Bivariate raising and lowering differential operators for eigenfunctions of a 2D Fourier transform
We define a two-dimensional (2D) Fourier transform that self-reproduces a one-parameter family of bivariate Hermite functions; these are eigenfunctions of a Hamiltonian differential operator of second order, whose exponential is that transform. We find explicit forms of the bivariate raising and lowering partial differential operators of first degree for the eigenfunctions of this 2D Fourier transform. (paper)
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. PMID:26150988
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates
Edem Dovlo; Natalie Baddour
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 th...
Toolbox for the Computation of 2D Fourier Transforms in Polar Coordinates via Maple
Edem Dovlo
2015-02-01
Full Text Available The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. A toolbox of functions for the computation of two dimensional Fourier transforms in polar coordinates with symbolic computer algebra (Maple was developed. The implementation of the 2D Fourier transform in polar coordinates within the toolbox is a combination of two significantly simpler transforms. A modular approach is used along with the idea of lookup tables to help avoid the issue of indeterminate results when attempting to directly evaluate the transform. This concept helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.
Tensor representation of color images and fast 2D quaternion discrete Fourier transform
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, a general, efficient, split algorithm to compute the two-dimensional quaternion discrete Fourier transform (2-D QDFT), by using the special partitioning in the frequency domain, is introduced. The partition determines an effective transformation, or color image representation in the form of 1-D quaternion signals which allow for splitting the N × M-point 2-D QDFT into a set of 1-D QDFTs. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. In particular, a proposed method of calculating the 2r × 2r -point 2-D QDFT uses 18N2 less multiplications than the well-known column-row method and method of calculation based on the symplectic decomposition. The proposed algorithm is simple to apply and design, which makes it very practical in color image processing in the frequency domain.
Generalized Fourier transforms classes
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....
Popescu, Maria-Cristina, E-mail: cpopescu@icmpp.ro [' Petru Poni' Institute of Macromolecular Chemistry (Romania); Gomez, Rafael; Mata, Fco Javier de la; Rasines, Beatriz [Universidad de Alcala, Departamento de Quimica Inorganica (Spain); Simionescu, Bogdan C. [' Petru Poni' Institute of Macromolecular Chemistry (Romania)
2013-06-15
Fourier transform infrared spectroscopy and 2D correlation spectroscopy were used to study the microstructural changes occurring on heating of a new carbosilane dendrimer with peripheral ammonium groups. Temperature-dependent spectral variations in the 3,010-2,710, 1,530-1,170, and 1,170-625 cm{sup -1} regions were monitored during the heating process. The dependence, on temperature, of integral absorptions and position of spectral bands was established and the spectral modifications associated with molecular conformation rearrangements, allowing molecular shape changes, were found. Before 180 Degree-Sign C, the studied carbosilane dendrimer proved to be stable, while at higher temperatures it oxidizes and Si-O groups appear. 2D IR correlation spectroscopy gives new information about the effect of temperature on the structure and dynamics of the system. Synchronous and asynchronous spectra indicate that, at low temperature, conformational changes of CH{sub 3} and CH{sub 3}-N{sup +} groups take place first. With increasing temperature, the intensity variation of the CH{sub 2}, C-N, Si-C and C-C groups from the dendritic core is faster than that of the terminal units. This indicates that, with increasing temperature, the segments of the dendritic core obtain enough energy to change their conformation more easily as compared to the terminal units, due to their internal flexibility.
Fourier transformation for pedestrians
Butz, Tilman
2015-01-01
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
Fast complexified quaternion Fourier transform
Said, Salem; Bihan, Nicolas le; Sangwine, Stephen J.
2006-01-01
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex quaternion-valued. It is shown how to compute the transform using four standard complex Fourier transforms and the properties of the transform are briefly discussed.
Fourier transforms principles and applications
Hansen, Eric W
2014-01-01
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.
On the Replica Fourier Transform
Carlucci, D. M.; De Dominicis, C.
1997-01-01
The Replica Fourier Transform introduced previously is related to the standard definition of Fourier transforms over a group. Its use is illustrated by block-diagonalizing the eigenvalue equation of a four-replica Parisi matrix.
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
Wavelet-fractional Fourier transforms
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
Ultrafast Fourier-transform parallel processor
Greenberg, W.L.
1980-04-01
A new, flexible, parallel-processing architecture is developed for a high-speed, high-precision Fourier transform processor. The processor is intended for use in 2-D signal processing including spatial filtering, matched filtering and image reconstruction from projections.
2D Regimes of Non-Fourier Convection
Papanicolaou, N. C.
2010-11-01
In this work, we investigate the 2D flow in a rectangular cavity subject to both vertical and horizontal temperature gradients. The linearized model is studied and the effect of thermal relaxation, as described by the Maxwell-Cattaneo law of heat conduction is examined. To this end, a spectral numerical model is created based on a Galerkin expansion. The basis is the Cartesian product of systems of beam functions and trigonometric functions. The natural modes of the system are derived for both the Fourier and non-Fourier models. The results are compared to earlier works for the plain Fourier law. Our computations show that for the same set of parameters, the Maxwell-Cattaneo law yields modes which are quantitatively different from the Fourier. It is found that the real parts of the eigenvalues increase with the Straughan number Sg, which quantifies the non-Fourier effects. This confirms the destabilizing effect of the MC-law on the convective flow.
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Slice Fourier transform and convolutions
Cnudde, Lander; De Bie, Hendrik
2015-01-01
Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel function of this integral transform is constructed using the Mehler formula. An explicit expression for the integral transform is obtained and allows for the study of its properties. In the second part, two kinds of corresponding convolutions are examined:...
Applying Quaternion Fourier Transforms for Enhancing Color Images
M.I. Khalil
2012-03-01
Full Text Available The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.
A More Accurate Fourier Transform
Courtney, Elya
2015-01-01
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals (EI) that define Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric $\\mathrm{CO_2}$ concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT's FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability t...
Logarithm of the Discrete Fourier Transform
Michael Aristidou
2007-01-01
Full Text Available The discrete Fourier transform defines a unitary matrix operator. The logarithm of this operator is computed, along with the projection maps onto its eigenspaces. A geometric interpretation of the discrete Fourier transform is also given.
Logarithm of the Discrete Fourier Transform
Michael Aristidou; Jason Hanson
2007-01-01
The discrete Fourier transform defines a unitary matrix operator. The logarithm of this operator is computed, along with the projection maps onto its eigenspaces. A geometric interpretation of the discrete Fourier transform is also given.
Fourier transform of momentum distribution in vanadium
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.)
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.
Novel Micro Fourier Transform Spectrometers
KONG Yan-mei; LIANG Jing-qiu; LIANG Zhong-zhu; WANG-Bo; ZHANG Jun
2008-01-01
The miniaturization of spectrometer opens a new application area with real-time and on-site measurements. The Fourier transform spectrometer(FTS) is much attractive considering its particular advantages among the approaches. This paper reviews the current status of micro FTS in worldwide and describes its developments; In addition, analyzed are the key problems in designing and fabricating FTS to be settled during the miniaturization. Finally, a novel model of micro FTS with no moving parts is proposed and analyzed, which may provide new concepts for the design of spectrometers.
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.
Optical fourier transform image processor
The primary objective of this project is to improve the signal to noise ratio of the X-ray shadow graphs and tomographs of human body using optical spatial filtering techniques. Helium Neon laser of 4 milli Watt has been used for the purpose. Spatial filtering of the beam has been done in the first step to eliminate the coherent noise produced by various laser modes. Conventional method of spatial filtering has been used to process simple achieved using conventional filters. Edge enhancement and improvement of signal to noise ratio of the X-ray shadow graphs has been done using lens and lens-less Fourier transform holographic filters and VanderLugt filters. VanderLugt filter has given the best edge-enhancement for the chest X-ray shadow graph. (author)
Fourier Transforms of Finite Chirps
Fickus Matthew
2006-01-01
Full Text Available Chirps arise in many signal processing applications. While chirps have been extensively studied as functions over both the real line and the integers, less attention has been paid to the study of chirps over finite groups. We study the existence and properties of chirps over finite cyclic groups of integers. In particular, we introduce a new definition of a finite chirp which is slightly more general than those that have been previously used. We explicitly compute the discrete Fourier transforms of these chirps, yielding results that are number-theoretic in nature. As a consequence of these results, we determine the degree to which the elements of certain finite tight frames are well distributed.
2D Fourier series representation of gravitational functionals in spherical coordinates
Ghobadi-Far, Khosro; Sharifi, Mohammad Ali; Sneeuw, Nico
2016-05-01
2D Fourier series representation of a scalar field like gravitational potential is conventionally derived by making use of the Fourier series of the Legendre functions in the spherical harmonic representation. This representation has been employed so far only in the case of a scalar field or the functionals that are related to it through a radial derivative. This paper provides a unified scheme to represent any gravitational functional in terms of spherical coordinates using a 2D Fourier series representation. The 2D Fourier series representation for each individual point is derived by transforming the spherical harmonics from the geocentric Earth-fixed frame to a rotated frame so that its equator coincides with the local meridian plane of that point. In the obtained formulation, each functional is linked to the potential in the spectral domain using a spectral transfer. We provide the spectral transfers of the first-, second- and third-order gradients of the gravitational potential in the local north-oriented reference frame and also those of some functionals of frequent use in the physical geodesy. The obtained representation is verified numerically. Moreover, spherical harmonic analysis of anisotropic functionals and contribution analysis of the third-order gradient tensor are provided as two numerical examples to show the power of the formulation. In conclusion, the 2D Fourier series representation on the sphere is generalized to functionals of the potential. In addition, the set of the spectral transfers can be considered as a pocket guide that provides the spectral characteristics of the functionals. Therefore, it extends the so-called Meissl scheme.
Two modified discrete chirp Fourier transform schemes
樊平毅; 夏香根
2001-01-01
This paper presents two modified discrete chirp Fourier transform (MDCFT) schemes.Some matched filter properties such as the optimal selection of the transform length, and its relationship to analog chirp-Fourier transform are studied. Compared to the DCFT proposed previously, theoretical and simulation results have shown that the two MDCFTs can further improve the chirp rate resolution of the detected signals.
Matrix Fourier transform with discontinuous coefficients
Yaremko, O.; Zhuravleva, E.
2013-01-01
The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of mathematical physics.Multidimensional integral transformations with non-separated variables for problems with discontinuous coefficients are constructed in this work. The coefficient discontinuities focused on the of parallel hyperplanes. In this work explicit formul...
On the $q$-Bessel Fourier transform
Dhaouadi, Lazhar
2013-01-01
In this work, we are interested by the $q$-Bessel Fourier transform with a new approach. Many important results of this $q$-integral transform are proved with a new constructive demonstrations and we establish in particular the associated $q$-Fourier-Neumen expansion which involves the $q$-little Jacobi polynomials.
Product Theorem for Quaternion Fourier Transform
Bahri, Mawardi
2014-01-01
In this paper we present the generalized convolution and correlation for the two-dim ensional discrete quaternion Fourier transform (DQFT). We provide several new properties of the generalizations. There results can be considered as the extension of correlation and convolution properties of real and complex Fourier transform to the DQFT domain.
The Table of Analytical Discrete Fourier Transforms
Briggs, William L.; Henson, Van Emden
1995-01-01
While most people rely on numerical methods (most notably the fast Fourier transform) for computing discrete Fourier transforms (DFTs), there is still an occasional need to have analytical DFTs close at hand. Such a table of analytical DFTs is provided in this paper, along with comments and observations, in the belief that it will serve as a useful resource or teaching aid for Fourier practioners.
On the positivity of Fourier transforms
Giraud, Bertrand G
2014-01-01
Characterizing in a constructive way the set of real functions whose Fourier transforms are positive appears to be yet an open problem. Some sufficient conditions are known but they are far from being exhaustive. We propose two constructive sets of necessary conditions for positivity of the Fourier transforms and test their ability of constraining the positivity domain. One uses analytic continuation and Jensen inequalities and the other deals with Toeplitz determinants and the Bochner theorem. Applications are discussed, including the extension to the two-dimensional Fourier-Bessel transform and the problem of positive reciprocity, i.e. positive functions with positive transforms.
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
Plasma Spectrochemistry with a Fourier Transform Spectrometer.
Manning, Thomas Joseph John
1990-01-01
This dissertation can be interpreted as being two-dimensional. The first dimension uses the Los Alamos Fourier Transform Spectrometer to uncover various physical aspects of a Inductively Coupled Plasma. The limits of wavenumber accuracy and resolution are pushed to measure line shifts and line profiles in an Inductively Coupled Argon Plasma. This is new physical information that the plasma spectroscopy community has been seeking for several years. Other plasma spectroscopy carried out includes line profile studies, plasma diagnostics, and exact identification of diatomic molecular spectra. The second aspect of the dissertation involves studies of light sources for Fourier Transform Spectroscopy. Sources developed use an inductively coupled plasma (ICP) power supply. New sources (neon ICP, closed cell ICP, and helium ICP) were developed and new methods to enhance the performance and understand a Fourier Transform Spectrometer were studied including a novel optical filter, a spectrum analyzer to study noises, and a standard to calibrate and evaluate a Fourier Transform Spectrometer.
Fractional Fourier transform of Lorentz beams
Zhou Guo-Quan
2009-01-01
This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.
From Complex Fractional Fourier Transform to Complex Fractional Radon Transform
FAN Hong-Yi; JIANG Nian-Quan
2004-01-01
We show that for n-dimensional complex fractional Fourier transform the corresponding complex fractional Radon transform can also be derived, however, it is different from the direct product of two n-dimensional real fractional Radon transforms. The complex fractional Radon transform of two-mode Wigner operator is calculated.
Fast Fourier Transforms of Piecewise Constant Functions
Sorets, Eugene
1995-02-01
We present an algorithm for the evaluation of the Fourier transform of piecewise constant functions of two variables. The algorithm overcomes the accuracy problems associated with computing the Fourier transform of discontinuous functions; in fact, its time complexity is O (N2 logN + NP log2 (1/ε) + V log3 (1/ε)), where ε is the accuracy, N is the size of the problem, P is the perimeter of the set of discontinuities, and V is its number of vertices. The algorithm is based on the Lagrange interpolation formula and the Green's theorem, which are used to preprocess the data before applying the fast Fourier transform. It readily generalizes to higher dimensions and to piecewise smooth functions.
High order generalized permutational fractional Fourier transforms
Ran Qi-Wen; Yuan Lin; Tan Li-Ying; Ma Jing; Wang Qi
2004-01-01
We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT),is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +∞,M = 4k (k is a natural number), and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
High order generalized permutational fractional Fourier transforms
Ran, Qi-Wen; Yuan, Lin; Tan, Li-Ying; Ma, Jing; Wang, Qi
2004-02-01
We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +infty, M = 4k (k is a natural number) and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
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. PMID:16138556
Fractional Fourier Transform of Cantor Sets
LIAO Tian-ne; GAO Qiong
2005-01-01
@@ A new kind of multifractal is constructed by fractional Fourier transform of Cantor sets. The wavelet transform modulus maxima method is applied to calculate the singularity spectrum under an operational definition of multifractal. In particular, an analysing procedure to determine the spectrum is suggested for practice. Nonanalyticities of singularity spectra or phase transitions are discovered, which are interpreted as some indications on the range of Boltzmann temperature q, on which the scaling relation of partition function holds.
Fourier transforms on an amalgam type space
Liflyand, E
2012-01-01
We introduce an amalgam type space, a subspace of $L^1(\\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the integrability of trigonometric series.
Directional Uncertainty Principle for Quaternion Fourier Transform
Hitzer, Eckhard
2013-01-01
This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric algebras with quaternion subalgebras. We demonstrate this with the example of a directional spacetime algebra function uncertainty principle related to multivector wave packets.
The PROSAIC Laplace and Fourier Transform
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
Debnath, Lokenath
2012-07-01
The profound study of nature is the most fertile source of mathematical discoveries. Not only does this study, by offering a definite goal to research, have the advantage of excluding vague questions and futile calculations, but it is also a sure means of moulding analysis itself, and discerning those elements in it which it is still essential to know and which science ought to conserve. These fundamental elements are those which recur in all natural phenomena. Joseph Fourier pure mathematics enables us to discover the concepts and laws connecting them, which gives us the key to the understanding of the phenomena of nature. Albert Einstein 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 to his splendid research contributions to mathematical physics, pure and applied mathematics and his unprecedented public service accomplishments in the history of France. This is followed by historical comments about the significant and major impact of Fourier analysis on mathematical physics, probability and mathematical statistics, mathematical economics and many areas of pure and applied mathematics including geometry, harmonic analysis, signal analysis, wave propagation and wavelet analysis. Special attention is also given to the Fourier integral formula, Brownian motion and stochastic processes and many examples of applications including isoparametric inequality, everywhere continuous but nowhere differentiable functions, Heisenberg uncertainty principle, Dirichlets' theorem on primes in arithmetic progression, the Poisson summation formula and solutions of wave and diffusion equations. It is also shown that Fourier coefficients c n (t) in the Fourier expansion of a scalar field
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Fourier Transform Infrared Spectroscopic Studies in Flotation
无
2001-01-01
Fourier transform infrared (FTIR) spectroscopy has been extensively employed in flotation research.The work done by the author and co-workers has been reported.A comparison has been made among the different FTIR spectroscopic techniques,e.g.,transmission FTIR spectroscopy,diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy,and attenuated total reflectance (ATR) FTIR spectroscopy.FTIR spectroscopy has been used to study the mechanism of interaction between the collector and the surfaces of different minerals,the mechanism of action of the depressant in improving the selectivity of flotation,and the mechanism of adsorption of the polymeric modifying reagent on mineral surfaces.The interaction between particles in mineral suspension has also been studied by FTIR spectroscopy.
Miniaturization of holographic Fourier-transform spectrometers.
Agladze, Nikolay I; Sievers, Albert J
2004-12-20
Wave propagation equations in the stationary-phase approximation have been used to identify the theoretical bounds of a miniature holographic Fourier-transform spectrometer (HFTS). It is demonstrated that the HFTS throughput can be larger than for a scanning Fourier-transform spectrometer. Given room- or a higher-temperature constraint, a small HFTS has the potential to outperform a small multichannel dispersive spectrograph with the same resolving power because of the size dependence of the signal-to-noise ratio. These predictions are used to analyze the performance of a miniature HFTS made from simple optical components covering a broad spectral range from the UV to the near IR. The importance of specific primary aberrations in limiting the HFTS performance has been both identified and verified. PMID:15646777
Fourier Transform Spectrometer Controller for Partitioned Architectures
Tamas-Selicean, Domitian; Keymeulen, D.; Berisford, D.; Carlson, R.; Hand, K.; Pop, Paul; Wadsworth, W.; Levy, R.
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......, 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....
CONTINUOUS QUATERNION FOURIER AND WAVELET TRANSFORMS
Bahri, Mawardi
2014-01-01
A two-dimensional quaternion Fourier transform (QFT) defined with the kernel $e^{-\\frac{\\boldsymbol{i} + \\boldsymbol{j} + \\boldsymbol{k}} {\\sqrt{3}} \\boldsymbol{\\omega} \\cdot \\boldsymbol{x} }$ is proposed. Some fundamental properties, such as convolution theorem, Plancherel theorem, and vector differential, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet tra...
An Imaging Fourier Transform Spectrometer for NGST
Graham, J R
1999-01-01
Due to its simultaneous deep imaging and integral field spectroscopic capability, an Imaging Fourier Transform Spectrograph (IFTS) is ideally suited to the Next Generation Space Telescope (NGST) mission, and offers opportunities for tremendous scientific return in many fields of astrophysical inquiry. We describe the operation and quantify the advantages of an IFTS for space applications. The conceptual design of the Integral Field Infrared Spectrograph (IFIRS) is a wide field (5'.3 x 5'.3) four-port imaging Michelson interferometer.
Fourier transform resampling: Theory and application
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)
Matrix isolation studies with Fourier transform ir
The combination of Fourier transform infrared (FT-IR) spectroscopy with the matrix-isolation techniques has advantages compared with the use of more conventional grating spectroscopy. Furthermore, the recent commercial availability of Fourier transform spectrometers has made FT-IR a practical alternative. Some advantages of the FT-IR spectrometer over the grating spectrometer are the result of the computerized data system that is a necessary part of the FT-IR spectrometer; other advantages are a consequence of the difference in optical arrangements and these represent the inherent advantages of the FT-IR method. In most applications with the matrix-isolation technique, the use of FT-IR spectroscopy results in either an improved signal-to-noise ratio or a shorter time for data collection compared with grating infrared spectroscopy. Fourier transform infrared spectroscopy has been used in the laboratory to study several molecular species in low-temperature matrices. Some species have been produced by high-temperature vaporization from Knudsen cells and others by sputtering. By sputtering, Ar and Kr matrices have been prepared which contain U atoms, UO, UO2, UO3, PuO, PuO2, UN, or UN2, depending upon the composition of the gas used to sputter as well as the identity of the metallic cathode. Infrared spectra of matrices containing these compounds are presented and discussed
Diffraction theory for an achromatic Fourier transformation
A three-lens achromatic Fourier transform system is analyzed in the contex of parazial Fresnel diffraction theory. From the analysis a general solution for the required wavelength dependence of the various lenses is found. A particular arrangement of the general system is then considered. Using first-order lens design principles, it is shown that each dispersive lens cand be fabricated using a holographic zone lens and glas element cascade. The parazial chromatic aberrations of the resulting system are calculated. It is found that this system design yields an achromatic transformation that is well corrected (parazially) over the entire visible spectrum
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
Quantum Optical Squeezing Transform for Generalizing Fractional Fourier Transform'
HU Li-Yun; FAN Hong-Yi
2008-01-01
By establishing the relation between the optical scaled fractional Fourier transform (FFT) and quantum mechanical squeezing-rotating operator transform, we employ the bipartite entangled state representation of two-mode squeezing operator to extend the scaled FFT to more general cases, such as scaled complex FFT and entangled scaled FFT. The additivity and eigenmodes are presented in quantum version. The relation between the scaled FFT and squeezing-rotating Wigner operator is studied.
Optical image encryption based on multifractional Fourier transforms.
Zhu, B; Liu, S; Ran, Q
2000-08-15
We propose a new image encryption algorithm based on a generalized fractional Fourier transform, to which we refer as a multifractional Fourier transform. We encrypt the input image simply by performing the multifractional Fourier transform with two keys. Numerical simulation results are given to verify the algorithm, and an optical implementation setup is also suggested. PMID:18066153
Fourier transform infrared spectroscopy of deuterated proteins
Marcano O., A.; Markushin, Y.; Melikechi, N.; Connolly, D.
2008-08-01
We report on Fourier transform spectra of deuterated proteins: Bovine Serum Albumin, Leptin, Insulin-like Growth Factor II, monoclonal antibody to ovarian cancer antigen CA125 and Osteopontin. The spectra exhibit changes in the relative amplitude and spectral width of certain peaks. New peaks not present in the non-deuterated sample are also observed. Ways for improving the deuteration of proteins by varying the temperature and dilution time are discussed. We propose the use of deuterated proteins to increase the sensitivity of immunoassays aimed for early diagnostic of diseases most notably cancer.
Alternating multivariate trigonometric functions and corresponding Fourier transforms
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group An, which is a subgroup of the permutation (symmetric) group Sn. 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
Alternating multivariate trigonometric functions and corresponding Fourier transforms
Klimyk, A U [Bogolyubov Institute for Theoretical Physics, Metrologichna str. 14b, Kiev 03680 (Ukraine); Patera, J [Centre de Recherches Mathematiques, Universite de Montreal, C.P. 6128-Centre ville, Montreal, H3C 3J7 Quebec (Canada)], E-mail: aklimyk@bitp.kiev.ua, E-mail: patera@crm.umontreal.ca
2008-04-11
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group A{sub n}, which is a subgroup of the permutation (symmetric) group S{sub 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.
Alternating multivariate trigonometric functions and corresponding Fourier transforms
Klimyk, A. U.; Patera, J.
2008-04-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group An, which is a subgroup of the permutation (symmetric) group Sn. 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.
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.
Compact Fourier transform spectrometer without moving parts
Huang, Chu-Yu; Estroff, B.; Wang, Wei-Chih
2012-04-01
Fourier transform spectroscopy (FTS) is a potent analytical tool for chemical and biological analysis, but is limited by system size, expense, and robustness. To make FTS technology more accessible, we present a compact, inexpensive FTS system based on a novel liquid crystal (LC) interferometer. This design is unique because the optical path difference (OPD) is controlled by voltage applied to the LC cell. The OPD is further improved by reflecting the polarized incident light through the LC several times before reaching the second polarizer and measurement. This paper presents the theoretical model and numerical simulations for the liquid crystal Fourier transform spectrometer (LCFTS), and experimental results from the prototype. Based on the experimental results, the LCFTS performs in accordance with the theoretical predictions, achieving a maximum OPD of 210μm and a resolution of 1nm at a wavelength of 630nm. The instrumental response refresh rate is just under 1 second. Absorbance measurements were conducted for single and mixed solutions of deionized water and isopropyl alcohol, demonstrating agreement with a commercial system and literature values. We also present the LCFTS transmission spectra for varying concentrations of potassium permanganate to show system sensitivity.
Research progress on discretization of fractional Fourier transform
TAO Ran; ZHANG Feng; WANG Yue
2008-01-01
As the fractional Fourier transform has attracted a considerable amount of atten-tion in the area of optics and signal processing,the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier trans-form.Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain,the discre-tization of the fractional Fourier transform has been investigated recently.A sum-mary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper.The discretizations include sampling in the fractional Fourier domain,discrete-time fractional Fourier transform,frac-tional Fourier series,discrete fractional Fourier transform (including 3 main types:linear combination-type;sampling-type;and eigen decomposition-type),and other discrete fractional signal transform.It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.
XFT: Extending the Digital Application of the Fourier Transform
Campos, Rafael G; Chávez, Edgar
2009-01-01
In recent years there has been a growing interest in the fractional Fourier transform driven by its great number of applications. The literature in this field follows two main routes. On the one hand the applications fields where the ordinary Fourier transform can be applied are being revisited to use this intermediate time-frequency representation of signals; and on the other hand fast algorithms for numerical computation of the fractional Fourier transform are devised. In this paper we derive a Gaussian-like quadrature of the continuous fractional Fourier transform. This quadrature is given in terms of the Hermite polynomials and their zeros. By using some asymptotic formulae we are able to solve the quadrature by a diagonal congruence transformation equivalent to a chirp-FFT-chirp transformation, yielding a fast discretization of the fractional Fourier transform and its inverse in closed form. We extend the range of the fractional Fourier transform by considering arbitrary complex values inside the unitary...
CONVOLUTION THEOREMS FOR CLIFFORD FOURIER TRANSFORM AND PROPERTIES
Mawardi Bahri
2014-10-01
Full Text Available The non-commutativity of the Clifford multiplication gives different aspects from the classical Fourier analysis.We establish main properties of convolution theorems for the Clifford Fourier transform. Some properties of these generalized convolutionsare extensions of the corresponding convolution theorems of the classical Fourier transform.
From fractional Fourier transformation to quantum mechanical fractional squeezing transformation
吕翠红; 范洪义; 李东韡
2015-01-01
By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hy-perbolic function, i.e., tanα→tanhα, sinα→sinhα, we find quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within ordered product of operators (IWOP) wederive the unitary operator responsible for the FrST, which is composite and is made of eiπa†a/2 and exp[ iα2 (a2+a†2)]. The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.
Motion analysis of optically trapped particles and cells using 2D Fourier analysis
Kristensen, Martin Verner; Ahrendt, Peter; Lindballe, Thue Bjerring;
2012-01-01
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...... of diffusion coefficients and the trapping forces....
Fourier transform spectrometer controller for partitioned architectures
Tamas-Selicean, D.; Keymeulen, D.; Berisford, D.; Carlson, R.; Hand, K.; Pop, P.; Wadsworth, W.; Levy, R.
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. Researchers at ESA and NASA advocated for the use of partitioned architecture to reduce this complexity. Partitioned architectures rely on platform mechanisms to provide robust temporal and spatial separation between applications. Such architectures have been successfully implemented in several industries, 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 infrared spectroscopy for Mars science
Anderson, Mark S.; Andringa, Jason M.; Carlson, Robert W.; Conrad, Pamela; Hartford, Wayne; Shafer, Michael; Soto, Alejandro; Tsapin, Alexandre I.; Dybwad, Jens Peter; Wadsworth, Winthrop; Hand, Kevin
2005-03-01
Presented here is a Fourier transform infrared spectrometer (FTIR) for field studies that serves as a prototype for future Mars science applications. Infrared spectroscopy provides chemical information that is relevant to a number of Mars science questions. This includes mineralogical analysis, nitrogen compound recognition, truth testing of remote sensing measurements, and the ability to detect organic compounds. The challenges and scientific opportunities are given for the in situ FTIR analysis of Mars soil and rock samples. Various FTIR sampling techniques are assessed and compared to other analytical instrumentation. The prototype instrument presented is capable of providing field analysis in a Mars analog Antarctic environment. FTIR analysis of endolithic microbial communities in Antarctic rocks and a Mars meteor are given as analytical examples.
Compact snapshot birefringent imaging Fourier transform spectrometer
Kudenov, Michael W.; Dereniak, Eustace L.
2010-08-01
The design and implementation of a compact multiple-image Fourier transform spectrometer (FTS) is presented. Based on the multiple-image FTS originally developed by A. Hirai, the presented device offers significant advantages over his original implementation. Namely, its birefringent nature results in a common-path interferometer which makes the spectrometer insensitive to vibration. Furthermore, it enables the potential of making the instrument ultra-compact, thereby improving the portability of the sensor. The theory of the birefringent FTS is provided, followed by details of its specific embodiment. A laboratory proof of concept of the sensor, designed and developed at the Optical Detection Lab, is also presented. Spectral measurements of laboratory sources are provided, including measurements of light-emitting diodes and gas-discharge lamps. These spectra are verified against a calibrated Ocean Optics USB2000 spectrometer. Other data were collected outdoors, demonstrating the sensor's ability to resolve spectral signatures in standard outdoor lighting and environmental conditions.
Optical correction using fourier transform heterodyne
Laubscher, Bryan E.; Nemzek, Robert J.; Cooke, Bradly J.; Olivas, Nicholas L.; Jorgensen, Anders M.; Smith, J. A.; Weisse-Bernstein, Nina R.
2005-08-01
In this paper we briefly present the theory of Fourier Transform Heterodyne (FTH), describe past verification experiments carried out, and discuss the experiment designed to use this new imaging technology to perform optical correction. FTH uses the scalar projection of a reference laser beam and a test laser beam onto a single element detector. The complex current in the detector yields the coefficient of the scalar projection. By projecting a complete orthonormal basis set of reference beams onto the test beam, the amplitude and phase of the test beam can be measured, allowing the reconstruction of the phasefront of the image. Experiments to determine this technique's applicability to optical correction and optical self-correction are continuing. Applications of this technique beyond optical correction include adaptive optics; interferometry; and active, high background, low signal imaging.
Uncertainty relation for the discrete Fourier transform.
Massar, Serge; Spindel, Philippe
2008-05-16
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation. PMID:18518426
Geometric interpretations of the Discrete Fourier Transform (DFT)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
Topology-Preserving Rigid Transformation of 2D Digital Images.
Ngo, Phuc; Passat, Nicolas; Kenmochi, Yukiko; Talbot, Hugues
2014-02-01
We provide conditions under which 2D digital images preserve their topological properties under rigid transformations. We consider the two most common digital topology models, namely dual adjacency and well-composedness. This paper leads to the proposal of optimal preprocessing strategies that ensure the topological invariance of images under arbitrary rigid transformations. These results and methods are proved to be valid for various kinds of images (binary, gray-level, label), thus providing generic and efficient tools, which can be used in particular in the context of image registration and warping. PMID:26270925
Fourier-Laguerre transform, convolution and wavelets on the ball
McEwen, J D
2013-01-01
We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling theorem on the ball. We study the definition of convolution on the ball in this context, showing explicitly how translation on the radial line may be viewed as convolution with a shifted Dirac delta function. We review the exact Fourier-Laguerre wavelet transform on the ball, coined flaglets, and show that flaglets constitute a tight frame.
Multifunctional metasurface lens for imaging and Fourier transform
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-06-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping.
Fiber Optic Fourier Transform White-Light Interferometry
Yi Jiang; Cai-Jie Tang
2008-01-01
Fiber optic Fourier transform white-light inter-fereometry is presented to interrogate the absolute optical path difference of an Mach-Zehnder inter-ferometer. The phase change of the interferometer caused by scanning wavelength can be calculated by a Fourier transform-based phase demodulation technique. A linear output is achieved.
CORRELATION THEOREMS FOR TYPE II QUATERNION FOURIER TRANSFORM
Bahri, Mawardi; Ashino, Ryuichi
2013-01-01
We present the correlation within the framework of the quaternion algebra. We establish the correlation theorem for type II quaternion Fourier transform (QFT) and obtain some important properties of the relationship between the quaternion correlation and the type II QFT. Keywords: quaternion correlation; quaternion Fourier transform
Implementation of 2-D Discrete Cosine Transform Algorithm on GPU
SHIVANG GHETIA, NAGENDRA GAJJAR, RUCHI GAJJAR
2013-07-01
Full Text Available Discrete Cosine Transform (DCT is a technique to get frequency separation. When DCT is applied on an image, it will give frequency segregation of an image since it is composed of DC value and range of low frequency values to high frequency values. DCT is very useful in image compression. When high frequency values are eliminated from image, it will give efficient compression at the cost of little degradation of image quality. But, the bottleneck is that when 2-Dimentional DCT is carried out on CPU, it takes much time since there is very high order of computation. To overcome this problem, Graphics Processing Unit (GPU has opened the door for parallel processing. In this paper, we have implemented 2-D DCT with parallel approach on NVIDIA GPU using CUDA (Compute Unified Device Architecture. By applying here presented 2-D DCT algorithm for image processing has narrowed down the time requirement and has achieved speed up by factor 97x including data transfer timing from CPU to GPU and again back to CPU. So, parallel processing of 2-D DCT algorithm on GPU has fulfilled the purpose of fast and efficient processing of an image.
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author)
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses
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.
Fast Inverse Nonlinear Fourier Transforms for Fiber Bragg Grating Design and Related Problems
Wahls, Sander
2016-01-01
The problem of constructing a fiber Bragg grating profile numerically such that the reflection coefficient of the grating matches a given specification is considered. The well-known analytic solution to this problem is given by a suitable inverse nonlinear Fourier transform (also known as inverse scattering transform) of the specificed reflection coefficient. Many different algorithms have been proposed to compute this inverse nonlinear Fourier transform numerically. The most efficient ones require $\\mathcal{O}(D^{2})$ floating point operations (flops) to generate $D$ samples of the grating profile. In this paper, two new fast inverse nonlinear Fourier transform algorithms that require only $\\mathcal{O}(D\\log^{2}D)$ flops are proposed. The merits of our algorithms are demonstrated in numerical examples, in which they are compared to a conventional layer peeling method, the Toeplitz inner bordering method and integral layer peeling. One of our two algorithms also extends to the design problem for fiber-assiste...
Fourier transforms of Dini-Lipschitz functions on Vilenkin groups
M. S. Younis
1992-09-01
Full Text Available In [4] we proved some theorems on the Fourier Transforms of functions satisfying conditions related to the Dini-Lipschitz conditions on the n-dimensional Euclidean space Rn and the torus group Tn. In this paper we extend those theorems for functions with Fourier series on Vilenkin groups.
q-Generalization of the inverse Fourier transform
Jauregui, M., E-mail: jauregui@cbpf.b [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro (Brazil); Tsallis, C. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro (Brazil); Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 (United States)
2011-05-23
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.
q-Generalization of the inverse Fourier transform
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.
Electro-Optic Imaging Fourier Transform Spectral Polarimeter Project
National Aeronautics and Space Administration — Boulder Nonlinear Systems, Inc. (BNS) proposes to develop an Electro-Optic Imaging Fourier Transform Spectral Polarimeter (E-O IFTSP). The polarimetric system is...
Quantum Fourier Transform and Phase Estimation in Qudit System
CAO Ye; PENG Shi-Guo; ZHENG Chao; LONG Gui-Lu
2011-01-01
The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc.In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case.They can be seen as subroutines in a main program run in a qudit quantum computer, and the quantum circuits are given.
Signature Recognition using Multi Scale Fourier Descriptor And Wavelet Transform
Ismail, Ismail A; danaf, Talaat S El; Samak, Ahmed H
2010-01-01
This paper present a novel off-line signature recognition method based on multi scale Fourier Descriptor and wavelet transform . The main steps of constructing a signature recognition system are discussed and experiments on real data sets show that the average error rate can reach 1%. Finally we compare 8 distance measures between feature vectors with respect to the recognition performance. Key words: signature recognition; Fourier Descriptor; Wavelet transform; personal verification
Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Ryuichi Ashino; Mawardi Bahri; Rémi Vaillancourt
2013-01-01
General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion al...
The quest for conformal geometric algebra Fourier transformations
Hitzer, Eckhard
2013-10-01
Conformal geometric algebra is preferred in many applications. Clifford Fourier transforms (CFT) allow holistic signal processing of (multi) vector fields, different from marginal (channel wise) processing: Flow fields, color fields, electro-magnetic fields, ... The Clifford algebra sets (manifolds) of √-1 lead to continuous manifolds of CFTs. A frequently asked question is: What does a Clifford Fourier transform of conformal geometric algebra look like? We try to give a first answer.
SAW chirp Fourier transform for MB-OFDM UWB receiver
HE Peng-fei; L(U) Ying-hua; ZHANG Hong-xin; WANG Ye-qiu; XU Yong
2006-01-01
In the conventional multiband orthogonal frequency division multiplexing ultra wideband (MB-OFDM UWB )receiver, the fast Fourier transform (FFT) algorithm is realized by the expensive and power-consuming digital signal processor (DSP) chips. In this article, the lower power, lower cost, and lower complexity real-time analog surface acoustic wave (SAW)chirp Fourier transform devices were used to replace the DSP part. A MB-OFDM UWB receiver based on the M-C-M SAW chirp Fourier transform was presented, and the step of signal transformation from input signals was also depicted. The simulation results show that the proposed receiver provides similar bit error performance compared to the fully digital receiver when used in the channel environments proposed by the IEEE 802.15SG3a.
Estimates for Fourier transform of measures supported on singular hypersurfaces
We consider hypersurfaces S is contained in R3 with zero Gaussian curvature at every ordinary point with surface measure dS and we define the surface measure dμ ψ(x)dS(x) for smooth function ψ with compact support. We obtain uniform estimates of Fourier transform of measures concentrated on such hypersurfaces. We show that due to the damping effect of the surface measure the Fourier transform decays faster than O(vertical bar ξ vertical bar-1/h), where h is the height of the phase function. In particular, Fourier transform of measures supported on the exceptional surfaces decays as O(vertical bar ξ vertical bar-1/2). (author)
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)
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)
The Formalization of Discrete Fourier Transform in HOL
Zhiping Shi
2015-01-01
Full Text Available Traditionally, Discrete Fourier Transform (DFT is performed with numerical or symbolic computation, which cannot guarantee 100% accurate analysis which may be necessary for safety-critical applications. Machine theorem proving is one of the formal methods that perform accurate analysis with completeness to some extent. This paper proposes the formalization of DFT in a higher-order logic theorem prover named HOL. We propose the formal definition of DFT and verify the fundamental properties of DFT. Two case studies are presented to illustrate usefulness and correctness of the formalized DFT, including formal verifications of Fast Fourier Transform (FFT and cosine frequency shift.
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
Multifractional Fourier Transform Method and Its Applications to Image Encryption
RANQiwen; WANGQi; MAJing; TANLiying
2003-01-01
The multiplicity of the fractional Fourier transform(FRFT),which is intrinsic in any fractional operator,has been claimed by several authors,but never across-the-board developed.Particularly,the weight-type FRFT(WFRFT) has not been investigated.Starting with defining the multifractional Fourier transform (MFRFT),we gained the generalization permutation matrix group (GPMG)representation and multiplicity of the MFRFT,and the relationships among the MFRFT the standard WFRFT and the standard CFRFT.Finally,as a application,a novel image encryption method hased on the MFRFT is propounded.Similation results show that this method is safe,practicable and impactful.
Extending Fourier transformations to Hamilton's quaternions and Clifford's geometric algebras
Hitzer, Eckhard
2013-10-01
We show how Fourier transformations can be extended to Hamilton's algebra of quaternions. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Hamilton's algebra of quaternions is only one example of the larger class of Clifford's geometric algebras, complete algebras encoding a vector space and all its subspace elements. We introduce how Fourier transformations are extended to Clifford algebras and applied in electromagnetism, and in the processing of images, color images, vector field and climate data.
Fourier transform photocurrent spectroscopy on non-crystalline semiconductors
Holovský, Jakub
Rijeka: InTech, 2011 - (Nikolic, G.), s. 257-282 ISBN 978-953-307-232-6 R&D Projects: GA ČR GD202/09/H041; GA MŠk(CZ) 7E09057; GA ČR GA202/09/0417 Grant ostatní: 7th FP(XE) CP-IP 214134-2 Institutional research plan: CEZ:AV0Z10100521 Keywords : Fourier transform * photocurrent * spectroscopy of semiconductors * thin film silicon * nanodiamond Subject RIV: BM - Solid Matter Physics ; Magnetism http://www.intechopen.com/articles/show/title/fourier-transform-photocurrent-spectroscopy-on-non-crystalline-semiconductors
Lensless Fourier-transform ghost imaging with classical incoherent light
The Fourier-transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a lensless scheme. The experimental results are in good agreement with the standard Fourier transform of the corresponding objects. This scheme provides a route toward aberration-free diffraction-limited three-dimensional images with classically incoherent thermal light (or neutrons), which have no resolution and depth-of-field limitations of lens-based tomographic systems
Lensless Fourier-Transform Ghost Imaging with Classical Incoherent Light
Zhang, M; Shen, X; Liu, Y; Liu, H; Cheng, J; Han, S; Zhang, Minghui; Wei, Qing; Shen, Xia; Liu, Yongfeng; Liu, Honglin; Cheng, Jing; Han, Shensheng
2006-01-01
The Fourier-Transform ghost imaging of both amplitude-only and pure-phase objects was experimentally observed with classical incoherent light at Fresnel distance by a new lensless scheme. The experimental results are in good agreement with the standard Fourier-transform of the corresponding objects. This scheme provides a new route towards aberration-free diffraction-limited 3D images with classically incoherent thermal light, which have no resolution and depth-of-field limitations of lens-based tomographic systems.
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
Recording Fractional Fourier Transform Hologram Using Holographic Zone Plate
高峰; 曾阳素; 张怡霄; 杨静; 高福华; 郭永康
2002-01-01
FRTH(fractional Fourier transform hologram) is a new kind of hologram that differs from common Fresnel holograms and Fourier transform holograms. Due to the flexibility of zone plate. A method that uses the -1 order diffraction wave of zone plate as the object wave and the 0 order diffraction wave as the reference wave to record FRTH is presented. It provides a new simple way to record FRTH. In this paper, the theory of achieving FRT and recording FRTH using holographic zone plate is presented and experimental results are given.
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.
Quaternion Fourier Transform on Quaternion Fields and Generalizations
Hitzer, Eckhard
2013-01-01
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear ($GL$) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging non-commutative multivector FT generalization...
Cesium ion desorption ionization with Fourier transform mass spectrometry
Cesium ions (Cs+) are used for the production of the feed ions necessary to obtain Fourier transform mass spectra (FTMS). The molecule chosen for the initial study of this Cs+ desorption ionization (DI-FTMS) was vitamin B-12 because of its nonvolatile, thermally labile character. 21 references
Fourier transformation methods in the field of gamma spectrometry
A Abdel-Hafiez
2006-09-01
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.
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.
A new stationary gridline artifact suppression method based on the 2D discrete wavelet transform
Tang, Hui, E-mail: corinna@seu.edu.cn [Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing 210096 (China); Key Laboratory of Computer Network and Information Integration (Southeast University), Ministry of Education, Nanjing 210000 (China); Centre de Recherche en Information Biomédicale sino-français, Laboratoire International Associé, Inserm, Université de Rennes 1, Rennes 35000 (France); Southeast University, Nanjing 210000 (China); Tong, Dan; Dong Bao, Xu [Laboratory of Image Science and Technology, School of Computer Science and Engineering, Southeast University, Nanjing 210096 (China); Dillenseger, Jean-Louis [INSERM, U1099, Rennes F-35000 (France); Université de Rennes 1, LTSI, Rennes F-35000 (France); Centre de Recherche en Information Biomédicale sino-français, Laboratoire International Associé, Inserm, Université de Rennes 1, Rennes 35000 (France); Southeast University, Nanjing 210000 (China)
2015-04-15
Purpose: In digital x-ray radiography, an antiscatter grid is inserted between the patient and the image receptor to reduce scattered radiation. If the antiscatter grid is used in a stationary way, gridline artifacts will appear in the final image. In most of the gridline removal image processing methods, the useful information with spatial frequencies close to that of the gridline is usually lost or degraded. In this study, a new stationary gridline suppression method is designed to preserve more of the useful information. Methods: The method is as follows. The input image is first recursively decomposed into several smaller subimages using a multiscale 2D discrete wavelet transform. The decomposition process stops when the gridline signal is found to be greater than a threshold in one or several of these subimages using a gridline detection module. An automatic Gaussian band-stop filter is then applied to the detected subimages to remove the gridline signal. Finally, the restored image is achieved using the corresponding 2D inverse discrete wavelet transform. Results: The processed images show that the proposed method can remove the gridline signal efficiently while maintaining the image details. The spectra of a 1D Fourier transform of the processed images demonstrate that, compared with some existing gridline removal methods, the proposed method has better information preservation after the removal of the gridline artifacts. Additionally, the performance speed is relatively high. Conclusions: The experimental results demonstrate the efficiency of the proposed method. Compared with some existing gridline removal methods, the proposed method can preserve more information within an acceptable execution time.
A new stationary gridline artifact suppression method based on the 2D discrete wavelet transform
Purpose: In digital x-ray radiography, an antiscatter grid is inserted between the patient and the image receptor to reduce scattered radiation. If the antiscatter grid is used in a stationary way, gridline artifacts will appear in the final image. In most of the gridline removal image processing methods, the useful information with spatial frequencies close to that of the gridline is usually lost or degraded. In this study, a new stationary gridline suppression method is designed to preserve more of the useful information. Methods: The method is as follows. The input image is first recursively decomposed into several smaller subimages using a multiscale 2D discrete wavelet transform. The decomposition process stops when the gridline signal is found to be greater than a threshold in one or several of these subimages using a gridline detection module. An automatic Gaussian band-stop filter is then applied to the detected subimages to remove the gridline signal. Finally, the restored image is achieved using the corresponding 2D inverse discrete wavelet transform. Results: The processed images show that the proposed method can remove the gridline signal efficiently while maintaining the image details. The spectra of a 1D Fourier transform of the processed images demonstrate that, compared with some existing gridline removal methods, the proposed method has better information preservation after the removal of the gridline artifacts. Additionally, the performance speed is relatively high. Conclusions: The experimental results demonstrate the efficiency of the proposed method. Compared with some existing gridline removal methods, the proposed method can preserve more information within an acceptable execution time
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.
Quasi- Chun- Ching Shih's Fractional Fourier Transform with Periodicity of 2,3 and M
FAN Xi-zhi
2004-01-01
Based on Chun-Ching Shih's idea, the basic transform was substituted and the quasi-ChunChing Shih's fractional Fourier transform with periodicity of 2, 3 and M was deduced. The two former transforms and the Chun-Ching Shih's fractional Fourier transform were only the particular cases of quasiChun-Ching Shih's fractional Fourier transform with periodicity of M.
Limitations on continuous variable quantum algorithms with Fourier transforms
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.
On the finite Fourier transforms of functions with infinite discontinuities
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.
A Student's Guide to Fourier Transforms - 2nd Edition
James, J. F.
2002-09-01
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science. Expanded to include more emphasis on applications An established successful textbook for undergraduate and graduate students Includes worked examples and copious diagrams throughout
Nanoscale Fourier-transform imaging with magnetic resonance force microscopy
We present a versatile method for Fourier encoding the spatial distribution of spins detected by magnetic resonance force microscopy. Shuttling a magnetic particle in synchrony with an rf pulse sequence causes spins in a constant-field slice near the particle to precess at a rate proportional to their x or y coordinate. A two-dimensional spin-density map is recovered by a linear Fourier transform of a set of integrated force signals. Performance of the rf sequence is demonstrated experimentally and numerical simulations show that the method can achieve nanoscale resolution. Our approach offers a new route to manipulating spin wave functions down to the atomic scale
Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer
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.
Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition
Yufeng Lu
2012-01-01
Full Text Available A fractional fourier transform (FrFT based chirplet signal decomposition (FrFT-CSD algorithm is proposed to analyze ultrasonic signals for NDE applications. Particularly, this method is utilized to isolate dominant chirplet echoes for successive steps in signal decomposition and parameter estimation. FrFT rotates the signal with an optimal transform order. The search of optimal transform order is conducted by determining the highest kurtosis value of the signal in the transformed domain. A simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chirp rate parameter in the simulated ultrasonic echoes. Benchmark and ultrasonic experimental data are used to evaluate the FrFT-CSD algorithm. Signal processing results show that FrFT-CSD not only reconstructs signal successfully, but also characterizes echoes and estimates echo parameters accurately. This study has a broad range of applications of importance in signal detection, estimation, and pattern recognition.
Multiparty Quantum Secret Sharing Using Quantum Fourier Transform
HUANG Da-Zu; CHEN Zhi-Gang; GUO Ying
2009-01-01
A (n, n )-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform.In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert.Furthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant.Security analysis shows that our scheme is secure.Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.
Matrix-Vector Based Fast Fourier Transformations on SDR Architectures
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.
Optimal color image restoration: Wiener filter and quaternion Fourier transform
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, we consider the model of quaternion signal degradation when the signal is convoluted and an additive noise is added. The classical model of such a model leads to the solution of the optimal Wiener filter, where the optimality with respect to the mean square error. The characteristic of this filter can be found in the frequency domain by using the Fourier transform. For quaternion signals, the inverse problem is complicated by the fact that the quaternion arithmetic is not commutative. The quaternion Fourier transform does not map the convolution to the operation of multiplication. In this paper, we analyze the linear model of the signal and image degradation with an additive independent noise and the optimal filtration of the signal and images in the frequency domain and in the quaternion space.
A GENERALIZED WINDOWED FOURIER TRANSFORM IN REAL CLIFFORD ALGEBRA CL0;N
Bahri, Mawardi
2011-01-01
The Clifford Fourier transform in Cl0;n (CFT) can be regarded as a generalization of the two-dimensional quaternionic Fourier transform (QFT), which is introduced from the mathematical aspect by Brackx at first. In this research paper, we propose the Clifford windowed Fourier transform using the kernel of the CFT. Some important properties of the transform are investigated.
Structural Characterization of Carbohydrates by Fourier Transform Tandem Mass Spectrometry
Zhou, Wen; Håkansson, Kristina
2011-01-01
Fourier transform tandem mass spectrometry (MS/MS) provides high mass accuracy, high sensitivity, and analytical versatility and has therefore emerged as an indispensable tool for structural elucidation of biomolecules. Glycosylation is one of the most common posttranslational modifications, occurring in ~50% of proteins. However, due to the structural diversity of carbohydrates, arising from non-template driven biosynthesis, achievement of detailed structural insight is highly challenging. T...
Quantum operation, quantum Fourier transform and semi-definite programming
Duan, Runyao; Ji, Zhengfeng; Feng, Yuan; Ying, Mingsheng
2003-01-01
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for this class of operations. A more general class of operations on qudits is also considered and its completely positive condition is reduced to the well-known semi-definite programming problem.
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.
Apparatus and methods for continuous beam fourier transform mass spectrometry
McLuckey, Scott A.; Goeringer, Douglas E.
2002-01-01
A continuous beam Fourier transform mass spectrometer in which a sample of ions to be analyzed is trapped in a trapping field, and the ions in the range of the mass-to-charge ratios to be analyzed are excited at their characteristic frequencies of motion by a continuous excitation signal. The excited ions in resonant motions generate real or image currents continuously which can be detected and processed to provide a mass spectrum.
Central limit theorem for Fourier transform of stationary processes
Peligrad, Magda
2009-01-01
We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish the central limit theorem (CLT) for almost all frequencies and also the annealed CLT. The theorems hold for all regular sequences. Our results shed new light on the foundation of spectral analysis and on the asymptotic distribution of periodogram, and it provides a nice blend of harmonic analysis, theory of stationary processes and theory of martingales.
Measured Quantum Fourier Transform of 1024 Qubits on Fiber Optics
Tomita, Akihisa; Nakamura, Kazuo
2004-01-01
Quantum Fourier transform (QFT) is a key function to realize quantum computers. A QFT followed by measurement was demonstrated on a simple circuit based on fiber-optics. The QFT was shown to be robust against imperfections in the rotation gate. Error probability was estimated to be 0.01 per qubit, which corresponded to error-free operation on 100 qubits. The error probability can be further reduced by taking the majority of the accumulated results. The reduction of error probability resulted ...
Optimizing holographic data storage using a fractional Fourier transform.
Pégard, Nicolas C; Fleischer, Jason W
2011-07-01
We demonstrate a method to optimize the reconstruction of a hologram when the storage device has a limited dynamic range and a minimum grain size. The optimal solution at the recording plane occurs when the object wave has propagated an intermediate distance between the near and far fields. This distance corresponds to an optimal order and magnification of the fractional Fourier transform of the object. PMID:21725476
Dispersive Fourier Transformation for Versatile Microwave Photonics Applications
Chao Wang
2014-01-01
Abstract: Dispersive Fourier transformation (DFT) maps the broadband spectrum of an ultrashort optical pulse into a time stretched waveform with its intensity profile mirroring the spectrum using chromatic dispersion. Owing to its capability of continuous pulse-by-pulse spectroscopic measurement and manipulation, DFT has become an emerging technique for ultrafast signal generation and processing, and high-throughput real-time measurements, where the speed of traditional optical instruments fa...
Design of high-resolution Fourier transform lens
Zhang, Lei; Zhong, Xing; Jin, Guang
2007-12-01
With the development of optical information processing, high-resolution Fourier transform lens has often been used in holographic data storage system, spatial filtering and observation of particles. This paper studies the optical design method of high-resolution Fourier transform optical lenses system, which could be used in particles observation and holographic data storage system. According to Fourier transform relation between object and its frequency plane and the theory of geometrical optics, the system with working wavelength 532nm and resolution 3μm was designed based on ZEMAX. A multi-configuration method was adopted to optimize the system's lenses. In the optical system, a diaphragm was placed at the system's spectrum plane and the system demanded a low vacuum to cut down the influences of atmosphere and other particles. The result of finite element analysis indicated that the influences of vacuum pumping to optics spacing and mirror surface shape very minor, and the imaging quality not being affected. This system has many advantages, such as simple structure, good image quality and a high resolution of 3μm. So it has a wide application prospect and can be used both in holographic data storage system and particles observation.
Fourier-transform Ghost Imaging with Hard X-rays
Yu, Hong; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming
2016-01-01
Knowledge gained through X-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. Atomic details of sample structures is achievable by X-ray crystallography, however, it is only applied to crystalline structures. Imaging techniques based on X-ray coherent diffraction or zone plates are capable of resolving the internal structure of non-crystalline materials at nanoscales, but it is still a challenge to achieve atomic resolution. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudo-thermal hard X-rays by measuring the second-order intensity correlation function of the light. We show that high resolution Fourier-transform diffraction pattern of a complex structure can be achieved at Fresnel region, and the amplitude and phase distributions of a sample in spatial domain can be retrieved successfully. The method of lensless X-ray Fourier-transform ghost imaging extends X-ray...
Wigner distribution moments in fractional Fourier transform systems.
Bastiaans, Martin J; Alieva, Tatiana
2002-09-01
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. Since Wigner distribution moments are identical to derivatives of the ambiguity function at the origin, a similar relation holds for these derivatives. The general input-output relationship is then broken down into a number of rotation-type input-output relationships between certain combinations of moments. It is shown how the Wigner distribution moments (or ambiguity function derivatives) can be measured as intensity moments in the output planes of a set of appropriate fractional Fourier transform systems and thus be derived from the corresponding fractional power spectra. The minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments is derived. As an important by-product we get a number of moment combinations that are invariant under (anamorphic) fractional Fourier transformation. PMID:12216870
Fourier transform method for evaluation resonance interaction effects
Resonance interaction effects are treated by the Fourier transform method. For the case of two interfering resonances, the slowing-down equation with temperature-dependent cross-sections is transformed to two coupled Fredholm integral equations. In the limit of zero temperature, it is shown that they reduce to coupled second order differential equations and are treated accurately by the WKB method. Temperature-dependent contributions to the resonance integrals are obtained from the solution of the integral equations using Gauss-Hermite quadrature formulae. Numerical results are presented for two interfering low-energy resonances of thorium 232. (orig.)
Fast 2-D 8×8 discrete cosine transform algorithm for image coding
JI XiuHua; ZHANG CaiMing; WANG JiaYe; BOEY S. H.
2009-01-01
A new fast two-dimension 8×8 discrete cosine transform (2D 8×8 DCT) algorithm based on the charac-teristics of the basic images of 2D DCT is presented. The new algorithm computes each DCT coefficient in turn more independently. Hence, the new algorithm is suitable for 2D DCT pruning algorithm of prun-ing away any number of high-frequency components of 2D DCT. The proposed pruning algorithm ls more efficient than the existing pruning 2D DCT algorithms in terms of the number of arithmetic opera-tions, especially the number of multiplications required in the computation.
A symplectic Poisson solver based on Fast Fourier Transformation. The first trial
A symplectic Poisson solver calculates numerically a potential and fields due to a 2D distribution of particles in a way that the symplecticity and smoothness are assured automatically. Such a code, based on Fast Fourier Transformation combined with Bicubic Interpolation, is developed for the use in multi-turn particle simulation in circular accelerators. Beside that, it may have a number of applications, where computations of space charge forces should obey a symplecticity criterion. Detailed computational schemes of all algorithms will be outlined to facilitate practical programming. (author)
A Comparison of 2-D Shape Retrieval Using Fourier Descriptors and Wavelet Descriptors
LIQin; JonathanEdwards
2005-01-01
Choosing an appropriate image retrieval tool is the primary problem for a multimedia application such as digital image library and online image retrieval. Shape is often regarded as the most important image feature. Fourier descriptors (FDs) are widely used in shape recognition and retrieval. However, as global descriptors, they are often blamed for not being able to describe local shape features[1,2]. Wavelet descriptors (WDs) are proposed to overcome this drawback. Unfortunately, the extra information such as the multi-resolution scheme and local shape features cause much more complicate shape matching algorithms. The efficient or effective use of WD srequires more effort. Experiments are executed to evaluate the retrieval performance of this two descriptors. Some conclusions and suggestions are given according to the experimental results and the literature reviewed.
Twin image elimination in digital holography by combination of Fourier transformations
Choudhury, Debesh
2013-01-01
We present a new technique for removing twin image in in-line digital Fourier holography using a combination of Fourier transformations. Instead of recording only a Fourier transform hologram of the object, we propose to record a combined Fourier transform hologram by simultaneously recording the hologram of the Fourier transform and the inverse Fourier transform of the object with suitable weighting coefficients. Twin image is eliminated by appropriate inverse combined Fourier transformation and proper choice of the weighting coefficients. An optical configuration is presented for recording combined Fourier transform holograms. Simulations demonstrate the feasibility of twin image elimination. The hologram reconstruction is sensitive to phase aberrations of the object, thereby opening a way for holographic phase sensing.
A novel algorithm and architecture of combined direct 2-D transform and quantization for H.264
无
2007-01-01
This paper proposes a novel high-performance direct 2-D transform algorithm which suitably arranges the data processing sequences adopted in row and column transforms of H.264 CODEC systems to finish the data transposition. Simultaneity, this paper proposes a new direct 2-D transform and quantization architectures for H.264 video coding standard. The induced new transform and quantization architecture greatly increases the data processing rate and eliminates transform multiplication and transpose memory, and select different mode and quantization according to AC coefficient, DC coefficient, chrominance block and Luminance block. And this architecture just need to storage one quantization tables for Integer transform and Hadamard transform, but it can do two types of forward transforms and quantization just in one block.
Denoise in the pseudopolar grid Fourier space using exact inverse pseudopolar Fourier transform
Wei, Fan Jun
2015-01-01
In this paper I show a matrix method to calculate the exact inverse pseudopolar grid Fourier transform, and use this transform to do noise removals in the k space of pseudopolar grids. I apply the Gaussian filter to this pseudopolar grid and find the advantages of the noise removals are very excellent by using pseudopolar grid, and finally I show the Cartesian grid denoise for comparisons. The results present the signal to noise ratio and the variance are much better when doing noise removals in the pseudopolar grid than the Cartesian grid. The noise removals of pseudopolar grid or Cartesian grid are both in the k space, and all these noises are added in the real space.
Atomic transition probabilities of Ce I from Fourier transform spectra
Atomic transition probabilities for 2874 lines of the first spectrum of cerium (Ce I) are reported. These data are from new branching fraction measurements on Fourier transform spectra normalized with previously reported radiative lifetimes from time-resolved laser-induced-fluorescence measurements (Den Hartog et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 085006). The wavelength range of the data set is from 360 to 1500 nm. Comparisons are made to previous investigations which are less extensive. Accurate Ce i transition probabilities are needed for lighting research and development on metal halide high-intensity discharge lamps.
Atomic transition probabilities of Ce I from Fourier transform spectra
Lawler, J E; Wood, M P; Den Hartog, E A [Department of Physics, University of Wisconsin, 1150 University Ave., Madison, WI 53706 (United States); Chisholm, J [Department of Physics, Boston College, 140 Commonwealth Ave., Chestnut Hill, MA 02467 (United States); Nitz, D E [Department of Physics, St. Olaf College, 1520 St. Olaf Ave., Northfield, MN 55057 (United States); Sobeck, J, E-mail: jelawler@wisc.ed, E-mail: chishojd@bc.ed, E-mail: nitz@stolaf.ed, E-mail: mpwood@wisc.ed, E-mail: jsobeck@uchicago.ed, E-mail: eadenhar@wisc.ed [Department of Astronomy and Astrophysics, University of Chicago, 5640 Ellis Ave., Chicago, IL 60637 (United States)
2010-04-28
Atomic transition probabilities for 2874 lines of the first spectrum of cerium (Ce I) are reported. These data are from new branching fraction measurements on Fourier transform spectra normalized with previously reported radiative lifetimes from time-resolved laser-induced-fluorescence measurements (Den Hartog et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 085006). The wavelength range of the data set is from 360 to 1500 nm. Comparisons are made to previous investigations which are less extensive. Accurate Ce i transition probabilities are needed for lighting research and development on metal halide high-intensity discharge lamps.
Ash melting behavior by Fourier transform infrared spectroscopy
LI Han-xu; QIU Xiao-sheng; TANG Yong-xin
2008-01-01
A Fourier Transform Infrared Spectroscopic (FTIR) method involving a Fe2O3 flux was used to learn how China's coal ash melts. The relationship between ash fusion temperature and chemical composition, as well as the effects of Fe2O3 flux on the ash fusion temperature were studied. The relationship between ash fusion temperature and chemical composition, mineralogical phases and functional groups was analyzed with the FTIR method. The results show that the ash fusion temperature is related to the location and transmittance of certain absorption peaks, which is of great significance for the study of ash behavior.
LPA1, LPA2, Deconvolution Program Using Fourier Transform
1 - Description of program or function: LPA1,LPA2 is a general deconvolution program suitable for application in applied mathematics, experimental physics, signal analytical system and some engineering application range, i.e. deconvolution spectrum, signal analysis and system property analysis, etc. 2 - Method of solution: It makes use of the Deconvolution Theorem and Fourier Transform algorithm (FFT). 3 - Restrictions on the complexity of the problem: The number of data points accepted is not greater than 1024 in this program. This can be increased by changing the data dimension in the program
Birefringent Fourier transform imaging spectrometer with a rotating retroreflector.
Bai, Caixun; Li, Jianxin; Shen, Yan; Zhou, Jianqiang
2016-08-01
A birefringent Fourier transform imaging spectrometer with a new lateral shearing interferometer is presented. The interferometer includes a Wollaston prism and a retroreflector. It splits an incident light beam into two shearing parallel parts to obtain interference fringe patterns of an imaging target, which is well established as an aid in reducing problems associated with optical alignment and manufacturing precision. Continuously rotating the retroreflector enables the spectrometer to acquire two-dimensional spectral images without spatial scanning. This technology, with a high work efficiency and low complexity, is inherently compact and robust. The effectiveness of the proposed method is demonstrated by the experimental results. PMID:27472640
Fourier transform infrared studies in solid egg white lysozyme
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
Fourier Transform Infrared Spectroscopic Analysis of Protein Secondary Structures
Jilie KONG; Shaoning YU
2007-01-01
Infrared spectroscopy is one of the oldest and well established experimental techniques for the analysis of secondary structure of polypeptides and proteins. It is convenient, non-destructive, requires less sample preparation, and can be used under a wide variety of conditions. This review introduces the recent developments in Fourier transform infrared (FTIR) spectroscopy technique and its applications to protein structural studies. The experimental skills, data analysis, and correlations between the FTIR spectroscopic bands and protein secondary structure components are discussed. The applications of FTIR to the secondary structure analysis, conformational changes, structural dynamics and stability studies of proteins are also discussed.
Multi-band Image Registration Method Based on Fourier Transform
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.
Dispersive Fourier transform spectroscopy with gases in the visible region
Kerl, K.; Häusler, H.
1984-05-01
The method of dispersive Fourier transform spectroscopy (DFTS) with gases in the visible wavenumber range is described in detail and compared with the method of scanning-wavelength interferometry (SWI). Measurements of the dispersion of the complex refractive index of gases can be performed successively in several minutes using the same apparatus and gas sample conditions for both methods. In the reported experiments with CH 4 a very simple mirror drive was used. Nevertheless, reasonable results are obtained for the dispersion of the real refractive index of CH 4 in the wavenumber range 16,000 ⩽ σ ⩽ 23,000 cm -1.
Fast Computation of Voigt Functions via Fourier Transforms
Mendenhall, M H
2006-01-01
This work presents a method of computing Voigt functions and their derivatives, to high accuracy, on a uniform grid. It is based on an adaptation of Fourier-transform based convolution. The relative error of the result decreases as the fourth power of the computational effort. Because of its use of highly vectorizable operations for its core, it can be implemented very efficiently in scripting language environments which provide fast vector libraries. The availability of the derivatives makes it suitable as a function generator for non-linear fitting procedures.
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
Klimyk, A.; Patera, J.
2007-09-01
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms involving the symmetric and antisymmetric multivariate sine and cosine functions.
Quantum control in two-dimensional Fourier-transform spectroscopy
We present a method that harnesses coherent control capability to two-dimensional Fourier-transform optical spectroscopy. For this, three ultrashort laser pulses are individually shaped to prepare and control the quantum interference involved in two-photon interexcited-state transitions of a V-type quantum system. In experiments performed with atomic rubidium, quantum control for the enhancement and reduction of the 5P1/2→ 5P3/2 transition was successfully tested in which the engineered transitions were distinguishably extracted in the presence of dominant one-photon transitions.
Remarks on a 2-D nonlinear backward heat problem using a truncated Fourier series method
Dang Duc Trong
2009-06-01
Full Text Available The inverse conduction problem arises when experimental measurements are taken in the interior of a body, and it is desired to calculate temperature on the surface. We consider the problem of finding, from the final data $u(x,y,T=varphi(x,y$, the initial data $u(x,y,0$ of the temperature function $u(x,y,t$, $(x,y in Uequiv (0,piimes (0,pi$, $tin [0,T]$ satisfying the nonlinear system $$displaylines{ u_t-Delta u= f(x,y,t,u(x,y, t,quad (x,y,tin Uimes (0,T,cr u(0,y,t= u(pi,y,t= u(x,0,t = u(x,pi,t = 0,quad (x,y,t in Uimes(0,T. }$$ This problem is known to be ill-posed, as the solution exhibits unstable dependence on the given data functions. Using the Fourier series method, we regularize the problem and to get some new error estimates. A numerical experiment is given.
The Non-uniform Fast Fourier Transform in Computed Tomography
Tang, Junqi
2016-01-01
This project is aimed at designing the fast forward projection algorithm and also the backprojection algorithm for cone beam CT imaging systems with circular X-ray source trajectory. The principle of the designs is based on utilizing the potential computational efficiency which the Fourier Slice Theorem and the Non-uniform Fast Fourier Transform (NUFFT) will bring forth. In this Masters report, the detailed design of the NUFFT based forward projector including a novel 3D (derivative of) Radon space resampling method will be given. Meanwhile the complexity of the NUFFT based forward projector is analysed and compared with the non-Fourier based CT projector, and the advantage of the NUFFT based forward projection in terms of the computational efficiency is demonstrated in this report. Base on the design of the forward algorithm, the NUFFT based 3D direct reconstruction algorithm will be derived. The experiments will be taken to test the performance of the forward algorithm and the backprojection algorithm to sh...
On the Fourier transformation of renormalization invariant coupling
Integral transformations of the QCD invariant (running) coupling and of some related objects are discussed. Special attention is paid to the Fourier transformation, that is to transition from the space-time to the energy-momentum representation. The conclusion is that the condition of possibility of such a transition provides us with one more argument against the real existence of unphysical singularities observed in the perturbative QCD. The second one relates to the way of 'translation' of some singular long-range asymptotic behaviours to the infrared momentum region. Such a transition has to be performed with due account of the Tauberian theorem. This comment relates to the recent ALPHA collaboration results on the asymptotic behavior of the QCD effective coupling obtained by lattice simulation
MR imaging of the knee : Three-dimensional fourier transform GRASS technique
Kim, Dong Joo; Lee, Young Uk; Youn, Eun Kyung; No, In Gye; Chin, Seoung Bum; Kim, Joon Sik; Choi, Jae Yeul [Kangbuk Samsung Hospital, Seoul (Korea, Republic of)
1996-04-01
To evaluate the usefulness of three-dimensional(3D) Fourier transform(FT) gradient refocused acquisition in steady state (GRASS) technique for MR imaging of the knee. Sixty-three knees in 61 patients were imaged on the 1.5T MR system. We compared 3DFT GRASS technique with 2D spin echo(SE) technique in terms of conspicuousness of the lesions of internal knee structures based on the results of arthroscopy or open surgery. As a SE technique, sagittal T1-and T2-weighted, and coronal fat-suppressed T2-weighted sequences were performed using 3D GRASS technique, and we also evaluated arbitrarily reformatted images produced from the original axial voxel images. For the depiction of the tear, 3DFT GRASS was superior to 2D SE in three cases of medial meniscus, one of lateral meniscus, and two of anterior cruciate ligament. Specificity of 3D GRASS was also higher than that of 2D SE in evaluation of lateral meniscus and anterior cruiciate ligament. There was no significant difference in MR diagnosis for tears of the posterior cruciate, medial collateral, and lateral collateral ligaments. 3D GRASS was superior in evaluating the extent and morphology of the torn menisci. The 3DFT GRASS technique was comparable or even superior to the 2D SE technique in the evaluation of the internal structure of the knee, and can be expected to supplement standard MR knee techniques, especially in complicated cases of meniscal or ligamentous tears.
MR imaging of the knee : Three-dimensional fourier transform GRASS technique
To evaluate the usefulness of three-dimensional(3D) Fourier transform(FT) gradient refocused acquisition in steady state (GRASS) technique for MR imaging of the knee. Sixty-three knees in 61 patients were imaged on the 1.5T MR system. We compared 3DFT GRASS technique with 2D spin echo(SE) technique in terms of conspicuousness of the lesions of internal knee structures based on the results of arthroscopy or open surgery. As a SE technique, sagittal T1-and T2-weighted, and coronal fat-suppressed T2-weighted sequences were performed using 3D GRASS technique, and we also evaluated arbitrarily reformatted images produced from the original axial voxel images. For the depiction of the tear, 3DFT GRASS was superior to 2D SE in three cases of medial meniscus, one of lateral meniscus, and two of anterior cruciate ligament. Specificity of 3D GRASS was also higher than that of 2D SE in evaluation of lateral meniscus and anterior cruiciate ligament. There was no significant difference in MR diagnosis for tears of the posterior cruciate, medial collateral, and lateral collateral ligaments. 3D GRASS was superior in evaluating the extent and morphology of the torn menisci. The 3DFT GRASS technique was comparable or even superior to the 2D SE technique in the evaluation of the internal structure of the knee, and can be expected to supplement standard MR knee techniques, especially in complicated cases of meniscal or ligamentous tears
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).
Radial Hilbert Transform in terms of the Fourier Transform applied to Image Encryption
In the present investigation, a mathematical algorithm under Matlab platform using Radial Hilbert Transform and Random Phase Mask for encrypting digital images is implemented. The algorithm is based on the use of the conventional Fourier transform and two random phase masks, which provide security and robustness to the system implemented. Random phase masks used during encryption and decryption are the keys to improve security and make the system immune to attacks by program generation phase masks
Tow-dimensional Strain Analysis by Fourier Transform Moire Interferometry
Moire interferometry using a diffraction grating and a laser is a powerful technique for analyzing small deformation of a specimen. In the method, the x and y-directional fringe patterns are obtained by using the x and y-directional sets of two beams. If the both sets of two beams are simultaneously incident to the specimen, the x and y-directional fringe patterns are super imposed. In this case, it is difficult to separate each directional fringe pattern. Therefore each fringe pattern has been separately recorded by selecting each set of two beams. In order to analyze a two-dimensional strain changing with time, Moire interferometry using the two-dimensional fourier transform method is proposed and the x and y-directional fringes are separated. By this method, the thermal deformation of a glass plate is analyzed
Spatially Resolved Fourier Transform Spectroscopy in the Extreme Ultraviolet
Jansen, G S M; Freisem, L; Eikema, K S E; Witte, S
2016-01-01
Coherent extreme ultraviolet (XUV) radiation produced by table-top high-harmonic generation (HHG) sources provides a wealth of possibilities in research areas ranging from attosecond physics to high resolution coherent imaging. However, it remains challenging to fully exploit the coherence of such sources for interferometry and Fourier transform spectroscopy (FTS). This is due to the need for a measurement system that is stable at the level of a wavelength fraction, yet allowing a controlled scanning of time delays. Here we demonstrate XUV interferometry and FTS in the 17-55 nm wavelength range using an ultrastable common-path interferometer suitable for high-intensity laser pulses that drive the HHG process. This approach enables the generation of fully coherent XUV pulse pairs with sub-attosecond timing variation, tunable time delay and a clean Gaussian spatial mode profile. We demonstrate the capabilities of our XUV interferometer by performing spatially resolved FTS on a thin film composed of titanium and...
Highly sensitive Fourier transform spectroscopy with LED sources
Serdyukov, V. I.; Sinitsa, L. N.; Vasil'chenko, S. S.
2013-08-01
It is shown that the use of high luminance LED emitters as a light source for Fourier transform spectrometers permits to enhance their threshold sensitivity in the visible range by orders of magnitude. Using a 2.5 W Edixeon EDEI-1LS3 emitter in the range of 11,350-11,700 cm-1 as a light source for the spectrometer with a 60-cm multipass cell during a 24-h measurement time, we have achieved a signal-to-noise ratio of 4.5 × 104 which corresponds to the minimal detectable absorption coefficient of 1.2 × 10-8 cm-1. Such enhanced sensitivity spectrometer has been used to measure the transition frequencies of CO2 vibrational bands 00051-00001 and 01151-01101 in the range of 11,400-11,500 cm-1.
Determination of total body water by Fourier transform infrared analysis
A new technique for determinig body water using deuterium isotope dilution for Fourier transform infrared (FTIR) analysis is described. The advantages of the FTIR over conventional dispersion and filter infrared instruments include greater flexibility through computer controlled operations and availability of 'on-line' analytical software. The technique was further improved by the development of a simple procedure for determining D2O concentration in untreated serum samples. A validation study of six normal adults showed that the fat-free-mass determined from the deuterium-space (total body water) correlated well with the results obtained by total body nitrogen (r = 0.997), total body potassium (r = 0.99f6) and anthropometric (r = 0.995) measurements. 17 refs., 4 tabs., 4 figs
Observing Extended Sources with the \\Herschel SPIRE Fourier Transform Spectrometer
Wu, Ronin; Etxaluze, Mireya; Makiwa, Gibion; Naylor, David A; Salji, Carl; Swinyard, Bruce M; Ferlet, Marc; van der Wiel, Matthijs H D; Smith, Anthony J; Fulton, Trevor; Griffin, Matt J; Baluteau, Jean-Paul; Benielli, Dominique; Glenn, Jason; Hopwood, Rosalind; Imhof, Peter; Lim, Tanya; Lu, Nanyao; Panuzzo, Pasquale; Pearson, Chris; Sidher, Sunil; Valtchanov, Ivan
2013-01-01
The Spectral and Photometric Imaging Receiver (SPIRE) on the European Space Agency's Herschel Space Observatory utilizes a pioneering design for its imaging spectrometer in the form of a Fourier Transform Spectrometer (FTS). The standard FTS data reduction and calibration schemes are aimed at objects with either a spatial extent much larger than the beam size or a source that can be approximated as a point source within the beam. However, when sources are of intermediate spatial extent, neither of these calibrations schemes is appropriate and both the spatial response of the instrument and the source's light profile must be taken into account and the coupling between them explicitly derived. To that end, we derive the necessary corrections using an observed spectrum of a fully extended source with the beam profile and the source's light profile taken into account. We apply the derived correction to several observations of planets and compare the corrected spectra with their spectral models to study the beam c...
Micro wishbone interferometer for Fourier transform infrared spectrometry
A miniature wishbone-type Si interferometer with electrically actuated rotary comb drive actuators is designed and fabricated to apply a Fourier transform infrared (FTIR) spectrometer. Corner cube mirrors are mounted on the end of the Si interferometer that is formed on a glass substrate. The total size of the interferometer is approximately 8 mm × 8 mm. The corner cube mirrors with sharp edges with a size of approximately 1 × 1 × 0.5 mm3 are fabricated using an indentation technique. The rotation angle of rotary comb drive actuators is approximately 11° with an applied voltage of 180 V. Hereby, the maximum optical path difference of approximately 2640 µm is achieved, which corresponds to the highest resolution of ∼4 cm−1 as a spectrometer
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.
Extreme-ultraviolet lensless Fourier-transform holography.
Lee, S H; Naulleau, P; Goldberg, K A; Cho, C H; Jeong, S; Bokor, J
2001-06-01
We demonstrate 100-nm-resolution holographic aerial image monitoring based on lensless Fourier-transform holography at extreme-UV (EUV) wavelengths, using synchrotron-based illumination. This method can be used to monitor the coherent imaging performance of EUV lithographic optical systems. The system has been implemented in the EUV phase-shifting point-diffraction interferometer recently developed at Lawrence Berkeley National Laboratory. Here we introduce the idea of the holographic aerial image-recording technique and present imaging performance characterization results for a 10x Schwarzschild objective, a prototype EUV lithographic optic. The results are compared with simulations, and good agreement is obtained. Various object patterns, including phase-shift-enhanced patterns, have been studied. Finally, the application of the holographic aerial image-recording technique to EUV multilayer mask-blank defect characterization is discussed. PMID:18357280
3-D Printed Slit Nozzles for Fourier Transform Microwave Spectroscopy
Dewberry, Chris; Mackenzie, Becca; Green, Susan; Leopold, Ken
2015-06-01
3-D printing is a new technology whose applications are only beginning to be explored. In this report, we describe the application of 3-D printing to the facile design and construction of supersonic nozzles. The efficacy of a variety of designs is assessed by examining rotational spectra OCS and Ar-OCS using a Fourier transform microwave spectrometer with tandem cavity and chirped-pulse capabilities. This work focuses primarily on the use of slit nozzles but other designs have been tested as well. New nozzles can be created for 0.50 or less each, and the ease and low cost should facilitate the optimization of nozzle performance (e.g., jet temperature or cluster size distribution) for the needs of any particular experiment.
Control Of Cryogenic Fourier Transform Spectrometer Scanning Mirrors
Tripathi, S. S.; Gowrinathan, S.
1981-12-01
The Perkin-Elmer Corporation has designed and built a cryogenically cooled Fourier transform spectrometer for spaceborne applications. In operation, the spectrometer requires mirrors moving at constant velocity in both forward and reverse directions. To maintain efficiency and accuracy, the time taken to reverse direction and the vibration induced due to this reversal must be kept within low limits. This paper deals with the control system design for maintaining a constant velocity during forward and reverse scans and for smooth direction reversals. The systems aspects of the problem are described, and time-domain techniques of modern control theory are applied for optimization of turn-around profile. The analysis leads to a suboptimal design easily implemented by using analog-type components. Test results of satisfactory performance are also included.
Radix-3 Algorithm for Realization of Discrete Fourier Transform
M.Narayan Murty
2016-07-01
Full Text Available In this paper, a new radix-3 algorithm for realization of discrete Fourier transform (DFT of length N = 3m (m = 1, 2, 3,... is presented. The DFT of length N can be realized from three DFT sequences, each of length N/3. If the input signal has length N, direct calculation of DFT requires O (N 2 complex multiplications (4N 2 real multiplications and some additions. This radix-3 algorithm reduces the number of multiplications required for realizing DFT. For example, the number of complex multiplications required for realizing 9-point DFT using the proposed radix-3 algorithm is 60. Thus, saving in time can be achieved in the realization of proposed algorithm.
Instrument concept of the imaging Fourier transform spectrometer GLORIA
F. Friedl-Vallon
2014-03-01
Full Text Available The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the Upper Troposphere/Lower Stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated in a gimbal. The assembly can be mounted in the belly pod of the German high altitude and long range research aircraft HALO and in instrument bays of the Russian M55 Geophysica. Measurements are made predominantly in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
Instrument concept of the imaging Fourier transform spectrometer GLORIA
F. Friedl-Vallon
2014-10-01
Full Text Available The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the upper troposphere/lower stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated into a gimbal. The assembly can be mounted in the belly pod of the German High Altitude and Long Range research aircraft (HALO and in instrument bays of the Russian M55 Geophysica. Measurements are made in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, and the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition, the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
[Influence of collimation system on static Fourier transform spectrometer].
Jiang, Cheng-Zhi; Liang, Jing-Qiu; Liang, Zhong-Zhu; Sun, Qiang; Wang, Wei-Biao
2014-01-01
Collimation system provides collimated light for the static Fourier-transform spectroscopy (SFTS). Its quality is crucial to the signal to noise ratio (SNR) of SFTS. In the present paper, the physical model of SFTS was established based on the Fresnel diffraction theory by means of numerical software. The influence of collimation system on the SFTS was discussed in detail focusing on the aberrations of collimation lens and the quality of extended source. The results of simulation show that the influences of different kinds of aberrations on SNR take on obvious regularity, and in particular, the influences of off-axis aberrations on SNR are closely related to the location of off-axis point source. Finally the extended source's maximum radius allowed was obtained by simulation, which equals to 0.65 mm. The discussion results will be used for the design of collimation system. PMID:24783575
Dispersive Fourier Transformation for Versatile Microwave Photonics Applications
Chao Wang
2014-12-01
Full Text Available Dispersive Fourier transformation (DFT maps the broadband spectrum of an ultrashort optical pulse into a time stretched waveform with its intensity profile mirroring the spectrum using chromatic dispersion. Owing to its capability of continuous pulse-by-pulse spectroscopic measurement and manipulation, DFT has become an emerging technique for ultrafast signal generation and processing, and high-throughput real-time measurements, where the speed of traditional optical instruments falls short. In this paper, the principle and implementation methods of DFT are first introduced and the recent development in employing DFT technique for widespread microwave photonics applications are presented, with emphasis on real-time spectroscopy, microwave arbitrary waveform generation, and microwave spectrum sensing. Finally, possible future research directions for DFT-based microwave photonics techniques are discussed as well.
Characterization of DNA adducts with fourier transform mass spectrometry
The sensitive detection and unambiguous structural characterization of modified nucleic acid constituents is vital for understanding the nature of DNA modification induced by carcinogenic agents. Fourier transform mass spectrometry (FTMS) combined with matrix-assisted laser desorption provides a powerful technique for examining picomole quantities of modified nucleosides, nucleotides, and oligonucleotides. The structures of these modified biomolecules can be probed in detail with a variety of gas phase processes, including collision-induced dissociation, ion-molecule reactions such as deuterium exchange, and selective cationization reactions. Each of these processes provides a wealth of structural information which can be used to not only identify the adduct present, but also determine its exact site of attachment to the nucleic acid constituent, thereby providing isomeric differentiation. This FTMS technique has been applied to the examination of DNA damage induced by high energy (x-rays) as well as low energy radiation (far ultraviolet)
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)
Adaptive motion mapping in pancreatic SBRT patients using Fourier transforms
Jones, Bernard L; Miften, Moyed
2015-01-01
Recent studies suggest that 4DCT is unable to accurately measure respiratory-induced pancreatic tumor motion. In this work, we assessed the daily motion of pancreatic tumors treated with SBRT, and developed adaptive strategies to predict and account for this motion. The daily motion trajectory of pancreatic tumors during CBCT acquisition was calculated using a model which reconstructs the instantaneous 3D position in each 2D CBCT projection image. We developed a metric (termed "Spectral Coherence," SC) based on the Fourier frequency spectrum of motion in the SI direction, and analyzed the ability of SC to predict motion-based errors and classify patients according to motion characteristics. The amplitude of daily motion exceeded the predictions of pre-treatment 4DCT imaging by an average of 3.0 mm, 2.3 mm, and 3.5 mm in the AP, LR, and SI directions. SC was correlated with daily motion differences and tumor dose coverage. In a simulated adaptive protocol, target margins were adjusted based on SC, resulting in...
OUYANG, Junlin; Coatrieux, Gouenou; Shu, Huazhong
2015-01-01
In this work, a novel robust image hashing scheme for image authentication is proposed based on the combination of the quaternion discrete Fourier transform (QDFT) with the log-polar transform. QDFT offers a sound way to jointly deal with the three channels of color images. The key features of the present method rely on (i) the computation of a secondary image using a log-polar transform; and (ii) the extraction from this image of low frequency QDFT coefficients' magnitude. The final image ha...
Chujun Zheng; Peng Han; Hongsen Chang
2006-01-01
@@ A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π,and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.
Identification of formation interfaces by using wavelet and Fourier transforms
Mukherjee, Bappa; Srivardhan, V.; Roy, P. N. S.
2016-05-01
The identification of formation interfaces is of prime importance from well log data. The interfaces are not clearly discernible due to the presence of high and low frequency noise in the log response. Accurate bed boundary information is very crucial in hydrocarbon exploration and the problem has received considerable attention and many techniques have been proposed. Frequency spectrum based filtering techniques aids us in interpretation, but usually leads to inaccurate amplification of unwanted components of the log response. Wavelet transform is very effective in denoising the log response and can be carried out to filter low and high frequency components of signal. The use of Fourier and Wavelet transform in denoising the log data for obtaining formation interfaces is demonstrated in this work. The feasibility of the proposed technique is tested so that it can be used in the industry to decipher formation interfaces. The work flow is demonstrated by testing on wells belonging to the Upper Assam Basin, which are self-potential, gamma ray, and resistivity log responses.
The use of Fourier reverse transforms in crystallographic phase refinement
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
The use of Fourier reverse transforms in crystallographic phase refinement
Ringrose, S.
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.
EXPRESSION PATTERN OF LUNG CANCER RELATED GENES IN MALIGNANT TRANSFORMATION OF BEP2D
范保星; 张开泰; 李刚; 谢玲; 马淑华; 葛世丽; 项小琼; 胡迎春; 王升启; 周平坤; 吴德昌
2002-01-01
Objective: To detect the expression difference of 60 lung cancer associated genes in human bronchial epithelial malignant transformation cell model (BEP2D) induced by alpha-particles. Methods: 60 lung cancer associated genes were collected and micro-arrayed onto the microscope slides using Cartesian PixSys5500 cDNA Microarray machine. Total RNA from BEP2D cells and passage 20 (Rl5H-20), passage 35 (R15H-35) cells derived from BEP2D following 1.5 Gy alpha-particles was extracted and labeled by fluorescent dye. The labeled probe was then hybridized with the cDNA. Results: 40, 47, 20 genes were detected in BEP2D, R15H-20 and R15H-35 respectively. The expression level of tumor suppressor genes decreased greatly in the transformed R15H-35. Most oncogenes decreased slightly in R15H-20. Most growth factors expressed only in R15H-20. Conclusion: In human bronchial epithelial malignant transformed cell model generated by alpha-particles, the loss-function of tumor suppressor genes at initiation stage was dominant, some related oncogenes and growth factors promoted the malignant transformation.
TMS320C25 Digital Signal Processor For 2-Dimensional Fast Fourier Transform Computation
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
[Biological Process Oriented Online Fourier Transform Infrared Spectrometer].
Xie, Fei; Wu, Qiong-shui; Zeng, Li-bo
2015-08-01
An online Fourier Transform Infrared Spectrometer and an ATR (Attenuated Total Reflection) probe, specifically at the application of real time measurement of the reaction substrate concentration in biological processes, were designed. (1) The spectrometer combined the theories of double cube-corner reflectors and flat mirror, which created a kind of high performance interferometer system. The light path folding way was utilized to makes the interferometer compact structure. Adopting double cube-corner reflectors, greatly reduces the influence of factors in the process of moving mirror movement such as rotation, tilt, etc. The parallelogram oscillation flexible support device was utilized to support the moving mirror moves. It cancelled the friction and vibration during mirror moving, and ensures the smooth operation. The ZnSe splitter significantly improved the hardware reliability in high moisture environment. The method of 60° entrance to light splitter improves the luminous flux. (2) An ATR in situ measuring probe with simple structure, large-flux, economical and practical character was designed in this article. The transmission of incident light and the light output utilized the infrared pipe with large diameter and innerplanted-high plating membrane, which conducted for the infrared transmission media of ATR probe. It greatly reduced the energy loss of infrared light after multiple reflection on the inner wall of the light pipe. Therefore, the ATR probe obtained high flux, improved the signal strength, which make the signal detected easily. Finally, the high sensitivity of MCT (Mercury Cadmium Telluride) detector was utilized to realize infrared interference signal collection, and improved the data quality of detection. The test results showed that the system yields the advantages of perfect moisture-proof performance, luminous flux, online measurement, etc. The designed online Fourier infrared spectrometer can real-time measured common reactant substrates
[Using Fourier transform to calculate gas concentration in DOAS].
Liu, Qian-lin; Wang, Li-shi; Huang, Xin-jian; Wu, Yan-dan; Xiao, Ming-wei
2008-12-01
Being an analysis tool of high sensitivity, high resolution, multicomponents, real-time and fast monitoring, the differential optical absorption spectrometry (DOAS) is becoming a new method in atmosphere pollution monitoring. In the DOAS technique, many gases spectra have periodicity evidently, such as those from SO2, NO, NH3 and NO2. Aiming at three kinds of main air-polluted gases, i.e., SO2, NO and NO2 in atmosphere, the DOAS technique is used to monitor them, and Fourier transform is used to analyse the above-mentioned absorption spectra. Under the condition of Hanning Windows, Fourier transforma is used to process various gases spectra which have periodicity. In the process, the value of the characteristic frequency has a linearity relation to the gas concentration. So a new analysis method of DOAS is proposed, which is utilizing the relation between the value of the characteristic frequency and the gas concentration to deduce a linearity formula to calculate the gas concentration. So the value of the characteristic frequency can be used to get the gas concentration. For the gases with evident spectrum periodicity, such as SO2 and NO, this method is good. But for some gases with periodicity not evident, the error in the calculated concentration is beyond the allowable value. So in this method, the important process is frequency separation. It is also the main part in the future study. In a word, this method frees itself from the basic theory in the DOAS technique, cuts down on the process of the concentration calculation and the spectral analysis, and deserves further study. PMID:19248493
Blacic, Tanya M.; Jun, Hyunggu; Rosado, Hayley; Shin, Changsoo
2016-02-01
In seismic oceanography, processed images highlight small temperature changes, but inversion is needed to obtain absolute temperatures. Local search-based full waveform inversion has a lower computational cost than global search but requires accurate starting models. Unfortunately, most marine seismic data have little associated hydrographic data and the band-limited nature of seismic data makes extracting the long wavelength sound speed trend directly from seismic data inherently challenging. Laplace and Laplace-Fourier domain inversion (LDI) can use rudimentary starting models without prior information about the medium. Data are transformed to the Laplace domain, and a smooth sound speed model is extracted by examining the zero and low frequency components of the damped wavefield. We applied LDI to five synthetic data sets based on oceanographic features and recovered smoothed versions of our synthetic models, showing the viability of LDI for creating starting models suitable for more detailed inversions.
Otten, Leonard John, III; Butler, Eugene W.; Rafert, Bruce; Sellar, R. Glenn
1995-06-01
Kestrel Corporation and the Florida Institute of Technology have designed, and are now manufacturing, a Fourier transform visible hyperspectral imager system for use in a single engine light aircraft. The system is composed of a Sagnac-based interferometer optical subsystem, a data management system, and an aircraft attitude and current position sybsystem. The system is designed to have better than 5 nm spectral resolution at 450 nm, operates over the 440 nm to 1150 nm spectral band and has a 2D spatial resolution of 0.8 mrad. An internal calibration source is recorded with every frame of data to retain radiometric accuracy. The entire system fits into a Cessna 206 and uses a conventional downward looking view port located in the baggage compartment. During operation, data are collected at a rate of 15 Mbytes per second and stored direct to a disk array. Data storage has been sized to accommodate 56 minutes of observations. Designed for environmental mapping, this Fourier transform imager has uses in emergency response and military operations.
Wang Chuandan; Zhang Zhongpei; Li Shaoqian
2007-01-01
The method of FRactional Fourier Transform (FRFT) is introduced to Transform Domain Communication System (TDCS) for signal transforming in the paper after theoretical analysis. The method yields optimal Basis Function (BF) by FRFT with optimal transform angle. The TDCS using the proposed method has wider usable spectrum, stronger robustness and better ability of anti non-stationary jamming than using usual methods, such as Fourier Transform (FT), Auto Regressive (AR), Wavelet Transform (WT), etc. The main simulation results are as follows. First, the Bit Error Rate (BER) Pb is close to theoretical bound of no jamming no matter in single tone or in linear chirp interference. Second, the interference-to-signal ratio J/E is at least 12dB more than that of Direct Spread Spectrum System (DSSS) under the same BER if the spectrum hopping-to-signal ratio is 1:20 in chirp plus hopping interfering. Third, the Eb/No (when estimation difference is 90% between transmitter and receiver) is about 3.5dB or about 0.5dB (when estimation difference is 10% between transmitter and receiver) more than that of theoretical result when no estimation difference under Pb = 10-2.
Gas Analysis by Fourier Transform Mm-Wave Spectroscopy
Harris, Brent J.; Steber, Amanda L.; Lehmann, Kevin K.; Pate, Brooks H.
2013-06-01
Molecular rotational spectroscopy of low pressure, room temperature gases offers high chemical selectivity and sensitivity with the potential for a wide range of applications in gas analysis. A strength of the technique is the potential to identify molecules that have not been previously studied by rotational spectroscopy by comparing experimental results to predictions of the spectroscopic parameters from quantum chemistry -6 so called library-free detection. The development of Fourier transform mm-wave spectrometers using high peak power (30 mW) active multiplier chain mm-wave sources brings new measurement capabilities to the analysis of complex gas mixtures. Strategies for gas analysis based on high-throughput mm-wave spectroscopy and arbitrary waveform generator driven mm-wave sources are described. Several new measurement capabilities come from the intrinsic time-domain measurement technique. High-sensitivity double-resonance measurements can be performed to speed the analysis of a complex gas sample containing several species. This technique uses a "pi-pulse" to selectively invert the population of two selected rotational energy levels and the effect of this excitation pulse on all other transitions in the spectrometer operating range is monitored using segmented chirped-pulse Fourier transform spectroscopy. This method can lead to automated determination of the molecular rotational constants. Rapid pulse duration scan experiments can be used to estimate the magnitude and direction of the dipole moment of the molecule from an unknown spectrum. Coherent pulse echo experiments, using the traditional Hahn sequence or two-color population recovery methods, can be used to determine the collisional relaxation rate of the unknown molecule. This rate determination improves the ability to estimate the mass of the unknown molecule from the determination of the Doppler dephasing rate. By performing a suite of automated, high-throughput measurements, there is the
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.
Quantitative analysis of iron oxides using Fourier transform infrared spectrophotometry
In this study, a systematic approach based on the application of Fourier transform infrared spectrophotometry (FTIR) was taken, in order to quantitatively analyze the corrosion products formed in the secondary cycle of pressurized water reactors (PWR). Binary mixtures of iron oxides were prepared with known compositions containing pure commercial magnetite (Fe3O4), maghemite (γ-Fe2O3), and hematite (α-Fe2O3) for calibration purposes. Calcium oxide (lime) was added to all samples as a standard reference in obtaining the calibration curves. Using regression analysis, relationships were developed for intensity versus concentration for absorption bands corresponding to each of the phases in their corresponding FTIR spectrum. Correlation coefficients, R2, of 0.82, 0.87, and 0.86 were obtained for maghemite-magnetite, hematite-magnetite, and hematite-maghemite systems, respectively. The calibration curves generated were used to quantify phases in multi-component unknown field samples that were obtained from different components (moisture separators, condensers, and high- and low- pressure heaters) of the two units (units 1 and 2) of the secondary cycle of the Comanche Peak PWR
Spectroscopic Stokes polarimetry based on Fourier transform spectrometer
Liu, Yeng-Cheng; Lo, Yu-Lung; Li, Chang-Ye; Liao, Chia-Chi
2015-02-01
Two methods are proposed for measuring the spectroscopic Stokes parameters using a Fourier transform spectrometer. In the first method, it is designed for single point measurement. The parameters are extracted using an optical setup comprising a white light source, a polarizer set to 0°, a quarter-wave plate and a scanning Michelson interferometer. In the proposed approach, the parameters are extracted from the intensity distributions of the interferograms produced with the quarter-wave plate rotated to 0°, 22.5°, 45° and -45°, respectively. For the second approach, the full-field and dynamic measurement can be designed based upon the first method with special angle design in a polarizer and a quarter-wave plate. Hence, the interferograms of two-dimensional detection also can be simultaneously extracted via a pixelated phase-retarder and polarizer array on a high-speed CCD camera and a parallel read-out circuit with a multi-channel analog to digital converter. Thus, a full-field and dynamic spectroscopic Stokes polarimetry without any rotating components could be developed. The validity of the proposed methods is demonstrated both numerically and experimentally. To the authors' knowledge, this could be the simplest optical arrangement in extracting the spectral Stokes parameters. Importantly, the latter one method avoids the need for rotating components within the optical system and therefore provides an experimentally straightforward means of extracting the dynamic spectral Stokes parameters.
X-ray Fourier-transform holographic microscope
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
Realization of a scalable coherent quantum Fourier transform
Debnath, Shantanu; Linke, Norbert; Figgatt, Caroline; Landsman, Kevin; Wright, Ken; Monroe, Chris
2016-05-01
The exponential speed-up in some quantum algorithms is a direct result of parallel function-evaluation paths that interfere through a quantum Fourier transform (QFT). We report the implementation of a fully coherent QFT on five trapped Yb+ atomic qubits using sequences of fundamental quantum logic gates. These modular gates can be used to program arbitrary sequences nearly independent of system size and distance between qubits. We use this capability to first perform a Deutsch-Jozsa algorithm where several instances of three-qubit balanced and constant functions are implemented and then examined using single qubit QFTs. Secondly, we apply a fully coherent five-qubit QFT as a part of a quantum phase estimation protocol. Here, the QFT operates on a five-qubit superposition state with a particular phase modulation of its coefficients and directly produces the corresponding phase to five-bit precision. Finally, we examine the performance of the QFT in the period finding problem in the context of Shor's factorization algorithm. This work is supported by the ARO with funding from the IARPA MQCO program and the AFOSR MURI on Quantum Measurement and Verification.
Calibration of the Herschel SPIRE Fourier Transform Spectrometer
Swinyard, B M; Hopwood, R; Valtchanov, I; Lu, N; Fulton, T; Benielli, D; Imhof, P; Marchili, N; Baluteau, J -P; Bendo, G J; Ferlet, M; Griffin, M J; Lim, T L; Makiwa, G; Naylor, D A; Orton, G S; Papageorgiou, A; Pearson, C P; Schulz, B; Sidher, S D; Spencer, L D; van der Wiel, M H D; Wu, R
2014-01-01
The Herschel 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 spatially extended source and uses the Herschel telescope as primary calibrator. Conversion from extended to point-source calibration is carried out using observations of the planet Uranus. The model of the telescope emission is shown to be accurate to within 6% and repeatable to better than 0.06% and, by comparison with models of Mars and Neptune, the Uranus model is shown to be accurate to within 3%. Multiple observations of a number of point-like sources show that the repeatability of the calibration is better than 1%, if the effects of the satellite absolu...
High-resolution wide-band Fast Fourier Transform spectrometers
Klein, Bernd; Krämer, Ingo; Bell, Andreas; Meyer, Klaus; Güsten, Rolf
2012-01-01
We describe the performance of our latest generations of sensitive wide-band high-resolution digital Fast Fourier Transform Spectrometer (FFTS). Their design, optimized for a wide range of radio astronomical applications, is presented. Developed for operation with the GREAT far infrared heterodyne spectrometer on-board SOFIA, the eXtended bandwidth FFTS (XFFTS) offers a high instantaneous bandwidth of 2.5 GHz with 88.5 kHz spectral resolution and has been in routine operation during SOFIA's Basic Science since July 2011. We discuss the advanced field programmable gate array (FPGA) signal processing pipeline, with an optimized multi-tap polyphase filter bank algorithm that provides a nearly loss-less time-to-frequency data conversion with significantly reduced frequency scallop and fast sidelobe fall-off. Our digital spectrometers have been proven to be extremely reliable and robust, even under the harsh environmental conditions of an airborne observatory, with Allan-variance stability times of several 1000 se...
Fourier transform infrared spectroscopy (FTIR) of laser-irradiated cementum
Rechmann, Peter; White, Joel M.; Cecchini, Silvia C. M.; Hennig, Thomas
2003-06-01
Utilizing Fourier Transform Infrared Spectroscopy (FTIR) in specular reflectance mode chemical changes of root cement surfaces due to laser radiation were investigated. A total of 18 samples of root cement were analyzed, six served as controls. In this study laser energies were set to those known for removal of calculus or for disinfection of periodontal pockets. Major changes in organic as well as inorganic components of the cementum were observed following Nd:YAG laser irradiation (wavelength 1064 nm, pulse duration 250 μs, free running, pulse repetition rate 20 Hz, fiber diameter 320 μm, contact mode; Iskra Twinlight, Fontona, Slovenia). Er:YAG laser irradiation (wavelength 2.94 μm, pulse duration 250 μs, free running, pulse repetition rate 6 Hz, focus diameter 620 μm, air water cooling 30 ml/min; Iskra Twinlight, Fontona, Slovenia) significantly reduced the Amid bands due to changes in the organic components. After irradiation with a frequency doubled Alexandrite laser (wavelength 377 nm, pulse duration 200 ns, q-switched, pulse repetition rate 20 Hz, beam diameter 800 μm, contact mode, water cooling 30 ml/min; laboratory prototype) only minimal reductions in the peak intensity of the Amide-II band were detected.
Liquid chromatography/Fourier transform IR spectrometry interface flow cell
Johnson, Charles C.; Taylor, Larry T.
1986-01-01
A zero dead volume (ZDV) microbore high performance liquid chromatography (.mu.HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a .mu.HPLC column end fitting to minimize the transfer volume of the effluents exiting the .mu.HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF.sub.2), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.
Single beam Fourier transform digital holographic quantitative phase microscopy
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
Single beam Fourier transform digital holographic quantitative phase microscopy
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.
Analysis of ovarian tumor pathology by Fourier Transform Infrared Spectroscopy
Mehrotra Ranjana
2010-12-01
Full Text Available Abstract Background Ovarian cancer is the second most common cancer among women and the leading cause of death among gynecologic malignancies. In recent years, infrared (IR spectroscopy has gained attention as a simple and inexpensive method for the biomedical study of several diseases. In the present study infrared spectra of normal and malignant ovarian tissues were recorded in the 650 cm-1 to 4000 cm-1 region. Methods Post surgical tissue samples were taken from the normal and tumor sections of the tissue. Fourier Transform Infrared (FTIR data on twelve cases of ovarian cancer with different grades of malignancy from patients of different age groups were analyzed. Results Significant spectral differences between the normal and the ovarian cancerous tissues were observed. In particular changes in frequency and intensity in the spectral region of protein, nucleic acid and lipid vibrational modes were observed. It was evident that the sample-to-sample or patient-to-patient variations were small and the spectral differences between normal and diseased tissues were reproducible. Conclusion The measured spectroscopic features, which are the spectroscopic fingerprints of the tissues, provided the important differentiating information about the malignant and normal tissues. The findings of this study demonstrate the possible use of infrared spectroscopy in differentiating normal and malignant ovarian tissues.
Multi-channel sampling theorems for band-limited signals with fractional Fourier transform
2008-01-01
Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies.
The Green's function for the three-dimensional linear Boltzmann equation via Fourier transform
Machida, Manabu
2016-04-01
The linear Boltzmann equation with constant coefficients in the three-dimensional infinite space is revisited. It is known that the Green's function can be calculated via the Fourier transform in the case of isotropic scattering. In this paper, we show that the three-dimensional Green's function can be computed with the Fourier transform even in the case of arbitrary anisotropic scattering.
Summation of the Fourier Transform of Measures and Four Denominator Estimates
In this paper we consider convergence exponent for the Fourier transform of surface-carried measures. We apply the obtained bound for the Fourier transform of measures to so-called four denominator estimate related to the Schroedinger operator on a lattice. (author)
The Clifford-Fourier transform $\\mathcal{F}_O$ and monogenic extensions
Lopez, Arnoldo Bezanilla; Sanchez, Omar Leon
2014-01-01
Several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding results of operational calculus. We obtain a technique to construct monogenic extensions of a certain type of continuous functions, and versions of the Paley-Wiener theorems are formulated.
Fractal surface synthesis based on two dimensional discrete Fourier transform
Zhou, Chao; Gao, Chenghui; Huang, Jianmeng
2013-11-01
The discrete Fourier transform(DFT) is used for fractional Brownian motion(FBM) surface synthesis in tribology(i.e., contact, sliding, and sealing, etc). However, the relationship between fractal parameters(fractal dimension and scale factor) and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface ( Sq) is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height( Sz), the skewness( Ssk) and the kurtosis( Sku) are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.
Geostationary Imaging Fourier Transform Spectrometer (GIFTS): science applications
Smith, W. L.; Revercomb, H. E.; Zhou, D. K.; Bingham, G. E.; Feltz, W. F.; Huang, H. L.; Knuteson, R. O.; Larar, A. M.; Liu, X.; Reisse, R.; Tobin, D. C.
2006-12-01
A revolutionary satellite weather forecasting instrument, called the "GIFTS" which stands for the "Geostationary Imaging Fourier Transform Spectrometer", was recently completed and successfully tested in a space chamber at the Utah State University's Space Dynamics Laboratory. The GIFTS was originally proposed by the NASA Langley Research Center, the University of Wisconsin, and the Utah State University and selected for flight demonstration as NASA's New Millennium Program (NMP) Earth Observing-3 (EO-3) mission, which was unfortunately cancelled in 2004. GIFTS is like a digital 3-d movie camera that, when mounted on a geostationary satellite, would provide from space a revolutionary four-dimensional view of the Earth's atmosphere. GIFTS will measure the distribution, change, and movement of atmospheric moisture, temperature, and certain pollutant gases, such as carbon monoxide and ozone. The observation of the convergence of invisible water vapor, and the change of atmospheric temperature, provides meteorologists with the observations needed to predict where, and when, severe thunderstorms, and possibly tornados, would occur, before they are visible on radar or in satellite cloud imagery. The ability of GIFTS to observe the motion of moisture and clouds at different altitudes enables atmospheric winds to be observed over vast, and otherwise data sparse, oceanic regions of the globe. These wind observations would provide the means to greatly improve the forecast of where tropical storms and hurricanes will move and where and when they will come ashore (i.e., their landfall position and time). GIFTS, if flown into geostationary orbit, would provide about 80,000 vertical profiles per minute, each one like a low vertical resolution (1-2km) weather balloon sounding, but with a spacing of 4 km. GIFTS is a revolutionary atmospheric sensing tool. A glimpse of the science measurement capabilities of GIFTS is provided through airborne measurements with the NPOESS Airborne
Fourier Transform Spectrometer measurements of Atmospheric Carbon Dioxide and Methane
Kivi, Rigel; Heikkinen, Pauli; Chen, Huilin; Hatakka, Juha; Laurila, Tuomas
2016-04-01
Ground based remote sensing measurements of column CO2 and CH4 using Fourier Transform Spectrometers (FTS) within the Total Carbon Column Observing Network (TCCON) are known for high precision and accuracy. These measurements are performed at various locations globally and they have been widely used in carbon cycle studies and validation of space born measurements. The relevant satellite missions include the Orbiting Carbon Observatory-2 (OCO-2) by the National Aeronautics and Space Administration (NASA); the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) by the European Space Agency (ESA); the Greenhouse gases Observing SATellite (GOSAT) by the Japan Aerospace Exploration Agency (JAXA) and the upcoming Sentinel-5 Precursor mission, which is an ESA mission and scheduled for launch in 2016. Results of the column CO2 and CH4 measurements at Sodankylä in northern Finland (at 67.4° N, 26.6° E) are reported in this study. The measurements have been performed on regular basis since the beginning of the program in early 2009. We also present evaluation of the data quality of the ground based measurements and comparisons with the available satellite based retrievals. In case of comparisons between the GOSAT and ground based retrievals of CO2 and CH4 no significant biases were found. Sodankylä is one of the northernmost stations in the TCCON network. However, the data coverage has been relatively good thanks to the progress towards automation of the FTS measurement system. At Sodankylä the retrievals have been also compared with the balloon borne AirCore measurements at the site. AirCore sampling system is directly related to the World Meteorological Organization in situ trace gas measurement scales. The balloon platform allows sampling in both stratosphere and troposphere, which is a benefit, compared to the aircraft in situ measurements.
The University of Toronto's balloon-borne Fourier transform spectrometer
Wunch, D.; Drummond, J. R.; Midwinter, C.; Taylor, J. R.; Fu, D.; Walker, K. A.; McElroy, C. T.; Strong, K.; Bernath, P.; Fast, H.
The University of Toronto s Fourier transform spectrometer U of T FTS derived from a Bomem DA5 Michelson-type interferometer was rebuilt and flown on the Middle Atmosphere Nitrogen TRend Assessment MANTRA high-altitude balloon platform in September 2004 The U of T FTS has a resolution of 0 02 cm -1 a spectral range covering 1200-5000 cm -1 and InSb and MCT detectors that measure simultaneously The spectrometer was originally built in the 1980s and purchased by the Meteorological Service of Canada To prepare the instrument for flight the original software was replaced with new LabVIEW control software creating a robust and easily-controlled instrument adaptable to either remote control or lab-based work As a result of replacing the software most of the electronics had to be replaced creating a lighter lower-power more robust instrument A description of the refurbishment will be presented Despite balloon launch and gondola pointing system failures during the MANTRA 2004 campaign two spectra were recorded on each detector during sunset from a float height of 35 km The data indicate that the instrument performed well throughout the flight and had the payload pointing been under control would have retrieved a full set of occultation data The data that were acquired will be shown The U of T FTS has since participated in a ground-based FTS inter-comparison campaign with two other FTS instruments the University of Toronto s Toronto Atmospheric Observatory TAO FTS a complementary NDACC station Network for the Detection of
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).
A Fourier transform infrared trace gas analyser for atmospheric applications
D. W. T. Griffith
2012-05-01
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 for 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 and accuracy. 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 Programme 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 application of the analyser in isotopic tracer experiments, for example ^{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.
Super-high-efficiency approximate calculation of series sum and discrete Fourier transform
Yan, Xin-Zhong
2013-01-01
We present a super-high-efficiency approximate computing scheme for series sum and discrete Fourier transform. The summation of a series sum or a discrete Fourier transform is approximated by summing over part of the terms multiplied by corresponding weights. The calculation is valid for the function under the transform being piecewise smooth in the continuum variable. The scheme reduces significantly the requirement for computer memory storage and enhances the numerical computation efficienc...
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
Campbell, Joel
2008-01-01
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
Rapid Bacterial Identification Using Fourier Transform Infrared Spectroscopy
Valentine, Nancy B.; Johnson, Timothy J.; Su, Yin-Fong; Forrester, Joel B.
2007-02-01
Recent studies at Pacific Northwest National Laboratory (PNNL) using infrared spectroscopy combined with statistical analysis have shown the ability to identify and discriminate vegetative bacteria, bacterial spores and background interferents from one another. Since the anthrax releases in 2001, rapid identification of unknown powders has become a necessity. Bacterial endospores are formed by some Bacillus species as a result of the vegetative bacteria undergoing environmental stress, e.g. a lack of nutrients. Endospores are formed as a survival mechanism and are extremely resistant to heat, cold, sunlight and some chemicals. They become airborne easily and are thus readily dispersed which was demonstrated in the Hart building. Fourier Transform Infrared (FTIR) spectroscopy is one of several rapid analytical methods used for bacterial endospore identification. The most common means of bacterial identification is culturing, but this is a time-consuming process, taking hours to days. It is difficult to rapidly identify potentially harmful bacterial agents in a highly reproducible way. Various analytical methods, including FTIR, Raman, photoacoustic FTIR and Matrix Assisted Laser Desorption/Ionization (MALDI) have been used to identify vegetative bacteria and bacterial endospores. Each has shown certain areas of promise, but each has shortcomings in terms of sensitivity, measurement time or portability. IR spectroscopy has been successfully used to distinguish between the sporulated and vegetative state. [1,2] It has also shown its utility at distinguishing between the spores of different species. [2-4] There are several Bacillus species that occur commonly in nature, so it is important to be able to distinguish between the many different species versus those that present an imminent health threat. The spectra of the different sporulated species are all quite similar, though there are some subtle yet reproducible spectroscopic differences. Thus, a more robust and
Thyroid lesions diagnosis by Fourier transformed infrared absorption spectroscopy (FTIR)
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 included
On the restriction of the Fourier transform to polynomial curves
Dendrinos, S.
2007-01-01
We prove a Fourier restriction theorem on curves parametrised by the mapping P(t) = (P1(t),..., Pn(t)), where each of the P1,..., Pn is a real-valued polynomial and t belongs to an interval on which each of the P1,..., Pn "resembles" a monomial.
Fourier transformation IR spectroscopy of rare earth hydrides and manganates
The publication describes IR optical investigations of rare earth hybrids and manganates. Both of these material systems have a pronounced interaction with light in the IR spectral region and are therefore well suited for Fourier transformation IR spectroscopy. Especially the spectra of the La1-xCaxMnO3 films contain many structures that derive both from the investigated film and the substrate. Quantitative information on the properties of the material system is obtained by separating the optical properties of LCMO from the substrate by means of adaptation using a multilayer formalism. The temperature dependence of the IR spectra was investigated down to the low-temperature range. Splitting and frequency shifts of the phonon modes were quantified, and the sensitive influence of the oxygen concentration of the samples on their optical properties was demonstrated. As representatives of the class of rare earth hybrids, various aspects of the material systems NdH2, EuH2 and YHx were investigated in thin film samples grown on substrates by means of molecular beam epitaxy. Detailed RHEED and Auger electron spectroscopy investigations provided information on the growth process, crystalline structure and chemical composition of the samples. By using a buffer layer between the rare earth metals and the palladium protective layer which is necessary with Nd and Eu, the minimum thickness of the Pd layer could be reduced about by half. The structural changes resulting from hydrogen loading are investigated by means of Raman measurements of the Nd hydride. The raman-active phonons that were observed for the first time by this method are strongly dependent on the crystal structure, i.e. the various phases are identified as a function of the hydrogen concentration. With the aid of the isotope effect, the origin of the phonons observed in the IR reflection and transmission spectra can be attributed to hydrogen oscillations. Evaluation of the spectra by multilayer formalism provides
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.
Improved method of generating bit reversed numbers for calculating fast fourier transform
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...
Implementation of Period-Finding Algorithm by Means of Simulating Quantum Fourier Transform
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.
Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.
Perkins, W. D.
1987-01-01
This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)
The Boundedness of Maximal Operators and Singular Integrals via Fourier Transform Estimates
Hong Hai LIU
2012-01-01
In this paper,the author studies the mapping properties for some general maximal operators and singular integrals on certain function spaces via Fourier transform estimates.Also,some concrete maximal operators and singular integrals are studied as applications.
Patino, A [Universidad Technologica de Bolivar, Cartagena de Indias (Colombia); Durand, P-E; Fogret, E; Pellat-Finet, P, E-mail: alberto.patino-vanegas@univ-ubs.fr [Laboratoire de mathematiques et applications des mathematiques, Universite de Bretagne Sud, B P 92116, 56321 Lorient cedex (France)
2011-01-01
According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.
AN ILLUMINATION INVARIANT FACE RECOGNITION USING 2D DISCRETE COSINE TRANSFORM AND CLAHE
A.Thamizharasi
2016-06-01
Full Text Available Automatic face recognition performance is affected due to the head rotations and tilt, lighting intensity and angle, facial expressions, aging and partial occlusion of face using Hats, scarves, glasses etc.In this paper, illumination normalization of face images is done by combining 2D Discrete Cosine Transform and Contrast Limited Adaptive Histogram Equalization. The proposed method selects certain percentage of DCT coefficients and rest is set to 0. Then, inverse DCT is applied which is followed by logarithm transform and CLAHE. Thesesteps create illumination invariant face image, termed as ‘DCT CLAHE’ image. The fisher face subspace method extracts features from ‘DCT CLAHE’ imageand features are matched with cosine similarity. The proposed method is tested in AR database and performance measures like recognition rate, Verification rate at 1% FAR and Equal Error Rate are computed. The experimental results shows high recognition rate in AR database.
Song, Xinbing; Qin, Hongwei; Li, Pengyun; Zhang, Xiangdong
2015-01-01
We perform Bell's measurement and perform quantum Fourier transform with the classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and nonquantum entanglement between the polarization and orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally, which is the crucial final step in Shor's algorithm
Muthuramalingam Uthaya Siva; Mohideen Abdul Badhul Haq; Deivasigamani Selvam; Ganesan Dinesh Babu; Rathinam Bakyaraj
2013-01-01
Objective: To investigate functional groups of toxic spines in stingray by Fourier transform infrared spectroscopic analysis. Methods: The venom extract of Himantura gerrardi, Himantura imbricata and Pastinachus sephen were centrifuged at 6 000 r/min for 10 min. The supernatant was collected and preserved separately in methanol, ethanol, chloroform, acetone (1:2) and then soaked in the mentioned solvents for 48 h. Then extracts were filtered and used for Fourier transform ...
CHEN Lin-Fei; ZHAO Dao-Mu
2006-01-01
@@ We propose a new method to add different images together by optical implementation that is realized by the multi-exposure based on fractional Fourier transform hologram. Partial image fusion is proposed and realized by this method. Multiple images encryption can also be implemented by the multi-exposure of the hologram based on fractional Fourier transform. Computer simulations prove that this method is valid.
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}.
Fourier-space inversion of the star transform
Zhao, Fan; Markel, Vadim A
2014-01-01
We define the star transform as a generalization of the broken ray transform introduced by us previously. The advantages of using the star transform include the possibility to reconstruct the absorption and the scattering coefficients of the medium separately and simultaneously (from the same data) and the possibility to utilize scattered radiation which, in the case of the conventional X-ray tomography, is discarded. In this paper, we derive the star transform from physical principles, discuss its mathematical properties and analyze numerical stability of inversion. In particular, it is shown that stable inversion of the star transform can be obtained only for configurations involving odd number of rays. Several computationally-efficient inversion algorithms are derived and tested numerically.
Kwieciena, P.; Richter, I.; Čtyroký, Jiří
Bellingham : SPIE, 2011, 83060Y. ISBN 978-0-8194-8953-1. [ Photonics , Devices, and Systems V. Praha (CZ), 24.08.2011-26.08.2011] Institutional research plan: CEZ:AV0Z20670512 Keywords : Fourier modal method * Bi-directional mode expansion propagation method * Bloch mode Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering
Factoring and Fourier Transformation with a Mach-Zehnder Interferometer
Summhammer, J
1997-01-01
The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for factoring N by means of an N-slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters the ratio of the coherence length to wavelength limits the numbers that can be factored. A conservative estimate permits $N \\approx 10^7$. It is furthermore shown, that sine and cosine Fourier coefficients of a real periodic function can be obtained with such an interferometer.
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.
Nonlinear Fourier transformation spectroscopy of small molecules with intense attosecond pulse train
We have developed an attosecond nonlinear molecular spectroscopic method called nonlinear Fourier transformation spectroscopy (NFTS) that uses an intense attosecond pulse train (APT) to induce multiphoton ionization processes. In the NFTS method, in addition to characterization of the temporal profile of attosecond pulses, the nonlinear molecular responses are encoded in the interferometric autocorrelation traces depending on the molecular species, their fragment ions and their kinetic energy distributions. The principle and applicability of the NFTS method are described in this paper along with the numerical simulations. The method is applied to diatomic molecules (N2 , D2 and O2) and polyatomic molecules (CO2, CH4 and SF6). Our results highlight the fact that nonlinear spectroscopic information of molecules in the short wavelength region can be obtained through the irradiation of intense APT by taking advantage of the broad spectral bandwidth of attosecond pulses. The development of the nonlinear spectroscopic method in attoseconds is expected to pave the way to investigate the ultrafast intramolecular electron motion such as ultrafast charge migration and electron correlation. (review article)
Nonlinear Fourier transformation spectroscopy of small molecules with intense attosecond pulse train
Okino, T.; Furukawa, Y.; Shimizu, T.; Nabekawa, Y.; Yamanouchi, K.; Midorikawa, K.
2014-06-01
We have developed an attosecond nonlinear molecular spectroscopic method called nonlinear Fourier transformation spectroscopy (NFTS) that uses an intense attosecond pulse train (APT) to induce multiphoton ionization processes. In the NFTS method, in addition to characterization of the temporal profile of attosecond pulses, the nonlinear molecular responses are encoded in the interferometric autocorrelation traces depending on the molecular species, their fragment ions and their kinetic energy distributions. The principle and applicability of the NFTS method are described in this paper along with the numerical simulations. The method is applied to diatomic molecules (N2 , D2 and O2) and polyatomic molecules (CO2, CH4 and SF6). Our results highlight the fact that nonlinear spectroscopic information of molecules in the short wavelength region can be obtained through the irradiation of intense APT by taking advantage of the broad spectral bandwidth of attosecond pulses. The development of the nonlinear spectroscopic method in attoseconds is expected to pave the way to investigate the ultrafast intramolecular electron motion such as ultrafast charge migration and electron correlation.
Yu, Lu; Sun, Su-qin; Zhou, Qun; Qin, Zhu
2006-12-01
Using multi-steps macro-fingerprint infrared (IR) spectroscopy, which combines three steps: conventional Fourier transform infrared spectroscopy (FTIR), second derivative spectroscopy, and two-dimensional infrared (2D-IR) correlation spectroscopy, the authors tracked dynamically the parching procedure of mustard seed to analyze the main transformation during the process. Compared with conventional IR spectra of samples parched for different time, the authors found that the characteristic peaks of protein decreased gradually, indicating the reduction of protein with the parching process, maybe because under a longtime parching procedure the heat denaturation occurred in protein compound. In addition, the essence of enzyme was protein, therefore, its transformation trend was closely related to that of protein, which also underwent heat denaturation. The absorption peak around 1 055 cm(-1), which was due to the vibrations of fibred saccharides, began to minish rapidly at early time, then vanished after ten minutes because of the decomposition of fibred saccharides at the beginning of the process. Moreover the results of second derivative spectroscopy and 2D IR correlation spectroscopy validated that of conventional IR spectroscopy, which also indicated the heat denaturation of enzyme and decomposition of saccharides. This multi-steps macro-fingerprint IR spectroscopy method can track dynamically the processing procedure of medicinal herbs and reveal the main transformations; it must play an important role in studying medicinal herbs in the future. PMID:17361704
Digital watermarking for still image based on discrete fractional fourier transform
无
2001-01-01
Presents a digital watermarking technique based on discrete fractional Fourier transform(DFRFT), discusses the transformation of the original image by DFRFT, and the modification of DFRFT coefficients of the original image by the information of watermark, and concludes from experimental results that the proposed tech nique is robust to lossy compression attack.
X-ray Coherent diffraction interpreted through the fractional Fourier transform
Bolloc'h, David Le; Sadoc, Jean-Francois
2011-01-01
Diffraction of coherent x-ray beams is treated through the Fractionnal Fourier transform. The transformation allow us to deal with coherent diffraction experiments from the Fresnel to the Fraunhofer regime. The analogy with the Huygens-Fresnel theory is first discussed and a generalized uncertainty principle is introduced.
Interpretation of gravity data using 2-D continuous wavelet transformation and 3-D inverse modeling
Roshandel Kahoo, Amin; Nejati Kalateh, Ali; Salajegheh, Farshad
2015-10-01
Recently the continuous wavelet transform has been proposed for interpretation of potential field anomalies. In this paper, we introduced a 2D wavelet based method that uses a new mother wavelet for determination of the location and the depth to the top and base of gravity anomaly. The new wavelet is the first horizontal derivatives of gravity anomaly of a buried cube with unit dimensions. The effectiveness of the proposed method is compared with Li and Oldenburg inversion algorithm and is demonstrated with synthetics and real gravity data. The real gravity data is taken over the Mobrun massive sulfide ore body in Noranda, Quebec, Canada. The obtained results of the 2D wavelet based algorithm and Li and Oldenburg inversion on the Mobrun ore body had desired similarities to the drill-hole depth information. In all of the inversion algorithms the model non-uniqueness is the challenging problem. Proposed method is based on a simple theory and there is no model non-uniqueness on it.
A two-step Hilbert transform method for 2D image reconstruction
Noo, Frederic; Clackdoyle, Rolf; Pack, Jed D [UCAIR, Department of Radiology, University of Utah, UT (United States)
2004-09-07
The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image. Formulae for performing the DBP step in fan-beam geometry are also presented. The advantage of this two-step Hilbert transform approach is that in certain situations, regions of interest (ROIs) can be reconstructed from truncated projection data. Simulation results are presented that illustrate very similar reconstructed image quality using the new method compared to standard filtered backprojection, and that show the capability to correctly handle truncated projections. In particular, a simulation is presented of a wide patient whose projections are truncated laterally yet for which highly accurate ROI reconstruction is obtained.
A two-step Hilbert transform method for 2D image reconstruction
The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image. Formulae for performing the DBP step in fan-beam geometry are also presented. The advantage of this two-step Hilbert transform approach is that in certain situations, regions of interest (ROIs) can be reconstructed from truncated projection data. Simulation results are presented that illustrate very similar reconstructed image quality using the new method compared to standard filtered backprojection, and that show the capability to correctly handle truncated projections. In particular, a simulation is presented of a wide patient whose projections are truncated laterally yet for which highly accurate ROI reconstruction is obtained
A two-step Hilbert transform method for 2D image reconstruction.
Noo, Frédéric; Clackdoyle, Rolf; Pack, Jed D
2004-09-01
The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image. Formulae for performing the DBP step in fanbeam geometry are also presented. The advantage of this two-step Hilbert transform approach is that in certain situations, regions of interest (ROIs) can be reconstructed from truncated projection data. Simulation results are presented that illustrate very similar reconstructed image quality using the new method compared to standard filtered backprojection, and that show the capability to correctly handle truncated projections. In particular, a simulation is presented of a wide patient whose projections are truncated laterally yet for which highly accurate ROI reconstruction is obtained. PMID:15470913
Orthonormal mode sets for the two-dimensional fractional Fourier transformation.
Alieva, Tatiana; Bastiaans, Martin J
2007-05-15
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 orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied. PMID:17440542
Fourier and Schur-Weyl transforms applied to XXX Heisenberg magnet
Similarities and differences between Fourier and Schur-Weyl transforms have been discussed in the context of a one-dimensional Heisenberg magnetic ring with N nodes. We demonstrate that main difference between them correspond to another partitioning of the Hilbert space of the magnet. In particular, we point out that application of the quantum Fourier transform corresponds to splitting of the Hilbert space of the model into subspaces associated with the orbits of the cyclic group, whereas, the Schur-Weyl transform corresponds to splitting into subspaces associated with orbits of the symmetric group.
Fourier transform microscope of the direct observation for nuclear emulsion
'The fourier transfom (FT) microscope of the direct observation' for tracks of charged particles in the nuclear emulsion is described. The working flow charts are given of the digital processing of the signals from the array of photodetectors disposed just behind the narrow transmitting slit in the FT plane. The general theory of this new device is presented. The net effect of the proposed processing algorithms is discussed. It is shown experimentally that with such a system we can detect the particle tracks with linear density of 40 silver grains per 100 μm with initial signal-to-noise ratio 1:3. The recommendations for the searching for the particle tracks of low ionization level in the nuclear emulsion by means of the FT microscope of the direct observation are described. 9 refs.; 15 figs.; 1 tab
The Logvinenko-Sereda Theorem for the Fourier-Bessel transform
Ghobber, Saifallah
2012-01-01
The aim of this paper is to establish an analogue of Logvinenko-Sereda's theorem for the Fourier-Bessel transform (or Hankel transform) $\\ff_\\alpha$ of order $\\alpha>-1/2$. Roughly speaking, if we denote by $PW_\\alpha(b)$ the Paley-Wiener space of $L^2$-functions with Fourier-Bessel transform supported in $[0,b]$, then we show that the restriction map $f\\to f|_\\Omega$ is essentially invertible on $PW_\\alpha(b)$ if and only if $\\Omega$ is sufficiently dense. Moreover, we give an estimate of the norm of the inverse map. As a side result we prove a Bernstein type inequality for the Fourier-Bessel transform.