain constant during a 30-s hold-up following each puff on the cigarettes.
Generation of Fourier-transform-limited heralded single photons
International Nuclear Information System (INIS)
U'Ren, Alfred B.; Jeronimo-Moreno, Yasser; Garcia-Gracia, Hipolito
2007-01-01
In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets
Surface analysis by Fourier-transform infrared (FTIR) spectroscopy
International Nuclear Information System (INIS)
Powell, G.L.; Smyrl, N.R.; Fuller, E.L.
1981-01-01
A diffuse-reflectance capability for the Fourier transform infrared spectrometer at the Y-12 Plant Laboratory has been implemented. A sample cell with a 25 to 400 0 C temperature-controlled sample stage and an ultrahigh-vacuum-to-atmospheric pressure gas-handling capability has been developed. Absorbance of light from the spectrometer beam, resulting from the beam being scattered from a powder sample, can be measured. This capability of detecting molecular species on and in powders is to be used to study chemisorption on actinide and rare-earth metals, alloys, and compounds. Cell design is described along with experiments demonstrating its performance in detecting moisture absorption on uranium oxide, moisture and carbon dioxide absorption on the lithium hydride/hydroxide system, and carbon dioxide absorption on potassium borohydride. 13 figures
Quantum copying and simplification of the quantum Fourier transform
Niu, Chi-Sheng
Theoretical studies of quantum computation and quantum information theory are presented in this thesis. Three topics are considered: simplification of the quantum Fourier transform in Shor's algorithm, optimal eavesdropping in the BB84 quantum cryptographic protocol, and quantum copying of one qubit. The quantum Fourier transform preceding the final measurement in Shor's algorithm is simplified by replacing a network of quantum gates with one that has fewer and simpler gates controlled by classical signals. This simplification results from an analysis of the network using the consistent history approach to quantum mechanics. The optimal amount of information which an eavesdropper can gain, for a given level of noise in the communication channel, is worked out for the BB84 quantum cryptographic protocol. The optimal eavesdropping strategy is expressed in terms of various quantum networks. A consistent history analysis of these networks using two conjugate quantum bases shows how the information gain in one basis influences the noise level in the conjugate basis. The no-cloning property of quantum systems, which is the physics behind quantum cryptography, is studied by considering copying machines that generate two imperfect copies of one qubit. The best qualities these copies can have are worked out with the help of the Bloch sphere representation for one qubit, and a quantum network is worked out for an optimal copying machine. If the copying machine does not have additional ancillary qubits, the copying process can be viewed using a 2-dimensional subspace in a product space of two qubits. A special representation of such a two-dimensional subspace makes possible a complete characterization of this type of copying. This characterization in turn leads to simplified eavesdropping strategies in the BB84 and the B92 quantum cryptographic protocols.
International Nuclear Information System (INIS)
Vilardy, Juan M; Millán, María S; Pérez-Cabré, Elisabet; Torres, Yezid
2014-01-01
We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations. (paper)
Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform.
Tang, Heng-He; Liu, Pu-Kun
2015-09-07
A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances.
Hennelly, Bryan M.; Sheridan, John T.
2005-05-01
By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.
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
Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform.
Mendlovic, D; Ozaktas, H M; Lohmann, A W
1994-09-10
Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.
Teaching stable two-mirror resonators through the fractional Fourier transform
International Nuclear Information System (INIS)
Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos
2010-01-01
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects.
Non-rigid registration of tomographic images with Fourier transforms
International Nuclear Information System (INIS)
Osorio, Ar; Isoardi, Ra; Mato, G
2007-01-01
Spatial image registration of deformable body parts such as thorax and abdomen has important medical applications, but at the same time, it represents an important computational challenge. In this work we propose an automatic algorithm to perform non-rigid registration of tomographic images using a non-rigid model based on Fourier transforms. As a measure of similarity, we use the correlation coefficient, finding that the optimal order of the transformation is n = 3 (36 parameters). We apply this method to a digital phantom and to 7 pairs of patient images corresponding to clinical CT scans. The preliminary results indicate a fairly good agreement according to medical experts, with an average registration error of 2 mm for the case of clinical images. For 2D images (dimensions 512x512), the average running time for the algorithm is 15 seconds using a standard personal computer. Summarizing, we find that intra-modality registration of the abdomen can be achieved with acceptable accuracy for slight deformations and can be extended to 3D with a reasonable execution time
TMS320C25 Digital Signal Processor For 2-Dimensional Fast Fourier Transform Computation
International Nuclear Information System (INIS)
Ardisasmita, M. Syamsa
1996-01-01
The Fourier transform is one of the most important mathematical tool in signal processing and analysis, which converts information from the time/spatial domain into the frequency domain. Even with implementation of the Fast Fourier Transform algorithms in imaging data, the discrete Fourier transform execution consume a lot of time. Digital signal processors are designed specifically to perform computation intensive digital signal processing algorithms. By taking advantage of the advanced architecture. parallel processing, and dedicated digital signal processing (DSP) instruction sets. This device can execute million of DSP operations per second. The device architecture, characteristics and feature suitable for fast Fourier transform application and speed-up are discussed
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)
Fan, Hong-yi; Hu, Li-yun
2012-06-01
By virtue of the new technique of performing integration over Dirac's ket-bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel-Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac's assertion: "...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory".
The use of Fourier reverse transforms in crystallographic phase refinement
Energy Technology Data Exchange (ETDEWEB)
Ringrose, Sharon [Iowa State Univ., Ames, IA (United States)
1997-10-08
Often a crystallographer obtains an electron density map which shows only part of the structure. In such cases, the phasing of the trial model is poor enough that the electron density map may show peaks in some of the atomic positions, but other atomic positions are not visible. There may also be extraneous peaks present which are not due to atomic positions. A method for determination of crystal structures that have resisted solution through normal crystallographic methods has been developed. PHASER is a series of FORTRAN programs which aids in the structure solution of poorly phased electron density maps by refining the crystallographic phases. It facilitates the refinement of such poorly phased electron density maps for difficult structures which might otherwise not be solvable. The trial model, which serves as the starting point for the phase refinement, may be acquired by several routes such as direct methods or Patterson methods. Modifications are made to the reverse transform process based on several assumptions. First, the starting electron density map is modified based on the fact that physically the electron density map must be non-negative at all points. In practice a small positive cutoff is used. A reverse Fourier transform is computed based on the modified electron density map. Secondly, the authors assume that a better electron density map will result by using the observed magnitudes of the structure factors combined with the phases calculated in the reverse transform. After convergence has been reached, more atomic positions and less extraneous peaks are observed in the refined electron density map. The starting model need not be very large to achieve success with PHASER; successful phase refinement has been achieved with a starting model that consists of only 5% of the total scattering power of the full molecule. The second part of the thesis discusses three crystal structure determinations.
Izadi Najafabadi, Mohammad
2017-11-06
A relatively high level of stratification (qualitatively: lack of homogeneity) is one of the main advantages of partially premixed combustion over the homogeneous charge compression ignition concept. Stratification can smooth the heat release rate and improve the controllability of combustion. In order to compare stratification levels of different partially premixed combustion strategies or other combustion concepts, an objective and meaningful definition of “stratification level” is required. Such a definition is currently lacking; qualitative/quantitative definitions in the literature cannot properly distinguish various levels of stratification. The main purpose of this study is to objectively define combustion stratification (not to be confused with fuel stratification) based on high-speed OH* chemiluminescence imaging, which is assumed to provide spatial information regarding heat release. Stratification essentially being equivalent to spatial structure, we base our definition on two-dimensional Fourier transforms of photographs of OH* chemiluminescence. A light-duty optical diesel engine has been used to perform the OH* bandpass imaging on. Four experimental points are evaluated, with injection timings in the homogeneous regime as well as in the stratified partially premixed combustion regime. Two-dimensional Fourier transforms translate these chemiluminescence images into a range of spatial frequencies. The frequency information is used to define combustion stratification, using a novel normalization procedure. The results indicate that this new definition, based on Fourier analysis of OH* bandpass images, overcomes the drawbacks of previous definitions used in the literature and is a promising method to compare the level of combustion stratification between different experiments.
Fourier Transform Infrared and Resonance Raman Spectroscopic Studies of Bacteriorhodopsin.
Earnest, Thomas Nixon
Fourier transform infrared and resonance Raman spectroscopy were used to investigate the structure and function of the light-activated, transmembrane proton pump, bacteriorhodopsin, from the purple membrane of Halobacterium halobium. Bacteriorhodopsin (bR) is a 27,000 dalton integral membrane protein consisting of 248 amino acids with a retinylidene chromophore. Absorption of a photon leads to the translocation of one or two protons from the inside of the cell to the outside. Resonance Raman spectroscopy allows for the study of the configuration of retinal in bR and its photointermediates by the selective enhancement of vibrational modes of the chromophore. This technique was used to determine that the chromophore is attached to lysine-216 in both the bR _{570} and the M _{412} intermediates. In bR with tyrosine-64 selectively nitrated or aminated, the chromophore appears to have the same configuration in that bR _{570} (all- trans) and M _{412} (13- cis) states as it does in unmodified bR. Polarized Fourier transform infrared spectroscopy (FTIR) permits the study of the direction of transition dipole moments arising from molecular vibrations of the protein and the retinal chromophore. The orientation of alpha helical and beta sheet components was determined for bR with the average helical tilt found to lie mostly parallel to the membrane normal. The beta sheet structures also exhibit an IR linear dichroism for the amide I and amide II bands which suggest that the peptide backbone is mostly perpendicular to the membrane plane although it is difficult to determine whether the bands originate from sheet or turn components. The orientation of secondary structure components of the C-1 (residues 72-248) and C-2 (residues 1-71) fragments were also investigated to determine the structure of these putative membrane protein folding intermediates. Polarized, low temperature FTIR -difference spectroscopy was then used to investigate the structure of bR as it undergoes
Directory of Open Access Journals (Sweden)
D. Seidl
1999-06-01
Full Text Available Among a variety of spectrogram methods Short-Time Fourier Transform (STFT and Continuous Wavelet Transform (CWT were selected to analyse transients in non-stationary tremor signals. Depending on the properties of the tremor signal a more suitable representation of the signal is gained by CWT. Three selected broadband tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli.
Fourier transform infrared spectroscopy for Kona coffee authentication.
Wang, Jun; Jun, Soojin; Bittenbender, H C; Gautz, Loren; Li, Qing X
2009-06-01
Kona coffee, the variety of "Kona typica" grown in the north and south districts of Kona-Island, carries a unique stamp of the region of Big Island of Hawaii, U.S.A. The excellent quality of Kona coffee makes it among the best coffee products in the world. Fourier transform infrared (FTIR) spectroscopy integrated with an attenuated total reflectance (ATR) accessory and multivariate analysis was used for qualitative and quantitative analysis of ground and brewed Kona coffee and blends made with Kona coffee. The calibration set of Kona coffee consisted of 10 different blends of Kona-grown original coffee mixture from 14 different farms in Hawaii and a non-Kona-grown original coffee mixture from 3 different sampling sites in Hawaii. Derivative transformations (1st and 2nd), mathematical enhancements such as mean centering and variance scaling, multivariate regressions by partial least square (PLS), and principal components regression (PCR) were implemented to develop and enhance the calibration model. The calibration model was successfully validated using 9 synthetic blend sets of 100% Kona coffee mixture and its adulterant, 100% non-Kona coffee mixture. There were distinct peak variations of ground and brewed coffee blends in the spectral "fingerprint" region between 800 and 1900 cm(-1). The PLS-2nd derivative calibration model based on brewed Kona coffee with mean centering data processing showed the highest degree of accuracy with the lowest standard error of calibration value of 0.81 and the highest R(2) value of 0.999. The model was further validated by quantitative analysis of commercial Kona coffee blends. Results demonstrate that FTIR can be a rapid alternative to authenticate Kona coffee, which only needs very quick and simple sample preparations.
Distributed Two-Dimensional Fourier Transforms on DSPs with an Application for Phase Retrieval
Smith, Jeffrey Scott
2006-01-01
Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The image-based approach has many benefits, yet it is a computational intensive solution for adaptive optic correction, where optical adjustments are made in real-time to correct for external (atmospheric turbulence) and internal (stability) aberrations, which cause image degradation. For phase retrieval, a type of image-based wavefront sensing, numerous two-dimensional Fast Fourier Transforms (FFTs) are used. To meet the required real-time specifications, a distributed system is needed, and thus, the 2-D FFT necessitates an all-to-all communication among the computational nodes. The 1-D floating point FFT is very efficient on a digital signal processor (DSP). For this study, several architectures and analysis of such are presented which address the all-to-all communication with DSPs. Emphasis of this research is on a 64-node cluster of Analog Devices TigerSharc TS-101 DSPs.
A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.
Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei
2015-09-01
A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress.
Fourier Transform Infrared Imaging analysis of dental pulp inflammatory diseases.
Giorgini, E; Sabbatini, S; Conti, C; Rubini, C; Rocchetti, R; Fioroni, M; Memè, L; Orilisi, G
2017-05-01
Fourier Transform Infrared microspectroscopy let characterize the macromolecular composition and distribution of tissues and cells, by studying the interaction between infrared radiation and matter. Therefore, we hypothesize to exploit this analytical tool in the analysis of inflamed pulps, to detect the different biochemical features related to various degrees of inflammation. IR maps of 13 irreversible and 12 hyperplastic pulpitis, together with 10 normal pulps, were acquired, compared with histological findings and submitted to multivariate (HCA, PCA, SIMCA) and statistical (one-way ANOVA) analysis. The fit of convoluted bands let calculate meaningful band area ratios (means ± s.d., P < 0.05). The infrared imaging analysis pin-pointed higher amounts of water and lower quantities of type I collagen in all inflamed pulps. Specific vibrational markers were defined for irreversible pulpitis (Lipids/Total Biomass, PhII/Total Biomass, CH 2 /CH 3 , and Ty/AII) and hyperplastic ones (OH/Total Biomass, Collagen/Total Biomass, and CH 3 Collagen/Total Biomass). The study confirmed that FTIR microspectroscopy let discriminate tissues' biological features. The infrared imaging analysis evidenced, in inflamed pulps, alterations in tissues' structure and composition. Changes in lipid metabolism, increasing amounts of tyrosine, and the occurrence of phosphorylative processes were highlighted in irreversible pulpitis, while high amounts of water and low quantities of type I collagen were detected in hyperplastic samples. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.
Mikkonen, Jopi J W; Raittila, Jussi; Rieppo, Lassi; Lappalainen, Reijo; Kullaa, Arja M; Myllymaa, Sami
2016-09-01
Saliva provides a valuable tool for assessing oral and systemic diseases, but concentrations of salivary components are very small, calling the need for precise analysis methods. In this work, Fourier transform infrared (FT-IR) spectroscopy using transmission and photoacoustic (PA) modes were compared for quantitative analysis of saliva. The performance of these techniques was compared with a calibration series. The linearity of spectrum output was verified by using albumin-thiocyanate (SCN(-)) solution at different SCN(-) concentrations. Saliva samples used as a comparison were obtained from healthy subjects. Saliva droplets of 15 µL were applied on the silicon sample substrate, 6 drops for each specimen, and dried at 37 ℃ overnight. The measurements were carried out using an FT-IR spectrometer in conjunction with an accessory unit for PA measurements. The findings with both transmission and PA modes mirror each other. The major bands presented were 1500-1750 cm(-1) for proteins and 1050-1200 cm(-1) for carbohydrates. In addition, the distinct spectral band at 2050 cm(-1) derives from SCN(-) anions, which is converted by salivary peroxidases to hypothiocyanate (OSCN(-)). The correlation between the spectroscopic data with SCN(-) concentration (r > 0.990 for transmission and r = 0.967 for PA mode) was found to be significant (P < 0.01), thus promising to be utilized in future applications. © The Author(s) 2016.
Relativistic elliptic matrix tops and finite Fourier transformations
Zotov, A.
2017-10-01
We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter η. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and η on an equal footing. Depending on the type of integrable reduction, any of the parameters can be chosen to be the spectral one. Then another one is the relativistic deformation parameter. As a by-product, we describe the model of N2 interacting GL(M) matrix tops and/or M2 interacting GL(N) matrix tops depending on a choice of the spectral parameter.
Fourier transform infrared spectroscopy in physics laboratory courses
International Nuclear Information System (INIS)
Möllmann, K-P; Vollmer, M
2013-01-01
Infrared spectrometry is one of the most important tools in the field of spectroscopic analysis. This is due to the high information content of spectra in the so-called spectroscopic fingerprint region, which enables measurement not only of gases, but also of liquids and solids. Today, infrared spectroscopy is almost completely dominated by Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy is able to detect minute quantities in the ppm and ppb ranges, and the respective analyses are now standard tools in science as well as industry. Therefore FTIR spectroscopy should be taught within the standard curriculum at university to physicists and engineers. Here we present respective undergraduate laboratory experiments designed for students at the end of their third year. Experiments deal first with understanding the spectrometer and second with recording and analysing spectra. On the one hand, transmission spectra of gases are treated which relate to environmental analytics (being probably the most prominent and well-known examples), and on the other hand, the focus is on the transmission and reflection spectra of solids. In particular, silicon wafers are studied—as is regularly done in the microelectronics industry—in order to characterize their thickness, oxygen content and phonon modes. (paper)
Convergence and summability of Fourier transforms and Hardy spaces
Weisz, Ferenc
2017-01-01
This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.
Toward a soft x-ray Fourier-transform spectrometer
International Nuclear Information System (INIS)
Howells, M.R.; Frank, K.; Hussain, Z.; Moler, E.J.; Reich, T.; Moeller, D.
1993-01-01
The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range ±1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330
Sparse-matrix factorizations for fast symmetric Fourier transforms
International Nuclear Information System (INIS)
Sequel, J.
1987-01-01
This work proposes new fast algorithms computing the discrete Fourier transform of certain families of symmetric sequences. Sequences commonly found in problems of structure determination by x-ray crystallography and in numerical solutions of boundary-value problems in partial differential equations are dealt with. In the algorithms presented, the redundancies in the input and output data, due to the presence of symmetries in the input data sequence, were eliminated. Using ring-theoretical methods a matrix representation is obtained for the remaining calculations; which factors as the product of a complex block-diagonal matrix times as integral matrix. A basic two-step algorithm scheme arises from this factorization with a first step consisting of pre-additions and a second step containing the calculations involved in computing with the blocks in the block-diagonal factor. These blocks are structured as block-Hankel matrices, and two sparse-matrix factoring formulas are developed in order to diminish their arithmetic complexity
Large Molecule Structures by Broadband Fourier Transform Molecular Rotational Spectroscopy
Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks
2016-06-01
Fourier transform molecular rotational resonance spectroscopy (FT-MRR) using pulsed jet molecular beam sources is a high-resolution spectroscopy technique that can be used for chiral analysis of molecules with multiple chiral centers. The sensitivity of the molecular rotational spectrum pattern to small changes in the three dimensional structure makes it possible to identify diastereomers without prior chemical separation. For larger molecules, there is the additional challenge that different conformations of each diastereomer may be present and these need to be differentiated from the diastereomers in the spectral analysis. Broadband rotational spectra of several larger molecules have been measured using a chirped-pulse FT-MRR spectrometer. Measurements of nootkatone (C15H22O), cedrol (C15H26O), ambroxide (C16H28O) and sclareolide (C16H26O2) are presented. These spectra are measured with high sensitivity (signal-to-noise ratio near 1,000:1) and permit structure determination of the most populated isomers using isotopic analysis of the 13C and 18O isotopologues in natural abundance. The accuracy of quantum chemistry calculations to identify diastereomers and conformers and to predict the dipole moment properties needed for three wave mixing measurements is examined.
Single beam Fourier transform digital holographic quantitative phase microscopy
Energy Technology Data Exchange (ETDEWEB)
Anand, A., E-mail: arun-nair-in@yahoo.com; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V. [Optics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390001 (India); Faridian, A.; Pedrini, G.; Osten, W. [Institut für Technische Optik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart (Germany); Dubey, S. K. [Siemens Technology and Services Pvt. Ltd, Corporate Technology—Research and Technology Centre, Bangalore 560100 (India); Javidi, B. [Department of Electrical and Computer Engineering, U-4157, University of Connecticut, Storrs, Connecticut 06269-2157 (United States)
2014-03-10
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
Hybrid fast Hankel transform implementation for optics simulation
Davis, Paul K.
2013-09-01
The most compute intensive part of a full optics simulation, especially including diffraction effects, is the Fourier transform between pupil and image spaces. This is typically performed as a two dimensional fast discrete transform. For a nearly radially symmetric system there are advantages to using polar coordinates, in which case the radial transform becomes a Hankel transform, using Bessel functions instead of circular functions. However, there are special difficulties in calculating and handling Bessel functions. Several solutions have been proposed. We present a hybrid Hankel transform which divides the domain, calculating a portion using Bessel function approximations but converting most of the domain into a one dimensional Fourier transform which can be handled by standard methods.
Application of finite Fourier transformation for the solution of the diffusion equation
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1991-01-01
The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)
On the moments of the Wigner distribution and the fractional Fourier transform
Alieva, T.; Bastiaans, M.J.; Veen, J.P.
2000-01-01
A Fourier transformation maps a one-dimensional time signal into a one-dimensional frequency function, the signal spectrum. Although the Fourier transform provides the signal's spectral content, it fails to indicate the time location of the spectral components, which is important, for example, when
2017-08-01
Fourier transform, discrete Fourier transform, digital array processing , antenna beamformers 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF...125 3.7 Simulation of 2-D Beams Cross Sections .................................................................... 125 3.7.1 8...unlimited. List of Figures Figure Page Figure 1: N-beam Array Processing System using a Linear Array
The RC Circuit: An Approach with Fourier Transforms In this article ...
Indian Academy of Sciences (India)
CLASSROOM. Mitrajyoti Ghosh. 83, Mitrapara 2nd Lane, Harinavi,. Kolkata 700148, West Bengal,. India. Email: mijospeakingnow@gmail.com. The RC Circuit: An Approach with Fourier Transforms. In this article we shall mathematically analyse the Resistor-. Capacitor (RC) circuit with the help of Fourier transforms. (FT).
Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes
Lin, Sian-Jheng; Al-Naffouri, Tareq Y.; Han, Yunghsiang S.; Chung, Wei-Ho
2016-01-01
In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h
An analogue of a theorem of Titchmarsh for Walsh-Fourier transformations
International Nuclear Information System (INIS)
Golubov, B I
1998-01-01
Let f-hat c be the Fourier cosine transform of f. Then, as proved for functions of class L p (R + ) in Titchmarsh's book 'Introduction to the theory of Fourier integrals' (1937), the Hardy operator and the Hardy-Littlewood operator can be defined. In the present paper similar equalities are proved for functions of class L p (R + ), 1< p≤2, and the Walsh-Fourier transformation
Ogawa, Takahiro; Haseyama, Miki
2013-03-01
A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.
Precise and fast spatial-frequency analysis using the iterative local Fourier transform.
Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook
2016-09-19
The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.
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
Directory of Open Access Journals (Sweden)
Siesler H. W.
2006-11-01
Full Text Available The recent extension of the Fourier-Transform (FT technique to the Raman effect has launched Raman spectroscopy into a new era of polymer chemical and physical applications. Thus, the increase in signal-to-noise ratio and the improvement in time resolution have largely enhanced the potential of FT-Raman spectroscopy for analytical applications, the characterization of time-dependent phenomena and the on-line combination with other techniques. Primarily the suppression of fluorescence by shifting the excitation line to the near-infrared (NIR region has contributed to the fast acceptance as an industrial routine tool. Furthermore, the application of fiber optics has opened up the areas of process-control and remote sensing. Les applications de la spectroscopie Raman dans le domaine des polymères sont entrées dans une ère nouvelle, grâce aux récents développements de la technique à transformée de Fourier avec excitation dans le proche infrarouge. L'augmentation du rapport signal sur bruit et l'amélioration de la résolution temporelle ont fortement renforcé les potentialités de la technique en ce qui concerne les applications analytiques, la caractérisation de phénomènes qui dépendent du temps et le couplage en ligne avec d'autres techniques. La suppression du phénomène de fluorescence par déplacement de la longueur d'onde de l'excitatrice dans le proche infrarouge a contribué à l'intégration rapide de l'outil en site industriel. L'emploi de fibres optiques a permis l'accroissement des applications dans le domaine du contrôle des procédés et d'analyser à distance.
Transformation optics and invisibility cloaks
DEFF Research Database (Denmark)
Qiu, Min; Yan, Min; Yan, Wei
2008-01-01
In this paper, we briefly summarize the theory of transformation optics and introduce its application in achieving perfect invisibility cloaking. In particular, we theoretically show how the task of realizing cylindrical invisibility cloaks can be eased by using either structural approximation...
Pipeline Analyzer using the Fractional Fourier Transform for Engine Control and Satellites Data
Directory of Open Access Journals (Sweden)
Darian M. Onchiș
2011-09-01
Full Text Available The aim of this paper is to present an algorithm for computing the fractional Fourier transform integrated into the pipeline of processing multi-variate and distributed data recorded by the engine control unit (ECU of a car and its satellites. The role of this transform is vital in establishing a time-variant filter and therefore it must be computed in a fast way. But for large scale time series, the application of the discrete fractional Fourier transform involves the computations of a large number of Hermite polynomials of increasingly order. The parallel algorithm presented will optimally compute the discrete Fourier-type transform for any given angle.
International Nuclear Information System (INIS)
Yamada, Yoshifumi; Liu, Na; Ito, Satoshi
2006-01-01
The signal in the Fresnel transform technique corresponds to a blurred one of the spin density image. Because the amplitudes of adjacent sampled signals have a high interrelation, the signal amplitude at a point between sampled points can be estimated with a high degree of accuracy even if the sampling is so coarse as to generate aliasing in the reconstructed images. In this report, we describe a new aliasless image reconstruction technique in the phase scrambling Fourier transform (PSFT) imaging technique in which the PSFT signals are converted to Fresnel transform signals by multiplying them by a quadratic phase term and are then interpolated using polynomial expressions to generate fully encoded signals. Numerical simulation using MR images showed that almost completely aliasless images are reconstructed by this technique. Experiments using ultra-low-field PSFT MRI were conducted, and aliasless images were reconstructed from coarsely sampled PSFT signals. (author)
Advanced multivariate data evaluation for Fourier transform infrared spectroscopy
International Nuclear Information System (INIS)
Diewok, J.
2002-12-01
The objective of the presented dissertation was the evaluation, application and further development of advanced multivariate data evaluation methods for qualitative and quantitative Fourier transform infrared (FT-IR) measurements, especially of aqueous samples. The focus was set on 'evolving systems'; i.e. chemical systems that change gradually with a master variable, such as pH, reaction time, elution time, etc. and that are increasingly encountered in analytical chemistry. FT-IR measurements on such systems yield 2-way and 3-way data sets, i.e. data matrices and cubes. The chemometric methods used were soft-modeling techniques, like multivariate curve resolution - alternating least squares (MCR-ALS) or principal component analysis (PCA), hard modeling of equilibrium systems and two-dimensional correlation spectroscopy (2D-CoS). The research results are presented in six publications and comprise: A new combination of FT-IR flow titrations and second-order calibration by MCR-ALS for the quantitative analysis of mixture samples of organic acids and sugars. A novel combination of MCR-ALS with a hard-modeled equilibrium constraint for second-order quantitation in pH-modulated samples where analytes and interferences show very similar acid-base behavior. A detailed study in which MCR-ALS and 2D-CoS are directly compared for the first time. From the analysis of simulated and experimental acid-base equilibrium systems, the performance and interpretability of the two methods is evaluated. Investigation of the binding process of vancomycin, an important antibiotic, to a cell wall analogue tripeptide by time-resolved FT-IR spectroscopy and detailed chemometric evaluation. Determination of red wine constituents by liquid chromatography with FT-IR detection and MCR-ALS for resolution of overlapped peaks. Classification of red wine cultivars from FT-IR spectroscopy of phenolic wine extracts with hierarchical clustering and soft independent modeling of class analogy (SIMCA
Fourier transform Raman spectroscopy of synthetic and biological calcium phosphates.
Sauer, G R; Zunic, W B; Durig, J R; Wuthier, R E
1994-05-01
Fourier-transform (FT) Raman spectroscopy was used to characterize the organic and mineral components of biological and synthetic calcium phosphate minerals. Raman spectroscopy provides information on biological minerals that is complimentary to more widely used infrared methodologies as some infrared-inactive vibrational modes are Raman-active. The application of FT-Raman technology has, for the first time, enabled the problems of high sample fluorescence and low signal-to-noise that are inherent in calcified tissues to be overcome. Raman spectra of calcium phosphates are dominated by a very strong band near 960 cm-1 that arises from the symmetric stretching mode (v1) of the phosphate group. Other Raman-active phosphate vibrational bands are seen at approximately 1075 (v3), 590 (v4), and 435 cm-1 (v2). Minerals containing acidic phosphate groups show additional vibrational modes. The different calcium phosphate mineral phases can be distinguished from one another by the relative positions and shapes of these bands in the Raman spectra. FT-Raman spectra of nascent, nonmineralized matrix vesicles (MV) show a distinct absence of the phosphate v1 band even though these structures are rich in calcium and phosphate. Similar results were seen with milk casein and synthetic Ca-phosphatidyl-serine-PO4 complexes. Hence, the phosphate and/or acidic phosphate ions in these noncrystalline biological calcium phosphates is in a molecular environment that differs from that in synthetic amorphous calcium phosphate. In MV, the first distinct mineral phase to form contained acidic phosphate bands similar to those seen in octacalcium phosphate. The mineral phase present in fully mineralized MV was much more apatitic, resembling that found in bones and teeth.(ABSTRACT TRUNCATED AT 250 WORDS)
International Nuclear Information System (INIS)
Ji, X.; Chen, Y.M.
1989-01-01
The boundary element method (BEM) is developed from the boundary integral equation method and the discretization techniques. Compared with other numerical method, BEM has been shown to be a versatile and efficient method for a wide variety of engineering problems, including the wave propagation in elastic media. The first formulation and solution of the transient elastodynamic problem by combining BEM and Laplace transform is due to Cruse. Further improvement was achieved by introducing Durbin's method instead of Papoulis method of numerical Laplace inverse transform. However, a great deal of computer time is still needed for the inverse transformation. The alternative integral transform approach is BEM combining with Fourier transform. The numerical Fourier inverse transformation is also computer time consuming, even if the fast Fourier transform is used. In the present paper, the authors use BEM combining with Fourier transform and Fourier eigen transform (FET). The new approach is very attractive in saving on computer time. This paper illustrates the application of FET to BEM of 2-dimensional transient elastodynamic problem. The example of a half plane subjected to a discontinuous boundary load is solved on ELXSI 6400 computer. The CPU time is less than one minute. If Laplace or Fourier transform is adopted, the CPU time will be more than 10 minutes
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)
International Nuclear Information System (INIS)
Kobayashi, Keisuke; Ishibashi, Hideo
1978-01-01
A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)
International Nuclear Information System (INIS)
Kobayashi, Keisuke
1975-01-01
A method of solution is presented for a monoenergetic diffusion equation in two-dimensional hexagonal cells by a finite Fourier transformation. Up to the present, the solution by the finite Fourier transformation has been developed for x-y, r-z and x-y-z geometries, and the flux and current at the boundary are obtained in terms of Fourier series. It is shown here that the method can be applied to hexagonal cells and the expansion of boundary values in a Legendre polynomials gives numerically a higher accuracy than is obtained by a Fourier series. (orig.) [de
Optical chirp z-transform processor with a simplified architecture.
Ngo, Nam Quoc
2014-12-29
Using a simplified chirp z-transform (CZT) algorithm based on the discrete-time convolution method, this paper presents the synthesis of a simplified architecture of a reconfigurable optical chirp z-transform (OCZT) processor based on the silica-based planar lightwave circuit (PLC) technology. In the simplified architecture of the reconfigurable OCZT, the required number of optical components is small and there are no waveguide crossings which make fabrication easy. The design of a novel type of optical discrete Fourier transform (ODFT) processor as a special case of the synthesized OCZT is then presented to demonstrate its effectiveness. The designed ODFT can be potentially used as an optical demultiplexer at the receiver of an optical fiber orthogonal frequency division multiplexing (OFDM) transmission system.
Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.
2012-01-01
By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.
Subwavelength Fourier-transform imaging without a lens or a beamsplitter
International Nuclear Information System (INIS)
Liu Rui-Feng; Yuan Xin-Xing; Fang Yi-Zhen; Zhang Pei; Zhou Yu; Gao Hong; Li Fu-Li
2014-01-01
The fourier-transform patterns of an object are usually observed in the far-field region or obtained in the near-field region with the help of lenses. Here we propose and experimentally demonstrate a scheme of Fourier-transform patterns in the Fresnel diffraction region with thermal light. In this scheme, neither a lens nor a beamsplitter is used, and only one single charge coupled device (CCD) is employed. It means that dividing one beam out of a light source into signal and reference beams is not as necessary as the one done by the use of a beamsplitter in usual ghost interference experiments. Moreover, the coincidence measurement of two point detectors is not necessary and data recorded on a single CCD are sufficient for reconstructing the ghost diffraction patterns. The feature of the scheme promises a great potential application in the fields of X-ray and neutron diffraction imaging processes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Zhang, B.; Sang, Jun; Alam, Mohammad S.
2013-03-01
An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.
Supersymmetric Transformations in Optical Fibers
Macho, Andrés; Llorente, Roberto; García-Meca, Carlos
2018-01-01
Supersymmetry (SUSY) has recently emerged as a tool to design unique optical structures with degenerate spectra. Here, we study several fundamental aspects and variants of one-dimensional SUSY in axially symmetric optical media, including their basic spectral features and the conditions for degeneracy breaking. Surprisingly, we find that the SUSY degeneracy theorem is partially (totally) violated in optical systems connected by isospectral (broken) SUSY transformations due to a degradation of the paraxial approximation. In addition, we show that isospectral constructions provide a dimension-independent design control over the group delay in SUSY fibers. Moreover, we find that the studied unbroken and isospectral SUSY transformations allow us to generate refractive-index superpartners with an extremely large phase-matching bandwidth spanning the S +C +L optical bands. These singular features define a class of optical fibers with a number of potential applications. To illustrate this, we numerically demonstrate the possibility of building photonic lanterns supporting broadband heterogeneous supermodes with large effective area, a broadband all-fiber true-mode (de)multiplexer requiring no mode conversion, and different mode-filtering, mode-conversion, and pulse-shaping devices. Finally, we discuss the possibility of extrapolating our results to acoustics and quantum mechanics.
Directory of Open Access Journals (Sweden)
Rachid El Ayachi
2012-03-01
Full Text Available Optical Character Recognition OCR is a tool that aims to provide opportunities for computers to read characters without human intervention. The objective of OCR is characterization of a character by invariant descriptors in translation, rotation and scaling. In this paper, the OCR developed use invariant moments and Fourier transform in extraction phase. In the recognition phase, dynamic programming and neural network are adopted. All tests are applied on Tifinaghe printed characters.
Thyroid lesions diagnosis by Fourier transformed infrared absorption spectroscopy (FTIR)
International Nuclear Information System (INIS)
Albero, Felipe Guimaraes
2009-01-01
Thyroid nodules are a common disorder, with 4-7% of incidence in the Brazilian population. Although the fine needle aspiration (FNA) is an accurate method for thyroid tumors diagnosis, the discrimination between benign and malignant neoplasm is currently not possible in some cases with high incidence of false negative diagnosis, leading to a surgical intervention due to the risk of carcinomas. The aim of this study was to verify if the Fourier Transform infrared spectroscopy (FTIR) can contribute to the diagnosis of thyroid carcinomas and goiters, using samples of tissue and aspirates. Samples of FNA, homogenates and tissues of thyroid nodules with histopathological diagnosis were obtained and prepared for FTIR spectroscopy analysis. The FNA and homogenates samples were measured by μ-FTIR (between 950 . 1750 cm -1 ), at a nominal resolution of 4 cm -1 and 120 scans). Tissue samples were analyzed directly by ATR-FTIR technique, at a resolution 2 cm -1 , with 60 scans in the same region. All spectra were corrected by the baseline and normalized by amides area (1550-1640 cm -1 ) in order to minimize variations of sample homogeneity. Then, spectra were converted into second derivatives using the Savitzk-Golay algorithm with a 13 points window. The Ward's minimum variance algorithm and Euclidean distances among the points were used for cluster analysis. Some FNA samples showed complex spectral pattern. All samples showed some cell pellets and large amount of hormone, represented by the bands of 1545 and 1655 cm -1 . Bands in 1409, 1412, 1414, 1578 and 1579 cm -1 were also found, indicating possible presence of sugar, DNA, citric acid or metabolic products. In this study, it was obtained an excellent separation between goiter and malign lesion for the samples of tissues, with 100% of specificity in specific cluster and 67% sensibility and 50 of specificity. In homogenate and FNA samples this sensibility and specificity were lower, because among these samples, it were
Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan
2012-02-15
Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.
Metamaterial-enabled transformation optics
Landy, Nathan
Transformation Optics is a design methodology that uses the form invariance of Maxwell's equations to distort electromagnetic fields. This distortion is imposed on a region of space by mimicking a curvilinear coordinate system with prescribed magnetoelectric material parameters. By simply specifying the correct coordinate transformation, researchers have created such exotic devices as invisibility cloaks, ``perfect'' lenses, and illusion devices. Unfortunately, these devices typically require correspondingly exotic material parameters that do not occur in Nature. Researchers have therefore turned to complex artificial media known as metamaterials to approximate the desired responses. However, the metamaterial design process is complex, and there are limitations on the responses that they achieve. In this dissertation, we explore both the applicability and limitations of metamaterials in Transformation Optics design. We begin in Chapter 2 by investigating the freedoms available to use in the transformation optics design process itself. We show that quasi-conformal mappings may be used to alleviate some of the complexity of material design in both two- and three-dimensional design. We then go on in Chapter 3 to apply this method to the design of a transformation-optics modified optic. We show that even a highly-approximate implementation of such a lens would retain many of the key performance feautures that we would expect from a full material prescription. However, the approximations made in the design of our lens may not be valid in other areas of transformation optical design. For instance, the high-frequency approximations of our lens design ignore the effects of impedance mismatch, and the approximation is not valid when the material parameters vary on the order of a wavelength. Therefore, in Chapter 4 we use other freedoms available to us to design a full-parameter cloak of invisibility. By tailoring the electromagnetic environment of our cloak, we are able to
Kuijpers, A.H.W.M.; Verbeek, G.; Verheij, J.W.
1997-01-01
Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be
Cross sections for electron-impact excitation of argon by fourier transform spectroscopy
International Nuclear Information System (INIS)
Chilton, J.E.; Boffard, J.B.; Chun C.L.
1996-01-01
The authors report absolute measurements of electron-impact excitation cross sections out of the ground level to the ten levels in the 3p 5 4p configuration of argon. The apparent excitation cross sections are determined by measuring the optical cross sections for the emission lines in the 3p 5 4p → 3p 5 4s manifold. For cascade corrections the authors measured the optical cross sections for the various 3p 5 5s → 3p 5 4p and 3p 5 4p infrared lines using a Fourier transform weak emission spectrometer to obtain the direct excitation cross sections from the optical data. Although the optical cross sections vary with pressure in the regime of 0.1 to 6 mTorr, the direct cross sections remain invariant. These pressure effects are understood within the framework of a radiation-reabsorption model. The excitation functions for the different transitions are also found to show considerable variation in shape
From the rectangular to the quincunx Gabor lattice via fractional Fourier transformation
Bastiaans, M.J.; Leest, van A.J.
1998-01-01
Transformations of Gabor lattices have been associated with operations on the window functions that arise in Gabor theory. In particular it has been shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function,
Rectangular-to-quincunx Gabor lattice conversion via fractional Fourier transformation
Bastiaans, M.J.; Leest, van A.J.
1998-01-01
Transformations of Gabor lattices are associated with operations on the window functions that arise in Gabor theory. In particular it is shown that transformation from a rectangular to a quincunx lattice can be associated with fractional Fourier transformation. Since a Gaussian function, which plays
Vector frequency-comb Fourier-transform spectroscopy for characterizing metamaterials
International Nuclear Information System (INIS)
Ganz, T; Brehm, M; Von Ribbeck, H G; Keilmann, F; Van der Weide, D W
2008-01-01
We determine infrared transmission amplitude and phase spectra of metamaterial samples at well-defined incidence and polarization with a vector ('asymmetric') frequency-comb Fourier-transform spectrometer (c-FTS) that uses no moving elements. The metamaterials are free-standing metallic hole arrays; we study their resonances in the 7-13 μm and 100-1000 μm wavelength regions due both to interaction with bulk waves (Wood anomaly) and with leaky surface plasmon polaritons (near-unity transmittance, coupling features and dispersion). Such complex-valued transmission and reflection spectra could be used to compute a metamaterial's complex dielectric function directly, as well as its magnetic and magneto-optical permeability functions.
Mesooptical Fourier transform microscope - a new device for high energy physics
International Nuclear Information System (INIS)
Astakhov, A.Ya.; Batusov, Yu.A.; Bencze, Gy.L.; Farago, I.; Kisvaradi, A.; Molnar, L.; Soroko, L.M.; Vegh, J.
1988-01-01
A new device for high energy physics, Mesooptical Fourier Transform Microscope (MFTM), designed for observation of straight-line particle tracks in nuclear emulsion is described. The MFTM works without any mechanical or electronical depth scanning and can be considered as a selectively viewing eye. The computer controlled system containing MFTM as the main unit is given. This system can be used for fast search particle tracks and events produced by high energy neutrinos from accelerators. The results of the first experimental test of the computer controlled MFTM are presented. The performances of this system are 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. As all operations in the MFTM go without any depth scanning this new system works at least two orders of magnitude faster than any known system with a traditional optical microscope
DEFF Research Database (Denmark)
Clausen, Sønnik; Morgenstjerne, Axel; Rathmann, Ole
1996-01-01
Surface temperatures are estimated with high precision based on a multitemperature method for Fourier-transform spectrometers. The method is based on Planck's radiation law and a nonlinear least-squares fitting algorithm applied to two or more spectra at different sample temperatures and a single...... of blackbody sources are estimated with an uncertainty of 0.2-2 K. The method is demonstrated for measuring the spectral emissivity of a brass specimen and an oxidized nickel specimen. (C) 1996 Optical Society of America...... measurement at a known sample temperature, for example, at ambient temperature. The temperature of the sample surface can be measured rather easily at ambient temperature. The spectrum at ambient temperature is used to eliminate background effects from spectra as measured at other surface temperatures...
Yi, Wei-song; Cui, Dian-sheng; Li, Zhi; Wu, Lan-lan; Shen, Ai-guo; Hu, Ji-ming
2013-01-01
The manuscript has investigated the application of near-infrared (NIR) spectroscopy for differentiation gastric cancer. The 90 spectra from cancerous and normal tissues were collected from a total of 30 surgical specimens using Fourier transform near-infrared spectroscopy (FT-NIR) equipped with a fiber-optic probe. Major spectral differences were observed in the CH-stretching second overtone (9000-7000 cm-1), CH-stretching first overtone (6000-5200 cm-1), and CH-stretching combination (4500-4000 cm-1) regions. By use of unsupervised pattern recognition, such as principal component analysis (PCA) and cluster analysis (CA), all spectra were classified into cancerous and normal tissue groups with accuracy up to 81.1%. The sensitivity and specificity was 100% and 68.2%, respectively. These present results indicate that CH-stretching first, combination band and second overtone regions can serve as diagnostic markers for gastric cancer.
D'Astous, Y.; Blanchard, M.
1982-05-01
In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)
Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...
How to use the Fast Fourier Transform in Large Finite Fields
Petersen, Petur Birgir
2011-01-01
The article contents suggestions on how to perform the Fast Fourier Transform over Large Finite Fields. The technique is to use the fact that the multiplicative groups of specific prime fields are surprisingly composite.
On the raising and lowering difference operators for eigenvectors of the finite Fourier transform
International Nuclear Information System (INIS)
Atakishiyeva, M K; Atakishiyev, N M
2015-01-01
We construct explicit forms of raising and lowering difference operators that govern eigenvectors of the finite (discrete) Fourier transform. Some of the algebraic properties of these operators are also examined. (paper)
Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...
Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform
Directory of Open Access Journals (Sweden)
Zohreh Moghareh Abed
2010-01-01
Full Text Available In this paper, we introduce quantum fourier transform as a key ingredient for many useful algorithms. These algorithms make a solution for problems which is considered to be intractable problems on a classical computer. Quantum Fourier transform is propounded as a key for quantum phase estimation algorithm. In this paper our aim is the implementation of period-finding algorithm.Quantum computer solves this problem, exponentially faster than classical one. Quantum phase estimation algorithm is the key for the period-finding problem .Therefore, by means of simulating quantum Fourier transform, we are able to implement the period-finding algorithm. In this paper, the simulation of quantum Fourier transform is carried out by Matlab software.
National Aeronautics and Space Administration — The Panchromatic Fourier Transform Spectrometer (PanFTS) is an imaging spectrometer that can measure pollutants, greenhouse gases, and aerosols as called for in the...
Improved method of generating bit reversed numbers for calculating fast fourier transform
Digital Repository Service at National Institute of Oceanography (India)
Suresh, T.
Fast Fourier Transform (FFT) is an important tool required for signal processing in defence applications. This paper reports an improved method for generating bit reversed numbers needed in calculating FFT using radix-2. The refined algorithm takes...
Fourier transform and mean quadratic variation of Bernoulli convolution on homogeneous Cantor set
Energy Technology Data Exchange (ETDEWEB)
Yu Zuguo E-mail: yuzg@hotmail.comz.yu
2004-07-01
For the Bernoulli convolution on homogeneous Cantor set, under some condition, it is proved that the mean quadratic variation and the average of Fourier transform of this measure are bounded above and below.
Hourani, Nadim; Andersson, Jan T.; Mö ller, Isabelle; Amad, Maan H.; Witt, Matthí as; Sarathy, Mani
2013-01-01
oil (VGO) and injected using the same method. The samples were analyzed using Fourier transform ion cyclotron resonance mass spectrometry (FTICR MS). RESULTS PASH model analytes were successfully ionized and mainly [M + H]+ ions were produced. The same
Fourier transform of delayed fluorescence as an indicator of herbicide concentration.
Guo, Ya; Tan, Jinglu
2014-12-21
It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. Copyright © 2014 Elsevier Ltd. All rights reserved.
Experimental demonstrations of the properties of Fourier transforms using diffraction phenomena
International Nuclear Information System (INIS)
Bazin, M.J.; Lucie, P.H.; Oliveira, S.M.M. de.
1984-01-01
The standard mathematical properties of Fourier transforms and the experimental characteristics of diffraction phenomena are systematically brought together. An experimental realization of a particular case of the convolution theorem is displayed in details. (Author) [pt
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.
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.
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.
Fourier-transform infrared spectroscopic studies of dithia ...
Indian Academy of Sciences (India)
Unknown
limited region 1000–1150 cm–1.10 Therefore, in the present paper we report and analyse Fourier-trans- form infrared (FT-IR) spectra of S2TPP and its chemically prepared cation. 2. Experimental. Dithia tetraphenyl porphyrine was received from. Professor A L Verma as a gift and used without fur- ther purification. However ...
Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing
Park, J. H.
1984-01-01
An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.
Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.
Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene
2017-08-01
Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.
Practical protocols for fast histopathology by Fourier transform infrared spectroscopic imaging
Keith, Frances N.; Reddy, Rohith K.; Bhargava, Rohit
2008-02-01
Fourier transform infrared (FT-IR) spectroscopic imaging is an emerging technique that combines the molecular selectivity of spectroscopy with the spatial specificity of optical microscopy. We demonstrate a new concept in obtaining high fidelity data using commercial array detectors coupled to a microscope and Michelson interferometer. Next, we apply the developed technique to rapidly provide automated histopathologic information for breast cancer. Traditionally, disease diagnoses are based on optical examinations of stained tissue and involve a skilled recognition of morphological patterns of specific cell types (histopathology). Consequently, histopathologic determinations are a time consuming, subjective process with innate intra- and inter-operator variability. Utilizing endogenous molecular contrast inherent in vibrational spectra, specially designed tissue microarrays and pattern recognition of specific biochemical features, we report an integrated algorithm for automated classifications. The developed protocol is objective, statistically significant and, being compatible with current tissue processing procedures, holds potential for routine clinical diagnoses. We first demonstrate that the classification of tissue type (histology) can be accomplished in a manner that is robust and rigorous. Since data quality and classifier performance are linked, we quantify the relationship through our analysis model. Last, we demonstrate the application of the minimum noise fraction (MNF) transform to improve tissue segmentation.
Accelerating the Non-equispaced Fast Fourier Transform on Commodity Graphics Hardware
DEFF Research Database (Denmark)
Sørensen, Thomas Sangild; Schaeffter, Tobias; Noe, Karsten Østergaard
2008-01-01
We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe the performa......We present a fast parallel algorithm to compute the Non-equispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform, which was previously its most time consuming part. We describe...
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.
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}.
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.
Energy Technology Data Exchange (ETDEWEB)
Laroche, G. [Laboratoire d' Ingenierie de Surface, Centre de Recherche sur les Materiaux Avances, Departement de genie des mines, de la metallurgie et des materiaux, Universite Laval, 1065, avenue de la Medecine, Quebec G1V 0A6 (Canada); Centre de recherche du CHUQ, Hopital St Francois d' Assise, 10, rue de l' Espinay, local E0-165, Quebec G1L 3L5 (Canada); Vallade, J. [Laboratoire Procedes, Materiaux et Energie Solaire, PROMES, CNRS, Technosud, Rambla de la Thermodynamique, F-66100 Perpignan (France); Agence de l' environnement et de la Ma Latin-Small-Letter-Dotless-I -carettrise de l' Energie, 20, avenue du Gresille, BP 90406, F-49004 Angers Cedex 01 (France); Bazinette, R.; Hernandez, E.; Hernandez, G.; Massines, F. [Laboratoire Procedes, Materiaux et Energie Solaire, PROMES, CNRS, Technosud, Rambla de la Thermodynamique, F-66100 Perpignan (France); Nijnatten, P. van [OMT Solutions bv, High Tech Campus 9, 5656AE Eindhoven (Netherlands)
2012-10-15
This paper describes an optical setup built to record Fourier transform infrared (FTIR) absorption spectra in an atmospheric pressure plasma with a spatial resolution of 2 mm. The overall system consisted of three basic parts: (1) optical components located within the FTIR sample compartment, making it possible to define the size of the infrared beam (2 mm Multiplication-Sign 2 mm over a path length of 50 mm) imaged at the site of the plasma by (2) an optical interface positioned between the spectrometer and the plasma reactor. Once through the plasma region, (3) a retro-reflector module, located behind the plasma reactor, redirected the infrared beam coincident to the incident path up to a 45 Degree-Sign beamsplitter to reflect the beam toward a narrow-band mercury-cadmium-telluride detector. The antireflective plasma-coating experiments performed with ammonia and silane demonstrated that it was possible to quantify 42 and 2 ppm of these species in argon, respectively. In the case of ammonia, this was approximately three times less than this gas concentration typically used in plasma coating experiments while the silane limit of quantification was 35 times lower. Moreover, 70% of the incoming infrared radiation was focused within a 2 mm width at the site of the plasma, in reasonable agreement with the expected spatial resolution. The possibility of reaching this spatial resolution thus enabled us to measure the gaseous precursor consumption as a function of their residence time in the plasma.
Optimal defocus selection based on normed Fourier transform for digital fringe pattern profilometry.
Kamagara, Abel; Wang, Xiangzhao; Li, Sikun
2017-10-01
Owing to gamma-effect robustness and high-speed imaging capabilities, projector defocusing of binary-coded fringe patterns is by far the most widely used and effective technique in generating sinusoidal fringe patterns for three-dimensional optical topography measurement with digital fringe projection techniques. However, this technique is not trouble-free. It is borne with uncertainty and challenges mainly because it remains somewhat difficult to quantify and ascertain the level of defocus required for desired fidelity in sinuousness of the projected fringe pattern. Too much or too little defocusing will affect the sinuosity accuracy of fringe patterns and consequently jeopardize the quality of the measurement results. In this paper, by combining intrinsic phase spectral sensitivities and normed Fourier transform, a method to quantify the amount of defocus and subsequently select the optimal degree of sinuosity for generating digital sinusoidal fringe patterns with projector defocusing for fringe pattern optical three-dimensional profilometry is proposed. Numerical simulations plus experiments give evidence of the feasibility and validity of the proposed method in enabling an improved digital binary defocusing technique for optical phase-shift profilometry using the digital fringe projection technique.
Image encryption based on fractal-structured phase mask in fractional Fourier transform domain
Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2018-04-01
We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.
Emoto, Akira; Fukuda, Takashi
2013-02-20
For Fourier transform holography, an effective random phase distribution with randomly displaced phase segments is proposed for obtaining a smooth finite optical intensity distribution in the Fourier transform plane. Since unitary phase segments are randomly distributed in-plane, the blanks give various spatial frequency components to an image, and thus smooth the spectrum. Moreover, by randomly changing the phase segment size, spike generation from the unitary phase segment size in the spectrum can be reduced significantly. As a result, a smooth spectrum including sidebands can be formed at a relatively narrow extent. The proposed phase distribution sustains the primary functions of a random phase mask for holographic-data recording and reconstruction. Therefore, this distribution is expected to find applications in high-density holographic memory systems, replacing conventional random phase mask patterns.
High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data
Morelli, Eugene A.
1997-01-01
Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.
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.
A Novel Fractional Fourier Transform-Based ASK-OFDM System for Underwater Acoustic Communications
Directory of Open Access Journals (Sweden)
Rami Ashri
2017-12-01
Full Text Available A key research area in wireless transmission is underwater communications. It has a vital role in applications such as underwater sensor networks (UWSNs and disaster detection. The underwater channel is very unique as compared to other alternatives of transmission channels. It is characterized by path loss, multipath fading, Doppler spread and ambient noise. Thus, the bit error rate (BER is increased to a large extent when compared to its counterpart of cellular communications. Acoustic signals are the current best solution for underwater communications. The use of electromagnetic or optical waves obviously entails a much higher data rate. However, they suffer from high attenuation, absorption or scattering. This paper proposes a novel fractional fast Fourier transform (FrFT—orthogonal frequency division multiplexing (FrFT-OFDM system for underwater acoustic (UWA communication—which employs the amplitude shift keying (ASK modulation technique (FrFT-ASK-OFDM. Specifically, ASK achieves a better bandwidth efficiency as compared to other commonly used modulation techniques, such as quadrature amplitude modulation (QAM and phase shift keying (PSK. In particular, the system proposed in this article can achieve a very promising BER performance, and can reach higher data rates when compared to other systems proposed in the literature. The BER performance of the proposed system is evaluated numerically, and is compared to the corresponding M-ary QAM system in the UWA channel for the same channel conditions. Moreover, the performance of the proposed system is compared to the conventional fast Fourier transform (FFT-OFDM (FFT-OFDM system in the absence and presence of the effect of carrier frequency offset (CFO. Numerical results show that the proposed system outperforms the conventional FFT-based systems for UWA channels, even in channels dominated by CFO. Moreover, the spectral efficiency and data rate of the proposed system are approximately double
Description of the electron-hydrogen collision by the Coulomb Fourier transform method
International Nuclear Information System (INIS)
Levin, S.B.
2005-01-01
A recently developed Coulomb Fourier Transform method is applied to the system containing one heavy ion and two electrons. The transformed Hamiltonian is described with a controlled accuracy in an effective finite basis set as a finite dimensional operator matrix. The kernels of interaction are formulated in terms of the so called Nordsieck integrals
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
Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
International Nuclear Information System (INIS)
Aerts, Diederik; Czachor, Marek; Kuna, Maciej
2016-01-01
Highlights: • Fractal arithmetic allows to define Fourier transforms on Cantor-like sets. • General construction is illustrated on the example of a sawtooth signal. • The formalism is much simpler than the approaches discussed so far in the literature. - Abstract: Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane
Huang, Lin; Lenells, Jonatan
2018-03-01
Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions a , b , A , B. The functions a (k) and b (k) are defined via a nonlinear Fourier transform of the initial data, whereas A (k) and B (k) are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques.
Does the entorhinal cortex use the Fourier transform?
Orchard, Jeff; Yang, Hao; Ji, Xiang
2013-01-01
Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4–12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed “theta precession.” Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415
Fourier transform and controlling of flux in scalar hysteresis measurement
International Nuclear Information System (INIS)
Kuczmann, Miklos
2008-01-01
The paper deals with a possible realization of eliminating the effect of noise in scalar hysteresis measurements. The measured signals have been transformed into the frequency domain, and, after applying digital filter, the spectrums of the filtered signals have been transformed back to the time domain. The proposed technique results in an accurate noise-removal algorithm. The paper illustrates a fast controlling algorithm applying the inverse of the actually measured hysteresis loop, and another proportional one to measure distorted flux pattern. By developing the mentioned algorithms, it aims at the controlling of a more complicated phenomena, i.e. measuring the vector hysteresis characteristics
Study of Fourier transform spectrometer based on Michelson interferometer wave-meter
Peng, Yuexiang; Wang, Liqiang; Lin, Li
2008-03-01
A wave-meter based on Michelson interferometer consists of a reference and a measurement channel. The voice-coiled motor using PID means can realize to move in stable motion. The wavelength of a measurement laser can be obtained by counting interference fringes of reference and measurement laser. Reference laser with frequency stabilization creates a cosine interferogram signal whose frequency is proportional to velocity of the moving motor. The interferogram of the reference laser is converted to pulse signal, and it is subdivided into 16 times. In order to get optical spectrum, the analog signal of measurement channel should be collected. The Analog-to-Digital Converter (ADC) for measurement channel is triggered by the 16-times pulse signal of reference laser. So the sampling rate is constant only depending on frequency of reference laser and irrelative to the motor velocity. This means the sampling rate of measurement channel signals is on a uniform time-scale. The optical spectrum of measurement channel can be processed with Fast Fourier Transform (FFT) method by DSP and displayed on LCD.
Portable Fourier Transform Spectroscopy for Analysis of Surface Contamination and Quality Control
Pugel, Diane
2012-01-01
Progress has been made into adapting and enhancing a commercially available infrared spectrometer for the development of a handheld device for in-field measurements of the chemical composition of various samples of materials. The intent is to duplicate the functionality of a benchtop Fourier transform infrared spectrometer (FTIR) within the compactness of a handheld instrument with significantly improved spectral responsivity. Existing commercial technology, like the deuterated L-alanine triglycine sulfide detectors (DLATGS), is capable of sensitive in-field chemical analysis. This proposed approach compares several subsystem elements of the FTIR inside of the commercial, non-benchtop system to the commercial benchtop systems. These subsystem elements are the detector, the preamplifier and associated electronics of the detector, the interferometer, associated readout parameters, and cooling. This effort will examine these different detector subsystem elements to look for limitations in each. These limitations will be explored collaboratively with the commercial provider, and will be prioritized to meet the deliverable objectives. The tool design will be that of a handheld gun containing the IR filament source and associated optics. It will operate in a point-and-shoot manner, pointing the source and optics at the sample under test and capturing the reflected response of the material in the same handheld gun. Data will be captured via the gun and ported to a laptop.
Large quantum Fourier transforms are never exactly realized by braiding conformal blocks
International Nuclear Information System (INIS)
Freedman, Michael H.; Wang, Zhenghan
2007-01-01
Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {U(2), controlled-NOT}, the discrete Fourier transforms F N =(ω ij ) NxN , i,j=0,1,...,N-1, ω=e 2πi at ∼sol∼ at N , can be realized exactly by quantum circuits of size O(n 2 ), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F N and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks
Jiang, Hongzhen; Liu, Xu; Liu, Yong; Li, Dong; Chen, Zhu; Zheng, Fanglan; Yu, Deqiang
2017-10-01
An effective approach for reconstructing on-axis lensless Fourier Transform digital hologram by using the screen division method is proposed. Firstly, the on-axis Fourier Transform digital hologram is divided into sub-holograms. Then the reconstruction result of every sub-hologram is obtained according to the position of corresponding sub-hologram in the hologram reconstruction plane with Fourier transform operation. Finally, the reconstruction image of on-axis Fourier Transform digital hologram can be acquired by the superposition of the reconstruction result of sub-holograms. Compared with the traditional reconstruction method with the phase shifting technology, in which multiple digital holograms are required to record for obtaining the reconstruction image, this method can obtain the reconstruction image with only one digital hologram and therefore greatly simplify the recording and reconstruction process of on-axis lensless Fourier Transform digital holography. The effectiveness of the proposed method is well proved with the experimental results and it will have potential application foreground in the holographic measurement and display field.
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...
Method of local pointed function reduction of original shape in Fourier transformation
International Nuclear Information System (INIS)
Dosch, H.; Slavyanov, S.Yu.
2002-01-01
The method for analytical reduction of the original shape in the one-dimensional Fourier transformation by the fourier image modulus is proposed. The basic concept of the method consists in the presentation of the model shape in the form of the local peak functions sum. The eigenfunctions, generated by the linear differential equations with the polynomial coefficients, are selected as the latter ones. This provides for the possibility of managing the Fourier transformation without numerical integration. This reduces the reverse task to the nonlinear regression with a small number of the evaluated parameters and to the numerical or asymptotic study on the model peak functions - the eigenfunctions of the differential tasks and their fourier images [ru
Transformation quantum optics: designing spontaneous emission using coordinate transformations
DEFF Research Database (Denmark)
Zhang, Jingjing; Wubs, Martijn; Ginzburg, Pavel
2016-01-01
Spontaneous decay is a fundamental quantum property of emitters that can be controlled in a material environment via modification of the local density of optical states (LDOS). Here we use transformation optics methods in order to design required density of states and thus spontaneous emission (S......, affect the LDOS in complex materials. Tailoring SE properties using transformation optics approach provides an innovative way for designing emission properties in a complex material environment needed for the development of active nanophotonic devices....
On Analog of Fourier Transform in Interior of the Light Cone
Directory of Open Access Journals (Sweden)
Tatyana Shtepina
2014-01-01
Full Text Available We introduce an analog of Fourier transform Fhρ in interior of light cone that commutes with the action of the Lorentz group. We describe some properties of Fhρ, namely, its action on pseudoradial functions and functions being products of pseudoradial function and space hyperbolic harmonics. We prove that Fhρ-transform gives a one-to-one correspondence on each of the irreducible components of quasiregular representation. We calculate the inverse transform too.
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 transform infrared spectroscopic estimation of crystallinity in ...
Indian Academy of Sciences (India)
We present here optical properties and crystallinity index of quartz (SiO2) in natural rocks samples from the Mikir and Khasi hills, Assam, India. Infrared spectroscopy has been used to study the structure of quartz in rock samples and estimate the mining quality of quartz mineral, which is substantiated by calculating the ...
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.
Computer Generation of Fourier Transform Libraries for Distributed Memory Architectures
2010-12-01
tractions used in quantum chemistry . It too performs algebraic transformations tominimize the operations count, and then optimizes code based on...existing parallel DFT algorithms, including their strengths and weaknesses. Four-stepFFT.The four-step algorithm [Hegland, 1994;Norton and Silberger , 1987...Sadayappan, and Alexander Sibiryakov. Synthesis of high-performance parallel programs for a class of ab initio quan- tum chemistry models. Proc. of
Fast Fourier transformation in vibration analysis of physically active systems
International Nuclear Information System (INIS)
Hafeez, T.; Amir, M.; Farooq, U.; Day, P.
2003-01-01
Vibration of all physical systems may be expressed as the summation of an infinite number of sine and cosine terms known as Fourier series. The basic vibration analysis tool used is the frequency 'spectrum' (a graph of vibration where the amplitude of vibration is plotted against frequency). When a particular rotating component begins to fail, its vibration tends to increase. Spectra graphs are powerful diagnostic tool for detecting components' degradation. Spectra obtained with accelerometers located at the various locations on the components and their analysis in practice from rotating machines enable early detecting of incipient failure. Consequence of unexpected failure can be catastrophic and costly. This study provides basis to relate defective component by its constituent frequencies and then to the known discrete frequency of its 'signature' or 'thumbprint' to predict and verify the sustained dynamic behavior of machine designs harmful effects of forced vibration. The spectra for gearbox of a vane with teeth damaged fault are presented here which signified the importance of FFT analysis as diagnostic tool. This may be helpful to predictive maintenance of the machinery. (author)
The su(2)α Hahn oscillator and a discrete Fourier-Hahn transform
International Nuclear Information System (INIS)
Jafarov, E I; Stoilova, N I; Van der Jeugt, J
2011-01-01
We define the quadratic algebra su(2) α which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2) α . We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2) α . It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this so-called discrete Fourier-Hahn transform is computed explicitly. The matrix of this discrete Fourier-Hahn transform has many interesting properties, similar to those of the traditional discrete Fourier transform. (paper)
Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions
Holmes, J. J.; Balanis, C. A.
1974-01-01
Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.
van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B
2015-12-01
Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.
Functional differential equations for the q-Fourier transform of q-Gaussians
International Nuclear Information System (INIS)
Umarov, S; Queiros, S M Duarte
2010-01-01
In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 ≤ q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.
Functional differential equations for the q-Fourier transform of q-Gaussians
Energy Technology Data Exchange (ETDEWEB)
Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)
2010-02-05
In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.
Study on sampling of continuous linear system based on generalized Fourier transform
Li, Huiguang
2003-09-01
In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.
Reduction and coding of synthetic aperture radar data with Fourier transforms
Tilley, David G.
1995-01-01
Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.
Goodman, Roe W
2016-01-01
This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
Hébert, Philippe-Jean; Cansot, E.; Pierangelo, C.; Buil, C.; Bernard, F.; Loesel, J.; Trémas, T.; Perrin, L.; Courau, E.; Casteras, C.; Maussang, I.; Simeoni, D.
2017-11-01
The SIFTI (Static Infrared Fourier Transform Interferometer) instrument aims at supporting an important part in a mission for atmospheric pollution sounding from space, by providing high spectral resolution and high Signal to Noise Ratio spectra of the atmosphere. They will allow to resolve tropospheric profiles of ozone (03) and carbon monoxide (C0), especially down to the planetary boundary layer (PBL), an altitude region of very high interest, though poorly monitored to date, for air quality and pollution monitoring. The retrieved profile of ozone, resp. C0, will contain 5 to 7, resp. 2.5 to 4, independent pieces of information. The French space agency CNES (Centre National d'Etudes Spatiales) has proposed and is studying an instrument concept for SIFTI based on a static interferometer, where the needed optical path are generated by a pair of crossed staircase fixed mirrors (replacing the moving reflector of dynamic Fourier transform interferometers like IASI or MIPAS). With the SIFTI design, a very high spectral resolution ( 0.1 cm-1 apodised) is achieved in a very compact optical setup, allowing a large throughput, hence a high SNR. The measurements are performed in the 9.5 μm band for 03 and in the 4.6 μm band for C0. The science return of the sounder can be further increased if an "intelligent pointing" process is implemented. This consists in combining the TIR sounder with a companion TIR imager, providing information on the cloud coverage in the next observed scene. 0nboard, real-time analysis of the IR image is used to command the sounder staring mirror to cloud free areas, which will maximize the probability for probing down to the surface. After the first part of the phase A, the architecture of SIFTI was studied as a trade-off between performance and resource budget. We review the main architecture and functional choices, and their advantages. The preliminary instrument concept is then presented in its main aspects and in terms of main subsystem
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.
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.
Design of an optical spatial interferometer with transformation optics
International Nuclear Information System (INIS)
Naghibi, Atefeh; Shokooh-Saremi, Mehrdad
2015-01-01
In this paper, we apply transformation optics to design an optical spatial interferometer. The transformation equations are described and two-dimensional finite element simulations are presented to numerically confirm the functionality of the device. It is shown that a small change in the refractive index can alter the interference pattern and hence can be detected. The design of the interferometer could expand transformation optics’ applications and make way for introduction of new structures with unique electromagnetic or optical functionalities. (paper)
Directory of Open Access Journals (Sweden)
Sarunya Kanjanawattana
2017-07-01
Full Text Available Image classification plays a vital role in many areas of study, such as data mining and image processing; however, serious problems collectively referred to as the course of dimensionality have been encountered in previous studies as factors that reduce system performance. Furthermore, we also confront the problem of different graph characteristics even if graphs belong to same types. In this study, we propose a novel method of graph-type classification. Using our approach, we open up a new solution of high-dimensional images and address problems of different characteristics by converting graph images to one dimension with a discrete Fourier transformation and creating numeric datasets using wavelet and Hough transformations. Moreover, we introduce a new classifier, which is a combination between artificial neuron networks (ANNs and support vector machines (SVMs, which we call ANNSVM, to enhance accuracy. The objectives of our study are to propose an effective graph-type classification method that includes finding a new data representative used for classification instead of two-dimensional images and to investigate what features make our data separable. To evaluate the method of our study, we conducted five experiments with different methods and datasets. The input dataset we focused on was a numeric dataset containing wavelet coefficients and outputs of a Hough transformation. From our experimental results, we observed that the highest accuracy was provided using our method with Coiflet 1, which achieved a 0.91 accuracy.
The Fourier transform as a signature for chaos in nuclear energy levels
International Nuclear Information System (INIS)
Bybee, C.R.; Mitchell, G.E.; Shriner, J.F. Jr.
1996-01-01
The Fourier transform of the autocorrelation function is an alternative test to characterize level statistics. For GOE statistics there is a suppression of the Fourier transform near the origin; this correlation hole is absent for Poisson statistics. Numerical modeling has been used to quantify the method and determine the dependence of the correlation-hole area on number, density, sampling interval, and fraction of missing or spurious levels. For large N the normalized correlation-hole area is a nearly universal constant and insensitive to missing and spurious levels. However, for the smaller sample sizes typical of nuclear data, application of the FT method yields ambiguous results. (orig.)
Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.
Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun
2009-05-01
Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.
Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation
International Nuclear Information System (INIS)
Aldea, N; Pintea, S; Rednic, V; Matei, F; Hu Tiandou; Xie Yaning
2009-01-01
The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe 3 O 4 core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.
Physiological response of Arundo donax to cadmium stress by Fourier transform infrared spectroscopy.
Yu, Shunhui; Sheng, Li; Zhang, Chunyan; Deng, Hongping
2018-06-05
The present paper deals with the physiological response of the changes in chemical contents of the root, stem and leaf of Arundo donax seedlings stressed by excess cadmium using Fourier transform infrared spectroscopy technique, cadmium accumulation in plant by atomic absorption spectroscopy were tested after different concentrations cadmium stress. The results showed that low cadmium concentrations (Fourier transform infrared spectroscopy technique for the non-invasive and rapid monitoring of the plants stressed with heavy metals, Arundo donax is suitable for phytoremediation of cadmium -contaminated wetland. Copyright © 2018 Elsevier B.V. All rights reserved.
The Fourier transform as a signature for chaos in nuclear energy levels
Energy Technology Data Exchange (ETDEWEB)
Bybee, C.R. [North Carolina State Univ., Raleigh, NC (United States)]|[Triangle Universities Nuclear Lab., Durham, NC (United States); Mitchell, G.E. [North Carolina State Univ., Raleigh, NC (United States)]|[Triangle Universities Nuclear Lab., Durham, NC (United States); Shriner, J.F. Jr. [Tennessee Technological Univ., Cookeville (United States)
1996-08-01
The Fourier transform of the autocorrelation function is an alternative test to characterize level statistics. For GOE statistics there is a suppression of the Fourier transform near the origin; this correlation hole is absent for Poisson statistics. Numerical modeling has been used to quantify the method and determine the dependence of the correlation-hole area on number, density, sampling interval, and fraction of missing or spurious levels. For large N the normalized correlation-hole area is a nearly universal constant and insensitive to missing and spurious levels. However, for the smaller sample sizes typical of nuclear data, application of the FT method yields ambiguous results. (orig.)
International Nuclear Information System (INIS)
Chen Wenhao; Chen Min; Xiao Tiqiao
2011-01-01
Effects of the incident angle offset on FT-IR spectra are investigated in this paper. The simulated FT-IR spectra are obtained by Fourier inverse transform. The results show that this frequency shift varies with the angle offset of the incident beam in FT-IR. As an example,the factors that affect the angle of incident IR light at SSRF are analyzed. According to performance specifications of the IR beamline, requirements of the optical component installation precision and position drift of the light source are given. (authors)
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.
National Research Council Canada - National Science Library
Graham, James R; Abrams, Mark; Bennett, C; Carr, J; Cook, K; Dey, A; Najita, J; Wishnow, E
1998-01-01
.... We consider the relationship between pixel size, spectral resolution, and diameter of the beam splitter for imaging and nonimaging Fourier transform spectrographs and give the condition required...
National Aeronautics and Space Administration — Fourier transform spectroscopy (FTS) in infrared wavelength range is an effective measure for global greenhouse gas monitoring. However, conventional FTS instruments...
Application of the fourier and wavelet transforms in noise reduction of the out of the ordinary data
International Nuclear Information System (INIS)
Tafreshi, M. A.; Sadeghi, Y.
2006-01-01
In this article the noise reduction of the experimental data by the Fourier and the wavelet transforms has been investigated. Using both simulated and experimental data (from the plasma focus facility, Dena), the sensitive features of the application of the Fourier transform are visualized and discussed. Then, the main idea of the wavelet transform and the results of the noise reduction with this transform are presented. Due to this investigation, for the cases such as the current derivative of the Dena facility, where the reliability of the Fourier transform can be doubtful, the wavelet transform can be considered as a more accurate alternative approach
International Nuclear Information System (INIS)
Ito, Satoshi; Kawawa, Yasuhiro; Yamada, Yoshifumi
2010-01-01
We propose an image reconstruction technique in which parallel image reconstruction is performed based on the sensitivity encoding (SENSE) algorithm using only a single set of signals. The signal obtained in the phase-scrambling Fourier transform (PSFT) imaging technique can be transformed to the signal described by the Fresnel transform of the objects, which is known as the diffracted wave-front equation of the object in acoustics or optics. Since the Fresnel transform is a convolution integral on the object space, the space where the PSFT signal exists can be considered as both in the Fourier domain and in the object domain. This notable feature indicates that weighting functions corresponding to the sensitivity of radiofrequency (RF) coils can be approximately given in the PSFT signal space. Therefore, we can obtain two folded images from a single set of signals with different weighting functions, and image reconstruction based on the SENSE parallel imaging algorithm is possible using a series of folded images. Simulation and experimental studies showed that almost alias-free images can be synthesized using a single signal that does not satisfy the sampling theorem. (author)
S-duality as Fourier transform for arbitrary ϵ1, ϵ2
International Nuclear Information System (INIS)
N Nemkov
2014-01-01
The Alday–Gaiotto–Tachikawa relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that, for the four-point conformal block, the modular transform up to the non-perturbative contributions can be written in the form of the ordinary Fourier transform when β ≡ −ϵ 1 /ϵ 2 = 1. Here I extend this conjecture to general values of ϵ 1 , ϵ 2 . Namely, I argue that, for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters ϵ 1 , ϵ 2 . The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant g 2 ≡ −ϵ 1 ϵ 2 and hypermultiplet masses. (paper)
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
UV Fourier transform measurements of tropospheric O3, NO2, SO2, benzene, and toluene
International Nuclear Information System (INIS)
Vandaele, A.C.; Tsouli, A.; Carleer, M.; Colin, R.
2002-01-01
Using the differential optical absorption spectroscopy (DOAS) technique and a Fourier transform spectrometer, NO 2 , SO 2 , O 3 , benzene, and toluene were measured during three measurement campaigns held in Brussels in 1995, 1996, and 1997. The O 3 concentrations could be explained as the results of the local photochemistry and the dynamical properties of the mixing layer. NO 2 concentrations were anti-correlated to the O 3 concentrations, is expected. SO 2 also showed a pronounced dependence on car traffic. Average benzene and toluene concentrations were, respectively 1.7 ppb and between 4.4 and 6.6 pbb, but high values of toluene up to 98.8 ppb were observed. SO 2 concentrations and to a lesser extent, those of NO 2 and O 3 , were dependent on the wind direction. Ozone in Brussels has been found to be influenced by the meteorological conditions prevailing in central Europe. Comparisons with other measurements have shown that O 3 and SO 2 data are in general in good agreement, but our NO 2 concentrations seem to be generally higher. (author)
Detection of emission sources using passive-remote Fourier transform infrared spectroscopy
International Nuclear Information System (INIS)
Demirgian, J.C.; Macha, S.M.; Darby, S.M.; Ditillo, J.
1995-01-01
The detection and identification of toxic chemicals released in the environment is important for public safety. Passive-remote Fourier transform infrared (FTIR) spectrometers can be used to detect these releases. Their primary advantages are their small size and ease of setup and use. Open-path FTIR spectrometers are used to detect concentrations of pollutants from a fixed frame of reference. These instruments detect plumes, but they are too large and difficult to aim to be used to track a plume to its source. Passive remote FTIR spectrometers contain an interferometer, optics, and a detector. They can be used on tripods and in some cases can be hand-held. A telescope can be added to most units. We will discuss the capability of passive-remote FTIR spectrometers to detect the origin of plumes. Low concentration plumes were released using a custom-constructed vaporizer. These plumes were detected with different spectrometers from different distances. Passive-remote spectrometers were able to detect small 10 cm on a side chemical releases at concentration-pathlengths at the low parts per million-meter (ppm-m) level
Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy.
Liu, Yan-De; Ying, Yi-Bin; Fu, Xia-Ping
2005-03-01
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 apples were tested and 80 of them were used to form a calibration data set. The influences of different data preprocessing and spectra treatments were also quantified. Calibration models based on smoothing spectra were slightly worse than that based on derivative spectra, and the best result was obtained when the segment length was 5 nm and the gap size was 10 points. Depending on data preprocessing and PLS method, the best prediction model yielded correlation coefficient of determination (r2) of 0.759, low root mean square error of prediction (RMSEP) of 0.0677, low root mean square error of calibration (RMSEC) of 0.0562. The results indicated the feasibility of FT-NIR spectral analysis for predicting apple valid acidity in a nondestructive way.
Fourier Transform Infrared spectrum of the OCD bending mode in methanol-D1
Mukhopadhyay, Indra
2016-03-01
The infrared (IR) spectra corresponding to OCD bending vibration of asymmetrically deuterated methanol species CH2DOH have been recorded with a Fourier Transform Spectrometer. The spectrum shows a typical structure of a parallel a-type band. This is expected because the bending vibration mainly executed parallel to the symmetry axis The Q-branch lines are grouped closely around 896 cm-1 and the P- and R-Branches show complex structure. Nonetheless it was possible to assign a-type P- and R-branch lines up to K value of 8 and J value up to about 20 in most cases. The Q-branch lines for higher K values can be followed to about J = 15, the presence of which confirmed the assignments. The observations suggest that in the OCD bend some energy levels are highly interacted by highly excited torsional state from the ground torsional state. A full catalogue is presented along with the effective molecular parameters. An intensity anomaly was also observed in the transitions. So far it has been possible to assign only transitions between e0 ← e0 states. Plausible explanations of intensity anomaly are presented. Lastly, a number of optically pumped far infrared (FIR) laser lines have been assigned either to exact or tentative quantum states. These assignments should prove valuable for production of new FIR laser lines.
High-resolution magnetic-domain imaging by Fourier transform holography at 21 nm wavelength
International Nuclear Information System (INIS)
Schaffert, Stefan; Pfau, Bastian; Günther, Christian M; Schneider, Michael; Korff Schmising, Clemens von; Eisebitt, Stefan; Geilhufe, Jan
2013-01-01
Exploiting x-ray magnetic circular dichroism at the L-edges of 3d transition metals, Fourier transform holography has become a standard technique to investigate magnetic samples with sub-100 nm spatial resolution. Here, magnetic imaging in the 21 nm wavelength regime using M-edge circular dichroism is demonstrated. Ultrafast pulses in this wavelength regime are increasingly available from both laser- and accelerator-driven soft x-ray sources. We explain the adaptations concerning sample preparation and data evaluation compared to conventional holography in the 1 nm wavelength range. We find the correction of the Fourier transform hologram to in-plane Fourier components to be critical for high-quality reconstruction and demonstrate 70 nm spatial resolution in magnetization imaging with this approach. (paper)
Novel Polynomial Basis with Fast Fourier Transform and Its Application to Reed-Solomon Erasure Codes
Lin, Sian-Jheng
2016-09-13
In this paper, we present a fast Fourier transform (FFT) algorithm over extension binary fields, where the polynomial is represented in a non-standard basis. The proposed Fourier-like transform requires O(h lg(h)) field operations, where h is the number of evaluation points. Based on the proposed Fourier-like algorithm, we then develop the encoding/ decoding algorithms for (n = 2m; k) Reed-Solomon erasure codes. The proposed encoding/erasure decoding algorithm requires O(n lg(n)), in both additive and multiplicative complexities. As the complexity leading factor is small, the proposed algorithms are advantageous in practical applications. Finally, the approaches to convert the basis between the monomial basis and the new basis are proposed.
Vibrational analysis of Fourier transform spectrum of the B u )–X g ...
Indian Academy of Sciences (India)
improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and r-centroid values. Keywords. Fourier transform spectroscopy; electronic spectrum of selenium dimer; vibrational analysis; Franck–Condon factor; r-centroid values.
Vibrational analysis of Fourier transform spectrum of the B 3− u (0
Indian Academy of Sciences (India)
... microwave, was recorded on BOMEM DA8 Fourier transform spectrometer at an apodized resolution of 0.035 cm-1. Vibrational constants were improved by putting the wave number of band origins in Deslandre table. The vibrational analysis was supported by determining the Franck–Condon factor and -centroid values.
PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY
Open-path Fourier transform infrared (OP-FT1R) spectroscopy is an accepted technology for measuring gaseous air contaminants. OP-FT1R absorbance spectra acquired during changing aerosols conditions reveal related changes in very broad baseline features. Usually, this shearing of ...
Fourier-transform ghost imaging with pure far-field correlated thermal light
International Nuclear Information System (INIS)
Liu Honglin; Shen Xia; Han Shensheng; Zhu Daming
2007-01-01
Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed
International Nuclear Information System (INIS)
Luederwald, I.
1977-01-01
Instrumentation and technology of Ion-Cyclotron-Resonance and Fourier-Transform-Ion-Cyclotron-Resonance Spectroscopy are described. The method can be applied to studies of ion/molecule reactions in gas phase, to obtain thermodynamic data as gas phase acidity or basicity, proton and electron affinity, and to establish reaction mechanisms and ion structures. (orig.) [de
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.
Applications of Fourier transform infrared spectroscopy to quality control of the epoxy matrix
Antoon, M. K.; Starkey, K. M.; Koenig, J. L.
1979-01-01
The object of the paper is to demonstrate the utility of Fourier transform infrared (FT-IR) difference spectra for investigating the composition of a neat epoxy resin, hardener, and catalysts. The composition and degree of cross-linking of the cured matrix is also considered.
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)
Directory of Open Access Journals (Sweden)
Fedotov A.
2017-02-01
Full Text Available The article proposes a method of mathematical simulation of electrical machines with thyristor exciters on the basis of the local Fourier transform. The present research demonstrates that this method allows switching from a variable structure model to a constant structure model. Transition from the continuous variables to the discrete variables is used. The numerical example is given in the paper.
Czech Academy of Sciences Publication Activity Database
Pivokonský, Radek; Filip, Petr; Zelenková, Jana
2016-01-01
Roč. 104, č. 8 (2016), s. 171-178 ISSN 0032-3861 Institutional support: RVO:67985874 Keywords : LAOS * fourier transform rheology * Giesekus model * PTT model * modified XPP model * poly(ethylene oxide) Subject RIV: BK - Fluid Dynamics Impact factor: 3.684, year: 2016
Fourier transform infrared emission spectra of atomic rubidium: g- and h-states
Czech Academy of Sciences Publication Activity Database
Civiš, Svatopluk; Ferus, Martin; Kubelík, Petr; Chernov, Vladislav E.; Zanozina, Ekaterina M.
2012-01-01
Roč. 45, č. 17 (2012), s. 175002 ISSN 0953-4075 R&D Projects: GA AV ČR IAAX00100903 Institutional support: RVO:61388955 Keywords : Fourier transform infrared emission spectra * atomic rubidium * physical chemistry Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.031, year: 2012
Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...
Soil science research is increasingly applying Fourier transform infrared (FTIR) spectroscopy for analysis of soil organic matter (SOM). However, the compositional complexity of soils and the dominance of the mineral component can limit spectroscopic resolution of SOM and other minor components. The...
On the Elliptic Nonabelian Fourier Transform for Unipotent Representations of p-Adic Groups
Ciubotaru, D.; Opdam, E.; Cogdell, J.; Kim, J.-L.; Zhu, C.-B.
2017-01-01
In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these
Fourier transform and the Verlinde formula for the quantum double of a finite group
Koornwinder, T.H.; Schroers, B.J.; Slingerland, J.K.; Bais, F.A.
1999-01-01
We define a Fourier transform $S$ for the quantum double $D(G)$ of a finite group $G$. Acting on characters of $D(G)$, $S$ and the central ribbon element of $D(G)$ generate a unitary matrix representation of the group $SL(2,Z)$. The characters form a ring over the integers under both the algebra
Nicolas, F.; Coëtmellec, S.; Brunel, M.; Allano, D.; Lebrun, D.; Janssen, A.J.E.M.
2005-01-01
The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by
Bronneberg, A. C.; Smets, A. H. M.; Creatore, M.; M. C. M. van de Sanden,
2011-01-01
Insight into the oxidation mechanism of microcrystalline silicon thin films has been obtained by means of Fourier transform infrared spectroscopy. The films were deposited by using the expanding thermal plasma and their oxidation upon air exposure was followed in time. Transmission spectra were
Superexponentially damped Vlasov plasma oscillations in the Fourier transformed velocity space
International Nuclear Information System (INIS)
Sedlacek, Z.; Nocera, L.
2002-01-01
The Landau (exponentially) damped solutions of the Vlasov-Poisson equation Fourier transformed with respect to velocity are genuine eigenmodes corresponding to complex eigenvalues. In addition there exist solutions decaying faster than exponentially which exhibit no oscillatory behaviour. A new characterization is given of the initial conditions that give rise to these solutions together with a numerical demonstration
Specification of the Fast Fourier Transform algorithm as a term rewriting system
Rodenburg, P.H.; Hoekzema, D.J.
1987-01-01
We specify an algorithm for multiplying polynomials with complex coefficients incorporating, the Fast Fourier Transform algorithm of Cooley and Tukey [CT]. The specification formalism we use is a variant of the formalism ASF described in. [BHK]. The difference with ASF is essentially a matter of
Bastiaans, M.J.; Alieva, T.
2002-01-01
It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. This general input-output relationship is then broken down into a
A fast Fourier transform program for the deconvolution of IN10 data
International Nuclear Information System (INIS)
Howells, W.S.
1981-04-01
A deconvolution program based on the Fast Fourier Transform technique is described and some examples are presented to help users run the programs and interpret the results. Instructions are given for running the program on the RAL IBM 360/195 computer. (author)
Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.
Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing
2016-10-01
The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.
3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography
Michael C. Martin; Charlotte Dabat-Blondeau; Miriam Unger; Julia Sedlmair; Dilworth Y. Parkinson; Hans A. Bechtel; Barbara Illman; Jonathan M. Castro; Marco Keiluweit; David Buschke; Brenda Ogle; Michael J. Nasse; Carol J. Hirschmugl
2013-01-01
We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical...
On the measurement of Wigner distribution moments in the fractional Fourier transform domain
Bastiaans, M.J.; Alieva, T.
2002-01-01
It is shown how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of fractional Fourier transform systems (generally anamorphic ones). The minimum number of (anamorphic) fractional power spectra that are needed
Fourier-transform imaging of cotton and botanical and field trash mixtures
Botanical and field cotton trash comingled with cotton lint can greatly reduce the marketability and quality of cotton. Trash can be found comingled with cotton lint during harvesting, ginning, and processing, thus this study is of interest. Attenuated Total Reflectance-Fourier Transform Infrared (A...
DEFF Research Database (Denmark)
Uceda Otero, E. P.; Eliel, G. S. N.; Fonseca, E. J. S.
2013-01-01
In this work we have used Fourier transform infrared (FTIR) / vibrational absorption (VA) spectroscopy to study two cancer cell lines: the Henrietta Lacks (HeLa) human cervix carcinoma and 5637 human bladder carcinoma cell lines. Our goal is to experimentally investigate biochemical changes...
Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform
Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos
2010-01-01
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…
Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere
International Nuclear Information System (INIS)
Sabbah, C
2004-01-01
It is shown that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies a polarizable regular twistor D-module if one considers only the part at finite distance. The associated holomorphic bundle defined away from the origin of the complex plane is therefore equipped with a natural harmonic metric having a tame behaviour near the origin
Prospects for the design of an ultraviolet imaging Fourier transform spectrometer
Lemaire, Philippe
2017-11-01
Recent results from solar observations in the far and extremeultraviolet (FUV/EUV) obtained from SOHO (SOlar and Heliospheric Observatory) and TRACE (Transition Region Camera) show the extreme variability of the solar atmosphere. Within the limited resolution of the instruments (1-2 arcseconds) horizontal and vertical velocities up-to 100 to 400 km s-1 have been measured. With an horizontal velocity of 100 km s-1 an one arsecond structure crosses the one arcsecond slit width of a classical slit spectrometer in less than 10 seconds. In the future, with higher angular resolution (e.g. 0.1 arcsecond), the capability to study small structures will be greatly reduced by a classical slit spectrometer. To be able to characterize the small scale solar atmospheric structures formed in the 104 K to 106 K temperature range (which emit in the 30 to 180 nm wavelength range) a spectrometer without slit (or with wide slit) is required. At the same time to obtain an accurate measurement of the doppler velocity an high spectral resolution is needed. The two requirements, high spectral resolution and large slit, are difficult to be simultaneously fulfilled with a classical slit spectrometer within the limited volume of a space instrumentation. Also, we propose to use an Imaging Fourier Transform Spectrometer (IFTS) to provide simultaneously a bidimensionnal field and an accurate determination of line profiles and positions. The development of Fourier Transform Spectrometers (FTS), although popular in the infrared, has been very limited in the UV/FUV by the lack of very high quality beam splitter. Since 10 years, the use of diffraction gratings as beam splitters has been suggested and few intruments have been built ([Chak 94]; [Clea 92]; [File 00]). These instruments illustrate some applications in the new wavelength domain opened by using a beam splitter grating, but do not yet provide the full capabilities of an FTS. In this paper we present several optical schemes which can
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
Study of dilution of Spin-On Glass by Fourier transform infrared spectroscopy
International Nuclear Information System (INIS)
Dominguez, Miguel; Rosales, Pedro; Torres, Alfonso; Moreno, Mario; Orduña, Abdu
2012-01-01
In this work, we study the dilution of Spin-On Glass (SOG) in order to obtain high quality SiO 2 films at 200 °C, with optical and electrical characteristics similar to those of the thermally grown SiO 2 . For the production of SiO 2 films we used 2-propanol and deionized water (DI) as diluents for the SOG and we compared the electrical and optical film properties with those of the films obtained from undiluted SOG. From Fourier transform infrared spectroscopy we observed a considerable reduction of Si-OH (920 cm −1 ), O-H (3490 cm −1 ) and C-H, C-O bonds (1139 cm −1 ) in the films produced from SOG diluted with DI. Besides the above, the insulator breakdown field was approximately 21 MV/cm, the refractive index and the dielectric constant were close to those of the thermally grown SiO 2 . Our results suggest that the film produced from SOG diluted with DI and cured at 200 °C is an excellent candidate to be used as insulator on flexible and large-area electronics. - Highlights: ► Preparation of high quality silicon oxide (SiO 2 ) films at 200 °C. ► Dilution of Spin-On Glass (SOG) solution was studied. ► Dilution of SOG is necessary to obtain high quality films annealed at 200 °C. ► n and k are close to those of the thermally grown SiO 2 .
Study of dilution of Spin-On Glass by Fourier transform infrared spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Dominguez, Miguel, E-mail: mdominguez@inaoep.mx [National Institute for Astrophysics, Optics and Electronics (INAOE), Electronics Department, Luis Enrique Erro No. 1, Puebla 72840 (Mexico); Rosales, Pedro; Torres, Alfonso; Moreno, Mario [National Institute for Astrophysics, Optics and Electronics (INAOE), Electronics Department, Luis Enrique Erro No. 1, Puebla 72840 (Mexico); Orduna, Abdu [CIBA-Tlaxcala, Instituto Politecnico Nacional, Tepetitla, Tlax. 90700 (Mexico)
2012-05-31
In this work, we study the dilution of Spin-On Glass (SOG) in order to obtain high quality SiO{sub 2} films at 200 Degree-Sign C, with optical and electrical characteristics similar to those of the thermally grown SiO{sub 2}. For the production of SiO{sub 2} films we used 2-propanol and deionized water (DI) as diluents for the SOG and we compared the electrical and optical film properties with those of the films obtained from undiluted SOG. From Fourier transform infrared spectroscopy we observed a considerable reduction of Si-OH (920 cm{sup -1}), O-H (3490 cm{sup -1}) and C-H, C-O bonds (1139 cm{sup -1}) in the films produced from SOG diluted with DI. Besides the above, the insulator breakdown field was approximately 21 MV/cm, the refractive index and the dielectric constant were close to those of the thermally grown SiO{sub 2}. Our results suggest that the film produced from SOG diluted with DI and cured at 200 Degree-Sign C is an excellent candidate to be used as insulator on flexible and large-area electronics. - Highlights: Black-Right-Pointing-Pointer Preparation of high quality silicon oxide (SiO{sub 2}) films at 200 Degree-Sign C. Black-Right-Pointing-Pointer Dilution of Spin-On Glass (SOG) solution was studied. Black-Right-Pointing-Pointer Dilution of SOG is necessary to obtain high quality films annealed at 200 Degree-Sign C. Black-Right-Pointing-Pointer n and k are close to those of the thermally grown SiO{sub 2}.
CIRS-lite, a Fourier Transform Spectrometer for Low-Cost Planetary Missions
Brasunas, J.; Bly, V.; Edgerton, M.; Gong, Q.; Hagopian, J.; Mamakos, W.; Morelli, A.; Pasquale, B.; Strojny, C.
2011-01-01
Passive spectroscopic remote sensing of planetary atmospheres and surfaces in the thermal infrared is a powerful tool for obtaining information about surface and atmospheric temperatures, composition, and dynamics (via the thermal wind equation). Due to its broad spectral coverage, the Fourier transform spectrometer (FTS) is particularly suited to the exploration and discovery of molecular species. NASA's Goddard Space Flight Center (GSFC) developed the CIRS (Composite Infrared Spectrometer) FTS for the NASA/ESA Cassini mission to the Saturnian system. CIRS observes Saturn, Titan, icy moons such as Enceladus, and the rings in thermal self-emission over the spectral range of 7 to 1000 ell11. CIRS has given us important new insights into stratospheric composition and jets on Jupiter and Saturn, the cryo-geyser and thermal stripes on Enceladus, and the winter polar vortex on Titan. CIRS has a mass of 43 kg, contrasted with the earlier GSFC FTS, pre-Voyager IRIS (14 kg). Future low-cost planetary missions will have very tight constraints on science payload mass, thus we must endeavor to return to IRIS-level mass while maintaining CIRS-level science capabilities ("do more with less"). CIRS-lite achieves this by pursuing: a) more sensitive infrared detectors (high Tc superconductor) to enable smaller optics. b) changed long wavelength limit from 1000 to 300 microns to reduce diffraction by smaller optics. c) CVD (chemical vapor deposition) diamond beam-splitter for broad spectral coverage. d) single FTS architecture instead of a dual FTS architecture. e) novel materials, such as single crystal silicon for the input telescope primary.
Intelligent Controller for a Compact Wide-Band Compositional Infrared Fourier Transform Spectrometer
Yiu, P.; Keymeulen, D.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.
2013-12-01
typically achieve very high wavelength resolution, the intended application of our instrument (spectroscopic investigation of Europa's surface) places higher emphasis on the greater wavelength band sensitivity in the 2-12 μm range provided by a rotating refractor design. The instrument's embedded microcontroller is implemented on a flight-qualified VIRTEX-5 FPGA with the aim of sampling the instrument's detector and optical rotary encoder in order to construct an interferogram. Subsequent signal processing, including a Fast Fourier Transform (FFT), noise reduction/averaging, and spectral calibration techniques are applied in real-time to compose the sample spectrum. Deployment of an FPGA eliminates the instrument's need to share computing resources with the main spacecraft computer and takes advantage of the low power consumption and high-throughput hardware parallelism intrinsic to FPGA applications. This parallelism facilitates the high speed, low latency sampling/signal processing critical to instrument precision with minimal power consumption to achieve highly sensitive spectra within the constraints of available spacecraft resources. The instrument is characterized in simulated space-flight conditions and we demonstrate that this technology is capable of meeting the strict volume, sensitivity, and power consumption requirements for implementation in scientific space systems.
Directory of Open Access Journals (Sweden)
A. Kleinert
2014-12-01
Full Text Available The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA is an imaging Fourier transform spectrometer that is capable of operating on various high-altitude research aircraft. It measures the atmospheric emission in the thermal infrared spectral region in limb and nadir geometry. GLORIA consists of a classical Michelson interferometer combined with an infrared camera. The infrared detector has a usable area of 128 × 128 pixels, measuring up to 16 384 interferograms simultaneously. Imaging Fourier transform spectrometers impose a number of challenges with respect to instrument calibration and algorithm development. The optical setup with extremely high optical throughput requires the development of new methods and algorithms for spectral and radiometric calibration. Due to the vast amount of data there is a high demand for scientifically intelligent optimisation of the data processing. This paper outlines the characterisation and processing steps required for the generation of radiometrically and spectrally calibrated spectra. Methods for performance optimisation of the processing algorithm are presented. The performance of the data processing and the quality of the calibrated spectra are demonstrated for measurements collected during the first deployments of GLORIA on aircraft.
The Fractional Fourier Transform and Its Application to Energy Localization Problems
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ter Morsche Hennie G
2003-01-01
Full Text Available Applying the fractional Fourier transform (FRFT and the Wigner distribution on a signal in a cascade fashion is equivalent to a rotation of the time and frequency parameters of the Wigner distribution. We presented in ter Morsche and Oonincx, 2002, an integral representation formula that yields affine transformations on the spatial and frequency parameters of the -dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. In this paper, we show how this representation formula can be used to solve certain energy localization problems in phase space. Examples of such problems are given by means of some classical results. Although the results on localization problems are classical, the application of generalized Fourier transform enlarges the class of problems that can be solved with traditional techniques.
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
Application of the fractional Fourier transform to image reconstruction in MRI.
Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo
2012-07-01
The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.
Reverse ray tracing for transformation optics.
Hu, Chia-Yu; Lin, Chun-Hung
2015-06-29
Ray tracing is an important technique for predicting optical system performance. In the field of transformation optics, the Hamiltonian equations of motion for ray tracing are well known. The numerical solutions to the Hamiltonian equations of motion are affected by the complexities of the inhomogeneous and anisotropic indices of the optical device. Based on our knowledge, no previous work has been conducted on ray tracing for transformation optics with extreme inhomogeneity and anisotropicity. In this study, we present the use of 3D reverse ray tracing in transformation optics. The reverse ray tracing is derived from Fermat's principle based on a sweeping method instead of finding the full solution to ordinary differential equations. The sweeping method is employed to obtain the eikonal function. The wave vectors are then obtained from the gradient of that eikonal function map in the transformed space to acquire the illuminance. Because only the rays in the points of interest have to be traced, the reverse ray tracing provides an efficient approach to investigate the illuminance of a system. This approach is useful in any form of transformation optics where the material property tensor is a symmetric positive definite matrix. The performance and analysis of three transformation optics with inhomogeneous and anisotropic indices are explored. The ray trajectories and illuminances in these demonstration cases are successfully solved by the proposed reverse ray tracing method.
Watanabe, A.; Furukawa, H.
2018-04-01
The resolution of multichannel Fourier transform (McFT) spectroscopy is insufficient for many applications despite its extreme advantage of high throughput. We propose an improved configuration to realise both performance using a two-dimensional area sensor. For the spectral resolution, we obtained the interferogram of a larger optical path difference by shifting the area sensor without altering any optical components. The non-linear phase error of the interferometer was successfully corrected using a phase-compensation calculation. Warping compensation was also applied to realise a higher throughput to accumulate the signal between vertical pixels. Our approach significantly improved the resolution and signal-to-noise ratio by factors of 1.7 and 34, respectively. This high-resolution and high-sensitivity McFT spectrometer will be useful for detecting weak light signals such as those in non-invasive diagnosis.
DEFF Research Database (Denmark)
Mogensen, Klaus Bo; Kwok, Y.C.; Eijkel, J.C.T.
2003-01-01
A microfabricated capillary electrophoresis device for velocity measurements of flowing particles is presented. It consists of a 1 x 128 planar waveguide beam splitter monolithically integrated with an electrically insulated fluidic channel network for fluorescence excitation at multiple points...... optics. The integrated planar waveguide beam splitter was, furthermore, permanently connected to the light source by a glued-on optical fiber, to achieve a robust and alignment-free operation of the system. The velocity was measured using a Fourier transformation with a Shah function, since the response...... of the fight array was designed to approximate a square profile. Deviations from this response were observed as a result of the multimode nature of the integrated waveguides....
Transformation optics on a silicon platform
International Nuclear Information System (INIS)
Gabrielli, Lucas H; Lipson, Michal
2011-01-01
Transformation optics allows the creation of innovative devices; however, its implementation in the optical domain remains challenging. We describe here our process to design and fabricate such devices using silicon as a platform for broad band operation in the optical domain. We discuss the approximations and methods employed to overcome the challenges of using dielectric materials as a platform for transformation optics, such as the anisotropy and gradient refractive index implementation. These encompass conformal and quasi-conformal mappings, and a dithering process to discretize and quantize the continuously inhomogeneous index function. We show examples of devices that we fabricated and tested, including the carpet invisibility cloak, a broad bandwidth light concentrator, and a perfect imaging device, known as Maxwell's fish eye lens. Finally, we touch on future directions under investigation to further develop transformation optics based on dielectric materials
Analysis of gamma-ray spectra by using fast Fourier transform
International Nuclear Information System (INIS)
Tominaga, Shoji; Nagata, Shojiro; Nayatani, Yoshinobu; Ueda, Isamu; Sasaki, Satoshi.
1977-01-01
In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform devised. The validity of the method was confirmed by a computer simulation for spectra of a NaI detector. The method uses the fact that spectral data can be represented by Fourier series with reduced number of terms. The estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features in the method and a general problem to be solved in a response matrix method are described. (auth.)
Use of fast Fourier transform in gamma-ray spectral analysis
International Nuclear Information System (INIS)
Tominaga, Shoji; Nayatani, Yoshinobu; Nagata, Shojiro; Sasaki, Takashi; Ueda, Isamu.
1978-01-01
In order to simplify the mass data processing in a response matrix method for γ-ray spectral analysis, a method using a Fast Fourier Transform has been devised. The validity of the method has been confirmed by computer simulation for spectra of a NaI detector. First, it is shown that spectral data can be represented by Fourier series with a reduced number of terms. Then the estimation of intensities of γ-ray components is performed by a matrix operation using the compressed data of an observation spectrum and standard spectra in Fourier coefficients. The identification of γ-ray energies is also easy. Several features of the method and a general problem to be solved in relation to a response matrix method are described. (author)
Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan
2016-01-01
Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.
Coulomb Fourier transformation: A novel approach to three-body scattering with charged particles
International Nuclear Information System (INIS)
Alt, E.O.; Levin, S.B.; Yakovlev, S.L.
2004-01-01
A unitary transformation of the three-body Hamiltonian which describes a system of two charged and one neutral particles is constructed such that the Coulomb potential which acts between the charged particles is explicitly eliminated. The transformed Hamiltonian and, in particular, the transformed short-range pair interactions are worked out in detail. Thereby it is found that, after transformation, the short-range potentials acting between the neutral and either one of the charged particles become simply Fourier transformed but, in addition, multiplied by a function that represents the Coulombic three-body correlations originating from the action of the other charged particle on the considered pair. This function which is universal as it does not depend on any property of the short-range interaction is evaluated explicitly and its singularity structure is described in detail. In contrast, the short-range potential between the charged particles remains of two-body type but occurs now in the 'Coulomb representation'. Specific applications to Yukawa and Gaussian potentials are given. Since the Coulomb-Fourier-transformed Hamiltonian does no longer contain the Coulomb potential or any other effective interaction of long range, standard methods of short-range few-body scattering theory are applicable
Directory of Open Access Journals (Sweden)
Eduardo O. Cerqueira
2000-10-01
Full Text Available Instrumental data always present some noise. The analytical data information and instrumental noise generally has different frequencies. Thus is possible to remove the noise using a digital filter based on Fourier transform and inverse Fourier transform. This procedure enhance the signal/noise ratio and consecutively increase the detection limits on instrumental analysis. The basic principle of Fourier transform filter with modifications implemented to improve its performance is presented. A numerical example, as well as a real voltammetric example are showed to demonstrate the Fourier transform filter implementation. The programs to perform the Fourier transform filter, in Matlab and Visual Basic languages, are included as appendices
A Fourier transform infrared trace gas and isotope analyser for atmospheric applications
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D. W. T. Griffith
2012-10-01
Full Text Available Concern in recent decades about human impacts on Earth's climate has led to the need for improved and expanded measurement capabilities of greenhouse gases in the atmosphere. In this paper we describe in detail an in situ trace gas analyser based on Fourier Transform Infrared (FTIR spectroscopy that is capable of simultaneous and continuous measurements of carbon dioxide (CO_{2}, methane (CH_{4}, carbon monoxide (CO, nitrous oxide (N_{2}O and ^{13}C in CO_{2} in air with high precision. High accuracy is established by reference to measurements of standard reference gases. Stable water isotopes can also be measured in undried airstreams. The analyser is automated and allows unattended operation with minimal operator intervention. Precision and accuracy meet and exceed the compatibility targets set by the World Meteorological Organisation – Global Atmosphere Watch for baseline measurements in the unpolluted troposphere for all species except ^{13}C in CO_{2}.
The analyser is mobile and well suited to fixed sites, tower measurements, mobile platforms and campaign-based measurements. The isotopic specificity of the optically-based technique and analysis allows its application in isotopic tracer experiments, for example in tracing variations of ^{13}C in CO_{2} and ^{15}N in N_{2}O. We review a number of applications illustrating use of the analyser in clean air monitoring, micrometeorological flux and tower measurements, mobile measurements on a train, and soil flux chamber measurements.
Cong, Lin-xiao; Huang, Min; Cai, Qi-sheng
2017-10-01
In this paper, a multi-line interferogram stitching method based on orthogonal shear using the Wollaston prism(WP) was proposed with a 2D projection interferogram recorded through the rotation of CCD, making the spectral resolution of Fourier-Transform spectrometer(FTS) of a limited spatial size increase by at least three times. The fringes on multi-lines were linked with the pixels of equal optical path difference (OPD). Ideally, the error of sampled phase within one pixel was less than half the wavelength, ensuring consecutive values in the over-sampled dimension while aliasing in another. In the simulation, with the calibration of 1.064μm, spectral lines at 1.31μm and 1.56μm of equal intensity were tested and observed. The result showed a bias of 0.13% at 1.31μm and 1.15% at 1.56μm in amplitude, and the FWHM at 1.31μm reduced from 25nm to 8nm after the sample points increased from 320 to 960. In the comparison of reflectance spectrum of carnauba wax within near infrared(NIR) band, the absorption peak at 1.2μm was more obvious and zoom of the band 1.38 1.43μm closer to the reference, although some fluctuation was in the short-wavelength region arousing the spectral crosstalk. In conclusion, with orthogonal shear based on the rotation of the CCD relative to the axis of WP, the spectral resolution of static FTS was enhanced by the projection of fringes to the grid coordinates and stitching the interferograms into a larger OPD, which showed the advantages of cost and miniaturization in the space-constrained NIR applications.
Dohe, S.; Sherlock, V.; Hase, F.; Gisi, M.; Robinson, J.; Sepúlveda, E.; Schneider, M.; Blumenstock, T.
2013-08-01
The Total Carbon Column Observing Network (TCCON) has been established to provide ground-based remote sensing measurements of the column-averaged dry air mole fractions (DMF) of key greenhouse gases. To ensure network-wide consistency, biases between Fourier transform spectrometers at different sites have to be well controlled. Errors in interferogram sampling can introduce significant biases in retrievals. In this study we investigate a two-step scheme to correct these errors. In the first step the laser sampling error (LSE) is estimated by determining the sampling shift which minimises the magnitude of the signal intensity in selected, fully absorbed regions of the solar spectrum. The LSE is estimated for every day with measurements which meet certain selection criteria to derive the site-specific time series of the LSEs. In the second step, this sequence of LSEs is used to resample all the interferograms acquired at the site, and hence correct the sampling errors. Measurements acquired at the Izaña and Lauder TCCON sites are used to demonstrate the method. At both sites the sampling error histories show changes in LSE due to instrument interventions (e.g. realignment). Estimated LSEs are in good agreement with sampling errors inferred from the ratio of primary and ghost spectral signatures in optically bandpass-limited tungsten lamp spectra acquired at Lauder. The original time series of Xair and XCO2 (XY: column-averaged DMF of the target gas Y) at both sites show discrepancies of 0.2-0.5% due to changes in the LSE associated with instrument interventions or changes in the measurement sample rate. After resampling, discrepancies are reduced to 0.1% or less at Lauder and 0.2% at Izaña. In the latter case, coincident changes in interferometer alignment may also have contributed to the residual difference. In the future the proposed method will be used to correct historical spectra at all TCCON sites.
Directory of Open Access Journals (Sweden)
S. Dohe
2013-08-01
Full Text Available The Total Carbon Column Observing Network (TCCON has been established to provide ground-based remote sensing measurements of the column-averaged dry air mole fractions (DMF of key greenhouse gases. To ensure network-wide consistency, biases between Fourier transform spectrometers at different sites have to be well controlled. Errors in interferogram sampling can introduce significant biases in retrievals. In this study we investigate a two-step scheme to correct these errors. In the first step the laser sampling error (LSE is estimated by determining the sampling shift which minimises the magnitude of the signal intensity in selected, fully absorbed regions of the solar spectrum. The LSE is estimated for every day with measurements which meet certain selection criteria to derive the site-specific time series of the LSEs. In the second step, this sequence of LSEs is used to resample all the interferograms acquired at the site, and hence correct the sampling errors. Measurements acquired at the Izaña and Lauder TCCON sites are used to demonstrate the method. At both sites the sampling error histories show changes in LSE due to instrument interventions (e.g. realignment. Estimated LSEs are in good agreement with sampling errors inferred from the ratio of primary and ghost spectral signatures in optically bandpass-limited tungsten lamp spectra acquired at Lauder. The original time series of Xair and XCO2 (XY: column-averaged DMF of the target gas Y at both sites show discrepancies of 0.2–0.5% due to changes in the LSE associated with instrument interventions or changes in the measurement sample rate. After resampling, discrepancies are reduced to 0.1% or less at Lauder and 0.2% at Izaña. In the latter case, coincident changes in interferometer alignment may also have contributed to the residual difference. In the future the proposed method will be used to correct historical spectra at all TCCON sites.