The Fourier Transform on Quantum Euclidean Space
NASA Astrophysics Data System (ADS)
Coulembier, Kevin
2011-05-01
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.
Quantum Fourier Transform in Computational Basis
S. S. Zhou; T. Loke; J. A. Izaac; J. B. Wang
2015-11-16
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum algorithm to encode the Fourier coefficients in the computational basis, with success probability $1-\\delta$ and desired precision $\\epsilon$. Its time complexity %$\\mathcal{O}\\big((\\log N)^2\\log(N/\\delta)/\\epsilon)\\big)$ depends polynomially on $\\log(N)$, where $N$ is the problem size, and linearly on $\\log(1/\\delta)$ and $1/\\epsilon$. We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
Purple bacteria and quantum Fourier transform
Samir Lipovaca
2007-02-22
The LH-II of purple bacteria Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila adopts a highly symmetrical ring shape, with a radius of about 7 nm. In the case of Rps. acidophila the ring has a ninefold symmetry axis, and in LH-II from Rs. molischianum the ring has an eightfold symmetry axis. These rings are found to exibit two bands of excitons. A simplified mathematical description of the exciton states is given in Hu, X. & Schulten, K. (1997) Physics Today 50, 28-34. Using this description, we will show, by suitable labeling of the lowest energy (Qy) excited states of individual BChls, that the resulting exciton states are the quantum Fourier transform of the BChls excited states. For Rs. molischianum ring exciton states will be modeled as the four qubit quantum Fourier transform and the explicit circuit will be derived. Exciton states for Rps. acidophila ring cannot be modeled with an integer number of qubits. Both quantum Fourier transforms are instances of the hidden subgroup problem and this opens up a possibility that both purple bacteria implement an efficient quantum circuit for light harvesting.
The Fourier Transform Approach to Quantum Coding
Hari Dilip Kumar; B. Sundar Rajan
2012-09-04
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from stabilizer codes, and Clifford codes. We analyze these in the framework of the Fourier inversion formula on a group algebra, the group in question being a subgroup of the error group considered. We study other possible code spaces that may be obtained via such an approach, obtaining codes that are the direct sums of translates of Clifford codes, and more general codes obtained from idempotents in the transform domain. We derive necessary and sufficient conditions for error detection by direct sums of translates of Clifford codes, and provide an example using an error group with non-Abelian index group.
Fourier transform spectra of quantum dots
NASA Astrophysics Data System (ADS)
Damian, V.; Ardelean, I.; Arm??elu, Anca; Apostol, D.
2010-05-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
Fourier transform spectra of quantum dots
NASA Astrophysics Data System (ADS)
Damian, V.; Ardelean, I.; Arm??elu, Anca; Apostol, D.
2009-09-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
Implementation of Quantum and Classical Discrete Fractional Fourier Transforms
Steffen Weimann; Armando Perez-Leija; Maxime Lebugle; Robert Keil; Malte Tichy; Markus Gräfe; Rene Heilmann; Stefan Nolte; Hector Moya-Cessa; Gregor Weihs; Demetrios N. Christodoulides; Alexander Szameit
2015-07-31
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the integrated configuration used in our experiments, the order of the transform is mapped onto the longitudinal coordinate, thus opening up the prospect of simultaneously observing all Transformation orders. In the context of classical optics, we implement discrete fractional Fourier transforms, both integer and fractional, of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to transform separable and highly entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools, such as quantum chemistry and biology, physics and mathematics.
Quantum fast Fourier transform using multilevel atoms ASHOK MUTHUKRISHNAN and C. R. STROUD, JR.
Stroud Jr., Carlos R.
Quantum fast Fourier transform using multilevel atoms ASHOK MUTHUKRISHNAN and C. R. STROUD, JR of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform packets amounts to a discrete quantum Fourier transform within each atom. The algorithm then reduces
Quantum control in two-dimensional Fourier-transform spectroscopy
Lim, Jongseok; Lee, Han-gyeol; Lee, Sangkyung; Ahn, Jaewook
2011-07-15
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 5P{sub 1/2}{yields} 5P{sub 3/2} transition was successfully tested in which the engineered transitions were distinguishably extracted in the presence of dominant one-photon transitions.
The amplified quantum Fourier transform: solving the local period problem
NASA Astrophysics Data System (ADS)
Cornwell, David J.
2013-02-01
This paper creates and analyzes a new quantum algorithm called the Amplified Quantum Fourier Transform (QFT) for solving the following problem: The Local Period Problem: Let L = {0,1 . . . N-1} be a set of N labels and let A be a subset of M labels of period P, i.e. a subset of the form A=\\{j:j=s+rP,r=0,1ldots M-1\\} where {P? sqrt{N}} and {M ? N}, and where M is assumed known. Given an oracle f : L? {0,1} which is 1 on A and 0 elsewhere, find the local period P and the offset s.
The Amplified Quantum Fourier Transform: solving the local period problem
David J. Cornwell
2012-08-12
This paper creates and analyses a new quantum algorithm called the Amplified Quantum Fourier Transform (Amplified-QFT) for solving the following problem: The Local Period Problem: Let L = {0,1...N-1} be a set of N labels and let A be a subset of M labels of period P, i.e. a subset of the form A = {j : j = s + rP; r = 0,1...M-1} where P {0,1} which is 1 on A and 0 elsewhere, find the local period P. A separate algorithm finds the offset s. The first part of the paper defines the Amplified-QFT algorithm. The second part of the paper summarizes the main results and compares the Amplified-QFT algorithm against the Quantum Fourier Transform (QFT) and Quantum Hidden Subgroup (QHS) algorithms when solving the local period problem. It is shown that the Amplified-QFT is, on average, quadratically faster than both the QFT and QHS algorithms. The third part of the paper provides the detailed proofs of the main results, describes the method of recovering P from an observation y and describes the method for recovering the offset s.
Fast parallel circuits for the quantum Fourier transform
Richard Cleve; John Watrous
2000-06-01
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n with error bounded by epsilon. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations with constant error. Moreover, our circuits have size O(n log (n/epsilon)). We also give an upper bound of O(n (log n)^2 log log n) on the circuit size of the exact QFT modulo 2^n, for which the best previous bound was O(n^2). As an application of the above depth bound, we show that Shor's factoring algorithm may be based on quantum circuits with depth only O(log n) and polynomial-size, in combination with classical polynomial-time pre- and post-processing. In the language of computational complexity, this implies that factoring is in the complexity class ZPP^BQNC, where BQNC is the class of problems computable with bounded-error probability by quantum circuits with poly-logarithmic depth and polynomial size. Finally, we prove an Omega(log n) lower bound on the depth complexity of approximations of the QFT with constant error. This implies that the above upper bound is asymptotically optimal (for a reasonable range of values of epsilon).
NASA Astrophysics Data System (ADS)
Krovi, Hari; Russell, Alexander
2015-03-01
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups [denoted , for a group G]. These induce a rich family of knot invariants and, additionally, are directly related to topological quantum computation. Regarding algorithms for these invariants, we develop quantum circuits for the quantum Fourier transform over ; in general, we show that when one can uniformly and efficiently carry out the quantum Fourier transform over the centralizers Z( g) of the elements of G, one can efficiently carry out the quantum Fourier transform over . We apply these results to the symmetric groups to yield efficient circuits for the quantum Fourier transform over . With such a Fourier transform, it is straightforward to obtain additive approximation algorithms for the related link invariant. As for hardness results, first we note that in contrast to those concerning the Jones polynomial—where the images of the braid group representations are dense in the unitary group—the images of the representations arising from are finite. This important difference appears to be directly reflected in the complexity of these invariants. While additively approximating "dense" invariants is -complete and multiplicatively approximating them is -complete, we show that certain invariants (such as invariants) are -hard to additively approximate, -hard to multiplicatively approximate, and -hard to exactly evaluate. To show this, we prove that, for groups (such as A n ) which satisfy certain properties, the probability of success of any randomized computation can be approximated to within any by the plat closure. Finally, we make partial progress on the question of simulating anyonic computation in groups uniformly as a function of the group size. In this direction, we provide efficient quantum circuits for the Clebsch-Gordan transform over for "fluxon" irreps, i.e., irreps of characterized by a conjugacy class of G. For general irreps, i.e., those which are associated with a conjugacy class of G and an irrep of a centralizer, we present an efficient implementation under certain conditions, such as when there is an efficient Clebsch-Gordan transform over the centralizers (this could be a hard problem for some groups). We remark that this also provides a simulation of certain anyonic models of quantum computation, even in circumstances where the group may have size exponential in the size of the circuit.
Implementation of the quantum Fourier transform on a hybrid qubit-qutrit NMR quantum emulator
Shruti Dogra; Arvind; Kavita Dorai
2015-03-23
The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a circuit decomposition of the QFT for hybrid qudits based on generalized Hadamard and generalized controlled-phase gates, which can be implemented using selective rotations in NMR. We experimentally implement the hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate a single qutrit coupled to two qubits.
Quantum suppression law in a 3-D photonic chip implementing the Fast Fourier Transform
Andrea Crespi; Roberto Osellame; Roberta Ramponi; Marco Bentivegna; Fulvio Flamini; Nicolò Spagnolo; Niko Viggianiello; Luca Innocenti; Paolo Mataloni; Fabio Sciarrino
2015-08-04
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multiparticle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transformation in the Fock space. In this work we develop a scalable approach for the implementation of quantum fast Fourier transform using 3-D photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the quantum suppression of a large number of output states with 4- and 8-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms.
Fourier Transform Pairs The Fourier transform transforms a function of
Masci, Frank
Fourier Transform Pairs The Fourier transform transforms a function of time, f(t), into a function of frequency, F(s): F {f(t)}(s) = F(s) = Z - f(t)e- j2st dt. The inverse Fourier transform transforms a func. The inverse Fourier transform of the Fourier trans- form is the identity transform: f(t) = Z - Z - f()e- j2s
Fourier Transform Infrared Spectroscopy
Nizkorodov, Sergey
FTIR - 1 Fourier Transform Infrared Spectroscopy FTIR DETERMINATION OF MTBE IN GASOLINE AND ETHANOL IN VODKA AND MOUTHWASH Last updated: June 17, 2014 #12;FTIR - 2 Fourier Transform Infrared Spectroscopy
Song, Xinbing; Sun, Yifan; Li, Pengyun; Qin, Hongwei; Zhang, Xiangdong
2015-01-01
We perform Bell's measurement for the non-separable correlation between polarization and orbital angular momentum from the same 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 non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally. PMID:26369424
Cavity QED implementation of the discrete quantum Fourier transform
Scully, Marlan O.; Zubairy, M. Suhail
2002-01-01
& to be the excited state and ub& to be the ground state. The correspond- ing time-evolution unitary operator is given by UI~ t !5expS2 i\\Vt D 5cos~Vt/2!~ ua&^au1ub&^bu! 2i sin~Vt/2!~e2ifua&^bu1eifub&^au!. ~8! This corresponds to the one-bit unitary gate ~2...! with u 5Vt/2. The quantum phase gate can be implemented via disper- sive coupling of a three-level atom with a cavity field @5#. We assume a three-level atom in V configuration with ub& to be the ground state and ua& and uc& to be the excited states...
Claude Sabbah FOURIER TRANSFORMATION AND
Sabbah, Claude
Claude Sabbah FOURIER TRANSFORMATION AND STOKES STRUCTURES CHICAGO, MAY 2012 WORK IN PROGRESS, 2013 #12;FOURIER TRANSFORMATION AND STOKES STRUCTURES CHICAGO, MAY 2012 WORK IN PROGRESS (VERSION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Fourier transformation: some analogies between arithmetic and complex algebraic geometry
Exhibition of the periodicity of Quantum Fourier Transformation in Nuclear Magnetic Resonance
Xinhua Peng; Xiwen Zhu; Ximing Fang; Mang Feng; Xiaodong Yang; Maili Liu; Kelin Gao
2002-02-01
The remarkable capability of quantum Fourier transformation (QFT) to extract the periodicity of a given periodic function has been exhibited by using nuclear magnetic resonance (NMR) techniques. Two separate sets of experiments were performed. In a full QFT, the periodicity were validated with state tomography and fidelity measurements. For a simplified QFT, the three-qubit pseudo-pure state was created by introducting an additional observer spin, and the spectra recorded on the observer spin showed intuitively the power of QFT\\ to find the periodicity. Experimentally realizing the QFT provides a critical step to implement the renowned Shor's quantum factoring algorithm and many other algorithms. Moveover, it can be applied to the study of quantum chaos and other quantum information processing.
Imaging Fourier transform spectrometer
Bennett, C.L.
1993-09-13
This invention is comprised of an imaging Fourier transform spectrometer having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer.
V. P. Shauro; V. E. Zobov
2012-11-21
We consider the problem of time-optimal realization of the quantum Fourier transform gate for a single qudit with number of levels d from 3 to 8. As a qudit the quadrupole nucleus with spin I > 1/2 controlled by NMR is considered. We calculate the dependencies of the gate error on the duration of radio-frequency pulse obtained by numerical optimization using Krotov-based algorithm. It is shown that the dependences of minimum time of QFT gate implementation on qudit dimension are different for integer and half-integer spins.
Enobio, Eli Christopher I.; Ohtani, Keita; Ohno, Yuzo; Ohno, Hideo
2013-12-02
We demonstrate the use of a Fourier Transform Infrared microscope system to detect and measure electroreflectance (ER) from mid-infrared quantum cascade laser (QCL) device. To characterize intersubband transition (ISBT) energies in a functioning QCL device, a microscope is used to focus the probe on the QCL cleaved mirror. The measured ER spectra exhibit resonance features associated to ISBTs under applied electric field in agreement with the numerical calculations and comparable to observed photocurrent, and emission peaks. The method demonstrates the potential as a characterization tool for QCL devices.
Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
1998-01-01
Understanding the global atmospheric changes is difficult with today's current technology. However, with high resolution and nearly continuous observations from a satellite, it's possible to transform our understanding of the atmosphere. To enable the next generation of atmospheric science, a new class of orbiting atmospheric sensors is being developed. The foundation of this advanced concept is the Fourier Transform Spectrometer, or FTS.
Discrete Fourier Transform Javier Montoya
Giger, Christine
Discrete Fourier Transform Javier Montoya Photogrammetry and Remote Sensing ETH Zurich March 16, 2012 1 Introduction The Discrete form of the Fourier transform is known as Discrete Fourier Transform domain using the Inverse Discrete Fourier Transform (IDFT): f(x) = 1 N N-1 x=0 F(u)ej 2 N ux for u = 0, 1
Claude Sabbah FOURIER TRANSFORMATION OF
Sabbah, Claude
Claude Sabbah FOURIER TRANSFORMATION OF D-MODULES AND APPLICATIONS LECTURE NOTES (CIRM, LUMINY://www.math.polytechnique.fr/~sabbah #12;FOURIER TRANSFORMATION OF D-MODULES AND APPLICATIONS LECTURE NOTES (CIRM, LUMINY, SEPT. 2010 of the Fourier transformation of holonomic D-modules. Firstly, a compar- ison is made with the usual Fourier
Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...
Fourier Transform Infrared (FTIR) Spectroscopy
Gerwert, Klaus
Fourier Transform Infrared (FTIR) Spectroscopy Klaus Gerwert, Lehrstuhl fu¨r Biophysik, Ruhr, Germany Based in part on the previous version of this Encyclopedia of Life Sciences (ELS) article, Fourier Transform IR by Johannes Orphal. Fourier transform infrared (FTIR) spectroscopy is an experimental technique
NASA Technical Reports Server (NTRS)
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Neural data Fourier transforms, spectral
Lin, Kevin K.
Neural data analysis - Session 2 Fourier transforms, spectral analysis #12;Why Fourier? A lot of these oscillations is often of interest Fourier analysis provides a way of identifying the frequencies of the oscillations present in a signal #12;Math review complex numbers #12;Waves - terminology #12;Fourier series
ContentsContents2424Fourier 1. The Fourier transform
Vickers, James
ContentsContents2424Fourier transforms 1. The Fourier transform 2. Properties of the Fourier Transform 3. Some Special Fourier Transform Pairs Learning outcomes needs doing Time allocation You mathematical topics this time may vary considerably. 1 #12;The Fourier Transform 24.1 Introduction
Fourier transforms from strongly complementary observables
Stefano Gogioso; William Zeng
2015-08-14
Ongoing work in quantum information emphasises the need for a structural understanding of quantum speedups: in this work, we focus on the quantum Fourier transform and the structures in quantum theory that enable it. We elucidate a general connection in any process theory between the Fourier transform and strongly complementary observables, i.e. Hopf algebras in dagger symmetric monoidal categories. We generalise the necessary tools of representation theory from fdHilb to arbitrary dagger symmetric monoidal categories. We define groups, characters and representations, and we prove their relation to strong complementarity. The Fourier transform is then defined in terms of pairs of strongly complementary observables, in both the abelian and non-abelian case. In the abelian case, we draw the connection with Pontryagin duality and provide categorical proofs of the Fourier Inversion Theorem, the Convolution Theory, and Pontryagin duality. Our work finds application in the novel characterisation of the Fourier transform for the category fRel of finite sets and relations. This is a result of interest for the study of categorical quantum algorithms, as the usual construction of the quantum Fourier transform in terms of Fourier matrices is shown to fail in fRel. Despite this, the process theoretic perspective on the Fourier transform is sensible in this setting. Furthermore, our categorical setting provides a generalisation of the abelian Fourier transform from finite-dimensional Hilbert spaces to finite-dimensional modules over arbitrary semirings, as well as a further generalisation to finite non-abelian groups, including a fully categorical generalisation of the Gelfand-Naimark theorem.
Fast Fourier transform telescope
Tegmark, Max; Zaldarriaga, Matias
2009-04-15
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog{sub 2}N rather than N{sup 2}) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Fourier Transform Spectrometer System
NASA Technical Reports Server (NTRS)
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
Some Special Fourier Transform Pairs
Vickers, James
Some Special Fourier Transform Pairs 24.3 Introduction ' & $ % Prerequisites Before starting to . . . #12;1. Parseval's Theorem Recall from Unit 2 on Fourier Series that for a periodic signal fT (t) with complex Fourier coefficients cn(n = 0, ±1, ±2, . . .) Parseval's Theorem holds: 1 T + T 2 - T 2 f2 T (t
Wavelets and Fourier Transforms, WISM453 Part 1: Fourier Theory
Sleijpen, Gerard
Wavelets and Fourier Transforms, WISM453 Part 1: Fourier Theory G.L.G. Sleijpen Department of Mathematics Utrecht University August 18, 2008 1 #12;i Preface Fourier Theory belongs to the basic who works in such a field should feel comfortable with Fourier transforms. But Fourier The- ory also
A NEW FOURIER TRANSFORM JONATHAN WANG
May, J. Peter
A NEW FOURIER TRANSFORM JONATHAN WANG Abstract. In order to define a geometric Fourier transform action of Gm, however, Laumon provides a uniform geometric construction of the Fourier transform in any the relation between this new functor and Laumon's homogeneous transform, the Fourier-Deligne transform
Fourier transforms of UD integrals
Igor Kondrashuk; Anatoly Kotikov
2008-02-23
UD integrals published by N. Usyukina and A. Davydychev in 1992-1993 are integrals corresponding to ladder-type Feynman diagrams. The results are UD functions $\\Phi^{(L)},$ where $L$ is the number of loops. They play an important role in N=4 supersymmetic Yang-Mills theory. The integrals were defined and calculated in the momentum space. In this paper the position space representation of UD functions is investigated. We show that Fourier transforms of UD functions are UD functions of space-time intervals but this correspondence is indirect. For example, the Fourier transform of the second UD integral is the second UD integral.
Fourier transform of confining potentials
Heiss, W.D.; Welke, G.M.
1986-04-01
The precise meaning of the Fourier transform of Vertical BarxVertical Bar/sup ..nu../ is examined. A general expression is given for real positive ..nu... For odd ..nu.., derivatives of principal value integrals are obtained, while even ..nu.. gives rise to derivatives of the delta function.
ERIC Educational Resources Information Center
Debnath, Lokenath
2012-01-01
This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…
Birefringent Fourier-transform imaging spectrometer
Harvey, Andy
Birefringent Fourier-transform imaging spectrometer Andrew Robert Harvey and David William Fletcher.r.Harvey@hw.ac.uk http://www.ece.eps.hw.ac.uk/~arharvey Abstract: Fourier-transform imaging spectrometers offer important, for application in harsh environments, deployment of Fourier-transform instruments based on traditional moving
Fourier transform channeled spectropolarimetry in the MWIR
Dereniak, Eustace L.
Fourier transform channeled spectropolarimetry in the MWIR Michael W. Kudenov,1 Nathan A. Hagen, 1 Abstract: A complete Fourier Transform Spectropolarimeter in the MWIR is demonstrated. The channeled and links 1. P. Griffiths and J. D. Haseth, "Fourier Transform Infrared Spectrometry," (John Wiley & Sons
The Fourier Transform -A Primer Hagit Shatkay
Learned, John
The Fourier Transform - A Primer Hagit Shatkay Department of Computer Science Brown University Providence, Rhode Island 02912 CS-95-37 November 1995 #12;#12;The Fourier Transform { A Primer Hagit Shatkay Department of Computer Science Brown University Providence, RI 02912 1 Introduction The Fourier transform
LOCAL FOURIER TRANSFORMS AND RIGIDITY FOR D-MODULES
Bloch, Spencer
LOCAL FOURIER TRANSFORMS AND RIGIDITY FOR D. Local Fourier transforms, analogous to the `-adic local Fourier transforms [14], are constructed infinitesimal rigidity condition is satisfied. As in [12], the argument uses local Fourier transforms
Fourier-transform optical microsystems
NASA Technical Reports Server (NTRS)
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.
Improved Fourier-transform profilometry
Mao Xianfu; Chen Wenjing; Su Xianyu
2007-02-10
An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object.
Fourier Transform, Riemann Surfaces and Indefinite Metric
Fominov, Yakov
Fourier Transform, Riemann Surfaces and Indefinite Metric P. G. Grinevich, S.P.Novikov Zakharov Park, College Park, USA #12;What is Fourier Transform in Riemann Surfaces? Which Problems need it? Discrete Analog of The Fourier/Laurent bases in Riemann Sur- faces was constructed by Krichever-Novikov (KN
The Fourier Transform A Primer Hagit Shatkay
The Fourier Transform A Primer Hagit Shatkay Department of Computer Science Brown University Providence, Rhode Island 02912 CS9537 November 1995 #12; #12; The Fourier Transform -- A Primer Hagit Shatkay Department of Computer Science Brown University Providence, RI 02912 1 Introduction The Fourier
The Fast Fourier Transform Telescope
Max Tegmark; Matias Zaldarriaga
2009-04-24
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of Fast Fourier Transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as N log N rather than N^2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large Fast Fourier Transform Telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Laser Field Imaging Through Fourier Transform Heterodyne
Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.
1999-04-05
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.
On Zeros of Fourier Transforms
Ruiming Zhang
2015-12-24
In this work we verify the sufficiency of a Jensen's necessary and sufficient condition for a class of genus 0 or 1 entire functions to have only real zeros. They are Fourier transforms of even, positive, indefinitely differentiable, and very fast decreasing functions. We also apply our result to several important special functions in mathematics, such as modified Bessel function $K_{iz}(a),\\ a>0$ as a function of variable $z$, Riemann Xi function $\\Xi(z)$, and character Xi function $\\Xi(z;\\chi)$ when $\\chi$ is a real primitive non-principal character satisfying $\\varphi(u;\\chi)\\ge0$ on the real line, we prove these entire functions have only real zeros.
Masci, Frank
The Fourier Transform The Fourier transform is crucial to any discussion of time series analysis: Fourier Series Fourier Transform Example and Interpretation Oddness and Evenness The Convolution Theorem Discrete Fourier Transforms Definitions Example Implementation Author Ã Fourier Series Recall the Fourier
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
ERIC Educational Resources Information Center
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
Fourier transform infrared (FTIR) spectroscopy.
Berthomieu, Catherine; Hienerwadel, Rainer
2009-01-01
Fourier transform infrared (FTIR) spectroscopy probes the vibrational properties of amino acids and cofactors, which are sensitive to minute structural changes. The lack of specificity of this technique, on the one hand, permits us to probe directly the vibrational properties of almost all the cofactors, amino acid side chains, and of water molecules. On the other hand, we can use reaction-induced FTIR difference spectroscopy to select vibrations corresponding to single chemical groups involved in a specific reaction. Various strategies are used to identify the IR signatures of each residue of interest in the resulting reaction-induced FTIR difference spectra. (Specific) Isotope labeling, site-directed mutagenesis, hydrogen/deuterium exchange are often used to identify the chemical groups. Studies on model compounds and the increasing use of theoretical chemistry for normal modes calculations allow us to interpret the IR frequencies in terms of specific structural characteristics of the chemical group or molecule of interest. This review presents basics of FTIR spectroscopy technique and provides specific important structural and functional information obtained from the analysis of the data from the photosystems, using this method. PMID:19513810
Safouhi, Hassan . E-mail: hassan.safouhi@ualberta.ca; Berlu, Lilian
2006-07-20
Molecular overlap-like quantum similarity measurements imply the evaluation of overlap integrals of two molecular electronic densities related by Dirac delta function. When the electronic densities are expanded over atomic orbitals using the usual LCAO-MO approach (linear combination of atomic orbitals), overlap-like quantum similarity integrals could be expressed in terms of four-center overlap integrals. It is shown that by introducing the Fourier transform of delta Dirac function in the integrals and using the Fourier transform approach combined with the so-called B functions, one can obtain analytic expressions of the integrals under consideration. These analytic expressions involve highly oscillatory semi-infinite spherical Bessel functions, which are the principal source of severe numerical and computational difficulties. In this work, we present a highly efficient algorithm for a fast and accurate numerical evaluation of these multicenter overlap-like quantum similarity integrals over Slater type functions. This algorithm is based on the SD-bar approach due to Safouhi. Recurrence formulae are used for a better control of the degree of accuracy and for a better stability of the algorithm. The numerical result section shows the efficiency of our algorithm, compared with the alternatives using the one-center two-range expansion method, which led to very complicated analytic expressions, the epsilon algorithm and the nonlinear D-bar transformation.
The Geostationary Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Key, Richard; Sander, Stanley; Eldering, Annmarie; Miller, Charles; Frankenberg, Christian; Natra, Vijay; Rider, David; Blavier, Jean-Francois; Bekker, Dmitriy; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for an earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. The GeoFTS instrument is a half meter cube size instrument designed to operate in geostationary orbit as a secondary "hosted" payload on a commercial geostationary satellite mission. The advantage of GEO is the ability to continuously stare at a region of the earth, enabling frequent sampling to capture the diurnal variability of biogenic fluxes and anthropogenic emissions from city to continental scales. The science goal is to obtain a process-based understanding of the carbon cycle from simultaneous high spatial resolution measurements of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) many times per day in the near infrared spectral region to capture their spatial and temporal variations on diurnal, synoptic, seasonal and interannual time scales. The GeoFTS instrument is based on a Michelson interferometer design with a number of advanced features incorporated. Two of the most important advanced features are the focal plane arrays and the optical path difference mechanism. A breadboard GeoFTS instrument has demonstrated functionality for simultaneous measurements in the visible and IR in the laboratory and subsequently in the field at the California Laboratory for Atmospheric Remote Sensing (CLARS) observatory on Mt. Wilson overlooking the Los Angeles basin. A GeoFTS engineering model instrument is being developed which will make simultaneous visible and IR measurements under space flight like environmental conditions (thermal-vacuum at 180 K). This will demonstrate critical instrument capabilities such as optical alignment stability, interferometer modulation efficiency, and high throughput FPA signal processing. This will reduce flight instrument development risk and show that the GeoFTS design is mature and flight ready.
The Geostationary Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Fourier Transform Heterodyne Techniques Applied To Astronomy
NASA Astrophysics Data System (ADS)
Laubscher, B. E.; Cooke, B. J.; Edwards, B. C.
1998-12-01
Fourier Transform Heterodyne (FTH) is a detection process capable of directly imaging the transverse amplitude and phase of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned systems, Fourier Transform Heterodyne (FTH) incorporates transverse spatial encoding of the local oscillator for image capture. Appropriate selection of spatial encoding functions (basis set) allows image retrieval by way of classic Fourier manipulations. Of practical interest: 1) Imaging is accomplished on a single element detector/sensor requiring no additional scanning or moving components. 2) Because detection is governed by heterodyne principles, near quantum limited performance is achievable. 3) The concept is general with the applicable electromagnetic spectrum encompassing the RF through optical. Although FTH is currently in its infancy, we believe this technique will provide new tools and concepts important to the development of future astronomical systems. For example: 1) An FTH-based optical or infrared interferometer (whether ground-based or space-based) can operate in direct analogy to VLBI radio astronomy systems. 2) FTH may be capable of measuring the atmospheric distortions of a target star to guide adaptive optical correction systems. 3) FTH may be used to determine the adjustments required to align a deployed structure in space and can remove aberrations from slight residual misalignments during operation. The work to be presented will include a brief introduction of the underlying principles governing FTH imaging, followed by cursory description of a simple proof-of-concept experiment carried out using a HeNe laser, a 69 element spatial phase modulator, and a 36 term Zernike basis set. Finally, astronomical applications will be discussed.
Nonlinear Radon and Fourier Transforms Franois Rouvire
Vallette, Bruno
Nonlinear Radon and Fourier Transforms François Rouvière Université de Nice Laboratoire Dieudonné, of the clas- sical Radon transform on hyperplanes. A function f on Rn can be reconstructed from nonlinear Radon transforms, obtained by integrating f and a ...nite num- ber of multiples x f over a family
A Primer of Fourier Transform NMR.
ERIC Educational Resources Information Center
Macomber, Roger S.
1985-01-01
Fourier transform nuclear magnetic resonance (NMR) is a new spectroscopic technique that is often omitted from undergraduate curricula because of lack of instructional materials. Therefore, information is provided to introduce students to the technique of data collection and transformation into the frequency domain. (JN)
FOURIER TRANSFORMS AND FROBENIUS EIGENVALUES FOR FINITE COXETER GROUPS
Malle, Gunter
FOURIER TRANSFORMS AND FROBENIUS EIGENVALUES FOR FINITE COXETER GROUPS group involves a certain non-abelian Fourier transformation. We construct analogous- ory of character sheaves. We also determine Fourier matrices for the "spetses" (in the sense
FOURIER TRANSFORM METHODS IN GEOPHYSICS David Sandwell, January, 2013
Sandwell, David T.
1 FOURIER TRANSFORM METHODS IN GEOPHYSICS David Sandwell, January, 2013 1. Fourier Transforms Fourier transform are use in many areas of geophysics such as image processing, time series analysis, and antenna design. Here we focus on the use of fourier transforms for solving linear partial differential
Fourier-Laguerre transform, Convolution and Wavelets on the Ball
McEwen, Jason
Fourier-Laguerre transform, Convolution and Wavelets on the Ball Jason D. McEwen and Boris Leistedt.leistedt.11}@ucl.ac.uk Abstract--We review the Fourier-Laguerre transform, an al- ternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits
Fractional discrete q-Fourier transforms
NASA Astrophysics Data System (ADS)
Muñoz, Carlos A.; Rueda-Paz, J.; Wolf, Kurt Bernardo
2009-09-01
The discrete Fourier transform (DFT) matrix has a manifold of fractionalizations that depend on the choice of its eigenbases. One prominent basis is that of Mehta functions; here we examine a family of fractionalizations of the DFT stemming from q-extensions of this basis. Although closed expressions are given, many results of our analysis derive from numerical computation and display. Thus we suggest that the account of fractional Fourier transformations applied on signals as presented by other authors—typically of a centred rectangle function—may be biased because the support of the function lies in the central part of the domain only. The phase and amplitude of the whole fractional DFT matrices reveal the location of departures from the continuous kernel of the fractional Fourier integral transform, whose phase and constant amplitude are well known.
Fast Fourier Transform algorithm design and tradeoffs
NASA Technical Reports Server (NTRS)
Kamin, Ray A., III; Adams, George B., III
1988-01-01
The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.
NASA Astrophysics Data System (ADS)
Cundiff, Steven; Bristow, Alan; Zhang, Tianhao; Siemens, Mark; Mirin, Richard
2011-03-01
Optical two-dimensional Fourier-transform spectroscopy is used to study the heavy- and light-hole excitonic resonances in GaAs quantum wells with weak structural disorder. Homogeneous and inhomogeneous broadening contribute differently to the two-dimensional resonance line shapes, allowing separation of homogeneous and inhomogeneous line widths. The heavy-hole exciton exhibits more inhomogeneous than homogeneous broadening, whereas the light-hole exciton shows the opposite. This situation arises from the interplay between the length scale of the disorder and the exciton Bohr radius, which affects the exciton localization and scattering. Utilizing this separation of line widths, excitation-density-dependent measurements reveal that many-body interactions alter the homogeneous dephasing, while disorder-induced dephasing is unchanged.
REMOTE FOURIER TRANSFORM INFRARED AIR POLLUTION STUDIES
A commercial Fourier transform infrared interferometer system has been installed in a van and used to make longpath absorption and single-ended emission measurements of gaseous pollutant concentrations at a variety of pollutant sources. The interferometer system is described and ...
Fourier Transform and Reflective Imaging Pyrometry
NASA Astrophysics Data System (ADS)
Stevens, Gerald
2011-06-01
A stationary Fourier transform pyrometer was used to record mid-wavelength IR spectra in dynamic shock experiments. The gated-IR camera used with this system was also used to record images of light produced and light reflected from shocked metals in order to constrain the dynamic emissivity and provide temperature estimates.
Fourier transform and reflective imaging pyrometry
NASA Astrophysics Data System (ADS)
Stevens, Gerald
2012-03-01
A stationary Fourier transform pyrometer was used to record mid-wavelength IR spectra in dynamic shock experiments. The gated-IR camera used with this system was also used to record images of light produced and light reflected from shocked metals in order to constrain the dynamic emissivity and provide temperature estimates. This technique will be referred to as reflective imaging pyrometry.
Comment on ``fourier transform coherent Raman spectroscopy''
NASA Astrophysics Data System (ADS)
Van Exter, Martin; Lagendijk, Ad
1988-05-01
Recently Felker and Hartland introduced an interesting non-linear optical CARS technique which they referred to as Fourier transform coherent Raman spectroscopy (FTCRS). We compare their approach with a time-resolved stimulated Raman technique that yields similar information. In this Comment we also extend the qualitative description of FTCRS beyond the region of pulse overlap between all the pulses involved.
Discrete Fourier transforms of nonuniformly spaced data
NASA Technical Reports Server (NTRS)
Swan, P. R.
1982-01-01
Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.
Electro-optic imaging Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
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.
LOCAL FOURIER TRANSFORMS AND RIGIDITY FOR SPENCER BLOCH AND H
Bloch, Spencer
LOCAL FOURIER TRANSFORMS AND RIGIDITY FOR D-MODULES SPENCER BLOCH AND H #19; EL #18; ENE ESNAULT To Armand Borel, in memoriam Abstract. Local Fourier transforms, analogous to the `-adic local Fourier if a certain in#12;nitesimal rigidity condition is satis#12;ed. As in [12], the argument uses local Fourier
Electro-optic Imaging Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin
2005-01-01
JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-O IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 micron (1000-4000/cm) to allow high-resolution, high-speed hyperspectral imaging applications. One application will be the remote sensing of the measurement of a large number of different atmospheric gases simultaneously in the same airmass. Due to the use of a combination of birefringent phase retarders and multiple achromatic phase switches to achieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventional Fourier transform spectrometer but without any moving parts. In this paper, the principle of operations, system architecture and recent experimental progress will be presented.
Electro-optic Imaging Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin
2005-01-01
JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-0IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 pm (1000 -4000 cm-') to allow high-resolution, high-speed hyperspectral imaging applications [l-51. One application will be theremote sensing of the measurement of a large number of different atmospheric gases simultaneously in the sameairmass. Due to the use of a combination of birefiingent phase retarders and multiple achromatic phase switches toachieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventionalFourier transform spectrometer but without any moving parts. In this paper, the principle of operations, systemarchitecture and recent experimental progress will be presen.
Fourier transform of a Gaussian measure on the Heisenberg group
Barczy, Mátyás
Fourier transform of a Gaussian measure on the Heisenberg group M´aty´as Barczy and Gyula Pap University of Debrecen, Hungary Abstract An explicit formula is derived for the Fourier transform measure. 1 Introduction Fourier transforms of probability measures on a locally compact topological group
Fourier transformation of D-modules and applications
Sabbah, Claude
Fourier transformation of D-modules and applications Claude Sabbah Centre de Math´ematiques Laurent Schwartz UMR 7640 du CNRS ´Ecole polytechnique, Palaiseau, France Fourier transformation of D-modules and applications p. 1/3 #12;Newton polygon Fourier transformation of D-modules and applications p. 2/3 #12
MICROMACHINED FOURIER TRANSFORM SPECTROMETER ON SILICON OPTICAL BENCH PLATFORM
Park, Namkyoo
MICROMACHINED FOURIER TRANSFORM SPECTROMETER ON SILICON OPTICAL BENCH PLATFORM Kyoungsik Yu1 a miniaturized Fourier transform spectrometer implemented on a silicon optical bench platform. The optical-etching. A spectral resolution of 45 nm near 1550 nm wavelength is demonstrated. Keywords: Fourier transform
Fourier Transform Heterodyne Spectroscopy of Liquid Interfaces A thesis presented
Mazur, Eric
Fourier Transform Heterodyne Spectroscopy of Liquid Interfaces A thesis presented by Doo Soo Chung Abstract This thesis describes the application of a novel Fourier transform heterodyne spectroscopy of fluid interfaces 3 1.4 Organization of this thesis 5 2 Fourier Transform Heterodyne Spectroscopy 7 2
An improved windowed Fourier transform filter algorithm
NASA Astrophysics Data System (ADS)
Zhao, Ran; Li, Xinglong; Sun, Ping
2015-11-01
In order to reduce the speckle noise in fringe patterns obtained by Electric Speckle Pattern Interferometry (ESPI), an improved windowed Fourier transform filter algorithm was proposed. The amplitude maximum of the fringe frequency scanned across a given window is set as the filtering criterion, which the optimum frequency image is obtained and the threshold window is not set in the window Fourier filter algorithm. The proposed algorithm is used to filter the fringe patterns obtained by ESPI. Experiment results show that the proposed algorithm has a better performance in reducing the speckle noise and has a high precision in phase calculation. The proposed algorithm can be used to filter other image as a low-pass filter.
The PROSAIC Laplace and Fourier Transform
Smith, G.A.
1994-11-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today`s emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting.
Analysis method for Fourier transform spectroscopy
NASA Technical Reports Server (NTRS)
Park, J. H.
1983-01-01
A fast Fourier transform technique is given for the simulation of those distortion effects in the instrument line shape of the interferometric spectrum that are due to errors in the measured interferogram. The technique is applied to analyses of atmospheric absorption spectra and laboratory spectra. It is shown that the nonlinear least squares method can retrieve the correct information from the distorted spectrum. Analyses of HF absorption spectra obtained in a laboratory and solar CO absorption spectra gathered by a balloon-borne interferometer indicate that the retrieved amount of absorbing gas is less than the correct value in most cases, if the interferogram distortion effects are not included in the analysis.
Noise figure of amplified dispersive Fourier transformation
NASA Astrophysics Data System (ADS)
Goda, Keisuke; Jalali, Bahram
2010-09-01
Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.
VLSI complexity of parallel Fourier transform algorithms
Baradaran Seyed, T.
1989-01-01
Scope and method of study. The purpose of this study is to present a set of new parallel algorithms for discrete Fourier transform and compare the VLSI time and area complexity of the associated designs with the existing designs. The proposed parallel algorithms may be implemented easily in pipeline and mesh-connected parallel processing systems. Findings and conclusions. Several parallel algorithms have been proposed and associated cell layout for VLSI implementation have been presented. Comparative analysis shows that two of the designs presented by this study have better area-time performance than the existing designs in their architectural category.
Fourier transform infrared spectroscopy of deuterated proteins
NASA Astrophysics Data System (ADS)
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.
Discrete Fourier transform in nanostructures using scattering Michael N. Leuenbergera)
Flatte, Michael E.
Discrete Fourier transform in nanostructures using scattering Michael N. Leuenbergera) and Michael that the discrete Fourier transform DFT can be performed by scattering a coherent particle or laser beam off the initial vector into the two-dimensional potential by means of electric gates, the Fourier
Imaging Fourier transform spectroscopy with multi-aperture telescopes
Fienup, James R.
Imaging Fourier transform spectroscopy with multi-aperture telescopes Samuel T. Thurman and James R Hanover St., Palo Alto, CA 94304 Abstract: Fourier spectroscopy can be performed with multi Society of America OCIS codes: (300.6300) Spectroscopy, Fourier transforms; (110.6770) Telescopes; (120
Fourier Transforms in Computer Science Daniel Stefankovi c
Stefankovic, Daniel
Fourier Transforms in Computer Science Daniel #20; Stefankovi#20;c Submitted to the Department of the Fourier coeÃ?- cients of AC 0 functions. [LMN93] (harmonic analysis over the #12;nite group Z n 2 ) #15.3 Random Restrictions and the Fourier Transform . . . . . . . . . . . . . . . . . . . . 11 1.4 AC 0
Nonlinear Fourier Analysis The Direct & Inverse Scattering Transforms
Christov, Ivan C.
Nonlinear Fourier Analysis The Direct & Inverse Scattering Transforms for the Kortewegde Vries by ONR/NRL funding. Nonlinear Fourier Analysis p.1/15 #12;Background & Introduction (I) 1895: Korteweg equations known as the Scattering Transform. Nonlinear Fourier Analysis p.2/15 #12;Background
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
ERIC Educational Resources Information Center
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…
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.
Fourier transform methods in local gravity modeling
NASA Technical Reports Server (NTRS)
Harrison, J. C.; Dickinson, M.
1989-01-01
New algorithms were derived for computing terrain corrections, all components of the attraction of the topography at the topographic surface and the gradients of these attractions. These algoriithms utilize fast Fourier transforms, but, in contrast to methods currently in use, all divergences of the integrals are removed during the analysis. Sequential methods employing a smooth intermediate reference surface were developed to avoid the very large transforms necessary when making computations at high resolution over a wide area. A new method for the numerical solution of Molodensky's problem was developed to mitigate the convergence difficulties that occur at short wavelengths with methods based on a Taylor series expansion. A trial field on a level surface is continued analytically to the topographic surface, and compared with that predicted from gravity observations. The difference is used to compute a correction to the trial field and the process iterated. Special techniques are employed to speed convergence and prevent oscillations. Three different spectral methods for fitting a point-mass set to a gravity field given on a regular grid at constant elevation are described. Two of the methods differ in the way that the spectrum of the point-mass set, which extends to infinite wave number, is matched to that of the gravity field which is band-limited. The third method is essentially a space-domain technique in which Fourier methods are used to solve a set of simultaneous equations.
Fourier Cosine and Sine Transform on fractal space
Guang-Sheng Chen
2011-10-21
In this paper, we establish local fractional Fourier Cosine and Sine Transforms on fractal space, considered some properties of local fractional Cosine and Sine Transforms, show applications of local fractional Fourier Cosine and Sine transform to local fractional equations with local fractional derivative.
Geometric interpretations of the Discrete Fourier Transform (DFT)
NASA Technical Reports Server (NTRS)
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.
Fast Fourier Transform of Sparse Spatial Data to Sparse Fourier Data W. C. Chew* and J.M. Song
Lanterman, Aaron
1 Fast Fourier Transform of Sparse Spatial Data to Sparse Fourier Data W. C. Chew* and J.M. Song of my mother who labored all her life for the next generation.) 1. Introduction Nonuniform Fast Fourier-3]. However, not much has been written on Fourier transforming sparse spatial data where the Fourier transform
Surface Inspection using fourier transform infrared spectroscopy
Powell, G.L.; Smyrl, N.R.; Williams, D.M.; Meyers, H.M. III; Barber, T.E.; Marrero-Rivera, M.
1994-08-08
The use of reflectance Fourier transform infrared (FTIR) spectroscopy as a tool for surface inspection is described. Laboratory instruments and portable instruments can support remote sensing probes that can map chemical contaminants on surfaces. Detection limits under the best of conditions are in the subnanometer range (i.e., near absolute cleanliness), excellent performance is obtained in the submicrometer range, and useful performance may exist for films tens of microns thick. Identifying and quantifying contamination such as mineral oils and greases, vegetable oils, and silicone oils on aluminum foil, galvanized sheet steel, smooth aluminum tubing, and gritblasted 7075 aluminum alloy and D6AC steel are described. The ability to map in time and space the distribution of oil stains on metals is demonstrated. Techniques for quantitatively applying oils to metals, subsequently verifying the application, and nonlinear relationships between reflectance and the quantity of oil are discussed.
Imaging Fourier transform spectrometry of chemical plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.; Gross, Kevin C.; Perram, Glen P.
2009-05-01
A midwave infrared (MWIR) imaging Fourier transform spectrometer (FTS), the Telops FIRST-MWE (Field-portable Imaging Radiometric Spectrometer Technology - Midwave Extended) has been utilized for the standoff detection and characterization of chemical plumes. Successful collection and analysis of MWIR hyperspectral imagery of jet engine exhaust has allowed us to produce spatial profiles of both temperature and chemical constituent concentrations of exhaust plumes. Successful characterization of this high temperature combustion event has led to the collection and analysis of hyperspectral imagery of lower temperature emissions from industrial smokestacks. This paper presents MWIR data from remote collection of hyperspectral imagery of methyl salicilate (MeS), a chemical warfare agent simulant, during the Chemical Biological Distributed Early Warning System (CBDEWS) test at Dugway Proving Grounds, UT in 2008. The data did not contain spectral lines associated with emission of MeS. However, a few broad spectral features were present in the background-subtracted plume spectra. Further analysis will be required to assign these features, and determine the utility of MWIR hyperspectral imagery for analysis of chemical warfare agent plumes.
Fourier transform spectroscopy for future planetary missions
NASA Astrophysics Data System (ADS)
Brasunas, John C.; Hewagama, Tilak; Kolasinski, John R.; Kostiuk, Theodor
2015-11-01
Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system.Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, NASA Goddard was funded via the Planetary Instrument Definition and Development Progrem (PIDDP) to develop CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. Following the initial validation of CIRS-lite operation in the laboratory, we have been acquiring atmospheric data in the 8-12 micron window at the 1.2 m telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) in Greenbelt, MD. Targets so far have included Earth's atmosphere (in emission, and in absorption against the moon), and Venus.We will present the roadmap for making CIRS-lite a viable candidate for future planetary missions.
Stepwise Iterative Fourier Transform: The SIFT
NASA Technical Reports Server (NTRS)
Benignus, V. A.; Benignus, G.
1975-01-01
A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.
A discrete Fourier transform for virtual memory machines
NASA Technical Reports Server (NTRS)
Galant, David C.
1992-01-01
An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.
Cryogenic Scan Mechanism for Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Brasunas, John C.; Francis, John L.
2011-01-01
A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear
Matrix probing, skeleton decompositions, and sparse Fourier transform
Chiu, Jiawei
2013-01-01
In this thesis, we present three different randomized algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with ...
Estimates for the Fourier-Bessel transforms of multivariate functions
NASA Astrophysics Data System (ADS)
Abilov, V. A.; Kerimov, M. K.
2012-06-01
Two estimates useful in applications are proved for the Fourier-Bessel (or Hankel) transform in the space {L}_2 ( {{R}_ + ^2 } ) for some classes of two-variable functions characterized by a generalized modulus of continuity.
Xgremlin: Interferograms and spectra from Fourier transform spectrometers analysis
NASA Astrophysics Data System (ADS)
Nave, G.; Griesmann, U.; Brault, J. W.; Abrams, M. C.
2015-11-01
Xgremlin is a hardware and operating system independent version of the data analysis program Gremlin used for Fourier transform spectrometry. Xgremlin runs on PCs and workstations that use the X11 window system, including cygwin in Windows. It is used to Fourier transform interferograms, plot spectra, perform phase corrections, perform intensity and wavenumber calibration, and find and fit spectral lines. It can also be used to construct synthetic spectra, subtract continua, compare several different spectra, and eliminate ringing around lines.
Automatic Fourier transform and self-Fourier beams due to parabolic potential
NASA Astrophysics Data System (ADS)
Zhang, Yiqi; Liu, Xing; Beli?, Milivoj R.; Zhong, Weiping; Petrovi?, Milan S.; Zhang, Yanpeng
2015-12-01
We investigate the propagation of light beams including Hermite-Gauss, Bessel-Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams-that is, the beams whose Fourier transforms are the beams themselves.
The Unified Discrete Fourier-Hartley Transforms Processor
Oraintara, Soontorn
, the architecture utilizes the general existing fast Fourier transform (FFT) IP-core working with pre- and post the FFT algorithms because of many commercial FPGA soft IP, DSP hardware and software available transform (FFT) IP-core [6, 7]. The proposed processor uses the existing FFT core to process the entire
The quantum Arnold transformation
Victor Aldaya; Francisco Cossio; Julio Guerrero; Francisco F. Lopez-Ruiz
2010-11-02
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with friction linear in velocity, can be related to the quantum free-particle dynamical system. This transformation provides a basic (Heisenberg-Weyl) algebra of quantum operators, along with well-defined Hermitian operators which can be chosen as evolution-like observables and complete the entire Schr\\"odinger algebra. It also proves to be very helpful in performing certain computations quickly, to obtain, for example, wave functions and closed analytic expressions for time-evolution operators.
Structure in Galaxy Distribution. III. Fourier Transforming the Universe
Scargle, Jeffrey D; Gazis, Paul
2015-01-01
We compute the complex 3D Fourier transform of the spatial galaxy distribution in a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields results quite similar to those from the FFT of finely binned galaxy positions. In both cases the sampling window function is deconvolved to yield an estimate of the true 3D transform. The Fourier amplitudes resulting from this simple procedure yield power spectrum estimates consistent with those from other more complicated approaches. We display also measurements of homogeneity, isotropy and Gaussianity, based on an analysis of the complex Fourier transform that is much simpler than the multi-point methods usually employed. Our model-independent analysis avoids statistical interpretations, which have no meaning without detailed assumptions about a hypothetical process generating the initial cosmic density fluctuations.
On q-extended eigenvectors of the integral and finite Fourier transforms
NASA Astrophysics Data System (ADS)
Atakishiyev, N. M.; Rueda, J. P.; Wolf, K. B.
2007-10-01
Mehta has shown that eigenvectors of the N × N finite Fourier transform can be written in terms of the standard Hermite eigenfunctions of the quantum harmonic oscillator (1987 J. Math. Phys. 28 781). Here, we construct a one-parameter family of q-extensions of these eigenvectors, based on the continuous q-Hermite polynomials of Rogers. In the limit when q ? 1 these q-extensions coincide with Mehta's eigenvectors, and in the continuum limit as N ? ? they give rise to q-extensions of eigenfunctions of the Fourier integral transform.
Electro-Optical Imaging Fourier-Transform Spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin; Zhou, Hanying
2006-01-01
An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.
Blind digital watermarking method in the fractional Fourier transform domain
NASA Astrophysics Data System (ADS)
Lang, Jun; Zhang, Zheng-guang
2014-02-01
In this paper, we proposed a novel blind digital image watermarking algorithm based on the fractional Fourier transform (FRFT), which is a generalization of the ordinary Fourier transform and its output has the mixed time and frequency components of the signal. The original image is segmented into non-overlapping blocks for watermarking, and each block is transformed by the two dimensional fractional Fourier transform with two fractional orders. Then each pixel value of binary watermark is embedded by modifying the back-diagonal FRFT coefficients of each image block at the same location with a random array. After perform an inverse two dimensional fractional Fourier transform, we can obtain the watermarked image and the transform orders can be consider as the encryption keys in this method. A series of attacking experiments are performed on the proposed method. The experiments results show that the proposed algorithm not only is of good imperceptibility and security and is very robust to JPEG compression noise attacks and image manipulation operations, but also can provide protection even under compound attacks.
Parallel fast Fourier transforms for non power of two data
Semeraro, B.D.
1994-09-01
This report deals with parallel algorithms for computing discrete Fourier transforms of real sequences of length N not equal to a power of two. The method described is an extension of existing power of two transforms to sequences with N a product of small primes. In particular, this implementation requires N = 2{sup p}3{sup q}5{sup r}. The communication required is the same as for a transform of length N = 2{sup p}. The algorithm presented is intended for use in the solution of partial differential equations, or in any situation in which a large number of forward and backward transforms must be performed and in which the Fourier Coefficients need not be ordered. This implementation is a one dimensional FFT but the techniques are applicable to multidimensional transforms as well. The algorithm has been implemented on a 128 node Intel Ipsc/860.
High resolution Fourier transform Raman spectroscopy with ultrashort laser pulses
NASA Astrophysics Data System (ADS)
Graener, H.; Laubereau, A.
1985-06-01
Coherent Raman scattering of delayed probing pulses after stimulated Raman excitation of molecular transitions is applied for a novel spectroscopy. Measuring the signal transient over long delay time intervals ? 10 -8 s numerical Fourier transformation yields precise spectroscopic information with a resolution ? 10 -3 cm -1. Experimental data are presented for the Q-band of the ? 1 vibration of CH 4 in the supersonic expansion. The potential of our Fourier transform Raman spectroscopy is demonstrated resolving the tensor splitting of the J = 2 transitions.
Modulated Fourier Transform Raman Fiber-Optic Spectroscopy
NASA Technical Reports Server (NTRS)
Jensen, Brian J. (Inventor); Cooper, John B. (Inventor); Wise, Kent L. (Inventor)
2000-01-01
A modification to a commercial Fourier Transform (FT) Raman spectrometer is presented for the elimination of thermal backgrounds in the FT Raman spectra. The modification involves the use of a mechanical optical chopper to modulate the continuous wave laser, remote collection of the signal via fiber optics, and connection of a dual-phase digital-signal-processor (DSP) lock-in amplifier between the detector and the spectrometer's collection electronics to demodulate and filter the optical signals. The resulting Modulated Fourier Transform Raman Fiber-Optic Spectrometer is capable of completely eliminating thermal backgrounds at temperatures exceeding 300 C.
Fourier-transform and global contrast interferometer alignment methods
Goldberg, Kenneth A. (Berkeley, CA)
2001-01-01
Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.
Application of Fourier transform spectroscopy to air pollution problems
NASA Astrophysics Data System (ADS)
Shaw, J. H.; Calvert, J. G.
1980-11-01
The nature of information that can be retrieved from spectra obtained with Fourier transform spectroscopy is discussed. Nonlinear, least squares analysis of spectra is capable of retrieving information that is beyond the reach of conventional methods and has improved precision and accuracy. Fourier transform infrared spectroscopy was used to study quantitatively the kinetics and mechanisms of several chemical reactions that are of interest to atmospheric chemists and are important in the development of air pollution control strategies. The systems studied include the metastable, reactive, gaseous species, peroxynitric acid, hypochlorous acid, and dimethylnitrosamine.
Fractional Fourier transform in temporal ghost imaging with classical light
Setaelae, Tero; Shirai, Tomohiro; Friberg, Ari T.
2010-10-15
We investigate temporal, second-order classical ghost imaging with long, incoherent, scalar plane-wave pulses. We prove that in rather general conditions, the intensity correlation function at the output of the setup is given by the fractional Fourier transform of the temporal object. In special cases, the correlation function is shown to reduce to the ordinary Fourier transform and the temporal image of the object. Effects influencing the visibility and the resolution are considered. This work extends certain known results on spatial ghost imaging into the time domain and could find applications in temporal tomography of pulses.
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
NASA Technical Reports Server (NTRS)
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.
Discrete Fourier Transform in a Complex Vector Space
NASA Technical Reports Server (NTRS)
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.
Fast Fourier Transform for Fitness Landscapes Dan Rockmorea, Peter Kosteleca, Wim Hordijkb, Peter F.
Stadler, Peter F.
Fast Fourier Transform for Fitness Landscapes Dan Rockmorea, Peter Kosteleca, Wim Hordijkb, Peter F of the Walsh/Fourier transforms are feasible for landscapes with up to 108 configurations using Fast Fourier as the generating set on Sn. Keywords. Spectral Analysis, Fast Fourier Transform, Walsh Functions, Cayley Graphs
Discrete Fourier Transform Analysis in a Complex Vector Space
NASA Technical Reports Server (NTRS)
Dean, Bruce H.
2009-01-01
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
ERIC Educational Resources Information Center
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
Recovering Missing Slices of the Discrete Fourier Transform using Ghosts
Shekhar Chandra; Imants Svalbe; Jeanpierre Guedon; Andrew Kingston; Nicolas Normand
2010-12-30
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called Ghosts. In this paper, a fast and exact method for de-convolving cyclic artefacts caused by missing slices of the DFT is presented. The slices discussed here originate from the exact partitioning of DFT space, under the projective Discrete Radon Transform, called the Discrete Fourier Slice Theorem. The method has a computational complexity of O(n log2 n) (where n = N^2) and is constructed from a new Finite Ghost theory. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. The paper concludes with a significant application to fast, exact, non-iterative image reconstruction from sets of discrete slices obtained for a limited range of projection angles.
Fourier transform ion cyclotron resonance precision atomic mass measurement limits
Kouzes, R.T.
1992-07-01
The application of Fourier Transform Ion Cylcotron Resonance Mass Spectroscopy to precision atomic mass measurements is considered. Limits on the mass accuracy of this technique for atomic masses are discussed, and plans for future developments with application to fundamental weak interaction physics are presented.
Fourier transform spectroscopy of cotton and cotton trash
Technology Transfer Automated Retrieval System (TEKTRAN)
Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...
Robustness of quadratic hedging strategies in finance via Fourier transforms
Vanmaele, Michèle
consider two models for the stock price process. The first model is a geometric L´evy process in which the robustness of the quadratic hedging strategies we use pricing and hedging formulas based on Fourier transform technically be performed under a related pricing measure that is a risk-neutral measure. Under this measure
APPLICATION OF FOURIER TRANSFORM SPECTROSCOPY TO AIR POLLUTION PROBLEMS
The nature of information that can be retrieved from spectra obtained with Fourier transform spectroscopy is discussed. Nonlinear, least-squares analysis of spectra is capable of retrieving information that is beyond the reach of conventional methods and has improved precision an...
Sparse Fourier Transform via Butterfly Algorithm Lexing Ying
Li, Tiejun
Sparse Fourier Transform via Butterfly Algorithm Lexing Ying Department of Mathematics, University the butterfly algorithm. The computation is further accelerated by exploiting the tensor- product property; Butterfly algorithm; Multiscale methods; Far field pat- tern. AMS subject classifications. 65R10, 65T50, 65Y
Chained Quantum Arnold Transformations
Francisco F. López-Ruiz; Julio Guerrero; Victor Aldaya
2011-09-06
We put forward the concatenation of Quantum Arnold Transformations as a tool to obtain the wave function of a particle subjected to a harmonic potential which is switched on and off successively. This simulates the capture and release process of an ion in a trap and provides a mathematical picture of this physical process.
A VLSI architecture for simplified arithmetic Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.
1992-01-01
The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.
Optimal color image restoration: Wiener filter and quaternion Fourier transform
NASA Astrophysics Data System (ADS)
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.
Fourier transform digital holographic adaptive optics imaging system
Liu, Changgeng; Yu, Xiao; Kim, Myung K.
2013-01-01
A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541
Development of Multi-Fourier Transform interferometer :Fundamental
Izumi S. Ohta; Makoto Hattori; Hiroshi Matsuo
2005-12-07
We propose the development of an instrument by the Martin & Puplett-type Fourier Transform Spectrometer to applying the aperture synthesis technique in millimeter and submillimeter waves. We call this equipment the Multi-Fourier Transform interferometer (MuFT). MuFT performs a wide band imaging, spectroscopy and polarimetry in millimeter and submillimeter wavelengths. We describe the fundamentals of MuFT, and give an example of one potential implementation. Full description of the observables by MuFT are provided. A physical explanation of the observability of the complex visibility by MuFT is given. Fundamental restrictions on observations with MuFT, eg. limits on spectral and spatial resolutions and field-of-view, are discussed. The advantages of MuFT are also summarized.
Development of a multi-Fourier-transform interferometer: fundamentals.
Ohta, Izumi S; Hattori, Makoto; Matsuo, Hiroshi
2006-04-20
We describe the development of an instrument that uses a Martin-Puplett-type Fourier-transform spectrometer to apply an aperture synthesis technique to millimeter and submillimeter waves. We call this instrument a multi-Fourier-transform interferometer (MuFT). The MuFT performs wideband imaging, spectroscopy, and polarimetry, at millimeter and submillimeter wavelengths. We describe the fundamentals of the MuFT and give an example of one potential implementation. A full description of the observables with a MuFT is provided. A physical explanation of the observability of complex visibility by the MuFT is given. Fundamental restrictions on observations with the MuFT, e.g., limits on spectral and spatial resolution and on fields of view, are discussed. The advantages of the MuFT are summarized. PMID:16633405
Signal estimation from modified short-time Fourier transform
NASA Astrophysics Data System (ADS)
Griffin, D. W.; Lim, J. S.
1984-04-01
An algorithm to estimate a signal from its modified short-time Fourier transform (STFT) is presented. This algorithm is computationally simple and is obtained by minimizing the mean squared error between the STFT of the estimated signal and the modified STFT. Using this algorithm, an iterative algorithm to estimate a signal from its modified STFT magnitude is also developed. The iterative algorithm is shown to decrease, in each iteration, the mean squared error between the STFT magnitude of the estimated signal and the modified STFT magnitude. The major computation involved in the iterative algorithm is the discrete Fourier transform computation, and the algorithm appears to be real-time implementable with current hardware technology. The algorithm developed has been applied to the time-scale modification of speech. The resulting system generates very high-quality speech, and appears to be better in performance than any existing method.
Fractional Fourier transforms of electromagnetic rectangular Gaussian Schell model beams
NASA Astrophysics Data System (ADS)
Liu, Xiayin; Zhao, Daomu
2015-06-01
We extend the scalar rectangular Gaussian Schell model (RGSM) beams to the electromagnetic domain and obtain the analytical expression for the propagation of the electromagnetic RGSM (EM RGSM) beams through an ABCD optical system. As a practical application, we illustrate how the spectral density, the spectral degree of polarization and the spectral degree of coherence of the EM RGSM beams through the fractional Fourier transform (FRFT) optical system depend on the FRFT order p and the value of beam profile M. It is found that the periods of the on-axis spectral density, the on-axis degree of polarization and the transverse degree of coherence for the FRFT order are all 2. In addition, it is of interest that the profiles of the transverse spectral intensity and the degree of polarization in the standard Fourier transform plane (i.e., p=1) are shown to form flat rectangular region which is wider for larger values of M.
Fourier spectroscopy with a one-million-point transformation
NASA Technical Reports Server (NTRS)
Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.
1972-01-01
A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.
Apparatus and methods for continuous beam fourier transform mass spectrometry
McLuckey, Scott A. (Oak Ridge, TN); Goeringer, Douglas E. (Oak Ridge, TN)
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.
Homology of balanced complexes via the Fourier transform
Meshulam, Roy
2011-01-01
Let G_0,...,G_k be finite abelian groups and let G_0*...*G_k be the join of the 0-dimensional complexes G_i. We give a characterization of the integral k-coboundaries of subcomplexes of G_0*...*G_k in terms of the Fourier transform on the group G_0 \\times ... \\times G_k. This leads to an extension of a recent result of Musiker and Reiner on a topological interpretation of the cyclotomic polynomial.
On the nature of the Tsallis-Fourier Transform
A. Plastino; M. C. Rocca
2015-07-21
By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map {\\it equivalence classes} of functions into other classes in a one-to-one fashion. This suggests that Tsallis' q-statistics may revolve around equivalence classes of distributions and not on individual ones, as orthodox statistics does. We solve here the qFT's non-invertibility issue, but discover a problem that remains open.
Wavelength-encoded tomography based on optical temporal Fourier transform
Zhang, Chi; Wong, Kenneth K. Y.
2014-09-01
We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150?-?m (ideally 36??m) resolution is achieved based on a 7.5-nm bandwidth swept-pump, using a conventional optical spectrum analyzer. This approach can potentially achieve up to 100-MHz or even higher frame rate with some proven ultrafast spectrum analyzer. We believe that this technique is innovative towards the next-generation ultrafast optical tomographic imaging application.
[Study of the fiber size in hardwood using Fourier transform].
Duo, Hua-qiong; Wang, Xi-ming
2009-09-01
Fourier transform image-processing technology was applied to measuring the fiber size of hardwood. In this method, each cell was mapped by the center point on the cell in the transverse section with extending up and down by four pixels (nine-pixel length in total) and by two pixels in width, and thereafter line convoluted dot map (LCDM) was obtained. Through Fourier transform, the frequency distribution of power spectrum pattern from both horizontal and vertical directions was obtained and the cell diameter in radial and tangential direction was known from the maximum value except 0 in the distribution. The result indicates that there is no significant difference from that by optical microscope or image-processing software. It suggests that the method can be applied to the cell measurement and expand the Fourier transform application domain. This method provides the new research direction for the microscopic analysis and cell identification, and also provides a theoretical basis for the establishment of the mathematical model to identify cell geometric parameter. PMID:19950633
Wavelength-encoded tomography based on optical temporal Fourier transform
NASA Astrophysics Data System (ADS)
Zhang, Chi; Wong, Kenneth K. Y.
2014-09-01
We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150 -?m (ideally 36 ?m) resolution is achieved based on a 7.5-nm bandwidth swept-pump, using a conventional optical spectrum analyzer. This approach can potentially achieve up to 100-MHz or even higher frame rate with some proven ultrafast spectrum analyzer. We believe that this technique is innovative towards the next-generation ultrafast optical tomographic imaging application.
Improved digital filters for evaluating Fourier and Hankel transform integrals
Anderson, Walter L.
1975-01-01
New algorithms are described for evaluating Fourier (cosine, sine) and Hankel (J0,J1) transform integrals by means of digital filters. The filters have been designed with extended lengths so that a variable convolution operation can be applied to a large class of integral transforms having the same system transfer function. A f' lagged-convolution method is also presented to significantly decrease the computation time when computing a series of like-transforms over a parameter set spaced the same as the filters. Accuracy of the new filters is comparable to Gaussian integration, provided moderate parameter ranges and well-behaved kernel functions are used. A collection of Fortran IV subprograms is included for both real and complex functions for each filter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms
Radon and Fourier transforms for D-modules Andrea D'Agnolo
D'Agnolo, Andrea
Radon and Fourier transforms for D-modules Andrea D'Agnolo and Michael Eastwood Version: July 17, 2002 Contents 1 Radon and Fourier transforms for D-modules 3 1.1 Review on algebraic D-modules . . . . . . . . . . . . . . . . 3 1.2 Review on the Fourier-Laplace transform . . . . . . . . . . 5 1.3 Review on the Radon
Fourier transform of the 3d NS equations The 3d NS equations are
Salmon, Rick
1 Fourier transform of the 3d NS equations The 3d NS equations are (1) vi t + vj vi xj = - p xi easily add it in at the end. Our interest is in the advection and pressure terms. Introducing the Fourier transforms (2) vi x( ) = ui k( )eikx k p x( ) = p k( )eikx k we obtain the Fourier transform of (1
Properties of Fourier transform Examples of standard cases with easy calculation
Collins, John
Properties of Fourier transform · Examples of standard cases with easy calculation: f(x) ~f(k) e, 2014 2/3 #12;Fourier transforms of distributions · After examination of distribution corresponding to ordinary function, define Fourier transform of distribution by ~[t] = [~t] · To make this work, we use
Fourier Transforms and the 2-adic Span of Periodic Binary Sequences
Klapper, Andy
" interpretation for the usual (complex) Fourier transform of a periodic binary sequence, but it also adds anotherFourier Transforms and the 2-adic Span of Periodic Binary Sequences Mark Goresky #3; Andrew Klapper the linear span of a sequence to its discrete Fourier transform. For comparison, let us recall this theorem
The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical
Prestin, JÃ¼rgen
which might be interpreted as an analogon to the classical Fourier slice theorem of the Radon transformThe Radon Transform on SO(3): A Fourier Slice Theorem and Numerical Inversion Ralf Hielscher inversion of the oneÂdimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete
Partial differential equation transform — Variational formulation and Fourier analysis
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-01-01
Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904
Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
Santa Maria, Odilyn L.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Radon and Fourier transforms for Dmodules Andrea D'Agnolo and Michael Eastwood
Radon and Fourier transforms for Dmodules Andrea D'Agnolo and Michael Eastwood Contents Introduction 2 Acknowledgements 2 1. Radon and Fourier transforms for Dmodules 3 1.1. Review on algebraic Dmodules 3 1.2. Review on the FourierLaplace transform 5 1.3. Review on the Radon transform(s) 6 1.4. Review
Coherent electromagnetic field imaging through Fourier transform heterodyne
Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Goeller, R.M.; Cafferty, M.; Briles, S.D.; Galbraith, A.E. |; Grubler, A.C. |
1998-12-31
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and if desired, Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LIDAR systems, Fourier Transform Heterodyne (FTH) incorporates transverse spatial encoding of the local oscillator for image capture. Appropriate selection of spatial encoding functions, or basis set, allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging is accomplished on a single element detector requiring no additional scanning or moving components, and (2) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection. In this paper, they introduce the underlying principles governing FTH imaging, followed by demonstration of concept via a simple experimental setup based on a HeNe laser and a 69 element spatial phase modulator.
A cascaded iterative Fourier transform algorithm for optical security applications
NASA Astrophysics Data System (ADS)
Situ, Guohai; Zhang, Jingjuan
A cascaded iterative Fourier transform (CIFT) algorithm is presented for optical security applications. Two phase-masks are designed and located in the input and the Fourier domains of a 4-f correlator respectively, in order to implement the optical encryption or authenticity verification. Compared with previous methods, the proposed algorithm employs an improved searching strategy: modifying the phase-distributions of both masks synchronously as well as enlarging the searching space. Computer simulations show that the algorithm results in much faster convergence and better image quality for the recovered image. Each of these masks is assigned to different person. Therefore, the decrypted image can be obtained only when all these masks are under authorization. This key-assignment strategy may reduce the risk of being intruded.
Fast Fourier Transform Notes 18.310, Fall 2005, Prof. Peter Shor
Shor, Peter W.
Fast Fourier Transform Notes 18.310, Fall 2005, Prof. Peter Shor 1 Introduction: Fourier Series Early in the Nineteenth century, Fourier studied sound and oscillatory motion and conceived of the idea the ordinary y = f(x) description of the shape of the string. This kind of representation is called a Fourier
EE261 The Fourier Transform and its Applications Syllabus and Schedule
Holub, Stepan
EE261 The Fourier Transform and its Applications Fall 2007 Syllabus and Schedule The following before coming to class. September 24 Introductions Periodicity and Fourier series (Sections 1.1 1.4) September 26 Fourier series and orthogonality Prob Set 1 handed out September 28 Fourier series, continued
Fourier-transform Raman spectroscopic study of human hair
NASA Astrophysics Data System (ADS)
Akhtar, W.; Edwards, H. G. M.; Farwell, D. W.; Nutbrown, M.
1997-07-01
Fourier-transform Raman microscopic spectra of normal, untreated and bleached hair fibres are presented. Vibrational assignments are made and differences are ascribed to the production of cysteic acid from cysteine. Changes in conformation associated with the disulphide bond in the keratotic component are noted from the ?(CSSC) vibrational modes at wave numbers near 500 cm -1. Raman spectra of hair root ends have also been investigated with a diminution in cysteine content being observed. Application of the technique to the biomedical investigation of healthy and diseased hair is proposed.
Sampling Theorem and Discrete Fourier Transform on the Hyperboloid
Manuel Calixto; Julio Guerrero; Juan Carlos Sánchez-Monreal
2011-09-09
Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\\mathbb D_1$), seen as a homogeneous space of the pseudo-unitary group SU(1,1). We provide a reconstruction formula for bandlimited functions, through a sinc-type kernel, and a discrete Fourier transform from $N$ samples properly chosen. We also study the case of undersampling of band-unlimited functions and the conditions under which a partial reconstruction from $N$ samples is still possible and the accuracy of the approximation, which tends to be exact in the limit $N\\to\\infty$.
Fourier transform spectrometry for fiber-optic sensor systems
NASA Technical Reports Server (NTRS)
Beheim, Glenn; Tuma, Margaret L.; Sotomayor, Jorge L.; Flatico, Joseph M.
1993-01-01
An integrated-optic Mach-Zehnder interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This type of spectrometer has an advantage over conventional grating spectrometers because it is better suited for use with time-division-multiplexed sensor networks. In addition, this spectrometer has the potential for low cost due to its use of a component that could be manufactured in large quantities for the optical communications industry.
Broadband stimulated Raman scattering with Fourier-transform detection.
Réhault, Julien; Crisafi, Francesco; Kumar, Vikas; Ciardi, Gustavo; Marangoni, Marco; Cerullo, Giulio; Polli, Dario
2015-09-21
We propose a new approach to broadband Stimulated Raman Scattering (SRS) spectroscopy and microscopy based on time-domain Fourier transform (FT) detection of the stimulated Raman gain (SRG) spectrum. We generate two phase-locked replicas of the Stokes pulse after the sample using a passive birefringent interferometer and measure by the FT technique both the Stokes and the SRG spectra. Our approach blends the very high sensitivity of single-channel lock-in balanced detection with the spectral coverage and resolution afforded by FT spectroscopy. We demonstrate our method by measuring the SRG spectra of different compounds and performing broadband SRS imaging on inorganic blends. PMID:26406721
Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.
2013-01-01
A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.
Beam profile for the Herschel-SPIRE Fourier transform spectrometer.
Makiwa, Gibion; Naylor, David A; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H D
2013-06-01
One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile. PMID:23736346
Fourier transform vibrational circular dichroism of small pharmaceutical molecules
NASA Astrophysics Data System (ADS)
Long, Fujin; Freedman, Teresa B.; Nafie, Laurence A.
1998-06-01
Fourier transform vibrational circular dichroism (FT-VCD) spectra of the small pharmaceutical molecules propanolol, ibuprofen and naproxen have been measured in the hydrogen stretching and mid-infrared regions to obtain information on solution conformation and to identify markers for absolute configuration determination. Ab initio molecular orbital calculations of low energy conformations, vibrational frequencies and VCD intensities for fragments of the drugs were utilized in interpreting the spectra. Features characteristic of five conformers of propranolol were identified. The weak positive CH stretching VCD signal in ibuprofen and naproxen is characteristic of the S-configuration of the chiral center common to these two analgesics.
Fourier transform infrared - attenuated total reflection for wheat grain
NASA Astrophysics Data System (ADS)
Suchowilska, E.; Kandler, W.; Wiwart, M.; Krska, R.
2012-04-01
Mid-infrared regions of the spectrum of grain of four Triticum species were analyzed using Fourier transform infrared - attenuated total reflection. Significant variations were noted in the absorbance of all studied taxa over four wavenumber ranges. The principal component analysis supported strong discrimination of the four examined species. The percentage of variation explained by the first two principal component analyses reached 95.04%, including principal components 1-72.16% and 2-22.88%. The applied method supports quick identification of the grains of various hulled species of wheat and it is a useful tool for evaluating the seeds and food products obtained from those cereal species.
Fiber-optic thermometer using Fourier transform spectroscopy
NASA Technical Reports Server (NTRS)
Beheim, Glenn; Sotomayor, Jorge L.; Flatico, Joseph M.; Azar, Massood T.
1991-01-01
An integrated-optic Mach-Zender interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This configuration provides a high degree of immunity to the effects of changes in the source spectrum, and it readily permits the interrogation of a number of different sensors using a single spectrometer. In addition, this system has a potentially low cost because it uses optical communications hardware that may in the future be manufactured in large quantities.
SCUBA-2 Fourier transform spectrometer (FTS-2) commissioning results
NASA Astrophysics Data System (ADS)
Gom, Brad G.; Naylor, David A.; Friberg, Per; Bell, Graham S.; Bintley, Daniel; Abdelazim, Sherif; Sherwood, Matt
2014-07-01
We present the latest commissioning results and instrument performance for the SCUBA-2 imaging Fourier Transform Spectrometer (FTS-2) installed at the James Clerk Maxwell Telescope (JCMT). This ancillary instrument provides intermediate spectral resolution (R ~10 to 5000) across both the 450 and 850 ?m atmospheric transmission windows with a FOV of ~5 arcmin2. The superconducting TES sensors and SQUID readout of SCUBA-2 present unique challenges for operation of an FTS; the sensitivity requirements demand high detector linearity and stability in addition to control of systematic atmospheric and optical spillover effects. We discuss the challenges encountered during commissioning and ongoing efforts to mitigate their effects.
Compact liquid-crystal-polymer Fourier-transform spectrometer.
Boer, Gerben; Ruffieux, Patrick; Scharf, Toralf; Seitz, Peter; Dändliker, René
2004-04-10
We present the optical design and realization of a low-resolution liquid-crystal (LC) Fourier-transform spectrometer (FTS). This FTS is based on a polarization interferometer that has a Wollaston prism made of a LC material as a key component. It has a compact design, a good acceptance angle, and low temperature dependence and can be fabricated with cost-effective LC technology. Because the LC is polymerized, it is robust, and the temperature dependence is drastically reduced. The performance of a compact handheld version of the spectrometer and the characteristics (angular dependence, resolution, stray light, and temperature dependence) will be discussed. PMID:15098820
Riemann zeros in radiation patterns: II. Fourier transforms of zeta
NASA Astrophysics Data System (ADS)
Berry, M. V.
2015-09-01
This extends a previous study (2012 J. Phys. A: Math. Theor. 45 302001) of two initial waveforms whose far-field radiation patterns possess sidelobes separated by the Riemann zeros. The analysis suffered from the disadvantage that the sidelobes were very weak, making it difficult to detect the zeros between them. To overcome this, new Fourier pairs are derived, whose sidelobes are not weak. These are transforms of the zeta function on the critical line, modulated by functions with no zeros on the line.
Soft x-ray microscope using Fourier transform holography
McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H. . Dept. of Physics; Lawrence Berkeley Lab., CA; Brookhaven National Lab., Upton, NY )
1989-01-01
A Fourier transform holographic microscope with an anticipated resolution of better than 100 nm has been built. Extensive testing of the apparatus has begun. Preliminary results include the recording of interference fringes using 3.6 nm x-rays. The microscope employs a charge-coupled device (CCD) detector array of 576 {times} 384 elements. The system is illuminated by soft x-rays from a high brightness undulator. The reference point source is formed by a Fresnel zone plate with a finest outer zone width of 50 nm. Sufficient temporal coherence for hologram formation is obtained by a spherical grating monochromator. The x-ray hologram intensities at the recording plane are to be collected, digitized and reconstructed by computer. Data acquisition is under CAMAC control, while image display and off-line processing takes place on a VAX graphics workstation. Computational models of Fourier transform hologram synthesis, and reconstruction in the presence of noise, have demonstrated the feasibility of numerical methods in two dimensions, and that three-dimensional information is potentially recoverable. 13 refs., 3 figs.
Ultrafast and versatile spectroscopy by temporal Fourier transform.
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E; Wong, Kenneth K Y
2014-01-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges. PMID:24939667
Ultrafast and versatile spectroscopy by temporal Fourier transform
NASA Astrophysics Data System (ADS)
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.
2014-06-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.
Ultrafast and versatile spectroscopy by temporal Fourier transform
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.
2014-01-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system – the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges. PMID:24939667
PHYSICAL REVIEW A 82, 033827 (2010) Noise figure of amplified dispersive Fourier transformation
Jalali. Bahram
2010-01-01
PHYSICAL REVIEW A 82, 033827 (2010) Noise figure of amplified dispersive Fourier transformation transformation (ADFT), also known as time-stretch amplified Fourier transformation [16], is a powerful technique in a dispersive medium using internal optical amplification. The amplification is realized using stimulated Raman
A direct digital synthesis chirped pulse Fourier transform microwave spectrometer
NASA Astrophysics Data System (ADS)
Finneran, Ian A.; Holland, Daniel B.; Carroll, P. Brandon; Blake, Geoffrey A.
2013-08-01
Chirped pulse Fourier transform microwave (CP-FTMW) spectrometers have become the instrument of choice for acquiring rotational spectra, due to their high sensitivity, fast acquisition rate, and large bandwidth. Here we present the design and capabilities of a recently constructed CP-FTMW spectrometer using direct digital synthesis (DDS) as a new method for chirped pulse generation, through both a suite of extensive microwave characterizations and deep averaging of the 10-14 GHz spectrum of jet-cooled acetone. The use of DDS is more suited for in situ applications of CP-FTMW spectroscopy, as it reduces the size, weight, and power consumption of the chirp generation segment of the spectrometer all by more than an order of magnitude, while matching the performance of traditional designs. The performance of the instrument was further improved by the use of a high speed digitizer with dedicated signal averaging electronics, which facilitates a data acquisition rate of 2.1 kHz.
Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere
Manuel Calixto; Julio Guerrero; Juan Carlos Sánchez-Monreal
2011-09-09
Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.
Molecular Structure and Chirality Detection by Fourier Transform Microwave Spectroscopy.
Lobsiger, Simon; Perez, Cristobal; Evangelisti, Luca; Lehmann, Kevin K; Pate, Brooks H
2015-01-01
We describe a three-wave mixing experiment using time-separated microwave pulses to detect the enantiomer-specific emission signal of the chiral molecule using Fourier transform microwave (FTMW) spectroscopy. A chirped-pulse FTMW spectrometer operating in the 2-8 GHz frequency range is used to determine the heavy-atom substitution structure of solketal (2,2-dimethyl-1,3-dioxolan-4-yl-methanol) through analysis of the singly substituted (13)C and (18)O isotopologue rotational spectra in natural abundance. A second set of microwave horn antennas is added to the instrument design to permit three-wave mixing experiments where an enantiomer-specific phase of the signal is observed. Using samples of R-, S-, and racemic solketal, the properties of the three-wave mixing experiment are presented, including the measurement of the corresponding nutation curves to demonstrate the optimal pulse sequence. PMID:26263113
Embeddings of fractional Sobolev spaces and estimates of Fourier transforms
Kolyada, V I
2001-08-31
Fractional anisotropic Sobolev-Liouville spaces L{sub p}{sup r{sub 1},...,r{sub n}}(R{sup n}) are investigated for 1{<=}p<{infinity} and positive r{sub k}. For functions in these spaces estimates of norms in modified spaces of Lorentz and Besov kinds, defined in terms of iterative rearrangements, are established. These estimates are used to prove inequalities for the Fourier transforms of functions in L{sub 1}{sup r{sub 1},...,r{sub n}}. This paper continues works of the author in which similar issues have been discussed for integer r{sub k}. The methods used in the paper are based on estimates of iterative rearrangements. This approach enables one to simplify proofs and at the same time to obtain stronger results. In particular, the analysis of the limit case p=1 becomes much easier.
Color image encryption based on joint fractional Fourier transform correlator
NASA Astrophysics Data System (ADS)
Lu, Ding; Jin, Weimin
2011-06-01
In this paper, an optical color image encryption/decryption technology based on joint fractional Fourier transform correlator and double random phase encoding (DRPE) is developed. In this method, the joint fractional power spectrum of the image to be encrypted and the key codes is recorded as the encrypted data. Different from the case with classical DRPE, the same key code was used both in the encryption and decryption. The security of the system is enhanced because of the fractional order as a new added key. This method takes full advantage of the parallel processing features of the optical system, and could optically realize single-channel color image encryption. The experimental results indicate that the new method is feasible.
Fourier transform microwave spectroscopy of CH(2)CFO.
Watanabe, Akihiro; Sumiyoshi, Yoshihiro; Endo, Yasuki
2009-06-14
Rotational spectra of the CH(2)CFO radical in the (2)A(") ground state with resolved fine and hyperfine structures have been observed for the first time by Fourier transform microwave spectroscopy. Rotational transitions are analyzed using the ordinary rigid asymmetric top Hamiltonian for doublet species with three nuclear spins. Seventeen molecular constants including the fine and hyperfine coupling constants have been determined. The CH(2)CFO radical is confirmed to be a planer molecule in the ground electronic state since it has a small positive inertial defect. From the hyperfine coupling constants of protons, the unpaired electron density on the CH(2) carbon atom is estimated to be about 85%. Thus, the formylmethyl-type resonance form (CH(2)CF=O) is a dominant structure in the ground electronic state, and fluorine substitution has negligible effect on the C-C-O pi conjugate system. PMID:19530765
Instrument concept of the imaging Fourier transform spectrometer GLORIA
NASA Astrophysics Data System (ADS)
Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.
2014-10-01
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.
Instrument concept of the imaging Fourier transform spectrometer GLORIA
NASA Astrophysics Data System (ADS)
Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.
2014-03-01
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.
Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)
NASA Technical Reports Server (NTRS)
Best, F. A.; Revercomb, H. E.; Bingham, G. E.; Knuteson, R. O.; Tobin, D. C.; LaPorte, D. D.; Smith, W. L.
2001-01-01
The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.
Optical design of the ATMOS Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Abel, I. R.; Reynolds, B. R.; Breckinridge, J. B.; Pritchard, J.
1979-01-01
The optical system design of the ATMOS Fourier transform spectrometer to be operated from Spacelab for the measurement of stratospheric trace molecules is described. The design contains features which can achieve the required fringe contrast of 80% and spectral resolution of 0.02/cm over a spectral range of 2-16 microns. In particular, the design is based on the following features which alleviate the usual requirements for alignment precision: (1) 'cat's eye' mirror configuration in the two arms of the interferometer for retroreflection stability, (2) tilt-compensated system of beamsplitter, compensator, and fold mirrors for wavefront directional stability, (3) paraboloidal 'cat's eye' primary mirror for wavefront stability against shear, (4) rotatable compensator for matching chromatic dispersion, and (5) wedged refractive components to avoid channel spectra due to the Fabry-Perot effect.
Homological mirror symmetry is Fourier-Mukai transform
Tu, Junwu
2012-01-01
We interpret symplectic geometry as certain sheaf theory by constructing a sheaf of curved A_\\infty algebras which in some sense plays the role of a "structure sheaf" for symplectic manifolds. An interesting feature of this "structure sheaf" is that the symplectic form itself is part of its curvature term. Using this interpretation homological mirror symmetry can be understood by well-known duality theories in mathematics: Koszul duality or Fourier- Mukai transform. In this paper we perform the above constructions over a small open subset inside the smooth locus of a Lagrangian torus fibration. In a subsequent work we shall use the language of derived geometry to obtain a global theory over the whole smooth locus. However we do not know how to extend this construction to the singular locus. As an application of the local theory we prove a version of homological mirror symmetry between a toric symplectic manifold and its Landau-Ginzburg mirror.
A rheumatoid arthritis study by Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
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.
Gas emission analysis based on Fourier transformed infrared spectroscopy
NASA Astrophysics Data System (ADS)
Shu, Xiaowen; Zhang, Xiaofu; Lian, Xu; Jin, Hui
2014-12-01
Solar occultation flux (SOF), a new optical technology to detect the gas based on the traditional Fourier transformed infrared spectroscopy (FTIR) developed quickly recently. In this paper, the system and the data analysis is investigated. First a multilayer transmission model of solar radiation is simulated. Then the retrieval process is illustrated. In the proceeding of the data analysis, the Levenberg-Marquardt non-linear square fitting is used to obtain the gas column concentration and the related emission ratio. After the theory certification, the built up system is conducted in a fertilizer plant in Hefei city .The results show SOF is available in the practice and the retrieved gas column concentration can give important information about the pollution emission and dispersion
Seismic data denoising based on the fractional Fourier transformation
NASA Astrophysics Data System (ADS)
Zhai, Ming-Yue
2014-10-01
Seismic data may suffer from too severe noise contamination to carry out further processing and interpretation procedure. In the paper, a new scheme was proposed based on the fractional Fourier transform (FrFT) in time frequency domain to mitigate noise. The scheme consists of two steps. In the first step, the seismic signal is filtered with the ordinary Butterworth filter in the frequency domain. The residual noises after frequency filtering are with the same frequencies with the filtered seismic signals. In order to mitigate the residual noises further, the FrFT filter is applied in the second step. The results from the simulated seismic signals and the measurements data verify the validity of the proposed scheme in both frequency and time-frequency domains.
Two-dimensional Fourier-transform spectroscopy of potassium vapor
Dai, X.; Bristow, A. D.; Karaiskaj, D.; Cundiff, S. T.
2010-11-15
Optical two-dimensional Fourier-transform (2DFT) spectroscopy is used to study the coherent optical response of potassium vapor in a thin transmission cell. Rephasing and nonrephasing spectra of the D{sub 1} and D{sub 2} transitions are obtained and compared to numerical simulations. Non-perturbative calculations using the optical Bloch equations give very good agreement with the experimental peak strengths and line shapes. Nonradiative Raman-like coherences are isolated using a different 2DFT projection. Comparison between the optical and Raman linewidths shows that dephasing is due to partially correlated energy fluctuations. Density-dependent measurements show distortion of 2DFT spectra due to pulse propagation effects.
On the abstracted dataflow complexity of Fast Fourier Transforms
Boehm, A.P.W.; Hiromoto, R.E.; Kelly, K.A.; Ashley, J.M.
1992-05-01
In this paper we develop and analyze the simulated performance of codes for the Fast Fourier Transform written in If and targeted for execution on Motorola`s dataflow machine Monsoon. The FFT application is of interest because of its computational parallelism, its requirement for global communications, and its array element data dependences. We use the parallel profiling simulator Id World to study the dataflow performance of various implementations. Our approach is comparative. We study two approaches, a recursive and an iterative one, and in each version we examine the effect of a variety of implementations. We contend that only through such comparative evaluations can significant insight be gained in understanding the computational and structural details of functional algorithms.
Dual-frequency fringe Fourier transform profilometry based on defocusing
NASA Astrophysics Data System (ADS)
Fu, Yanjun; Wang, Yonglong; Wu, Jianfeng; Jiang, Guangyu
2013-05-01
Dual-frequency fringe Fourier transform profilometry (FTP) is used to measure steep objects. The dual-frequency fringe can easily be obtained through software programming. However, due to the nonlinear gamma of the projector, the second harmonic generated by the nonlinear response of the camera and the presence of noise, digital filtering becomes difficult and measurement errors are introduced, thus reducing measurement accuracy. Therefore a novel method to generate dual-frequency fringe is presented in this study to solve the aforementioned problems. A binary square wave is projected onto the measured objects. By properly defocusing, the fundamental frequency and the third harmonic components can be preserved. The generated dual-frequency fringe is used to measure the 3-D profile of a computer mouse. The experimental results verify the feasibility of this method. The proposed method has higher measurement accuracy compared with the traditional dual-frequency fringe FTP.
Universal calculation formula and calibration method in Fourier transform profilometry
Wen Yongfu; Li Sikun; Cheng Haobo; Su Xianyu; Zhang Qican
2010-12-01
We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.
Adaptive Controller for Compact Fourier Transform Spectrometer with Space Applications
NASA Astrophysics Data System (ADS)
Keymeulen, D.; Yiu, P.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.; Conroy, M.
2014-12-01
Here we present noise mitigation techniques developed as part of an adaptive controller for a very compact Compositional InfraRed Interferometric Spectrometer (CIRIS) implemented on a stand-alone field programmable gate array (FPGA) architecture with emphasis on space applications in high radiation environments such as Europa. CIRIS is a novel take on traditional Fourier Transform Spectrometers (FTS) and replaces linearly moving mirrors (characteristic of Michelson interferometers) with a constant-velocity rotating refractor to variably phase shift and alter the path length of incoming light. The design eschews a monochromatic reference laser typically used for sampling clock generation and instead utilizes constant time-sampling via internally generated clocks. This allows for a compact and robust device, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 µm) on planetary exploration missions. The instrument's embedded microcontroller is implemented on a VIRTEX-5 FPGA and a PowerPC with the aim of sampling the instrument's detector and optical rotary encoder in order to construct interferograms. Subsequent onboard signal processing provides spectral immunity from the noise effects introduced by the compact design's removal of a reference laser and by the radiation encountered during space flight to destinations such as Europa. A variety of signal processing techniques including resampling, radiation peak removal, Fast Fourier Transform (FFT), spectral feature alignment, dispersion correction and calibration processes are applied to compose the sample spectrum in real-time with signal-to-noise-ratio (SNR) performance comparable to laser-based FTS designs in radiation-free environments. The instrument's FPGA controller is demonstrated with the FTS to characterize its noise mitigation techniques and highlight its suitability for implementation in space systems.
Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups
Guedes, Carlos; Oriti, Daniele; Raasakka, Matti; LIPN, Institut Galilée, Université Paris-Nord, 99, av. Clement, 93430 Villetaneuse
2013-08-15
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-product carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.
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.
NASA Astrophysics Data System (ADS)
Maccone, Claudio
2007-04-01
The present article describes that the range of any radiotelescope (and radar in general) may be increased by virtue of software, if one replaces the fast Fourier transform by the Karhunen Loève transform. The range increases with the inverse of the fourth root of the signal-to-noise ratio when this ratio decreases. Thus, the range on any radiotelescope (and radar) may be increased without changing the hardware at all, but by changing the software only. This improvement in the range of the radiotelescope is currently implemented at the 32-m antenna located at Medicina, near Bologna, in Italy, for both SETI and general radioastronomy.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Paul, J.; Dey, P.; Tokumoto, T.; Reno, J. L.; Hilton, D. J.; Karaiskaj, D.
2014-10-07
The dephasing of excitons in a modulation doped single quantum well was carefully measured using time integrated four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. These are the first 2DFT measurements performed on a modulation doped single quantum well. The inhomogeneous and homogeneous excitonic line widths were obtained from the diagonal and cross-diagonal profiles of the 2DFT spectra. The laser excitation density and temperature were varied and 2DFT spectra were collected. A very rapid increase of the dephasing decay, and as a result, an increase in the cross-diagonal 2DFT linewidths with temperature was observed. The lineshapes of the 2DFT spectra suggest the presence of excitation induced dephasing and excitation induced shift.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Paul, J.; Dey, P.; Tokumoto, T.; Reno, J. L.; Hilton, D. J.; Karaiskaj, D.
2014-10-07
The dephasing of excitons in a modulation doped single quantum well was carefully measured using time integrated four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. These are the first 2DFT measurements performed on a modulation doped single quantum well. The inhomogeneous and homogeneous excitonic line widths were obtained from the diagonal and cross-diagonal profiles of the 2DFT spectra. The laser excitation density and temperature were varied and 2DFT spectra were collected. A very rapid increase of the dephasing decay, and as a result, an increase in the cross-diagonal 2DFT linewidths with temperature was observed. The lineshapes of the 2DFTmore »spectra suggest the presence of excitation induced dephasing and excitation induced shift.« less
Cohen, Ronald C.
Fourier transform microwave spectrum of the propane-water complex: A prototypical water) The Fourier transform microwave spectrum of the propane-water complex (C3H,-H,O) has been observed and analyzed. This spectrum includes transitions assigned to propane complexed with both the ortho and para
An Incremental Algorithm for Signal Reconstruction from Short-Time Fourier Transform Magnitude
Ezzat, Tony
An Incremental Algorithm for Signal Reconstruction from Short-Time Fourier Transform Magnitude Jake@mit.edu Abstract We present an algorithm for reconstructing a time-domain signal from the magnitude of a short-domain signal from only the magnitude of the short-time Fourier transform (STFT) is a common prob- lem in speech
Matrix Fourier transform in dynamic theory of elasticity of piecewise homogeneous medium
O. Yaremko.; E. Mogileva
2013-09-24
The analytical solving dynamic problems of elasticity theory for piecewise homogeneous half-space is found. 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 in the heterogeneous environments is developed on an example of the dynamic problems of the elasticity theory.
The Green's function for the three-dimensional linear Boltzmann equation via Fourier transform
Manabu Machida
2015-10-03
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.
NASA Astrophysics Data System (ADS)
Xia, Xiang-Gen; Wang, Genyuan; Chen, Victor C.
2001-03-01
This paper first reviews some basic properties of the discrete chirp-Fourier transform and then present an adaptive chirp- Fourier transform, a generalization of the amplitude and phase estimation of sinusoids (APES) algorithm proposed by Li and Stoica for sinusoidal signals. We finally applied it to the ISAR imaging of maneuvering targets.
Dordevic, Sasha V.
conductivity S.V. Dordevic n Department of Physics, The University of Akron, Akron, Ohio 44325, USA a r t i c l Keywords: Optical conductivity Inverse Fourier Transform Heavy Fermions a b s t r a c t Inverse Fourier Transform of optical conductivity is used for studies of quasiparticle relaxation in Heavy Fermions in time
Fourier transform infrared spectroscopy for Kona coffee authentication.
Wang, Jun; Jun, Soojin; Bittenbender, H C; Gautz, Loren; Li, Qing X
2009-06-01
Kona coffee, the variety of "Kona typica" grown in the north and south districts of Kona-Island, carries a unique stamp of the region of Big Island of Hawaii, U.S.A. The excellent quality of Kona coffee makes it among the best coffee products in the world. Fourier transform infrared (FTIR) spectroscopy integrated with an attenuated total reflectance (ATR) accessory and multivariate analysis was used for qualitative and quantitative analysis of ground and brewed Kona coffee and blends made with Kona coffee. The calibration set of Kona coffee consisted of 10 different blends of Kona-grown original coffee mixture from 14 different farms in Hawaii and a non-Kona-grown original coffee mixture from 3 different sampling sites in Hawaii. Derivative transformations (1st and 2nd), mathematical enhancements such as mean centering and variance scaling, multivariate regressions by partial least square (PLS), and principal components regression (PCR) were implemented to develop and enhance the calibration model. The calibration model was successfully validated using 9 synthetic blend sets of 100% Kona coffee mixture and its adulterant, 100% non-Kona coffee mixture. There were distinct peak variations of ground and brewed coffee blends in the spectral "fingerprint" region between 800 and 1900 cm(-1). The PLS-2nd derivative calibration model based on brewed Kona coffee with mean centering data processing showed the highest degree of accuracy with the lowest standard error of calibration value of 0.81 and the highest R(2) value of 0.999. The model was further validated by quantitative analysis of commercial Kona coffee blends. Results demonstrate that FTIR can be a rapid alternative to authenticate Kona coffee, which only needs very quick and simple sample preparations. PMID:19646032
SAR-based vibrometry using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Campbell, Justin B.; Wang, Qi; Ade-Bello, Jelili; Caudana, Humberto; Trujillo, Nicole B.; Bhatta, Ishwor; Dunkel, Ralf; Atwood, Thomas; Doerry, Armin; Gerstle, Walter H.; Santhanam, Balu; Hayat, Majeed M.
2015-05-01
A fundamental assumption when applying Synthetic Aperture Radar (SAR) to a ground scene is that all targets are motionless. If a target is not stationary, but instead vibrating in the scene, it will introduce a non-stationary phase modulation, termed the micro-Doppler effect, into the returned SAR signals. Previously, the authors proposed a pseudosubspace method, a modification to the Discrete Fractional Fourier Transform (DFRFT), which demonstrated success for estimating the instantaneous accelerations of vibrating objects. However, this method may not yield reliable results when clutter in the SAR image is strong. Simulations and experimental results have shown that the DFRFT method can yield reliable results when the signal-to-clutter ratio (SCR) > 8 dB. Here, we provide the capability to determine a target's frequency and amplitude in a low SCR environment by presenting two methods that can perform vibration estimations when SCR < 3 dB. The first method is a variation and continuation of the subspace approach proposed previously in conjunction with the DFRFT. In the second method, we employ the dual-beam SAR collection architecture combined with the extended Kalman filter (EKF) to extract information from the returned SAR signals about the vibrating target. We also show the potential for extending this SAR-based capability to remotely detect and classify objects housed inside buildings or other cover based on knowing the location of vibrations as well as the vibration histories of the vibrating structures that house the vibrating objects.
Ribosomal DNA Nanoprobes studied by Fourier Transform Infrared spectroscopy
NASA Astrophysics Data System (ADS)
Fagundes, Jaciara; Castilho, Maiara L.; Téllez Soto, Claudio A.; Vieira, Laís de Souza; Canevari, Renata A.; Fávero, Priscila P.; Martin, Airton A.; Raniero, Leandro
2014-01-01
Paracoccidioides brasiliensis (P. brasiliensis) is a thermo-dimorphic fungus that causes paracoccidioidomycosis. Brazil epidemiological data shows that endemic areas are the subtropical regions, especially where agricultural activities predominate such as the Southeast, South, and Midwest. There are several tests to diagnose paracoccidioidomycosis, but they have many limitations such as low sensitivity, high cost, and a cross-reacting problem. In this work, gold nanoprobes were used to identify P. brasiliensis as an alternative diagnostic technique, which is easier to apply, costs less, and has great potential for application. The specific Ribosomal sequence of P. brasiliensis DNA was amplified and used to design the nanoprobes using a thiol-modified oligonucleotide. The results of positive and negative tests were done by UV-visible and Fourier Transform Infrared (FT-IR) measurements. The deconvolution of FT-IR sample spectra showed differences in the vibrational modes from the hydrogen bridge NHN and NHO bands that form the double helix DNA for samples matching the DNA sequence of nanoprobes that could be used to classify the samples.
Fourier Transform Microwave Spectra of n-BUTANOL and Isobutanol
NASA Astrophysics Data System (ADS)
Uzuyama, Taigo; Tanaka, Yugo; Kawashima, Yoshiyuki; Hirota, Eizi
2009-06-01
We have investigated two butanols, normal (1-butanol) and iso (2-methyl-1-propanol), by Fourier transform microwave spectroscopy, focusing attention mainly to internal motion and rotational isomerism. We anticipate that n-butanol exists in fourteen rotational isomers with the combination of the following conformations: trans (T) and gauche (G) with respect to the CH_3CH_2-CH_2CH_2OH bond, trans (t) and two gauche's (g, g') to the CH_3CH_2CH_2-CH_2OH bond, and two or three potential minima in the internal rotation of OH, and that isobutanol in five. We scanned the frequency region from 7 to 25 GHz using a heated nozzle, and detected six and three isomers for n-butanol and isobutanol, respectively: three with Ar as a buffer gas and three with Ne instead of Ar for n-butanol, whereas Ar was employed for isobutanol. The observed spectral lines were assigned by comparing the experimental moments of inertia and the observed spectral intensities with those calculated by ab initio MO at the MP2/6-311++G(d,p) level. We thus concluded that five conformers detected for n-butanol are T-form and one G-form and that three observed isomers of isobutanol are gauche with respect to the H(CH_3)_2C-CH_2OH bond and one isomer lacking a-type spectra to trans to the CH_2-OH bond.
Liquid chromatography/Fourier transform IR spectrometry interface flow cell
Johnson, C.C.; Taylor, L.T.
1985-01-04
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.
Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS)
NASA Technical Reports Server (NTRS)
Sromovsky, L. A.
2002-01-01
This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).
Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability
NASA Technical Reports Server (NTRS)
Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.
2007-01-01
The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.
Single beam Fourier transform digital holographic quantitative phase microscopy
NASA Astrophysics Data System (ADS)
Anand, A.; Faridian, A.; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Dubey, S. K.; Pedrini, G.; Osten, W.; Javidi, B.
2014-03-01
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.
Applications of Fourier transform-infrared spectroscopy to edible oils.
Vlachos, N; Skopelitis, Y; Psaroudaki, M; Konstantinidou, V; Chatzilazarou, A; Tegou, E
2006-07-28
Recent developments in Fourier transform infrared (FT-IR) spectroscopy instrumentation extend the application of this technique to the field of food research, facilitating particularly the studies on edible oils and fats. In this work, FT-IR spectroscopy is used as an effective analytical tool in order: (a) to determine extra virgin olive oil adulteration with lower priced vegetable oils (sunflower oil, soyabean oil, sesame oil, corn oil) and (b) to monitor the oxidation process of corn oil samples undergone during heating or/and exposure to ultraviolet radiation. A band shift observed at 3009 cm(-1) assigned to the C_H stretching vibration of the cis-double bond, allows the determination of extra virgin olive oil adulteration. Changes in the 3050-2800 and 1745 cm(-1) spectral region appear after heating at elevated temperatures and aid the oxidation process monitoring. In addition, an analytical technique for the measurement of carbonylic compounds in oils, produced after heating, is applied. The possible antioxidant effect of oregano is also discussed. PMID:17723561
Fourier transform infrared spectroscopic analysis of cell differentiation
NASA Astrophysics Data System (ADS)
Ishii, Katsunori; Kimura, Akinori; Kushibiki, Toshihiro; Awazu, Kunio
2007-02-01
Stem cells and its differentiations have got a lot of attentions in regenerative medicine. The process of differentiations, the formation of tissues, has become better understood by the study using a lot of cell types progressively. These studies of cells and tissue dynamics at molecular levels are carried out through various approaches like histochemical methods, application of molecular biology and immunology. However, in case of using regenerative sources (cells, tissues and biomaterials etc.) clinically, they are measured and quality-controlled by non-invasive methods from the view point of safety. Recently, the use of Fourier Transform Infrared spectroscopy (FT-IR) has been used to monitor biochemical changes in cells, and has gained considerable importance. The objective of this study is to establish the infrared spectroscopy of cell differentiation as a quality control of cell sources for regenerative medicine. In the present study, as a basic study, we examined the adipose differentiation kinetics of preadipocyte (3T3-L1) and the osteoblast differentiation kinetics of bone marrow mesenchymal stem cells (Kusa-A1) to analyze the infrared absorption spectra. As a result, we achieved to analyze the adipose differentiation kinetics using the infrared absorption peak at 1739 cm-1 derived from ester bonds of triglyceride and osteoblast differentiation kinetics using the infrared absorption peak at 1030 cm-1 derived from phosphate groups of calcium phosphate.
Fourier Transform Microwave and Infrared Spectroscopic Investigation of Propiolactone
NASA Astrophysics Data System (ADS)
Chen, Ziqiu; van Wijngaarden, Jennifer
2009-06-01
The pure rotational spectrum of the four-membered ester ring propiolactone (C{_3}H{_4}O{_2}) has been measured in a supersonic jet between 7 and 22 GHz using Fourier transform microwave (FTMW) spectroscopy. For the normal isotopologue, a total of 19 a- and b-type transitions have been recorded. Fifteen transitions due to three different ^{13}C isotopologues have also been observed. The microwave spectrum was analyzed to obtain an improved set of ground state rotational constants in comparison to earlier microwave experiments. The new set of rotational parameters was used to predict the rovibrational band structure of the lowest frequency modes of propiolactone. A total of 12 vibrational band origins have been observed between 400 and 1500 cm^{-1} using the far infrared beamline of the Canadian Light Source coupled to a Bruker IFS125HR spectrometer. The spectra were recorded with a resolution of 0.000969 cm^{-1} and although the intensities of the bands vary, 9 bands are of sufficient quality for complete rovibrational assignment. The progress of the assignment of this rich spectrum will be discussed. D. W. Boone, C O. Britt and J. E. Boggs J. Chem. Phys. 43 (1190), 1965.
Single beam Fourier transform digital holographic quantitative phase microscopy
Anand, A. Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Faridian, A.; Pedrini, G.; Osten, W.; Dubey, S. K.; Javidi, B.
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.
External Second Gate-Fourier Transform Ion Mobility Spectrometry.
Tarver, Edward E., III
2005-01-01
Ion mobility spectrometry (IMS) is recognized as one of the most sensitive and versatile techniques for the detection of trace levels of organic vapors. IMS is widely used for detecting contraband narcotics, explosives, toxic industrial compounds and chemical warfare agents. Increasing threat of terrorist attacks, the proliferation of narcotics, Chemical Weapons Convention treaty verification as well as humanitarian de-mining efforts has mandated that equal importance be placed on the analysis time as well as the quality of the analytical data. (1) IMS is unrivaled when both speed of response and sensitivity has to be considered. (2) With conventional (signal averaging) IMS systems the number of available ions contributing to the measured signal to less than 1%. Furthermore, the signal averaging process incorporates scan-to-scan variations decreasing resolution. With external second gate Fourier Transform ion mobility spectrometry (FT-IMS), the entrance gate frequency is variable and can be altered in conjunction with other data acquisition parameters to increase the spectral resolution. The FT-IMS entrance gate operates with a 50% duty cycle and so affords a 7 to 10-fold increase in sensitivity. Recent data on high explosives are presented to demonstrate the parametric optimization in sensitivity and resolution of our system.
Liquid chromatography/Fourier transform IR spectrometry interface flow cell
Johnson, Charles C. (Fairfield, OH); Taylor, Larry T. (Blacksburg, VA)
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.
Applications of the VUV Fourier Transform Spectrometer at Synchrotron Soleil
NASA Astrophysics Data System (ADS)
de Oliveira, Nelson; Joyeux, Denis; Ito, Kenji; Gans, Berenger; Nahon, Laurent
2015-06-01
Fourier transform spectrometers (FTS) are usually based upon amplitude division interferometers through beamsplitters (BS) as in the Michelson interferometer geometry. However, the manufacture of broadband BS is difficult and even impossible in the far VUV (below ? = 140 nm). We therefore conceived an instrument based upon an original design involving only reflective plane surfaces, giving access to the whole VUV range without the restrictions associated with BS. The VUV- FTS is a permanent endstation connected to one of the three experimental branches of the DESIRS beamline and devoted to high resolution photoabsorption in the UV-VUV spectral range, typically between ? = 300 and 40 nm Since 2008, a large international community of users interested in laboratory measurements with applications in astrophysics, molecular physics or planetary atmospheres has been attracted by the VUV - FTS capabilities including its efficiency in terms of signal to noise ratio, even when high spectral resolution was not an issue. A large number of dedicated gas phase sample environments have been developed including a windowless cell that can be cooled down, a heated windowless cell, a free molecular jet set-up and various windowed cells. Besides, a new discharge gas cell for production and study of transient species gave recently its first results. As an illustration, the VUV absorption spectrum of the CH_3 radical down to 140 nm will be shown in this presentation. Nahon et al., J. Synchrotron Radiat., 19, 508(2012) De Oliveira et al., Nat. Photonics, 5, 149(2011)
Optimal Padding for the Two-Dimensional Fast Fourier Transform
NASA Technical Reports Server (NTRS)
Dean, Bruce H.; Aronstein, David L.; Smith, Jeffrey S.
2011-01-01
One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications.
Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Heisler, R.
1978-01-01
A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.
NASA Astrophysics Data System (ADS)
Chen, Ziqiu; van Wijngaarden, Jennifer
2009-10-01
The pure rotational spectrum of ?-propiolactone (c-C 2H 4COO) has been recorded between 7 and 21 GHz using a pulsed jet Fourier transform microwave spectrometer. The resulting ground state spectroscopic constants guided the analysis of the rotationally-resolved infrared spectra of two bands that were collected using the far infrared beamline at the Canadian Light Source synchrotron. The observed modes correspond to motions best described as ring deformation ( ?12) at 747.2 cm -1 and CO ring stretching ( ?8) at 1095.4 cm -1. A global fit of 4430 a- and b-type transitions from the microwave spectrum and the two infrared bands provided an accurate set of ground state and excited state spectroscopic parameters. To complement the experimental results, the harmonic and anharmonic vibrational frequencies of all 21 infrared active modes of ?-propiolactone have been calculated using the DFT B3LYP method (6-311+G(d,p), 6-311++G(2d,3p) basis sets).
Xiao-Jun Yang
2011-07-23
It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.
NASA Astrophysics Data System (ADS)
Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.
2012-06-01
By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H_2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct. Q. Ma, R. H. Tipping, and N. N. Lavrentieva, JQSRT dio:10.1016/j.jqsrt.2012.02.012 (2012).
NASA Technical Reports Server (NTRS)
Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.
2012-01-01
By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.
Systematic characterization of the Herschel SPIRE Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Hopwood, R.; Polehampton, E. T.; Valtchanov, I.; Swinyard, B. M.; Fulton, T.; Lu, N.; Marchili, N.; van der Wiel, M. H. D.; Benielli, D.; Imhof, P.; Baluteau, J.-P.; Pearson, C.; Clements, D. L.; Griffin, M. J.; Lim, T. L.; Makiwa, G.; Naylor, D. A.; Noble, G.; Puga, E.; Spencer, L. D.
2015-05-01
A systematic programme of calibration observations was carried out to monitor the performance of the Spectral and Photometric Imaging REceiver (SPIRE) Fourier Transform Spectrometer (FTS) instrument on board the Herschel Space Observatory. Observations of planets (including the prime point-source calibrator, Uranus), asteroids, line sources, dark sky and cross-calibration sources were made in order to monitor repeatability and sensitivity, and to improve FTS calibration. We present a complete analysis of the full set of calibration observations and use them to assess the performance of the FTS. Particular care is taken to understand and separate out the effect of pointing uncertainties, including the position of the internal beam steering mirror for sparse observations in the early part of the mission. The repeatability of spectral-line centre positions is <5 km s-1, for lines with signal-to-noise ratios >40, corresponding to <0.5-2.0 per cent of a resolution element. For spectral-line flux, the repeatability is better than 6 per cent, which improves to 1-2 per cent for spectra corrected for pointing offsets. The continuum repeatability is 4.4 per cent for the SPIRE Long Wavelength spectrometer (SLW) band and 13.6 per cent for the SPIRE Short Wavelength spectrometer (SSW) band, which reduces to ˜1 per cent once the data have been corrected for pointing offsets. Observations of dark sky were used to assess the sensitivity and the systematic offset in the continuum, both of which were found to be consistent across the FTS-detector arrays. The average point-source calibrated sensitivity for the centre detectors is 0.20 and 0.21 Jy [1?; 1 h], for SLW and SSW. The average continuum offset is 0.40 Jy for the SLW band and 0.28 Jy for the SSW band.
Calibration of the Herschel SPIRE Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Swinyard, B. M.; Polehampton, E. T.; Hopwood, R.; Valtchanov, I.; Lu, N.; Fulton, T.; Benielli, D.; Imhof, P.; Marchili, N.; Baluteau, J.-P.; Bendo, G. J.; Ferlet, M.; Griffin, 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.
2014-06-01
The Herschel Spectral and Photometric REceiver (SPIRE) instrument consists of an imaging photometric camera and an imaging Fourier Transform Spectrometer (FTS), both operating over a frequency range of ˜450-1550 GHz. In this paper, we briefly review the FTS design, operation, and data reduction, and describe in detail the approach taken to relative calibration (removal of instrument signatures) and absolute calibration against standard astronomical sources. The calibration scheme assumes a 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 per cent and repeatable to better than 0.06 per cent and, by comparison with models of Mars and Neptune, the Uranus model is shown to be accurate to within 3 per cent. Multiple observations of a number of point-like sources show that the repeatability of the calibration is better than 1 per cent, if the effects of the satellite absolute pointing error (APE) are corrected. The satellite APE leads to a decrement in the derived flux, which can be up to ˜10 per cent (1 ?) at the high-frequency end of the SPIRE range in the first part of the mission, and ˜4 per cent after Herschel operational day 1011. The lower frequency range of the SPIRE band is unaffected by this pointing error due to the larger beam size. Overall, for well-pointed, point-like sources, the absolute flux calibration is better than 6 per cent, and for extended sources where mapping is required it is better than 7 per cent.
Phase retrieval using iterative Fourier transform and convex optimization algorithm
NASA Astrophysics Data System (ADS)
Zhang, Fen; Cheng, Hong; Zhang, Quanbing; Wei, Sui
2015-05-01
Phase is an inherent characteristic of any wave field. Statistics show that greater than 25% of the information is encoded in the amplitude term and 75% of the information is in the phase term. The technique of phase retrieval means acquire phase by computation using magnitude measurements and provides data information for holography display, 3D field reconstruction, X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Mathematically, solving phase retrieval problem is an inverse problem taking the physical and computation constraints. Some recent algorithms use the principle of compressive sensing, such as PhaseLift, PhaseCut and compressive phase retrieval etc. they formulate phase retrieval problems as one of finding the rank-one solution to a system of linear matrix equations and make the overall algorithm a convex program over n × n matrices. However, by "lifting" a vector problem to a matrix one, these methods lead to a much higher computational cost as a result. Furthermore, they only use intensity measurements but few physical constraints. In the paper, a new algorithm is proposed that combines above convex optimization methods with a well known iterative Fourier transform algorithm (IFTA). The IFTA iterates between the object domain and spectral domain to reinforce the physical information and reaches convergence quickly which has been proved in many applications such as compute-generated-hologram (CGH). Herein the output phase of the IFTA is treated as the initial guess of convex optimization methods, and then the reconstructed phase is numerically computed by using modified TFOCS. Simulation results show that the combined algorithm increases the likelihood of successful recovery as well as improves the precision of solution.
Air quality monitoring based on Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Zheng, Wei; Wang, Yan; Wang, Rui
2006-09-01
The use of optical techniques to identify and quantify atmospheric pollutants has been focused within the past two decades. Fourier Transform Infrared (FTIR) spectroscopy has proven to be a powerful tool for multi-component analysis of air quality monitoring. The technique has been used for gaseous samples by extractive sampling as well as in the open-path configuration. The present contribution has described the application of FTIR to analyze gaseous pollutants in ambient air in detail. The study for the detection limits of the interested gas, the design of the multipass White mirror system, and the experimental results are described. The White cell is employed to increase the absorbance relative to noise in the absorbance spectrum by increasing the path length without proportional loss of signal. A classical least squares (CLS) fit is used to match the scaled standards or previously measured absorption profiles to those of the observed spectrum in the specified spectral analysis regions for simultaneous quantification of the compounds of interest, plus several other ambient air constituents. The regions were chosen carefully to provide optimum detection of the compounds of interest with minimum interference by other compounds. Specially, spectrum subtraction and differential absorption concepts are introduced into FTIR data analysis. The optimal window for CO, S0 II, NO II, NO and CO II would be the region at 2250-2020 cm -1, 1230-1070 cm -1, 2940-2840 cm -1, 1965-1775 cm -1, and around 668.24 cm -1 respectively. Deviations from traditional measured results for all approaches are in 10%.
Fourier transform Raman lidar for trace gas detection and quantification
Sentell, J.C.
1994-12-31
The Raman technique, while a valuable tool in chemical and combustion research, is limited in many remote sensing applications because of the low Raman scattering cross-section, which may be three to five orders of magnitude below the Rayleigh (elastic) values. Two concepts for increasing the signal level are discussed. First, use a range-gated Fourier transform spectrometer to increase the system throughput and allow multiplexing advantages. The spectrum is obtained by performing a FFT on the resulting interferogram. Second, since the cross section goes as the fourth power of the optical frequency, use ultra-violet laser illumination, and separate the resulting fluorescence radiation by placing a known dispersion on the transmitted waveform. The techniques for achieving this function, and the mathematical formulation for the phase-modulated auto-correlation which result, are not evaluated in this paper. However, the approach does not appreciably lower the available resolution because the limits are imposed by the sampling function inherent to the finite-duration Michelson mirror scan. A conceptual design using a long-pulse, flashlamp-pumped dye laser is shown, and typical performance equations in the detection of Freon 12, CCl{sub 2}F{sub 2}, are presented. For a one joule laser and a thirty (30) cm aperture operating in darkness, a concentration of 10{sup 23} molecules/m{sup 3} can be detected in a 60 km visibility at a range of 3.4 km. Much greater performance is obtained against molecules exhibiting the resonance Raman effect, such as nitrogen dioxide.
Two-dimensional Fourier transform electronic correlation and relaxation spectroscopy
NASA Astrophysics Data System (ADS)
Jonas, David
2000-03-01
We have detected optical electric fields to develop femtosecond 2D Fourier transform electronic spectroscopy, which has similarities to 2D NMR and a complementary relationship to single molecule spectroscopy. The two frequency axes represent the initial dipole oscillation frequency after the first excitation pulse and the final dipole oscillation frequency after the last pulse. The 2D spectrum shows correlations between these initial and final frequencies on single molecular complexes. The real and imaginary parts of the 2D spectra represent absorption and dispersion changes induced by the initial excitation. A three pulse sequence allows an adjustable relaxation time between the two frequency measurements that generate the 2D spectrum. The relaxation time can be used to probe electronic relaxation (energy transfer, electron transfer), vibrational relaxation, or chemical reactions. On a femtosecond timescale this relaxation time allows study of nuclear wavepacket motion, which alters the electronic frequency in accord with the Franck-Condon principle. Because the 2D spectrum is determined by free dipole oscillation between pulses, 2D spectra can reveal motions hidden under the broad spectra of femtosecond pulses or obscured by motion during a femtosecond pulse. The excitation pulses act as spectral filters that provide a window onto the undistorted dynamics revealed in a 2D spectrum. Slices of the 2D correlation spectrum at zero relaxation time each reveal the dynamics of separate initial molecular configurations. 2D spectra of the solvatochromic dye IR144 in solution have been used to probe femtosecond polar solvation dynamics as a function of the initial solvent coordinate. These studies have allowed us to measure the inertial response of methanol to a sudden change in solute charge distribution and provide a test of the linear response assumption in electron transfer theory.
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
NASA Technical Reports Server (NTRS)
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.
Liouville transformations and quantum reflection
Gabriel Dufour; Romain Guérout; Astrid Lambrecht; Serge Reynaud
2015-02-21
Liouville transformations of Schr\\"odinger equations preserve the scattering amplitudes while changing the effective potential. We discuss the properties of these gauge transformations and introduce a special Liouville gauge which allows one to map the problem of quantum reflection of an atom on an attractive Casimir-Polder well into that of reflection on a repulsive wall. We deduce a quantitative evaluation of quantum reflection probabilities in terms of the universal probability which corresponds to the solution of the $V_4=-C_4/z^4$ far-end Casimir-Polder potential.
This is an author preprint of: J. P. Haldar, R. M. Leahy. "Linear Transforms for Fourier Data
Leahy, Richard M.
This is an author preprint of: J. P. Haldar, R. M. Leahy. "Linear Transforms for Fourier Data;Linear Transforms for Fourier Data on the Sphere: Application to High Angular Resolution Diffusion MRI in three- dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk
Ghosh, Sandip
Application of a Fourier transform based filtering technique to improve signal-to-noise ratio of a fast Fourier transform FFT based simplified filtering procedure to improve S/N ratio, thereby enabling) is the Fourier transform of the above data. The frequency scale has been normalized with respect to the Nyquist
Franchetti, Franz
Fast Fourier Transform on FPGA: Design Choices and Evaluation Peter A. Milder, Franz Franchetti University Pittsburgh, PA, U.S.A. {pam, franzf, jhoe, pueschel}@ece.cmu.edu The discrete Fourier transform algorithms for computing the DFT, called fast Fourier transforms (FFTs), exhibit concurrency and regularity
Stadler, Peter F.
Fast Fourier Transform for Fitness Landscapes Dan Rockmore a , Peter Kostelec a , Wim Hordijk b that explicit computations of the Walsh/Fourier transforms are feasible for landscapes with up to 10 8 configurations using Fast Fourier Transform techniques. We find that the cost function of a linear sum assignment
Inversion of weighted Radon transforms via finite Fourier series weight approximations
Guillement, Jean-Pol
Inversion of weighted Radon transforms via finite Fourier series weight approximations J Moscow, Russia e-mail: novikov@cmap.polytechnique.fr Abstract. We consider weighted Radon transforms approach by numerical examples for the case of the attenuated Radon transforms in the framework
Time-domain surface profile imaging via a hyperspectral Fourier transform spectrometer
the HS-FTS. © 2008 Optical Society of America OCIS codes: 240.0310, 110.4234, 120.2830. The development using a hyperspectral Fourier transform spectrometer (HS-FTS). This technique measures the frequency of a hyperspectral Fourier trans- form spectrometer (HS-FTS) for surface profile imag- ing with a primary application
The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.
ERIC Educational Resources Information Center
King, Roy W.; Williams, Kathryn R.
1989-01-01
Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)
This project explored the feasibility of developing new techniques for evaluation of the effects of environmental toxic materials on complex biopolymer systems using high sensitivity Fourier transform nuclear magnetic resonance (nmr) spectroscopy. Commercial instrumentation avail...
Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...
A commercial Fourier transform infrared (FTIR) spectrometer, modified for automated analysis of particulate-associated sulfate, was used to obtain transmission spectra samples of particulate matter collected from the ambient air onto Teflon filters. n evaluation of this instrumen...
Arc Fault Signal Detection - Fourier Transformation vs. Wavelet Decomposition Techniques using Abstract -- Arc faults are a significant reliability and safety concern for photovoltaic (PV) systems faults in deployed systems are seemingly random and challenging to faithfully create experimentally
NASA Technical Reports Server (NTRS)
Bowman, K.; Worden, H.; Beer, R.
1999-01-01
Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.
NASA Technical Reports Server (NTRS)
Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.
2000-01-01
A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).
Calcium floride, magnesium fluoride, sulfur, silver bromide, silver chloride, and five different particle sizes of diamond powder were studied for use as matrix materials for diffuse reflectance Fourier transform infrared spectrometry. Potassium chloride was used as a reference b...
Wolfe, Alexander P.
CHARACTERIZING MODERN AND FOSSIL GYMNOSPERM EXUDATES USING MICRO-FOURIER TRANSFORM INFRARED spectroscopy have direct implications for the assessment of the fossil potential and the chemotaxonomic interpretation of modern and fossil gymnosperm exudates. Keywords: chemotaxonomy, plant resin, gum, conifers
Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.
ERIC Educational Resources Information Center
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)
SPECIATION OF HAZARDOUS INORGANIC COMPOUNDS BY FOURIER TRANSFORM INFRARED (FTIR) SPECTROSCOPY
The report describes an extension of the application of infrared methodology to characterize hazardous inorganic compounds in solid inorganic emissions, based on recent advances in instrumentation for Fourier transform infrared (FTIR) spectroscopy. The improved instrumentation, c...
Broadband Mid-Infrared Comb-Resolved Fourier Transform Spectroscopy
NASA Astrophysics Data System (ADS)
Lee, Kevin; Mills, Andrew; Mohr, Christian; Jiang, Jie; Fermann, Martin; Maslowski, Piotr
2014-06-01
We report on a comb-resolved, broadband, direct-comb spectroscopy system in the mid-IR and its application to the detection of trace gases and molecular line shape analysis. By coupling an optical parametric oscillator (OPO), a 100 m multipass cell, and a high-resolution Fourier transform spectrometer (FTS), sensitive, comb-resolved broadband spectroscopy of dilute gases is possible. The OPO has radiation output at 3.1-3.7 and 4.5-5.5 ?m. The laser repetition rate is scanned to arbitrary values with 1 Hz accuracy around 417 MHz. The comb-resolved spectrum is produced with an absolute frequency axis depending only on the RF reference (in this case a GPS disciplined oscillator), stable to 1 part in 10^9. The minimum detectable absorption is 1.6x10-6 wn Hz-1/2. The operating range of the experimental setup enables access to strong fundamental transitions of numerous molecular species for applications based on trace gas detection such as environmental monitoring, industrial gas calibration or medical application of human breath analysis. In addition to these capabilities, we show the application for careful line shape analysis of argon-broadened CO band spectra around 4.7 ?m. Fits of the obtained spectra clearly illustrate the discrepancy between the measured spectra and the Voigt profile (VP), indicating the need to include effects such as Dicke narrowing and the speed-dependence of the collisional width and shift in the line shape model, as was shown in previous cw-laser studies. In contrast to cw-laser based experiments, in this case the entire spectrum (˜ 250 wn) covering the whole P and R branches can be measured in 16 s with 417 MHz resolution, decreasing the acquisition time by orders of magnitude. The parallel acquisition allows collection of multiple lines simultaneously, removing the correlation of possible temperature and pressure drifts. While cw-systems are capable of measuring spectra with higher precision, this demonstration opens the door for fast, massively parallel line shape parameters retrieval combined with analysis reaching beyond the VP and with absolute frequency calibration delivered by frequency combs. R. Wehr et al. J. Mol. Spec. 235 54-68 (2003) A. Cygan, et al. Eur. Phys. J. Special Topics 222 2119-2142 (2013)
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 reliable method is needed for differentiation. Using chemometrics, a classification scheme was developed and performed on samples sporulated in glucose broth. PNNL has demonstrated that vegetative bacteria and endospores have unique infrared (IR) signatures that can be used to identify to the species-, and in some cases, even to the strain-level. We have shown that the IR spectra of spores of different species tend to be quite similar, yet the small but reproducible differences in the spectra allow for a certain degree of differentiation. Further studies have shown that the culture medium can also have an effect on the spectra. For the distinction between vegetative and endospores, we have consistently observed a series of four peaks at 766, 725, 702, and a fairly sharp peak (FWHM 7 cm-1) at 660 cm-1, present only in the endospore spectra.
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.
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
Fourier transform infrared and mass spectrometry studies of a photoirradiated KxC60 film
NASA Astrophysics Data System (ADS)
Onoe, J.; Hashi, Y.; Esfarjani, K.; Kawazoe, Y.; Takeuchi, K.
A photoirradiated potassium-doped C60 film has been studied by Fourier transform mass spectrometry (FT-MS) and by in situ high-resolution Fourier transform infrared spectroscopy (FT-IR) in combination with tight-binding IR calculations. The results of FT-MS and FT-IR strongly suggest that C120 bucky peanuts, which have been theoretically predicted to be stable, were formed in the photoirradiated film.
Hopkinson, J; Moustou, C; Charlwood, K A; Newbery, J E; Charlwood, B V
1985-12-01
A method has been developed to determine the reflectance Fourier Transform Infrared spectra of plant cells grown in vitro and of the protoplasts released from such cells by enzymatic digestion. It is demonstrated that there is a smooth and reproducible transition in spectral detail as enzymatic digestion procedes. Reflectance Fourier Transform Infrared spectroscopy has been used to monitor the progress of protoplast release during enzymatic digestion of cell wall material. PMID:24254073
Wang, Ruhang; Huang, Jianguo; Ma, Tian; Zhang, Qunfei
2010-12-01
This letter presents an improved space time prewhitening method for linear frequency modulation (LFM) reverberation. The proposed method transforms the reverberation to fractional Fourier domain to whiten using fractional Fourier transform. The linear varying frequency in LFM reverberation is focused on a stationary frequency, and the adjacent block signal is used as the reference signal of prewhitening. Finally, experiment results with real reverberation data verify that the proposed method improves the detection performance of active sonar in shallow sea significantly. PMID:21218858
Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing
NASA Technical Reports Server (NTRS)
Park, J. H.
1984-01-01
An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.
Fourier transform spectroscopy of chemiluminescence from system of SrOq
Le Roy, Robert J.
Fourier transform spectroscopy of chemiluminescence from the A01 PÂX1 RÃ¾ system of SrOq Randall H a Broida flow reactor using a Fourier transform spectrometer. In total, 32 bands from 88 SrO, 87 SrO, 86 SrO. The A01 P state of SrO was first investigated by Field [10] through his interpretation
Alternative path to the boundary: The CFT as the Fourier transform in AdS space
Tolfree, Ian M.
2008-11-15
In this paper we shed new light on the AdS/CFT duality by interpreting the CFT as the Fourier transform in AdS space. We make use of well-known integral geometry techniques to derive the Fourier transformation of a function defined on the AdS hyperboloid. We show that the Fourier transformation of a function on the hyperboloid is a function defined on the boundary. We find that the Green's functions from the literature are actually the Fourier weights (i.e. plane wave solutions) of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier components of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD-like theories. In addition, we consider possible implications involving understanding the dual of AdS black holes.
Baddour, Natalie
2010-10-01
For functions that are best described with spherical coordinates, the three-dimensional Fourier transform can be written in spherical coordinates as a combination of spherical Hankel transforms and spherical harmonic series. However, to be as useful as its Cartesian counterpart, a spherical version of the Fourier operational toolset is required for the standard operations of shift, multiplication, convolution, etc. This paper derives the spherical version of the standard Fourier operation toolset. In particular, convolution in various forms is discussed in detail as this has important consequences for filtering. It is shown that standard multiplication and convolution rules do apply as long as the correct definition of convolution is applied. PMID:20922005
Pilgrim, Richard Allen
1994-01-01
The performance characteristics of the wavelet transform and the short-time Fourier transform (STFT) for transient detection are examined by means of computer simulation. The STFT uses a power-of-two decimation-in-time FFT with various frame sizes...
Fourier transform infrared emission spectra of MgH and MgD A. Shayesteh and D. R. T. Appadoo
Le Roy, Robert J.
Fourier transform infrared emission spectra of MgH and MgD A. Shayesteh and D. R. T. Appadoo, Ontario, N2L 3G1, Canada Received 9 February 2004; accepted 8 March 2004 High resolution Fourier transform the emission spectrum of the A 2 X 2 transition of MgH using a magnesium hollow cathode discharge and a Fourier
A Graphical Presentation to Teach the Concept of the Fourier Transform
ERIC Educational Resources Information Center
Besalu, E.
2006-01-01
A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.
X-ray Coherent diffraction interpreted through the fractional Fourier transform
Bolloc'h, david Le
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.
Evaluation of Fourier cosine/sine transforms using exponentially positioned samples
NASA Astrophysics Data System (ADS)
Kong, F. N.
2012-04-01
The digital filter technique using exponentially positioned samples has been widely used in evaluating Hankel transforms. However it is not so widely used in evaluating Fourier transforms (FT). Published actual filters for FT evaluation are rather limited. We therefore present filters in lengths: 21, 61 and 101, which may be useful in evaluating FT for calculating e.g., the electromagnetic fields from a line source and from a dipole source, etc. It is shown that the filter technique can be more efficient (i.e., using fewer samples) than using digital Fourier transform (DFT) in evaluating FT related to 2D and 3D Green's functions.
Boal, David
PHYS 385 Lecture 3 - Fourier transforms 3 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 3 - Fourier transforms What's important: · discrete Fourier transforms · continuous Fourier transforms Text: Gasiorowicz, App. A The two
Lab 7: Fourier analysis and synthesis Fourier series (periodic phenomena)
Gustafsson, Torgny
Lab 7: Fourier analysis and synthesis · Fourier series (periodic phenomena) · Fourier transform (aperiodic phenomena) · Fast Fourier transform (FFT) The Fourier Transform and its Applications Brad G A powerful analytic tool that has many applications.... #12;Applications of Fourier analysis Periodic
Operational and convolution properties of two-dimensional Fourier transforms in polar coordinates.
Baddour, Natalie
2009-08-01
For functions that are best described in terms of polar coordinates, the two-dimensional Fourier transform can be written in terms of polar coordinates as a combination of Hankel transforms and Fourier series-even if the function does not possess circular symmetry. However, to be as useful as its Cartesian counterpart, a polar version of the Fourier operational toolset is required for the standard operations of shift, multiplication, convolution, etc. This paper derives the requisite polar version of the standard Fourier operations. In particular, convolution-two dimensional, circular, and radial one dimensional-is discussed in detail. It is shown that standard multiplication/convolution rules do apply as long as the correct definition of convolution is applied. PMID:19649111
Products of multiple Fourier series with application to the multiblade transformation
NASA Technical Reports Server (NTRS)
Kunz, D. L.
1981-01-01
A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.
Fourier-transform Ghost Imaging for pure phase object based on Compressive Sampling algorithm
Hui Wang; Shensheng Han
2009-11-20
A special algorithm for the Fourier-transform Ghost Imaging (GI) scheme is discussed based on the Compressive Sampling (CS) theory. Though developed mostly in real space, CS algorithm could also be used for the Fourier spectrum reconstruction of pure phase object by setting a proper sensing matrix. This could find its application in diffraction imaging of X-ray, neutron and electron with higher efficiency and resolution. Simulation and experiment results are also presented to prove the feasibility.
q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity
NASA Astrophysics Data System (ADS)
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.
2009-10-01
It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.
Image encryption based on nonseparable fractional Fourier transform and chaotic map
NASA Astrophysics Data System (ADS)
Ran, Qiwen; Yuan, Lin; Zhao, Tieyu
2015-08-01
In this paper an image cryptosystem is constructed by using double random phase masks and a chaotic map together with a novel transform which is similar to fractional Fourier transform and gyrator transform to some extent. The new transform is not periodic with respect to the transform order and cannot be expressed as a tensor product of two one-dimensional transforms neither in the space domain nor in the Wigner space-frequency domain. In the cryptosystem, the parameters of Arnold map, transform orders of the proposed transform and phase information serve as the main keys. The numerical simulations have demonstrated the validity and high security level of the image cryptosystem based on the proposed transform.
Study on sampling of continuous linear system based on generalized Fourier transform
NASA Astrophysics Data System (ADS)
Li, Huiguang
2003-09-01
In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.
Experimental validation of Fourier-transform wave-front reconstruction at the Palomar Observatory.
Poyneer, Lisa A; Troy, Mitchell; Macintosh, Bruce; Gavel, Donald T
2003-05-15
Wave-front reconstruction with use of the Fourier transform has been validated through theory and simulation. This method provides a dramatic reduction in computational costs for large adaptive (AO) systems. Because such a reconstructor can be expressed as a matrix, it can be used as an alternative in a matrix-based AO control system. This was done with the Palomar Observatory AO system on the 200-in. Hale telescope. Results of these tests indicate that Fourier-transform wave-front reconstruction works in a real system. For both bright and dim stars, a Hudgin-geometry Fourier-transform method produced performance comparable to that of the Palomar Adaptive Optics least squares. The Fried-geometry method had a noticeable Strehl ratio performance degradation of 0.043 in the K band (165-nm rms wave-front error added in quadrature) on a dim star. PMID:12779150
Representation of the Fourier transform as a weighted sum of the complex error functions
S. M. Abrarov; B. M. Quine
2015-08-05
In this paper we show that a methodology based on a sampling with the Gaussian function of kind $h\\,{e^{ - {{\\left( {t/c} \\right)}^2}}}/\\left( {{c}\\sqrt \\pi } \\right)$, where ${c}$ and $h$ are some constants, leads to the Fourier transform that can be represented as a weighted sum of the complex error functions. Due to remarkable property of the complex error function, the Fourier transform based on the weighted sum can be significantly simplified and expressed in terms of a damping harmonic series. In contrast to the conventional discrete Fourier transform, this methodology results in a non-periodic wavelet approximation. Consequently, the proposed approach may be useful and convenient in algorithmic implementation.
NASA Astrophysics Data System (ADS)
van Agthoven, Maria A.; Barrow, Mark P.; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A.; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B.
2015-07-01
Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules.
van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B
2015-12-01
Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ?. PMID:26184984
Sun, Zhiwei; Hou, Peipei; Zhi, Ya'nan; Sun, Jianfeng; Zhou, Yu; Xu, Qian; Lu, Zhiyong; Liu, Liren
2014-03-20
A two-dimensional (2D) Fourier transform algorithm for the image reconstruction of synthetic-aperture imaging ladar (SAIL) collected data is suggested. This algorithm consists of quadratic phase compensation in azimuth direction and 2D fast Fourier transform. Based on this algorithm and the parallel 2D Fourier transform capability of spherical lens, an optical principle scheme that processes the SAIL data is proposed. The basic principle, design equations, and necessary analysis are presented. To verify this principle scheme, an experimental optical SAIL processor setup is constructed. The imaging results of SAIL data obtained by our SAIL demonstrator are presented. The optical processor is compact, lightweight, and consumes low power. This optical processor can also provide inherent parallel and speed-of-light computing capability, and thus has potential applications in on-board and satellite-borne SAIL systems. PMID:24663462
Wavelets as alternative to short-time Fourier transform in signal-averaged electrocardiography.
Gramatikov, B; Georgiev, I
1995-05-01
The paper reports experience of using the wavelet transform to build time-frequency distributions of the terminal portion of the QRS-complex. We used wavelets of Morlet at 12 scales, grouped in three sets, to analyse the frequency range 33-404 Hz. On the same patient data we applied the short-time Fourier transform and compared the results. Both representations reflected the time-frequency contents and detected irregular structures in the terminal portion of the QRS complex. The wavelet transform revealed more adequately QRS prolongations characteristic of patients prone to ventricular tachycardia. We may conclude that the wavelet transform can be a flexible alternative to short-time Fourier transform. PMID:7666698
Reduction and coding of synthetic aperture radar data with Fourier transforms
NASA Technical Reports Server (NTRS)
Tilley, David G.
1995-01-01
Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.
Does the entorhinal cortex use the Fourier transform?
Orchard, Jeff; Yang, Hao; Ji, Xiang
2013-01-01
Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4–12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed “theta precession.” Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415
NASA Astrophysics Data System (ADS)
Fan, Hong-yi; Hu, Li-yun
2012-06-01
By virtue of the new technique of performing integration over Dirac's ket-bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel-Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac's assertion: "...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory".
Digital holographic moiré-like patterns and an application to Fourier transform profilometry
NASA Astrophysics Data System (ADS)
de Oliveira, G. N.; de Oliveira, M. E.; da Rocha Freire, R. B.; dos Santos, P. A. M.
2015-11-01
In the present work, the production of digital holographic moiré-like patterns in a well-controlled digital Fourier transform holographic experiment is reported, and this technique is then applied to profilometry. A simple implementation of the digital Fourier transform holographic setup is used to produce these interference patterns. This setup allows us to control certain parameters, namely the incident angle of the reference beams and the spatial frequency of the moiré-like patterns. These digital moiré-like patterns could have promising applications in relevant optical interferometric fields such as profilometry, as demonstrated here, along with other industrial optomechanical applications.
The Los Alamos Fourier-transform spectrometer: Applications to molecular spectroscopy
Palmer, B.A.; McDowell, R.S.
1989-01-01
We outline design considerations and operating characteristics of the Los Alamos Fourier-transform spectrometer, a state-of-the-art instrument operating from 200 nm to 20 ..mu..m with a resolution of 0.0026 cm/sup /minus/1/ and very high wave number and intensity accuracy. Recent work in molecular spectroscopy carried out with this instrument will be discussed, including N/sub 2//sup +/ spectra obtained in inductively-coupled plasmas; high-temperature spectra of diatomic molecules of astrophysical interest; high-resolution rovibrational fine structure; and Fourier-transform Raman spectroscopy of species in expansion-cooled gases. 8 refs., 5 figs., 4 tabs.
Fast transform from an adaptive multi-wavelet representation to a partial Fourier representation
Jia, Jun; Harrison, Robert J; Fann, George I
2010-01-01
We present a fast algorithm to compute the partial transformation of a function represented in an adaptive pseudo-spectral multi-wavelet representation to a partial Fourier representation. Such fast transformations are useful in many contexts in physics and engineering, where changes of representation from a piece wise polynomial basis to a Fourier basis. The algorithm is demonstrated for a Gaussian in one and in three dimensions. For 2D, we apply this approach to a Gaussian in a periodic domain. The accuracy and the performance of this method is compared with direct summation.
NASA Astrophysics Data System (ADS)
Kulkarni, Rishikesh; Rastogi, Pramod
2015-07-01
This paper proposes a novel method for the simultaneous estimation of multiple interference phases from a single recording of the interference field in a multi-wave digital holographic interferometry set-up. The method involves the separation of signal components from the recorded interference field based on windowed Fourier transform based filtering and amplitude discrimination criteria. The proposed method possesses the advantages offered by windowed Fourier transform based filtering such as noise robustness and a high quality reconstruction of the signal components. The performance of the method is validated with numerical and experimental examples.
Goda, Keisuke; Jalali, Bahram
2008-01-01
Dispersive Fourier transformation is a powerful technique in which the spectrum of an optical pulse is mapped into a time-domain waveform using chromatic dispersion. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector. This simplifies the system and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcode reader and displacement sensor that employs internally-amplified dispersive Fourier transformation. This technique amplifies and simultaneously maps the spectrally encoded barcode into a temporal waveform. It achieves a record acquisition speed of 25 MHz -- four orders of magnitude faster than the current state-of-the-art.
Quantum Memory as Light Pulses Quantum States Transformer
NASA Astrophysics Data System (ADS)
Vetlugin, A. N.; Sokolov, I. V.
2015-09-01
Quantum memory can operate not only as a write-in/readout device [1] for quantum light pulses and non-classical states generation [2] device but also as a quantum states of light transformer. Here the addressable parallel quantum memory [3] possibilities for this type of transformation are researched. Quantum memory operates as a conventional N-port interferometer with N equals to the number of the involved spin waves. As example we consider the ability to transform quantum states of two light pulses - in this case the quantum memory works as a mirror with a controlled transmission factor.
Grid-Based Fourier Transform Phase Contrast Imaging
NASA Astrophysics Data System (ADS)
Tahir, Sajjad
Low contrast in x-ray attenuation imaging between different materials of low electron density is a limitation of traditional x-ray radiography. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One recently developed phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a technique recently demonstrated by Bennett et al. that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 microm spot Mo source, a CCD with 22 microm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the grid in the Fourier domain. A Matlab code was written to perform the image processing. For the first time, the effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the window function type used to separate the harmonics, and the window widths, were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and new methods investigated to form improved phase contrast images.
S-duality as Fourier transform for arbitrary $?_1,?_2$
N. Nemkov
2013-07-09
The AGT relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that for the four-point conformal block the modular transform up to the non-perturbative contributions can be written in form of the ordinary Fourier transform when $\\beta\\equiv-\\epsilon_1/\\epsilon_2=1$. Here we extend this conjecture to general values of $\\epsilon_1,\\epsilon_2$. Namely, we argue that for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters $\\epsilon_1,\\epsilon_2$. The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant $g^2\\equiv-\\epsilon_1\\epsilon_2$ and hypermultiplet masses.
Fourier-transform spectroscopy and potential construction of the (2){sup 1}? state in KCs
Birzniece, I.; Nikolayeva, O.; Tamanis, M.; Ferber, R.
2015-04-07
The paper presents an empirical pointwise potential energy curve (PEC) of the (2){sup 1}? state of the KCs molecule constructed by applying the Inverted Perturbation Approach routine. The experimental term values in the energy range E(v?, J?) ? [15?407; 16?579] cm{sup ?1} involved in the fit were based on Fourier-Transform spectroscopy data obtained with 0.01 cm{sup ?1} accuracy from the laser-induced (2){sup 1}? ? X{sup 1}?{sup +} fluorescence spectra. Buffer gas Ar was used to facilitate the appearance of rotation relaxation lines in the spectra, thus enlarging the (2){sup 1}? data set and allowing determination of the ?-splitting constants. The data set included vibrational v? ? [0, 28] and rotational J? ? [7, 274] quantum numbers covering about 67% of the potential well. The present PEC reproduces the overall set of data included in the fit with a standard deviation of 0.5 cm{sup ?1}. The obtained value of the ?-doubling constant q = + 1.8 × 10{sup ?6} cm{sup ?1} for J? > 50 and v? ? [0, 6] is in an excellent agreement with q = + 1.84 × 10{sup ?6} cm{sup ?1} reported in Kim, Lee, and Stolyarov [J. Mol. Spectrosc. 256, 57-67 (2009)].
Fourier transform spectroscopy of CO2 isotopologues at 1.6 ?m: Line positions and intensities
NASA Astrophysics Data System (ADS)
Jacquemart, D.; Borkov, Yu. G.; Lyulin, O. M.; Tashkun, S. A.; Perevalov, V. I.
2015-07-01
The line positions and intensities of carbon dioxide isotopologues have been retrieved between 5900 and 6400 cm-1 region from Fourier transform spectra of 17O- and 18O-enriched carbon dioxide recorded in LADIR (Paris, France) with the Bruker IFS 125-HR. In total 1634 line positions and intensities of 20 bands of the 5 major CO2 isotopologues present in our sample 16O12C17O (39.48%), 17O12C17O (27.73%), 16O12C16O (15.20%), 16O12C18O (7.32%) and 17O12C18O (8.25%) are retrieved. All studied bands belong to the ?P=8 (only for asymmetric species) and 9 series of transitions, where P = 2V1 +V2 + 3V3 is the polyad number (Vi are vibrational quantum numbers). The accuracy of the line position determination is about 0.3×10-3 cm-1 for the unblended and not very weak lines and the accuracy for the line intensities varies from 4% to 30% depending on the intensity of the line and on the extent of the line overlapping. For the 16O12C17O, 17O12C17O, 16O12C18O and 17O12C18O isotopologues the systematic comparisons have been performed with the recent CRDS measurements.
Technology Transfer Automated Retrieval System (TEKTRAN)
A new chemometric method based on absorbance ratios from Fourier transform infrared spectra was devised to analyze multicomponent biodegradable plastics. The method uses the BeerLambert law to directly compute individual component concentrations and weight losses before and after biodegradation of c...
Tabletop soft-x-ray Fourier transform holography with 50 nm resolution
Miao, Jianwei "John"
-harmonic source, while resolutions of 71 nm were obtained us- ing a 46.9 nm SXR laser [11,12]. Fourier transform-ray source. By applying curvature correction to compensate for the large angles inherent in high-NA coherent. This technique will enable biological and materials microscopy with simultaneously high spa- tial and temporal
Technology Transfer Automated Retrieval System (TEKTRAN)
The automated quantification of three greenhouse gases, ammonia, methane and nitrous oxide, in the vicinity of a large dairy farm by open-path Fourier transform infrared (OP/FT-IR) spectrometry at intervals of 5 minutes is demonstrated. Spectral pretreatment, including the detection and correction ...
Technology Transfer Automated Retrieval System (TEKTRAN)
Over 32,000 interferograms measured during open-path Fourier transform infrared (OP/FT-IR) measurements at dairy and hog farms were evaluated for anomalies. Five types of anomalies could be distinguished: a reduction in the interferogram intensity because of weather-related optical misalignment; an ...
Fourier Transformed Spectral Bio-imaging for Studying the Intracellular Fate of Liposomes
van Vliet, Lucas J.
Fourier Transformed Spectral Bio-imaging for Studying the Intracellular Fate of Liposomes Ulrich of liposomal drug targeting systems, it is necessary to understand the mechanism of liposome uptake by the cell and to follow the intracellular fate of internalized liposomes and their contents. Methods: We applied multiple
ATMOSPHERIC MEASUREMENTS OF TRACE POLLUTANTS; LONG PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY
Described are the results of a four-year study to measure trace pollutant concentrations in polluted atmospheres by kilometer pathlength Fourier transform infrared (FT-IR) absorption spectroscopy. The study covers selected smog episodes during the years 1976 to 1979. During 1976 ...
The United States Environmental Protection Agency (U.S. EPA) requires reference spectra to support its gas chromatography/Fourier transform infrared (GC/FT-IR) routine environmental monitoring program. Although on-the-fly (OTF) techniques are needed to satisfy the Agency's high s...
Far infrared Fourier-transform spectroscopy of mono-deuterated hydrogen peroxide HOOD
Giesen, Thomas
Far infrared Fourier-transform spectroscopy of mono-deuterated hydrogen peroxide HOOD Doris-1, Tsukuba, Ibaraki 305-8569, Japan a r t i c l e i n f o Keywords: Deuterated hydrogen peroxide Far infrared phase spectrum of singly deuterated hydrogen peroxide, HOOD, in its vibrational ground state, recorded
Iterative reconstruction of speech from short-time Fourier transform phase and magnitude spectra
Iterative reconstruction of speech from short-time Fourier transform phase and magnitude spectra dimensional, signal reconstruction (specifically speech signals) from the magnitude spectrum and the phase magnitude spectrum, and (iii) a signal can be reconstructed to within a scale factor from its magnitude
Degradation of polymer/substrate interfaces an attenuated total reflection Fourier transform. The durability of such polymer coated adhesively bonded joint structures depends upon the stability of the interfaces between the polymer and the substrate it is coated on. It is economically important to have
Several field tests of a Fourier transform infrared (FTIR) spectrometer have been conducted. he results indicate that effective use of this type of instrument in the field of continuous emissions monitoring (CEM) is possible under the proper conditions, and within limits currentl...
A test for second order stationarity of a time series based on the Discrete Fourier Transform
Subba Rao, Suhasini
A test for second order stationarity of a time series based on the Discrete Fourier Transform property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic is approximately a chi square distribution
PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY
Open-path Fourier transform infrared (OP-FT1R) spectroscopy is an accepted technology for measuring gaseous air contaminants. OP-FT1R absorbance spectra acquired during changing aerosols conditions reveal related changes in very broad baseline features. Usually, this shearing of ...
Applications of Fourier transform infrared spectroscopy to quality control of the epoxy matrix
NASA Technical Reports Server (NTRS)
Antoon, M. K.; Starkey, K. M.; Koenig, J. L.
1979-01-01
The object of the paper is to demonstrate the utility of Fourier transform infrared (FT-IR) difference spectra for investigating the composition of a neat epoxy resin, hardener, and catalysts. The composition and degree of cross-linking of the cured matrix is also considered.
Fourier-Transform Infrared Spectroscopy Analysis of Modified Cotton Trash Extracts
Technology Transfer Automated Retrieval System (TEKTRAN)
In a previous study, Fourier transform infrared spectroscopy (FTIR) was utilized in identifying different types of botanical cotton trash as each was subjected to simulations of ginning and textile processing. Changes in the infrared spectra that occurred after heat treatment indicated that the nee...
Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform
ERIC Educational Resources Information Center
Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos
2010-01-01
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…
Discrete Fourier Transform Compiler for FPGA and CPU/FPGA Partitioned Implementations
Franchetti, Franz
Discrete Fourier Transform Compiler for FPGA and CPU/FPGA Partitioned Implementations Paolo D automatically high-quality HW only and HW/SW partitioned implementations. Generating DFT IP blocks Approach core generator ([1]) specific for the Pease DFT algorithms. Extending the SPIRAL formula generation
As part of the Online Surface Cleanliness Project, the Naval Facilities Engineering Service Center (NFESC) conducted a study of grazing-angle reflectance Fourier Transform Infrared (FTIR) Spectroscopy as a tool for online cleanliness verification at Department of Defense (DoD) cl...
Technology Transfer Automated Retrieval System (TEKTRAN)
Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...
Fourier-Borel Transforms in Clifford Analysis and the Dual Fischer Decomposition
Sommen, Franciscus C.
2008-09-01
In this presentation we introduce several generalizations to Clifford analysis of the classical Fourier-Borel transform for analytic of holomorphic functionals. We also prove that every analytic or holomorphic functional admits a unique decomposition as a series of Dirac derivatives of monogenic functionals, a result which is dual to the Fischer decomposition.
CaJ!'ll'eLV:L{li Compact snapshot birefringent imaging Fourier transform
Dereniak, Eustace L.
. Merlet, M. T. Gruneisen, M. Dusek, J. G. Rarity, G. J. Bishop, J. Gonglewski, Proc. of SPIE Vol. 8542a CaJ!'ll'eLV:L{li .7Ktlif1=: Compact snapshot birefringent imaging Fourier transform spectrometer for remote sensing and endoscopy Michael W. Kudenov1 , Bhaskar Banerjee2 , Victoria C. Chan2 , and Eustace L
Rendering falling snow using an inverse Fourier transform Michael S. Langer
Langer, Michael
Rendering falling snow using an inverse Fourier transform Michael S. Langer School of Computer snow, non-photorealistic rendering Methods for rendering falling snow typically use particle sys- tems we present an alter- native method for rendering falling snow which does not use parti- cles
Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding
NASA Technical Reports Server (NTRS)
Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.
1977-01-01
An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.
Technology Transfer Automated Retrieval System (TEKTRAN)
This study deals with transferring the near-infrared (NIR) calibration models for quality assessment of barley between two instruments with different resolutions and number of data points, a Fourier transform instrument (master) and a dispersive instrument (slave). A file of spectra from 206 ground ...
A commercial Fourier transform interferometer system with telescopic optics has been installed in a van and used to make long-path absorption and single-ended emission measurements of gaseous pollutant concentrations at a number of geographical locations. The system covers the in...
USE OF A FOURIER TRANSFORM SPECTROMETER AS A REMOTE SENSOR AT SUPERFUND SITES
A Fourier transform infrared remote sensor (FTIR-RS) was used to measure chemical emissions at the Shaver's Park Superfund site in northwestern Georgia. he system was bistatic with a source/receiver at one end of a 250 path and a retroreflector at the other end. he source/receive...
THE FOURIER-SERIES METHOD FOR INVERTING TRANSFORMS OF PROBABILITY DISTRIBUTIONS
Whitt, Ward
Ward Whitt 900 Hammond Road AT&T Bell Laboratories Ridgewood, NJ 07450-2908 Room 2C-178 Murray Hill, NJ FOURIER-SERIES METHOD FOR INVERTING TRANSFORMS OF PROBABILITY DISTRIBUTIONS by Joseph Abate Ward Whitt 900 Hammond Road AT&T Bell Laboratories Ridgewood, NJ 07450-2908 Room 2C-178 Murray Hill, NJ 07974
ERIC Educational Resources Information Center
Perkins, W. D.
1986-01-01
Discusses: (1) the design of the Fourier Transform-Infrared Spectroscopy (FT-IR) spectrometer; (2) the computation of the spectrum from the interferogram; and (3) the use of apodization. (Part II will discuss advantages of FT-IR over dispersive techniques and show applications of FT-IR to difficult spectroscopic measurements.) (JN)
Fourier transform spectroscopy around 3 microns with a broad difference frequency comb
Meek, Samuel A; Guelachvili, Guy; Hänsch, Theodor W; Picqué, Nathalie
2013-01-01
We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.2 microns. High power per comb mode (>10-7 W/mode) is obtained over a broad spectral span (>700 nm). The source is used for direct absorption spectroscopy with a Michelson-based Fourier transform interferometer.
Jalali. Bahram
Amplified dispersive Fourier-transform imaging for ultrafast displacement sensing and barcode and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcode. This technique amplifies and simultaneously maps the spectrally encoded barcode into a temporal waveform
Achromatic optical Fourier transformer with planar-integrated free-space optics
Jahns, Jürgen
or ultrafast lasers) or the emission wavelength drifts with temperature (as with vertical-cavity surfaceAchromatic optical Fourier transformer with planar-integrated free-space optics Gladys Mi system for the realization of planar-integrated, free-space optics. In particular we demonstrate
Nikolay I. Agladz, John Klopf, Gwyn Williams, Albert J. Sievers
2010-06-01
By use of coherent terahertz synchrotron radiation, we experimentally tested a holographic Fourier transform spectrometer coupled to an array detector to determine its viability as a spectral device. Somewhat surprisingly, the overall performance strongly depends on the absorptivity of the birefringent lithium tantalate pixels in the array detector.
Hielscher, Andreas
Evaluation of Fourier Transform Coefficients for The Diagnosis of Rheumatoid Arthritis From Diffuse: Diffuse Optical Tomography, Computer-Aided Diagnosis, Rheumatoid Arthritis 1. INTRODUCTION Rheumatoid arthritis (RA) is an autoimmune disorder that affects 0.5-1.0% of adults in industrialized countries
Submillimeter Fourier-transform spectrometer measurements of atmospheric opacity above Mauna Kea
Pardo-Carrión, Juan R.
Submillimeter Fourier-transform spectrometer measurements of atmospheric opacity above Mauna Kea E Observatory on Mauna Kea, Hawaii. These measurements cover the 0.90.3-mm wavelength range and are the first of the Mauna Kea site provides access to extremely low zenith water-vapor columns, permitting atmospheric
Faster GPS via the Sparse Fourier Transform Haitham Hassanieh Fadel Adib Dina Katabi Piotr Indyk
Faster GPS via the Sparse Fourier Transform Haitham Hassanieh Fadel Adib Dina Katabi Piotr Indyk, fadel, dk, indyk}@mit.edu ABSTRACT GPS is one of the most widely used wireless systems. A GPS re- ceiver the fastest GPS locking algorithm to date. The algorithm reduces the locking complexity to O(n log n). Fur
Fourier-transform ghost imaging with pure far-field correlated thermal light
Liu Honglin; Shen Xia; Han Shensheng; Zhu Daming
2007-11-15
Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed.
NASA Astrophysics Data System (ADS)
Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin
2015-03-01
The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.
Santos, Cledir; Fraga, Marcelo E; Kozakiewicz, Zofia; Lima, Nelson
2010-03-01
Fourier transform infrared is considered a powerful technique for characterizing chemical compositions of complex probes such as microorganisms. It has successfully been applied to fungal identification. In this paper, the current state of identification and characterization of filamentous fungi and yeasts by Fourier transform infrared is reviewed. PMID:20079832
Modified radon-Fourier transform for reflective tomography laser radar imaging
NASA Astrophysics Data System (ADS)
Jin, Xiaofeng; Sun, Jianfeng; Yan, Yi; Zhou, Yu; Liu, Liren
2011-06-01
This paper presents imaging result of computer simulation using a modified Radon-Fourier transform algorithm to reconstruct images from reflective tomography data. Since the signal returned is reflected off the illuminated outer surface of an opaque target, only information about the exterior of the target can be obtained, and the images reconstructed using reflective tomography techniques is an outline view of the target cross section. The projection p(r,? ) and p(r,? + 180°) contain different information about the target surface, and will lead different Fourier estimates along the same line through the origin based on the standard Fourier-Slice tomography theorem. Here, using the functional similarity between transmission tomography and reflective tomography, we add the collinear reflective projections to become corresponding transmissive projections before Fourier transform. Then the target can be reconstructed from the Fourier domain using the same operations in transmission tomography. The computer simulation result demonstrates the effectiveness of this modified algorithm to reconstruct image in reflective tomography using the diffuse reflection model (lamberts body). Future research will include the development of image reconstruction based on this modified algorithm for targets with much more complicated reflective characters.
Program for the analysis of time series. [by means of fast Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Brown, T. J.; Brown, C. G.; Hardin, J. C.
1974-01-01
A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.
Photon echo quantum memory and state transformation
NASA Astrophysics Data System (ADS)
Abazari, Ahdiyeh Delfan
Quantum memory, as an essential part of a quantum repeater, is the key element for extending quantum communication beyond its current distance limit of around 100 km. In addition to memories, quantum communication tasks require state manipulation and measurement. This is generally accomplished by means of interferometric optical setups, which often suffer from the requirement of phase stabilization. In this thesis we investigate a novel, particularly robust and versatile quantum state transformation approach based on photon-echo type atom-light interaction that allows combining storage with controlled transformation of quantum states. The possibility of modifying a 100% efficient quantum memory protocol to perform this operation is studied and an experimental test-bed based on the traditional stimulated photon echo process is proposed. The method is demonstrated through simulations and experimental studies of nonorthogonal state discrimination, which is of special interest for quantum information processing from the fundamental as well as practical point of view.
A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC
NASA Technical Reports Server (NTRS)
White, Michael J.
2006-01-01
This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.
High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform
Chan, Kenny K. H.; Tang, Shuo
2010-01-01
The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551
Imaging Fourier transform endospectroscopy for in vivo and in situ multispectral imaging.
Zhang, Hongming; Yuan, Jing; Fu, Ling
2012-10-01
We report the design and implementation of a multispectral imaging Fourier transform endospectroscopy (IFTES) system. The IFTES system employs a flexible fiber bundle catheter coupled to a home-built imaging Fourier transform spectroscope. The instrument enables the performance of non- or minimally invasive subsurface imaging and multispectral imaging at the cellular level in vivo and in situ. A maximum spectral resolution of 0.2 nm at 632.8 nm and a lateral resolution of 4.4 ?m were proved. Preliminary results of a standard resolution target, ex-vivo small animal tissue, single wavelength laser, fluorescence solution, in-vivo mouse skin, microspheres mixture, and in-vivo transgenic mouse brain were given to demonstrate the potential of the technique. PMID:23188298
The X(1)?g(+) ground state of Mg2 studied by Fourier-transform spectroscopy.
Knöckel, H; Rühmann, S; Tiemann, E
2013-03-01
The A(1)?u(+) - X(1)?g(+) UV spectrum of Mg2 has been investigated with high resolution Fourier-transform spectroscopy. Mg2 vapor was created in a heat pipe. Various spectroscopic methods have been employed, such as conventional absorption spectroscopy with light from a broad band lamp and laser-induced fluorescence. The high resolution of the Fourier-transform spectrometer, together with computer aided evaluation methods of the spectra, yields precise transition frequencies. The new data and data available from earlier investigations are applied in direct potential fits of lower and upper electronic states. Various representations of potential energy curves for the ground state X(1)?g(+) have been employed and their benefits in terms of smallest number of parameters are discussed. Scattering lengths are derived for the homonuclear isotopologues and compared with previous results. PMID:23485290
Foliage Plant Retrieval using Polar Fourier Transform, Color Moments and Vein Features
Kadir, Abdul; Susanto, Adhi; Santosa, Paulus Insap
2011-01-01
This paper proposed a method that combines Polar Fourier Transform, color moments, and vein features to retrieve leaf images based on a leaf image. The method is very useful to help people in recognizing foliage plants. Foliage plants are plants that have various colors and unique patterns in the leaf. Therefore, the colors and its patterns are information that should be counted on in the processing of plant identification. To compare the performance of retrieving system to other result, the experiments used Flavia dataset, which is very popular in recognizing plants. The result shows that the method gave better performance than PNN, SVM, and Fourier Transform. The method was also tested using foliage plants with various colors. The accuracy was 90.80% for 50 kinds of plants.
S. M. Abrarov; B. M. Quine
2015-11-03
This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only $17$ summation terms the obtained rational approximation of the complex error function provides accuracy ${10^{ - 15}}$ over the most domain of practical importance $0 \\le x \\le 40,000$ and ${10^{ - 4}} \\le y \\le {10^2}$ required for the HITRAN-based spectroscopic applications. Since the rational approximation does not contain trigonometric or exponential functions dependent upon the input parameters $x$ and $y$, it is rapid in computation. Such an example demonstrates that the considered methodology of the Fourier transform may be advantageous in practical applications.
Nagler, Peter C; Kogut, Alan; Tucker, Gregory S
2015-01-01
The detection of the primordial B-mode polarization signal of the cosmic microwave background (CMB) would provide evidence for inflation. Yet as has become increasingly clear, the detection of a such a faint signal requires an instrument with both wide frequency coverage to reject foregrounds and excellent control over instrumental systematic effects. Using a polarizing Fourier transform spectrometer (FTS) for CMB observations meets both these requirements. In this work, we present an analysis of instrumental systematic effects in polarizing Fourier transform spectrometers, using the Primordial Inflation Explorer (PIXIE) as a worked example. We analytically solve for the most important systematic effects inherent to the FTS - emissive optical components, misaligned optical components, sampling and phase errors, and spin synchronous effects - and demonstrate that residual systematic error terms after corrections will all be at the sub-nK level, well below the predicted 100 nK B-mode signal.
Applications of near-infrared spectroscopy to process analysis using fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Watari, Masahiro
2010-05-01
The applications of near-IR spectroscopy to process analysis using a Fourier transform spectrometer are described. In recent years, process analysis based on near-IR spectroscopy has received keen interest from a growing number of industries. Some configurations of Fourier transform near infrared (FT-NIR) interferometers used for process analysis are introduced as special optical systems for the realization of stable and reproducible performance. Moreover, the applications of NIR spectroscopy to process analysis using FT-NIR spectrometers are overviewed and two examples of applications are described in more detail. Furthermore, process analytical technology (PAT) for the pharmaceutical industry is introduced as a future trend of the application of FT-NIR spectroscopy, and a dual-wavelength system that can combine NIR and IR spectra is discussed as a newly proposed PAT tool for understanding processes.
MightySat II.1 Fourier-transform hyperspectral imager payload performance
NASA Astrophysics Data System (ADS)
Otten, Leonard J.; Sellar, R. Glenn; Rafert, J. Bruce
1995-12-01
Using a new microsat called MightySat II as a platform, Kestrel Corporation is designing and building the first Fourier transform hyperspectral imager (FTHSI) to be operated from a spacecraft. This payload will also be the first to fly on the Phillips Laboratory MightySat II spacecraft series, a new, innovative approach, to affordable space testing of high risk, high payoff technologies. Performance enhancements offered by the Fourier transform approach have shown it to be one of the more promising spaceborne hyperspectral concepts. Simulations of the payload's performance have shown that the instrument is capable of separating a wide range of subtle spectral differences. Variations in the return from the Georges Bank and shoals are discernible and various types of coastal grasses (sea oats and spartina) can be isolated against a sand background.
Cao, Julie; Ng, Elizabeth S.; McNaughton, Donald; Stanley, Edouard G.; Elefanty, Andrew G.; Tobin, Mark J.; Heraud, Philip
2013-01-01
Fourier transform infrared (FTIR) microspectroscopy shows potential as a benign, objective and rapid tool to screen pluripotent and multipotent stem cells for clinical use. It offers a new experimental approach that provides a holistic measurement of macromolecular composition such that a signature representing the internal cellular phenotype is obtained. The use of this technique therefore contributes information that is complementary to that acquired by conventional genetic and immunohistochemical methods. PMID:24065090
Novel all-reflective Fourier transform imaging spectrometer based on Fresnel double-mirror
NASA Astrophysics Data System (ADS)
Zhang, Dan; Liao, Ningfang; Liang, Minyong; Lin, Yu; Luo, Yongdao; Cui, Deqi
2007-11-01
In order to develop new technology during the spaceborne remote sensing mission, we introduce a novel all-reflective Fourier Transform Imaging Spectrometer(FTIS) based on Fresenel Double Mirror (FDM). Using all reflective parts, the system can work in visible and infrared waveband. Besides, the novel optical configuration which is involved can lead to the characters of the high spatial, spectral resolution and large field of view. The basic performance of the system was analyzed based on the test results.
Isotropic Spin Trap EPR Spectra Simulation by Fast Fourier Transform (FFT)
NASA Astrophysics Data System (ADS)
Laachir, S.; Moussetad, M.; Adhiri, R.; Fahli, A.
2005-03-01
The detection and investigation of free radicals forming in living systems became possible due to the introduction of the method of spin traps. In this work, the electron spin resonance (ESR) spectra of DMPO/HO(.) and MGD-Fe-NO adducts are reproduced by simulation, based on the Fast Fourier Transform (FFT). The calculated spectral parameters as the hyperfine coupling constants, agree reasonably with the experimental data and the results are discussed.
Metabolic fingerprinting of lichen Usnea baileyi by Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Bakar, Siti Zaharah Abu; Latip, Jalifah; bin Din, Laily; Samsuddin, Mohd Wahid
2014-09-01
The lichen Usnea baileyi collected from different environments was characterised using Fourier transform infrared spectroscopy. This preliminary study was done to determine the effects of different environment populations on U. baileyi chemical composition. Results showed that the absorbance peaks of Golf Course 2 (GCU2) are more intense compared to Taman Awana (TA), Jalan Awana (JA) and Jalan Gohtong (JG). U. baileyi contains of dibenzofurans, depsides, depsidones, xanthones and terpenoids.
Toney, M.L.
1999-07-01
The purpose of this testing program is to obtain uncontrolled and controlled hydrogen chloride (HCl) and speciated hydrocarbon Hazardous Air Pollutants (HAPs) emissions data from lime production plants to support a national emission standard for hazardous air pollutants (NESHAP). This report presents data from the Fourier Transform Infrared Spectroscopy (FTIR) measurements. FTIR source testing was conducted for the following purposes: Quantify HCl emission levels; and Gather screening (i.e., qualitative) data on other HAP emissions.
Single-channel color image encryption based on iterative fractional Fourier transform and chaos
NASA Astrophysics Data System (ADS)
Sui, Liansheng; Gao, Bo
2013-06-01
A single-channel color image encryption is proposed based on iterative fractional Fourier transform and two-coupled logistic map. Firstly, a gray scale image is constituted with three channels of the color image, and permuted by a sequence of chaotic pairs which is generated by two-coupled logistic map. Firstly, the permutation image is decomposed into three components again. Secondly, the first two components are encrypted into a single one based on iterative fractional Fourier transform. Similarly, the interim image and third component are encrypted into the final gray scale ciphertext with stationary white noise distribution, which has camouflage property to some extent. In the process of encryption and description, chaotic permutation makes the resulting image nonlinear and disorder both in spatial domain and frequency domain, and the proposed iterative fractional Fourier transform algorithm has faster convergent speed. Additionally, the encryption scheme enlarges the key space of the cryptosystem. Simulation results and security analysis verify the feasibility and effectiveness of this method.
On q-EXTENSIONS of Mehta's Eigenvectors of the Finite Fourier Transform
NASA Astrophysics Data System (ADS)
Atakishiyev, Natig M.
Mehta has shown that eigenvectors Fj(k) of the finite Fourier transform with the matrix Aj,k(N): = (1)/(? {N)}exp ((2? i)/(N)jk; ), 0 ? j, k ? N-1, can be defined in terms of the classical Hermite functions { H}k(x) := Hk(x)exp (-x2/2) as Fj(k):= ? n=-? ? { H}k(x_n(j)), where xn(j) := ? {(2? )/(N)}(nN+j). We argue that the finite Fourier transform Aj,k(N) does actually govern also some q-extensions of Mehta's eigenvectors Fj(k), associated with certain well-known orthogonal q-polynomial families. For the pairs of the continuous q-Hermite and q-1-Hermite polynomials, the Rogers-Szeg? and Stieltjes-Wigert polynomials, and the discrete q-Hermite polynomials of types I and II such links are explicitly derived. In the limit when the base q ? 1 these q-extensions coincide with Mehta's eigenvectors Fj(k), whereas in the continuous limit (i.e. when the parameter N ? ?) they correspond to the classical Fourier integral transforms between the above-mentioned pairs of q-polynomial families.
A compact Fourier transform imaging spectrometer employing a variable gap Fabry-Perot interferometer
NASA Astrophysics Data System (ADS)
Lucey, Paul G.; Akagi, Jason; Bingham, Adam L.; Hinrichs, John L.; Knobbe, Edward T.
2014-05-01
Fourier transform spectroscopy is a widely employed method for obtaining visible and infrared spectral imagery, with applications ranging from the desktop to remote sensing. Most fielded Fourier transform spectrometers (FTS) employ the Michelson interferometer and measure the spectrum encoded in a time-varying signal imposed by the source spectrum interaction with the interferometer. A second, less widely used form of FTS is the spatial FTS, where the spectrum is encoded in a pattern sampled by a detector array. Recently we described using a Fabry-Perot interferometer, with a deliberately wedged gap geometry and engineered surface reflectivities, to produce an imaging spatial FTS. The Fabry-Perot interferometer can be much lighter and more compact than a conventional interferometer configuration, thereby making them suitable for portable and handheld applications. This approach is suitable for use over many spectral regimes of interest, including visible and infrared regions. Primary efforts to date have focused on development and demonstration of long wave infrared (LWIR) spectral imagers. The LWIR version of the miniaturized Fabry-Perot has been shown to be effective for various applications including spectral imaging-based chemical detection. The compact LWIR spectral imager employs uncooled optics and a microbolometer camera; a handheld version is envisioned for future development. Recent advancements associated with the spatial Fourier Transform imaging spectrometer system are described.
Holland, Alexander; Aboy, Mateo
2009-07-01
We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb-Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations. PMID:19247700
Lasalde Dominicc, Jose A. - Department of Biology, Universidad de Puerto Rico
Fourier transform coupled to tryptophan-scanning mutagenesis: Lessons from its application 20 February 2008 Although Fourier transform (FT) and tryptophan-scanning mutagenesis (TrpScanM) have: Tryptophan-scanning mutagenesis Fourier transform Ligand-gated ion channel Lipid-exposed transmembrane domain
The parallel implementation of the one-dimensional Fourier transformed Vlasov Poisson system
NASA Astrophysics Data System (ADS)
Eliasson, Bengt
2005-08-01
A parallel implementation of an algorithm for solving the one-dimensional, Fourier transformed Vlasov-Poisson system of equations is documented, together with the code structure, file formats and settings to run the code. The properties of the Fourier transformed Vlasov-Poisson system is discussed in connection with the numerical solution of the system. The Fourier method in velocity space is used to treat numerical problems arising due the filamentation of the solution in velocity space. Outflow boundary conditions in the Fourier transformed velocity space removes the highest oscillations in velocity space. A fourth-order compact Padé scheme is used to calculate derivatives in the Fourier transformed velocity space, and spatial derivatives are calculated with a pseudo-spectral method. The parallel algorithms used are described in more detail, in particular the parallel solver of the tri-diagonal systems occurring in the Padé scheme. Program summaryTitle of program:vlasov Catalogue identifier:ADVQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating system under which the program has been tested: Sun Solaris; HP-UX; Read Hat Linux Programming language used: FORTRAN 90 with Message Passing Interface (MPI) Computers: Sun Ultra Sparc; HP 9000/785; HP IPF (Itanium Processor Family) ia64 Cluster; PCs cluster Number of lines in distributed program, including test data, etc.:3737 Number of bytes in distributed program, including test data, etc.:18 772 Distribution format: tar.gz Nature of physical problem: Kinetic simulations of collisionless electron-ion plasmas. Method of solution: A Fourier method in velocity space, a pseudo-spectral method in space and a fourth-order Runge-Kutta scheme in time. Memory required to execute with typical data: Uses typically of the order 10 5-10 6 double precision numbers. Restriction on the complexity of the problem: The program uses periodic boundary conditions in space. Typical running time: Depends strongly on the problem size, typically few hours if only electron dynamics is considered and longer if both ion and electron dynamics is important. Unusual features of the program: No
Niida, Chisato; Nakajima, Masakazu; Endo, Yasuki; Sumiyoshi, Yoshihiro; Ohshima, Yasuhiro; Kohguchi, Hiroshi
2014-03-14
Pure rotational transitions of the Ar–CS van der Waals complex have been observed by Fourier Transform Microwave (FTMW) and FTMW-millimeter wave double resonance spectroscopy. Rotational transitions of v{sub s} = 0, 1, and 2 were able to be observed for normal CS, together with those of C{sup 34}S in v{sub s} = 0, where v{sub s} stands for the quantum number of the CS stretching vibration. The observed transition frequencies were analyzed by a free rotor model Hamiltonian, where rovibrational energies were calculated as dynamical motions of the three nuclei on a three-dimensional potential energy surface, expressed by analytical functions with 57 parameters. Initial values for the potential parameters were obtained by high-level ab initio calculations. Fifteen parameters were adjusted among the 57 parameters to reproduce all the observed transition frequencies with the standard deviation of the fit to be 0.028 MHz.
Schrottke, L. Lü, X.; Grahn, H. T.
2015-04-21
We present a self-consistent model for carrier transport in periodic semiconductor heterostructures completely formulated in the Fourier domain. In addition to the Hamiltonian for the layer system, all expressions for the scattering rates, the applied electric field, and the carrier distribution are treated in reciprocal space. In particular, for slowly converging cases of the self-consistent solution of the Schrödinger and Poisson equations, numerous transformations between real and reciprocal space during the iterations can be avoided by using the presented method, which results in a significant reduction of computation time. Therefore, it is a promising tool for the simulation and efficient design of complex heterostructures such as terahertz quantum-cascade lasers.
Camino, Fernando E.; Nam, Chang-Yong; Pang, Yutong T.; Hoy, Jessica; Eisaman, Matthew D.; Black, Charles T.; Sfeir, Matthew Y.
2014-01-01
We present a methodology for probing light-matter interactions in prototype photovoltaic devices consisting of an organic semiconductor active layer with a semitransparent metal electrical contact exhibiting surface plasmon-based enhanced optical transmission. We achieve high-spectral irradiance in a spot size of less than 100??m using a high-brightness laser-driven light source and appropriate coupling optics. Spatially resolved Fourier transform photocurrent spectroscopy in the visible and near-infrared spectral regions allows us to measure external quantum efficiency with high sensitivity in small-area devices (<1?mm2). This allows for rapid fabrication of variable-pitch sub-wavelength hole arrays in metal films for use as transparent electrical contacts, and evaluation of the evanescent and propagating mode coupling to resonances in the active layer. PMID:25705085
Indyk, Piotr
representation in O(n log n) time. However, the emergence of big data problems, in which the processed datasets a subset of the input data required by the FFT. Recent efforts in the area of Fourier sampling have focusedSample-Optimal Average-Case Sparse Fourier Transform in Two Dimensions Badih Ghazi Haitham
NASA Astrophysics Data System (ADS)
Li, Hai; Yang, Chuping
2011-02-01
A two-dimensional multiscale windowed Fourier transform (2D-MWFT), based on two-dimensional Gabor wavelet transform (2D-GWT), for the phase extraction from a spatial fringe pattern in fringe projection profilometry is presented. First, the instantaneous frequencies on x and y direction of the modulated fringe pattern are determined by 2D-GWT, and then the local stationary lengths are obtained. The 2D-MWFT with different two-dimensional Gaussian windows whose width is set according to the local stationary length is preformed for each section of the modulated fringe pattern to achieve multiresolution analysis and phase demodulation. Comparing the result of the phase demodulated by 2D-GWT and two-dimensional windowed Fourier transform (2D-WFT) with that by 2D-MWFT in a numerical simulation, we show that the 2D-MWFT method is superior to these methods, especially for the local non-stationary signal with low frequency. The theory and the results of a simulation and experiment are shown.
Potential-Field Forward Modeling and Inversion Using 3D Fast Fourier Transforms
NASA Astrophysics Data System (ADS)
Phillips, J. D.; Caratori Tontini, F.; Cocchi, L.
2008-12-01
Although 1D and 2D fast Fourier transforms (FFTs) have long been used for the filtering, interpretation, and modeling of potential-field data, 3D FFTs have not enjoyed similar popularity. This may change with the recent discovery (Caratori Tontini et al., in press, JGR) that simple 3D FFT filters can be used to transform distributions of density (or magnetization) within a box-shaped 3D volume into gravity (or magnetic) fields within the same volume. For example, the continuous 3D Fourier transform of the vertical gravity anomaly ?gz(x,y,z) in a volume is related to the 3D Fourier transform of the density ?(x,y,z) in the volume by ?[?gz] = i4?G(kz/ | k | 2)?[?]; | k | ?0, (1) where G is the gravitational constant, kx, ky, kz are wavenumbers, and | k | 2 = kx2+ ky2+ kz2. (2) Translating (1) into a digital FFT filtering operation requires careful consideration of the periodicity of the density distribution and the gravity field. Nevertheless, (1) provides a highly efficient way to calculate the vertical gravity anomaly of a 3D density distribution within a few minutes. The calculated gravity anomaly can be sampled at random points or on an arbitrary surface using tri-linear interpolation. An equivalent space- domain calculation of the gravity field on an arbitrary surface can take many hours. The inverse relation to (1) does not appear to offer a practical approach for calculating a reliable density distribution from observed gravity data. This is because the data would have to cover a substantial portion of the model volume, and because the transformation is undefined on the plane kz = 0, where both the denominator of the filter kernel and the Fourier transform of the gravity field are identically zero. Numerical experiments show that the density distribution resulting from the power on the plane kz = 0 represents a classic Parker annihilator. This annihilator can be calculated from the density distribution but not from the gravity field, as would be required for direct inversion. In forward modeling mode, equations such as (1) permit rapid testing of geological models against observed potential-field data. The calculation speed of the 3D FFT suggests that a practical iterative inversion algorithm could be developed from (1) using Markov perturbation of an initial density model. Such an algorithm would have immediate application to problems of hydrogeology, resource assessment, and tunnel detection.
Technology Transfer Automated Retrieval System (TEKTRAN)
Analysis of DNA samples of Salmonella serotypes (Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky) were performed using Fourier transform infrared spectroscopy (FT-IR) spectrometer by placing directly in contact with a diamond attenua...
A portable Fourier transform infrared gas analyzer with a photoacoustic detector performed reliably during pollution prevention research at two industrial facilities. It exhibited good agreement (within approximately 6%) with other analytical instruments (dispersive infrared and ...
Abeysekera, Chamara
This second paper in a series of two reports on the performance of a new instrument for studying chemical reaction dynamics and kinetics at low temperatures. Our approach employs chirped-pulse Fourier-transform microwave ...
A Fourier transform telescope for sub-arcsecond imaging of X-rays and gamma rays
NASA Technical Reports Server (NTRS)
Crannell, C. J.; Orwig, L. E.; Hurford, G. J.; Prince, T. A.
1986-01-01
This paper describes a Fourier transform telescope designed to image solar flare X-rays and gamma rays at energies up to 1 MeV with arcsec resolution. The imaging technique makes use of a bigrid collimator divided into a number of smaller areas called subcollimators. The grids in each subcollimator consist of a set of linear apertures so configured that each subcollimator provides a measurement of a single Fourier component of the angular distribution of the source. The imaging concept is therefore a mathematical analog to aperture synthesis in radio astronomy. For X-ray and gamma-ray astronomy, this approach has significant advantages in terms of relaxed requirements for astronomy, this approach has significant advantages in terms of relaxed requirements for position sensitivity in the detector and for control of grid alignment in the large scale telescope structure. The concept of the Fourier transform telescope will be illustrated with numerical parameters of a version now under study for the Pinhole/Occulter Facility.
A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws
Levenhagen, R. S.
2014-12-10
Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (? Eri).
NASA Astrophysics Data System (ADS)
Zhou, Nanrun; Wang, Yixian; Gong, Lihua; He, Hong; Wu, Jianhua
2011-06-01
A new color image encryption algorithm based on fractional Fourier transform (FrFT) and chaos is proposed. The colors of the original color image are converted to HSI (hue-saturation-intensity), and the S component is transformed by the random-phase encoding based on FrFT to obtain a new random phase. The I component is transformed by double random-phase encoding based on FrFT using the H component and the new random phase as two phase plates. Then chaos scrambling technology is used to encrypt the image, which makes the resulting image nonlinear and disorder both in spatial domain and frequency domain. Additionally, the ciphertext is not a color image but a combination of a gray image and a phase matrix, so the ciphertext has camouflage property to some extent. The results of numerical simulations demonstrate the effectiveness and the security of this algorithm.
Digital watermarking algorithm research of color images based on quaternion Fourier transform
NASA Astrophysics Data System (ADS)
An, Mali; Wang, Weijiang; Zhao, Zhen
2013-10-01
A watermarking algorithm of color images based on the quaternion Fourier Transform (QFFT) and improved quantization index algorithm (QIM) is proposed in this paper. The original image is transformed by QFFT, the watermark image is processed by compression and quantization coding, and then the processed watermark image is embedded into the components of the transformed original image. It achieves embedding and blind extraction of the watermark image. The experimental results show that the watermarking algorithm based on the improved QIM algorithm with distortion compensation achieves a good tradeoff between invisibility and robustness, and better robustness for the attacks of Gaussian noises, salt and pepper noises, JPEG compression, cropping, filtering and image enhancement than the traditional QIM algorithm.
Precise measurement of the resolution in light microscopy using Fourier transform
Vainrub, Arnold
2008-04-15
The resolution power of light microscope has been accurately measured ({+-}5%) by Fourier transform of various object images and further evaluation of the highest spatial frequency in Fourier spectrum. Any unknown shape plane object with a shape feature's size smaller than the resolution to be measured was shown to provide a reliable resolution test. This simple method gives a direct measurement of the resolution power as defined by Abbe [Archiv. F. Mikroskopische Anat. 9, 413 (1873)]. The results have been justified by comparison to a standard resolution measurement by using calibrated periodic line patterns. Notably, the approach is applicable in super-resolution light microscopy (transmission, reflection, and fluorescence), where calibrated resolution targets do not occur. It was conveniently implemented by using a compact disk as a test object and free IMAGEJ imaging software.
Rice, S.B.; Freund, H.; Huang, W.L.; Clouse, J.A.; Isaacs, C.M.
1995-10-02
An important goal in silica diagenesis research is to understand the kinetics of opal transformation from noncrystalline opal-A to the disordered silica polymorph opal-CT. Because the conventional technique for monitoring the transformation, powder X-ray diffraction (XRD), is applicable only to phases with long-range order, the authors used Fourier transform infrared spectroscopy (FTIR) to monitor the transformation. They applied this technique, combined with XRD and TEM, to experimental run products and natural opals from the Monterey Formation and from siliceous deposits in the western Pacific Ocean. Using a ratio of two infrared absorption intensities ({omega} = I{sub 472 cm{sup {minus}1}}/I{sub 500 cm{sup {minus}1}}), the relative proportions of opal-A and opal-CT can be determined. The progress of the transformation is marked by changes in slope of {omega} vs. depth or time when a sufficient stratigraphic profile is available. There are three stages in the opal-A to opal-CT reaction: (1) opal-A dissolution; (2) opal-CT precipitation, whose end point is marked by completion of opal-A dissolution; and (3) opal-CT ordering, during which tridymite stacking is eliminated in favor of crystobalite stacking.
NASA Astrophysics Data System (ADS)
Galizzi, Gustavo E.; Cuadrado-Laborde, Christian
2015-10-01
In this work we study the joint transform correlator setup, finding two analytical expressions for the extensions of the joint power spectrum and its inverse Fourier transform. We found that an optimum efficiency is reached, when the bandwidth of the key code is equal to the sum of the bandwidths of the image plus the random phase mask (RPM). The quality of the decryption is also affected by the ratio between the bandwidths of the RPM and the input image, being better as this ratio increases. In addition, the effect on the decrypted image when the detection area is lower than the encrypted signal extension was analyzed. We illustrate these results through several numerical examples.
Fourier Transform Microwave Spectrum of CO{_2} -(CH{_3}){_2} S
NASA Astrophysics Data System (ADS)
Kawashima, Yoshiyuki; Moritani, Takayuki; Hirota, Eizi
2012-06-01
In spite of the fact that the oxygen and sulfur atoms belong to the same group in the periodic table, oxygen-containing molecules and their corresponding sulfur analogues often exhibit characteristic differences in their chemical and physical properties. We have been interested in these differences and have investigated, in a systematic way using Fourier transform microwave (FTMW) spectroscopy combined with ab initio molecular orbital calculations, complexes consisting of dimethyl ether (DME)/dimethyl sulfide (DMS) and ethylene oxide (EO)/ ethylene sulfide (ES), each being attached to either one of rare gas atoms (Rg), CO, N{_2}, or CO{_2}. Among others the CO{_2}-DMS complex should be mentioned, which, in sharp contrast with its counterpart: CO{_2}-DME behaves anomalously, presumably because of low-frequency internal motions, and we have decided to explore it in detail by a FTMW spectrometer. We have generated the CO{_2}-DMS complex by supersonic expansion of a CO{_2} and DMS mixture diluted with Ar, and have scanned the frequency region from 5 to 24 GHz to record the rotational spectra of the complex. We have found it difficult to fit the observed transition frequencies to the ordinary rotational Hamiltonian, but have succeeded to assign 75 transitions by sum rules among the observed transition frequencies. We are suspecting the anomalous behavior of the complex to be caused by a low-frequency torsion of the moieties. In the case of the CO{_2}-DME, the internal rotations of the two methyl groups of the DME were shown to be locked to the CO{_2} by hydrogen bonding, whereas, for the CO{_2}-DMS, we have observed internal-rotation splittings of the two methyl groups of the DMS, indicating the structure of the CO{_2}-DMS complex being considerably different from that of the CO{_2}-DME. We will report the structure at the potential minima and the internal motion of the CO{_2}-DMS, in comparison with the results predicted by quantum chemical calculations. Y. Kawashima, A. Sato, Y. Orita, and E. Hirota J. Phys. Chem. A 116, 1224 2012. J. J. Newby, R. A. Peebles, and S. A. Peebles J. Phys. Chem. A 108, 11234 2004.
Quantum simulation of noncausal kinematic transformations.
Alvarez-Rodriguez, U; Casanova, J; Lamata, L; Solano, E
2013-08-30
We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean boosts or spatial and time parity operations in the simulated dynamics. This framework provides us with a flexible toolbox that enhances the versatility of quantum simulation theory, allowing the direct access to dynamical quantities that would otherwise require full tomography. Furthermore, this method enables the study of noncausal kinematics and phenomena beyond special relativity in a quantum controllable system. PMID:24033011
Slit Function Measurement of An Imaging Spectrograph Using Fourier Transform Techniques
NASA Technical Reports Server (NTRS)
Park, Hongwoo; Swimyard, Bruce; Jakobsen, Peter; Moseley, Harvey; Greenhouse, Matthew
2004-01-01
Knowledge of a spectrograph slit function is necessary to interpret the unresolved lines in an observed spectrum. A theoretical slit function can be calculated from the sizes of the entrance slit, the detector aperture when it functions as an exit slit, the dispersion characteristic of the disperser, and the point spread function of the spectrograph. A measured slit function is preferred to the theoretical one for the correct interpretation of the spectral data. In a scanning spectrometer with a single exit slit, the slit function is easily measured. In a fixed grating/or disperser spectrograph, illuminating the entrance slit with a near monochromatic light from a pre-monochrmator or a tunable laser and varying the wavelength of the incident light can measure the slit function. Even though the latter technique had been used successfully for the slit function measurements, it had been very laborious and it would be prohibitive to an imaging spectrograph or a multi-object spectrograph that has a large field of view. We explore an alternative technique that is manageable for the measurements. In the proposed technique, the imaging spectrograph is used as a detector of a Fourier transform spectrometer. This method can be applied not only to an IR spectrograph but also has a potential to a visible/UV spectrograph including a wedge filter spectrograph. This technique will require a blackbody source of known temperature and a bolometer to characterize the interferometer part of the Fourier Transform spectrometer. This pa?er will describe the alternative slit function measurement technique using a Fourier transform spectrometer.
Vehicle Classification Using the Discrete Fourier Transform with Traffic Inductive Sensors.
Lamas-Seco, José J; Castro, Paula M; Dapena, Adriana; Vazquez-Araujo, Francisco J
2015-01-01
Inductive Loop Detectors (ILDs) are the most commonly used sensors in traffic management systems. This paper shows that some spectral features extracted from the Fourier Transform (FT) of inductive signatures do not depend on the vehicle speed. Such a property is used to propose a novel method for vehicle classification based on only one signature acquired from a sensor single-loop, in contrast to standard methods using two sensor loops. Our proposal will be evaluated by means of real inductive signatures captured with our hardware prototype. PMID:26516855
Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Lu, Ming-Feng; Zhang, Feng; Tao, Ran; Ni, Guo-Qiang; Bai, Ting-Zhu; Yang, Wen-Ming
2015-11-01
Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton's rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.
NASA Technical Reports Server (NTRS)
Parsons, C. L.; Gerlach, J. C.; Whitehurst, M.
1982-01-01
The development of a prototype, ground-based, Sun-pointed Michelson interferometric spectrometer is described. Its intended use is to measure the atmospheric amount of various gases which absorb in the near-infrared, visible, and near-ultraviolet portions of the electromagnetic spectrum. Preliminary spectra which contain the alpha, 0.8 micrometer, and rho sigma tau water vapor absorption bands in the near-infrared are presented to indicate the present capability of the system. Ultimately, the spectrometer can be used to explore the feasible applications of Fourier transform spectroscopy in the ultraviolet where grating spectrometers were used exclusively.
NASA Astrophysics Data System (ADS)
Lu, Ding; Jin, Weimin
2010-11-01
A novel single-channel color image encryption technique based on joint fractional Fourier transform correlator(JFRTC) and phase retrieval algorithm (PRA) is proposed. The target color image is decomposed into three red, green, blue (RGB) components. A joint image is formed and encoded into two random phase masks (RPM) iteratively. The security of the system is enhanced because of the fractional order as a new added key. The system and the operation procedure are simplified. Simulation experiments show that the algorithm converges rapidly and has great design flexibility. The decryption can be realized by digital or optical methods.
NASA Astrophysics Data System (ADS)
Azour, Halima; Derouault, Jean; Lauroua, Pierre; Vezon, Gérard
2000-07-01
In order to remedy the limitations of state-of-the-art methods for red blood cells grouping and antibody screening we have tried to develop a new type of immunosensors based upon a metallic substrate. The first two steps of the manufacturing of such a sensor consist in the anodization and in the silanization of the metal surface. Fourier transform infrared spectroscopy (FTIR) has been used to investigate aluminum samples treated with the above process. FTIR analysis allows the accurate determination of the grafted species, and thus to perform the optimization of the experimental parameters.
Applications of asynoptic space - Time Fourier transform methods to scanning satellite measurements
NASA Technical Reports Server (NTRS)
Lait, Leslie R.; Stanford, John L.
1988-01-01
A method proposed by Salby (1982) for computing the zonal space-time Fourier transform of asynoptically acquired satellite data is discussed. The method and its relationship to other techniques are briefly described, and possible problems in applying it to real data are outlined. Examples of results obtained using this technique are given which demonstrate its sensitivity to small-amplitude signals. A number of waves are found which have previously been observed as well as two not heretofore reported. A possible extension of the method which could increase temporal and longitudinal resolution is described.
Solouki, T; Russell, D H
1992-01-01
Matrix-assisted laser desorption ionization is used to obtain Fourier-transform ion cyclotron resonance mass spectra of model peptides (e.g., gramicidin S, angiotensin I, renin substrate, melittin, and bovine insulin). Matrix-assisted laser desorption ionization yields ions having appreciable kinetic energies. Two methods for trapping the high kinetic energy ions are described: (i) the ion signal for [M+H]+ ions is shown to increase with increasing trapping voltages, and (ii) collisional relaxation is used for the detection of [M+H]+ ions of bovine insulin. Images PMID:1378614
Numerical simulations of turbulent fluid flows. I - Fast Fourier transform method
NASA Astrophysics Data System (ADS)
Sakai, K.; Sekiya, T.
1984-10-01
A brief review on turbulent flow problems is presented. The large eddy simulation technique is promising for detail numerical analyses of turbulent flows using existing computers. A computer program TURBINE has been developed, in which the Poisson equation for pressure is solved by using the fast Fourier transform technique and the tri-diagonal matrix algorithm to improve numerical accuracy and cpu time. The program was tested with use of an exactly solvable problem proposed by Taylor. Good numerical accuracy was obtained and cpu time was decreased to about 1/30 as compared with SOLA program based on a pressure iteration technique.
NASA Astrophysics Data System (ADS)
Dordevic, S. V.
2012-11-01
Inverse Fourier Transform of optical conductivity is used for studies of quasiparticle relaxation in Heavy Fermions in time domain. We demonstrate the usefulness of the procedure on model spectra and then use it to study quasiparticle relaxation in two Heavy Fermions YbFe4Sb12 and CeRu4Sb12. Optical conductivity in time domain reveals details of quasiparticle relaxation close to the Fermi level, not readily accessible from the spectra in the frequency domain. In particular, we find that the relaxation of heavy quasiparticles does not start instantaneously, but typically after a few hundred femto-seconds.
Aizikov, Konstantin; Mathur, Raman; O’Connor, Peter B.
2009-01-01
The spontaneous loss of coherence catastrophe (SLCC) is a frequently observed, yet poorly studied, space-charge related effect in Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS). This manuscript presents an application of the filter diagonalization method (FDM) in the analysis of this phenomenon. The temporal frequency behavior reproduced by frequency shift analysis using the FDM shows the complex nature of the SLCC, which can be explained by a combination of factors occurring concurrently, governed by electrostatics and ion packet trajectories inside the ICR cell. PMID:19013078
NASA Technical Reports Server (NTRS)
Beecken, Brian P.; Kleinman, Randall R.
2004-01-01
New developments in infrared sensor technology have potentially made possible a new space-based system which can measure far-infrared radiation at lower costs (mass, power and expense). The Stationary Imaging Fourier Transform Spectrometer (SIFTS) proposed by NASA Langley Research Center, makes use of new detector array technology. A mathematical model which simulates resolution and spectral range relationships has been developed for analyzing the utility of such a radically new approach to spectroscopy. Calculations with this forward model emulate the effects of a detector array on the ability to retrieve accurate spectral features. Initial computations indicate significant attenuation at high wavenumbers.
Improving imaging resolution of shaking targets by Fourier-transform ghost diffraction
NASA Astrophysics Data System (ADS)
Zhang, Cong; Gong, Wenlin; Han, Shensheng
2013-01-01
For conventional imaging, shaking of the imaging system or the target leads to the degradation of imaging resolution. The influence of the target's shaking to Fourier-transform ghost diffraction (FGD) is investigated and phase-retrieval method is used to recover the target's imaging. The analytical results, which are backed up by numerical simulation and experiments, demonstrate that the quiver of target has no effect on the resolution of FGD and high-resolution imaging can be always achieved by phase-retrieval method from FGD patterns. This approach can be applied in high-precision imaging systems, to overcome the influence of the system's shaking to imaging resolution.
Fourier transform C-13 NMR analysis of some free and potassium-ion complexed antibiotics.
NASA Technical Reports Server (NTRS)
Ohnishi, M.; Fedarko, M.-C.; Baldeschwieler, J. D.; Johnson, L. F.
1972-01-01
Fourier transforms of the noise-decoupled, natural abundance C-13 NMR free induction decays of the cyclic antibiotic valinomycin and its potassium-ion complex have been obtained at 25.2 MHz. Comparisons are made with C-13 NMR spectra taken at 22.6 MHz of the cyclic antibiotic nonactin and the synthetic polyether dicyclohexyl-18-crown-6 and their potassium complexes. The results obtained suggest that conformational rearrangements of the molecule as a whole can compete with direct interactions between carbons and the potassium ion in determining C-13 chemical shift differences between the free and complexed species.
High-resolution Fourier Transform Spectroscopy of Nb I in the Near-Infrared
NASA Astrophysics Data System (ADS)
Er, A.; Güzelçimen, F.; Ba?ar, Gö.; Öztürk, I. K.; Tamanis, M.; Ferber, R.; Kröger, S.
2015-11-01
In this study, a Fourier Transform spectrum of Niobium (Nb) is investigated in the near-infrared spectral range from 6000 to 12,000 cm?1 (830–1660 nm). The Nb spectrum is produced using a hollow cathode discharge lamp in an argon atmosphere. Both Nb and Ar spectral lines are visible in the spectrum. A total of 110 spectral lines are assigned to the element Nb. Of these lines, 90 could be classified as transitions between known levels of atomic Nb. From these classified Nb i transitions, 27 have not been listed in literature previously. Additionally, 8 lines are classified for the first time.
First measurements using the ALS Soft X-ray Fourier Transform spectrometer
Moler, E.J.; Duarte, R.M.; Howells, M.R.; Hussain, Z.; Spring, J.
1997-08-01
Commissioning of a Fourier Transform Soft X-ray spectrometer (FT-SX) is under way at the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory, as a branch of beamline 9.3.2. The spectrometer is a novel soft x-ray interferometer designed for ultra-high resolution spectroscopy in the photon experimental results which sensitively test models of correlated electron processes in atomic and molecular physics. The design criteria and consequent technical challenges posed by the short wavelengths of x-rays and desired resolving power are discussed. The fundamental and practical aspects of soft x-ray interferometry are also explored.
Realization of a NIR compact static Fourier transform spectrometer in glass integrated optics
NASA Astrophysics Data System (ADS)
Martin, B.; Morand, A.; Jocou, L.; Benech, P.; Grosa, G.; Le Coarer, E.; Kern, P.
2010-02-01
The realization and characterization of the leaky loop integrated Fourier transform spectrometer (LLIFTS) in integrated optics are described. The component is compact, costless with no moveable parts. The principle lies on a two-beam interferometer in planar design using a leaky loop waveguide structure. The radiated part leaking from the loop induces an interference pattern at the end of the component. The structure has the advantage of controlling the shape of the interference pattern. Ion exchange technology used here requires only a single lithography step. Measurements have been made in the near infrared domain with wavelength resolution of 11 nm.
NASA Astrophysics Data System (ADS)
Creux, A.; Morand, A.; Benech, P.; Martin, B.; Grosa, G.; Cassagnettes, C.; Barbier, D.; Le Coarer, E.
2013-03-01
A leaky loop Fourier Transform spectrometer is presented in 700-1000nm spectral bandwidth. This integrated optic spectrometer is made without moveable parts. The contrast and the shape of the interferogram created at the end of the component are controlled by the gap evolution between the bend waveguide and the planar waveguide. Glass ion exchange has been chosen to obtain a high fringe contrast. A linear camera set directly at the end of the component allows interferences capture from 780nm to 850nm and the light vertical scattering due to the waveguides surface roughness is used to characterize the optical loop behavior.
Three-dimensional profiling using the Fourier transform method with a hexagonal grating projection
Iwata, Koichi; Kusunoki, Fuminori; Moriwaki, Kousuke; Fukuda, Hiroki; Tomii, Takaharu
2008-04-20
We present three-dimensional profilometry based on triangulation in which a hexagonal pattern is projected on the object. To obtain an accurate result with a one-shot photographic image, the Fourier transform method and method of excess fraction are adopted. The three grating components of the hexagonal pattern are used. For compactness a new pattern projection scheme is introduced. The experimental results show that the constructed optical system works well for measuring the profile of a mannequin with a height resolution of {approx} {+-} 1 mm.
Fourier-transform microwave spectroscopy of an alkyl substituted Criegee intermediate anti-CH3CHOO
NASA Astrophysics Data System (ADS)
Nakajima, Masakazu; Yue, Qiang; Endo, Yasuki
2015-04-01
Pure rotational transitions of the anti-form of the simplest alkyl-substituted Criegee intermediate, anti-CH3CHOO, were observed by Fourier-transform microwave spectroscopy. The observed transition frequencies in the A and E levels of the ground vibrational state were analyzed together, and molecular constants including parameters which characterize the internal rotation of the methyl rotor were determined. The experimentally determined barrier height of the three-fold potential for the methyl internal rotation is 399.1 cm-1, less than a half of that of the other conformer, syn-CH3CHOO (Nakajima and Endo, 2014).
Planetary infrared astronomy using a cryogenic postdisperser on Fourier transform spectrometers
NASA Technical Reports Server (NTRS)
Jennings, D. E.; Kunde, V. G.; Hanel, R. A.; Maguire, W. C.; Lamb, G. M.
1986-01-01
High resolution infrared spectra of planets from ground-based observatories were analyzed and instrumentation to improve sensitivity was developed. A cryogenic postdisperser (a narrow bandpass spectral filter) for use with Fourier transform spectrometers (FTS's) at facility observatories was constructed. This instrument has improved the sensitivity of FTS observations at 8 to 20 microns by about an order of magnitude. Spectra of Jupiter, Saturn and Comet Halley were obtained using the postdisperser with FTS facilities at the Kitt Peak 4-meter and McMath telescopes. Spectral resolution as high as 0.01/cm was achieved.
Vehicle Classification Using the Discrete Fourier Transform with Traffic Inductive Sensors
Lamas-Seco, José J.; Castro, Paula M.; Dapena, Adriana; Vazquez-Araujo, Francisco J.
2015-01-01
Inductive Loop Detectors (ILDs) are the most commonly used sensors in traffic management systems. This paper shows that some spectral features extracted from the Fourier Transform (FT) of inductive signatures do not depend on the vehicle speed. Such a property is used to propose a novel method for vehicle classification based on only one signature acquired from a sensor single-loop, in contrast to standard methods using two sensor loops. Our proposal will be evaluated by means of real inductive signatures captured with our hardware prototype. PMID:26516855
Vilkov, Andrey N.; Gamage, Chaminda M.; Misharin, Alexander S.; Doroshenko, Vladimir M.; Tolmachev, Dmitry A.; Tarasova, Irina A.; Kharybin, Oleg N.; Novoselov, Konstantin P.; Gorshkov, Michael V.
2007-01-01
A new Fourier Transform Ion Cyclotron Resonance mass spectrometer based on a permanent magnet with an atmospheric pressure ionization source was designed and constructed. A mass resolving power (full-width-at-half-maximum) of up to 80,000 in the electron ionization mode and 25,000 in the electrospray mode was obtained. Also, a mass measurement accuracy at low-ppm level has been demonstrated for peptide mixtures in a mass range of up to 1,200 m/z in the isotopically resolved mass spectra. PMID:17587594
Sloan, J.M.
1986-07-01
Fourier-transform infrared spectroscopy (FT-IR) using a photoacoustic sampling cell was used to obtain high-quality infrared spectra of various fiber-reinforced epoxy composites and the corresponding resin matrixes. Photoacoustic spectroscopy (PAS) offers the advantages of having little or no sample preparation for high-quality spectra to be obtained, and no alignment of the infrared incident beam is necessary. This makes PAS an ideal sampling method for in-field testing of composite laminates. The spectra revealed information on the degree of cure of the resin system by monitoring the 915/cm absorption band and the type of reinforcement material used (glass or Kevlar).
Zhang, Kang; Kang, Jin U.
2010-01-01
We implemented fast Gaussian gridding (FGG)-based non-uniform fast Fourier transform (NUFFT) on the graphics processing unit (GPU) architecture for ultrahigh-speed, real-time Fourier-domain optical coherence tomography (FD-OCT). The Vandermonde matrix-based non-uniform discrete Fourier transform (NUDFT) as well as the linear/cubic interpolation with fast Fourier transform (InFFT) methods are also implemented on GPU to compare their performance in terms of image quality and processing speed. The GPU accelerated InFFT/NUDFT/NUFFT methods are applied to process both the standard half-range FD-OCT and complex full-range FD-OCT (C-FD-OCT). GPU-NUFFT provides an accurate approximation to GPU-NUDFT in terms of image quality, but offers >10 times higher processing speed. Compared with the GPU-InFFT methods, GPU-NUFFT has improved sensitivity roll-off, higher local signal-to-noise ratio and immunity to side-lobe artifacts caused by the interpolation error. Using a high speed CMOS line-scan camera, we demonstrated the real-time processing and display of GPU-NUFFT-based C-FD-OCT at a camera-limited rate of 122 k line/s (1024 pixel/A-scan). PMID:21164690
Blackford, Jennifer Urbano; Salomon, Ronald M.; Waller, Niels G.
2009-01-01
Treatment-related changes in neurobiological rhythms are of increasing interest to psychologists, psychiatrists, and biological rhythms researchers. New methods for analyzing change in rhythms are needed, as most common methods disregard the rich complexity of biological processes. Large time series data sets reflect the intricacies of underlying neurobiological processes, but can be difficult to analyze. We propose the use of Fourier methods with multivariate permutation test (MPT) methods for analyzing change in rhythms from time series data. To validate the use of MPT for Fourier-transformed data, we performed Monte Carlo simulations and compared statistical power and family-wise error for MPT to Bonferroni-corrected and uncorrected methods. Results show that MPT provides greater statistical power than Bonferroni-corrected tests, while appropriately controlling family-wise error. We applied this method to human, pre-and post-treatment, serially-sampled neurotransmitter data to confirm the utility of this method using real data. Together, Fourier with MPT methods provides a statistically powerful approach for detecting change in biological rhythms from time series data. PMID:19212840
Real-time Fourier transform spectrometry for fluorescence imaging and flow cytometry
Buican, T.N.
1990-01-01
We present a Fourier transform (FT) spectrometer that is suitable for real-time spectral analysis in fluorescence imaging and flow cytometry. The instrument consists of a novel type of interferometer that can be modulated at frequencies of up to 100 kHz and has a high light throughput; and a dedicated, parallel array processor for the real-time computation of spectral parameters. The data acquisition array processor can be programmed by a host computer to perform any desired linear transform on the interferogram and can thus separate contributions from multiple fluorescence microscopy. The integration of a flow cytometer and a spectral imaging fluorescence microscope is discussed, and the concepts of direct and reversed virtual sorting'' are introduced. 9 refs., 8 figs.
A fast fourier transform algorithm for surface profiler based on scanning white-light interferometry
NASA Astrophysics Data System (ADS)
Zou, Wendong; Du, Nan; Fu, Yanjun; Xiao, Huirong; Du, Qiang
2006-01-01
In this paper, we introduce a fast Fourier transform algorithm for three-dimension surface analysis in a scanning white-light interferometry system. The interferograms, one for each pixel of the interference image, representing the variation in intensity as a function of scan position, are transformed into the spatial frequency domain and the relative surface height information for each point is extracted from the complex phase as a function of frequency. For optimal speed and efficiency with a minimum of resources, a simple frequency-based discriminator is used in data acquisition to identify the modulation region and a circular buffer technique is adopted for retaining the complete interferogram efficiently. Applying this method to the mapping of the endface topography of fiber connector, we've achieved high measurement repeatability and speed.
Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform.
Tang, Heng-He; Liu, Pu-Kun
2015-09-01
A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of ?/5 (? is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances. PMID:26368459
The price tag for a fast Fourier transform on any sample size
NASA Astrophysics Data System (ADS)
Cheek, James B.
1991-09-01
A computer program that makes a time-to-frequency domain transformation on a signal sampled with any number of equally spaced points has been available for over 10 years. That program, Glassman's discrete Fourier transform (DFT), is not generally used. Perhaps this low use is due to the wide and unpredictable variations in the processing time caused by small changes in the sample size. This paper examines that program and shows how the sample size controls the processing time. The procedure described in this paper establishes the relative computation cost of any sample size and shows that small adjustments to the sample size will provide the DFT capability at an affordable cost. So, this paper is largely about the workings of a computer-based signal processing tool and how to use it effectively.
, properties, Discrete and Fast Fourier Transforms, Z Transform, Digital Filter Design and Multi-rate Digital 220 Outcomes Students will be able to: A-3. Determine if a discrete time system is linear, time-invariant may be applied to determine the course letter grades. Composition of final grade: Your course grade
NASA Astrophysics Data System (ADS)
Allen, Matthew S.; Mayes, Randall L.
2010-10-01
This work presents time-frequency signal processing methods for detecting and characterizing nonlinearity in transient response measurements. The methods are intended for systems whose response becomes increasingly linear as the response amplitude decays. The discrete Fourier transform of the response data is found with various sections of the initial response set to zero. These frequency responses, dubbed zeroed early-time fast Fourier transforms (ZEFFTs), acquire the usual shape of linear frequency response functions (FRFs) as more of the initial nonlinear response is nullified. Hence, nonlinearity is evidenced by a qualitative change in the shape of the ZEFFT as the length of the initial nullified section is varied. These spectra are shown to be sensitive to nonlinearity, revealing its presence even if it is active in only the first few cycles of a response, as may be the case with macro-slip in mechanical joints. They also give insight into the character of the nonlinearity, potentially revealing nonlinear energy transfer between modes or the modal amplitudes below which a system behaves linearly. In some cases one can identify a linear model from the late time, linear response, and use it to reconstruct the response that the system would have executed at previous times if it had been linear. This gives an indication of the severity of the nonlinearity and its effect on the measured response. The methods are demonstrated on both analytical and experimental data from systems with slip and impact nonlinearities.
Fourier Transform Infrared Emission Spectroscopy and AB Initio Study of Hbo and BO
NASA Astrophysics Data System (ADS)
Li, G.; Hargreaves, R. J.; Bernath, P. F.
2010-06-01
The Fourier-transform infrared emission spectra of HBO and BO were recorded using a Bruker IFS-125HR Fourier transform spectrometer. HBO molecules were synthesized using a high temperature tube furnace at 1450 °C. Our spectra of the HBO molecule in the 1200-4000 cm-1 region contain the v1 and v3 fundamental vibrational modes plus numerous hot bands. An accurate potential energy surface using the MRCI method with correlation consistent core-valence basis sets aug-cc-PCVnZ (n=3, 4, 5) is being calculated and a vibrational configuration interaction (VCI) calculation based on this surface will be performed to assist in the assignment of the HBO hot bands. BO molecules were produced by applying a DC discharge to the furnace containing HBO. Our spectrum of BO in the 1200-2100 cm-1 region contains the fundamental bands of both isotopic species, 11BO, 10BO, and one hot band of the main isotopologue 11BO. The fundamental band of 11BO contains 95 lines roughly equally distributed between the P and R branches. A combined least-squares fit with ground state microwave data was performed to determine the spectroscopic constants. Further results on this ongoing project will be presented.
A fractional Fourier transform analysis of the scattering of ultrasonic waves
Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony
2015-01-01
Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967
A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.
Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei
2015-09-01
A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at ?max = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress. PMID:26414526
NASA Astrophysics Data System (ADS)
Isobe, Keisuke; Suda, Akira; Tanaka, Masahiro; Kannari, Fumihiko; Kawano, Hiroyuki; Mizuno, Hideaki; Miyawaki, Atsushi; Midorikawa, Katsumi
2008-06-01
We propose a technique for distinguishing the origin of a four-wave mixing (FWM) signal. This technique is based on nonlinear Fourier-transform spectroscopy (FTS) combined with the use of a broadband pulse. We theoretically analyze FWM-FTS and show that the response function in FWM is obtained from the FWM power spectrum calculated by the Fourier transform of an interferometric autocorrelation signal. When a broadband pulse is employed as an excitation light source, the FWM power spectrum shows not only Raman resonance but also two-photon electronic resonance. By comparing the FWM power spectrum of a resonant sample with that of a nonresonant reference sample, the origin of FWM is identified. By employing theoretical analysis, we experimentally demonstrate FWM-FTS using a 5-fs broadband pulse. By combining the use of a 5-fs pulse with nonlinear FTS based on two-photon excited fluorescence, we also successfully measured a two-photon excitation spectrum with a bandwidth of 300 nm.
NASA Technical Reports Server (NTRS)
Hewagama, TIlak; Aslam, Shahid; Talabac, Stephen; Allen, John E., Jr.; Annen, John N.; Jennings, Donald E.
2011-01-01
Fourier transform spectrometers have a venerable heritage as flight instruments. However, obtaining an accurate spectrum exacts a penalty in instrument mass and power requirements. Recent advances in a broad class of non-scanning Fourier transform spectrometer (FTS) devices, generally called spatial heterodyne spectrometers, offer distinct advantages as flight optimized systems. We are developing a miniaturized system that employs photonics lightwave circuit principles and functions as an FTS operating in the 7-14 micrometer spectral region. The inteferogram is constructed from an ensemble of Mach-Zehnder interferometers with path length differences calibrated to mimic scan mirror sample positions of a classic Michelson type FTS. One potential long-term application of this technology in low cost planetary missions is the concept of a self-contained sensor system. We are developing a systems architecture concept for wide area in situ and remote monitoring of characteristic properties that are of scientific interest. The system will be based on wavelength- and resolution-independent spectroscopic sensors for studying atmospheric and surface chemistry, physics, and mineralogy. The self-contained sensor network is based on our concept of an Addressable Photonics Cube (APC) which has real-time flexibility and broad science applications. It is envisaged that a spatially distributed autonomous sensor web concept that integrates multiple APCs will be reactive and dynamically driven. The network is designed to respond in an event- or model-driven manner or reconfigured as needed.
Teaching stable two-mirror resonators through the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos
2010-03-01
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects.
NASA Astrophysics Data System (ADS)
Lanyi, G.; Kahn, R.
1997-01-01
An algorithm is presented for detection of very weak spacecraft tones generated by an onboard auxiliary oscillator with stability specifications similar to those of the small deep space transponder. Signal power is evaluated via discrete Fourier transforms, and detection is determined by comparing the measured power with a predetermined threshold. Limited oscillator stability precludes coherent integration of the signal over time scales longer than a few seconds; thus, the Fourier transform is performed independently on successive segments of data. Resulting power spectra are then averaged; potential frequency drift is accounted for by shifting the spectra when forming the average. The detection scheme is well suited to the proposed automated spacecraft monitoring system, in which a spacecraft sends a carrier signal modulated with one of four subcarrier frequencies to indicate the spacecraft's current state. Analysis based on theory and measurements indicates that reliable detection in a 1000-s interval can be achieved at a power signal to-noise-density level, P=N_0, as low as - 1 dB-Hz.
Identification of Earthquake Induced Damage Areas Using Fourier Transform and SPOT HRVIR Pan Images
Sertel, Elif
2009-01-01
A devastating earthquake with a magnitude of Mw 7.4 occurred on the North Anatolian Fault Zone (NAFZ) of Turkey on August 17, 1999 at 00:01:39 UTC (3:01 a.m. local time). The aim of this study is to propose a new approach to automatically identify earthquake induced damage areas which can provide valuable information to support emergency response and recovery assessment procedures. This research was conducted in the Adapazari inner city, covering a 3 × 3 km area, where 11,373 buildings collapsed as a result of the earthquake. SPOT high resolution visible infrared (HRVIR) Pan images obtained before (25 June 1999) and after (4 October 1999) the earthquake were used in the study. Five steps were employed to conduct the research and these are: (i) geometric and radiometric correction of satellite images, (ii) Fast Fourier Transform (FFT) of pre- and post-earthquake images and filtering the images in frequency domain, (iii) generating difference image using Inverse Fast Fourier Transform (IFFT) pre- and post- earthquake images, (iv) application of level slicing to difference image to identify the earthquake-induced damages, (v) accuracy assessment of the method using ground truth obtained from a 1/5,000 scale damage map. The total accuracy obtained in the research is 80.19 %, illustrating that the proposed method can be successfully used to automatically identify earthquake-induced damage areas. PMID:22573966
3D-printed slit nozzles for Fourier transform microwave spectroscopy
NASA Astrophysics Data System (ADS)
Dewberry, Christopher T.; Mackenzie, Rebecca B.; Green, Susan; Leopold, Kenneth R.
2015-06-01
3D printing is a new technology whose applications are only beginning to be explored. In this report, we describe the application of 3D printing to the design and construction of supersonic nozzles. Nozzles can be created for 0.50 or less, and the ease and low cost can facilitate the optimization of nozzle performance for the needs of any particular experiment. The efficacy of a variety of designs is assessed by examining rotational spectra of OCS (carbonyl sulfide) and Ar-OCS using a Fourier transform microwave spectrometer with tandem cavity and chirped-pulse capabilities. A slit geometry which, to the best of our knowledge has not been used in conjunction with Fourier transform microwave spectrometers, was found to increase the signal-to-noise ratio for the J = 1?0 transition of OCS, by a factor of three to four compared with that obtained using our standard circular nozzle. Corresponding gains for the Ar-OCS complex were marginal, at best, but further optimization of nozzle geometry should be possible. The spectrometer itself is designed to allow rapid switching between cavity and chirped-pulse modes of operation without the need to break vacuum. This feature, as well as the newly incorporated chirped-pulse capability, is described in detail.
NASA Astrophysics Data System (ADS)
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.
Instrumental phase-based method for Fourier transform spectrometer measurements processing
Saggin, Bortolino; Scaccabarozzi, Diego; Tarabini, Marco
2011-04-20
Phase correction is a critical procedure for most space-borne Fourier transform spectrometers (FTSs) whose accuracy (owing to often poor signal-to-noise ratio, SNR) can be jeopardized from many uncontrollable environmental conditions. This work considers the phase correction in an FTS working under significant temperature change during the measurement and affected by mechanical disturbances. The implemented method is based on the identification of an instrumental phase that is dependent on the interferometer temperature and on the extraction of a linear phase component through a least-squares approach. The use of an instrumental phase parameterized with the interferometer temperature eases the determination of the linear phase that can be extracted using only a narrow spectral region selected to be immune from disturbances. The procedure, in this way, is made robust against phase errors arising from instrumental effects, a key feature to reduce the disturbances through spectra averaging. The method was specifically developed for the Mars IR Mapper spectrometer, that was designed for operation onboard a rover on the Mars surface; the validation was performed using ground and in-flight measurements of the Fourier transform IR spectrometer planetary Fourier spectrometer, onboard the MarsExpress mission. The symmetrization has been exploited also for the spectra calibration, highlighting the issues deriving from the cases of relevant beamsplitter emission. The applicability of this procedure to other instruments is conditional to the presence in the spectra of at least one spectral region with a large SNR along with a negligible (or known) beamsplitter emission. For the PFS instrument, the processing of data with relevant beamsplitter emission has been performed exploiting the absorption carbon dioxide bands present in Martian spectra.
Instrumental phase-based method for Fourier transform spectrometer measurements processing.
Saggin, Bortolino; Scaccabarozzi, Diego; Tarabini, Marco
2011-04-20
Phase correction is a critical procedure for most space-borne Fourier transform spectrometers (FTSs) whose accuracy (owing to often poor signal-to-noise ratio, SNR) can be jeopardized from many uncontrollable environmental conditions. This work considers the phase correction in an FTS working under significant temperature change during the measurement and affected by mechanical disturbances. The implemented method is based on the identification of an instrumental phase that is dependent on the interferometer temperature and on the extraction of a linear phase component through a least-squares approach. The use of an instrumental phase parameterized with the interferometer temperature eases the determination of the linear phase that can be extracted using only a narrow spectral region selected to be immune from disturbances. The procedure, in this way, is made robust against phase errors arising from instrumental effects, a key feature to reduce the disturbances through spectra averaging. The method was specifically developed for the Mars IR Mapper spectrometer, that was designed for operation onboard a rover on the Mars surface; the validation was performed using ground and in-flight measurements of the Fourier transform IR spectrometer planetary Fourier spectrometer, onboard the MarsExpress mission. The symmetrization has been exploited also for the spectra calibration, highlighting the issues deriving from the cases of relevant beamsplitter emission. The applicability of this procedure to other instruments is conditional to the presence in the spectra of at least one spectral region with a large SNR along with a negligible (or known) beamsplitter emission. For the PFS instrument, the processing of data with relevant beamsplitter emission has been performed exploiting the absorption carbon dioxide bands present in Martian spectra. PMID:21509063
A quantum algorithm for the quantum Schur-Weyl transform
Sonya Berg
2012-05-17
We construct an efficient quantum algorithm to compute the quantum Schur-Weyl transform for any value of the quantum parameter $q \\in [0,\\infty]$. Our algorithm is a $q$-deformation of the Bacon-Chuang-Harrow algorithm, in the sense that it has the same structure and is identically equal when $q=1$. When $q=0$, our algorithm is the unitary realization of the Robinson-Schensted-Knuth (or RSK) algorithm, while when $q=\\infty$ it is the dual RSK algorithm together with phase signs. Thus, we interpret a well-motivated quantum algorithm as a generalization of a well-known classical algorithm.
Ma, Q.; Tipping, R. H.
2014-03-14
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS{sub 1} ? S{sub 2} introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the S-circumflex operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters’ two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
NASA Technical Reports Server (NTRS)
Ma, Q.; Boulet, C.; Tipping, R. H.
2014-01-01
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
NASA Astrophysics Data System (ADS)
Graf, Robert N.; Chen, Xiaoxin; Brown, William; Wax, Adam
2008-02-01
Fourier Domain Low Coherence Interferometry (fLCI) is a promising technique which combines the depth resolution of low coherence interferometry with the sensitivity of light scattering spectroscopy for probing the health of epithelial tissue layers. Our new fLCI system configuration utilizes a white light Xe arc lamp source and a 4-f interferometer which re-images light scattered from the sample onto the detection plane. The system employs an imaging spectrometer at the detection plane to acquire depth resolved profiles from 252 adjacent spatial points without the need for any scanning. The limited spatial coherence of the light source requires the resolution of adjacent spatial points for the generation of depth information. Depth-resolved spectral information is recovered by performing a short-time Fourier transform on the detected spectra, similar to spectroscopic optical coherence tomography. Wavelength dependent variations in scattering intensity are analyzed as a function of depth to obtain information about the neoplastic transformation of the probed cells. Previous studies have demonstrated fLCI as an excellent technique for probing the scatterer morphology of simple phantoms and of in vitro cancer cell monolayers. We now seek to assess the ability of the new fLCI system to measure the health of subsurface tissue layers using the hamster cheek pouch model. Seven hamsters will have one cheek pouch treated with the known carcinogen DMBA. At the conclusion of the 24 week treatment period the animals will be anesthetized and the cheek pouches will be extracted. We will use the fLCI optical system to measure the neoplastic transformation of the in situ subsurface tissue layers in both the normal and DMBA-treated cheek pouches. Traditional histological analysis will be used to verify the fLCI measurements. We expect our results to establish the feasibility of fLCI to distinguish between healthy and dysplastic epithelial tissues in the hamster cheek pouch.
Introduction to Quantum Simulation
NASA Technical Reports Server (NTRS)
Williams, Colin P.
2005-01-01
This viewgraph presentation addresses the problem of efficiently simulating the evolution of a quantum system. The contents include: 1) Quantum Simulation; 2) Extracting Answers from Quantum Simulations; 3) Quantum Fourier Transform; 4) Eigenvalue Estimation; 5) Fermionic Simulations.
Optical Fresnel transformation and quantum tomography
NASA Astrophysics Data System (ADS)
Fan, Hong-Yi; Hu, Li-yun
2009-09-01
Corresponding to optical Fresnel transformation characteristic of a ray transfer matrix (A,B,C,D),AD-BC=1, there exists Fresnel operator F(A,B,C,D) in quantum optics, we show that under the Fresnel transformation the pure-state position density ?x> sp=??-??dp'dx'?p-Ax'-Cp')?x',p', where ?p>
Liu, Derek Sloboda, Ron S.
2014-05-15
Purpose: Boyer and Mok proposed a fast calculation method employing the Fourier transform (FT), for which calculation time is independent of the number of seeds but seed placement is restricted to calculation grid points. Here an interpolation method is described enabling unrestricted seed placement while preserving the computational efficiency of the original method. Methods: The Iodine-125 seed dose kernel was sampled and selected values were modified to optimize interpolation accuracy for clinically relevant doses. For each seed, the kernel was shifted to the nearest grid point via convolution with a unit impulse, implemented in the Fourier domain. The remaining fractional shift was performed using a piecewise third-order Lagrange filter. Results: Implementation of the interpolation method greatly improved FT-based dose calculation accuracy. The dose distribution was accurate to within 2% beyond 3 mm from each seed. Isodose contours were indistinguishable from explicit TG-43 calculation. Dose-volume metric errors were negligible. Computation time for the FT interpolation method was essentially the same as Boyer's method. Conclusions: A FT interpolation method for permanent prostate brachytherapy TG-43 dose calculation was developed which expands upon Boyer's original method and enables unrestricted seed placement. The proposed method substantially improves the clinically relevant dose accuracy with negligible additional computation cost, preserving the efficiency of the original method.
Davis, Benjamin L.; Berrier, Joel C.; Shields, Douglas W.; Kennefick, Julia; Kennefick, Daniel; Seigar, Marc S.; Lacy, Claud H. S.; Puerari, Ivanio
2012-04-01
A logarithmic spiral is a prominent feature appearing in a majority of observed galaxies. This feature has long been associated with the traditional Hubble classification scheme, but historical quotes of pitch angle of spiral galaxies have been almost exclusively qualitative. We have developed a methodology, utilizing two-dimensional fast Fourier transformations of images of spiral galaxies, in order to isolate and measure the pitch angles of their spiral arms. Our technique provides a quantitative way to measure this morphological feature. This will allow comparison of spiral galaxy pitch angle to other galactic parameters and test spiral arm genesis theories. In this work, we detail our image processing and analysis of spiral galaxy images and discuss the robustness of our analysis techniques.
Cheng, Cun-gui; Ruan, Yong-ming; Li, Bing-lan
2004-11-01
This paper uses Fourier transform infrared spectrometer with OMNI sampler to distinguish Fructus amomi from their confusable varieties, i. e. Amomum aurantiacum H. T. Tsai et S. W. Zhao, Amomum chinense Chun ex T. L. Wu, Alpinia chinensis (Ketz.) Rosc and Alpinia japonica (Thunb.) Miq. IRs of Amomum villosum Lour., Amomum longiligulare T. L. Wu and Amomum villosum Lour. Var xanthioides T. L. Wu et Senjen are resemble, and they are markedly different from the FTIR of the confusable varieties. Repeat experiments were processed with different samples of the same set, and the probability is 1.000. The result shows that FTIR can be directly used to distinguish Fructus amomi from their confusable varieties. PMID:15762475
NASA Astrophysics Data System (ADS)
Brasunas, John C.
2004-12-01
Planetary Fourier transform spectroscopy (FTS) has a long history at the Goddard Space Flight Center. Dr. Rudy Hanel developed a series of such instruments for Earth, Mars and the two Voyager spacecraft. More recently as part of the Cassini mission, the CIRS (Composite Infrared Spectrometer) FTS was launched in 1997 for the 2000-2001 Jupiter flyby and the 2004-2008+ Saturn tour. At about 40 kg, CIRS is both too heavy and too light for future planetary missions. It is too heavy for future Discovery and New Frontier missions, where the emphasis is on low-mass, low-power instrumentation. On the other hand, CIRS could be heavier to take full advantage of future Prometheus missions such as JIMO. Here we discuss future development of CIRS-like FTS"s for both Discovery/New Frontier and for Prometheus flight opportunities. We also briefly discuss possible applications in the Moon/Mars exploration initiative.
Ibrahim, Amr; PredoiCross, Adriana; Teillet, P. M.
2010-10-29
Seven different techniques in dealing the problem of channel spectra in Fourier transform Spectroscopy utilizing synchrotron source were examined and compared. Five of these techniques deal with the artifacts (spikes) in the recorded interferogram which in turn result in channel spectra within the spectral domain. Such interferogram editing method include replacing these spikes with zeros, straight line, fitted polynomial curve, rescaled spike and spike reduced with Gauss Function. Another two techniques try to target this issue in the spectral domain instead by either generating a synthetic background simulating the channels or measuring the channels parameters (amplitude, spacing and phase) to use in the spectral fitting program. Results showed spectral domain techniques produces higher quality results in terms of signal to noise and fitting residual. The effect of each method on the line parameters such as position, intensity are air broadening are also measured and discussed.
NASA Technical Reports Server (NTRS)
Zimmerman, G. A.; Gulkis, S.
1991-01-01
The sensitivity of a matched filter-detection system to a finite-duration continuous wave (CW) tone is compared with the sensitivities of a windowed discrete Fourier transform (DFT) system and an ideal bandpass filter-bank system. These comparisons are made in the context of the NASA Search for Extraterrestrial Intelligence (SETI) microwave observing project (MOP) sky survey. A review of the theory of polyphase-DFT filter banks and its relationship to the well-known windowed-DFT process is presented. The polyphase-DFT system approximates the ideal bandpass filter bank by using as few as eight filter taps per polyphase branch. An improvement in sensitivity of approx. 3 dB over a windowed-DFT system can be obtained by using the polyphase-DFT approach. Sidelobe rejection of the polyphase-DFT system is vastly superior to the windowed-DFT system, thereby improving its performance in the presence of radio frequency interference (RFI).
NASA Technical Reports Server (NTRS)
Verber, C. M.; Vahey, D. W.; Wood, V. E.; Kenan, R. P.; Hartman, N. F.
1977-01-01
The possibility of producing an integrated optics data processing device based upon Fourier transformations or other parallel processing techniques, and the ways in which such techniques may be used to upgrade the performance of present and projected NASA systems were investigated. Activities toward this goal include; (1) production of near-diffraction-limited geodesic lenses in glass waveguides; (2) development of grinding and polishing techniques for the production of geodesic lenses in LiNbO3 waveguides; (3) development of a characterization technique for waveguide lenses; and (4) development of a theory for corrected aspheric geodesic lenses. A holographic subtraction system was devised which should be capable of rapid on-board preprocessing of a large number of parallel data channels. The principle involved is validated in three demonstrations.
NASA Astrophysics Data System (ADS)
McNaughton, Don; Godfrey, Peter D.; Jahn, Michaela K.; Dewald, David A.; Grabow, Jens-Uwe
2011-04-01
The pure rotational spectra of the bicyclic aromatic nitrogen heterocycle molecules, quinazoline, quinoxaline, and phthalazine, have been recorded and assigned in the region 13-87 GHz. An analysis, guided by ab initio molecular orbital predictions, of frequency-scanned Stark modulated, jet-cooled millimeter wave absorption spectra (48-87 GHz) yielded a preliminary set of rotational and centrifugal distortion constants. Subsequent spectral analysis at higher resolution was carried out with Fourier transform microwave (FT-MW) spectroscopy (13-18 GHz) of a supersonic rotationally cold molecular beam. The high spectral resolution of the FT-MW instrument provided an improved set of rotational and centrifugal distortion constants together with nitrogen quadrupole coupling constants for all three species. Density functional theory calculations at the B3LYP/6-311+G** level of theory closely predict rotational constants and are useful in predicting quadrupole coupling constants and dipole moments for such species.
Largo-Gosens, Asier; Hernández-Altamirano, Mabel; García-Calvo, Laura; Alonso-Simón, Ana; Álvarez, Jesús; Acebes, José L.
2014-01-01
Fourier transform mid-infrared (FT-MIR) spectroscopy has been extensively used as a potent, fast and non-destructive procedure for analyzing cell wall architectures, with the capacity to provide abundant information about their polymers, functional groups, and in muro entanglement. In conjunction with multivariate analyses, this method has proved to be a valuable tool for tracking alterations in cell walls. The present review examines recent progress in the use of FT-MIR spectroscopy to monitor cell wall changes occurring in muro as a result of various factors, such as growth and development processes, genetic modifications, exposition or habituation to cellulose biosynthesis inhibitors and responses to other abiotic or biotic stresses, as well as its biotechnological applications. PMID:25071791
Label-free identification of individual bacteria using Fourier transform light scattering
Jo, YoungJu; Kim, Min-hyeok; Park, HyunJoo; Kang, Suk-Jo; Park, YongKeun
2015-01-01
Rapid identification of bacterial species is crucial in medicine and food hygiene. In order to achieve rapid and label-free identification of bacterial species at the single bacterium level, we propose and experimentally demonstrate an optical method based on Fourier transform light scattering (FTLS) measurements and statistical classification. For individual rod-shaped bacteria belonging to four bacterial species (Listeria monocytogenes, Escherichia coli, Lactobacillus casei, and Bacillus subtilis), two-dimensional angle-resolved light scattering maps are precisely measured using FTLS technique. The scattering maps are then systematically analyzed, employing statistical classification in order to extract the unique fingerprint patterns for each species, so that a new unidentified bacterium can be identified by a single light scattering measurement. The single-bacterial and label-free nature of our method suggests wide applicability for rapid point-of-care bacterial diagnosis.
Mitochondrial Metabolomics Using High-Resolution Fourier-Transform Mass Spectrometry
Go, Young-Mi; Uppal, Karan; Roede, James R.; Jones, Dean P.; Tran, ViLinh; Walker, Douglas I.; Dury, Lauriane; Strobel, Frederick H.; Baubichon-Cortay, Hélène; Pennell, Kurt D.
2015-01-01
Summary High-resolution Fourier-transform mass spectrometry (FTMS) provides important advantages in studies of metabolism because more than half of common intermediary metabolites can be measured in 10 min with minimal pre-detector separation and without ion-dissociation. This allows unprecedented opportunity to study complex metabolic systems, such as mitochondria. Analysis of mouse liver mitochondria using FTMS with liquid chromatography shows that sex and genotypic differences in mitochondrial metabolism can be readily distinguished. Additionally, differences in mitochondrial function are readily measured, and many of the mitochondria-related metabolites are also measurable in plasma. Thus, application of high-resolution mass spectrometry provides an approach for integrated studies of complex metabolic processes of mitochondrial function and dysfunction in disease. PMID:25270922
Suto, Hiroshi; Yoshida, Jun; Desbiens, Raphael; Kawashima, Takahiro; Kuze, Akihiko
2013-07-10
Microvibrations onboard greenhouse gases observing satellite (GOSAT) cause scan speed variations in the TANSO Fourier transform spectrometer. The associated periodic sampling errors generate ghost features in O2 A-band spectra, where surface pressure and aerosol properties are retrieved to determine the optical path through the atmosphere. A correction algorithm has been developed to re-compute the interferograms at equally spaced sampling intervals. The key is to determine iteratively the amplitude and phase of sinusoidal perturbations with predetermined frequencies to minimize the magnitude of the out-of-band ghosts artifacts after correction of the sampling grid. This correction algorithm drastically reduces errors in retrieved surface pressure and improves agreement with ground-based observations. PMID:23852213
Yoshida, Yukio; Oguma, Hiroyuki; Morino, Isamu; Suto, Hiroshi; Kuze, Akihiko; Yokota, Tatsuya
2010-01-01
The absorption spectra of surface-scattered solar radiation were measured from the top of Mount Tsukuba (altitude 833 m) in the short wavelength infrared region using a Fourier transform spectrometer (FTS). The FTS used in this experiment was the breadboard model of the FTS on the Greenhouse Gases Observing Satellite, which was launched on 23 January 2009. In situ measurement of carbon dioxide (CO(2)) from a Cessna airplane was performed simultaneously with the FTS observation. The CO(2) column abundances were retrieved from the observed spectra under the assumption of the absence of aerosol. The retrieved CO(2) column abundances over a few minutes dispersed within 1%. The remaining bias was considered to be caused by the no-aerosol assumption. PMID:20062492
Accelerating the two-point and three-point galaxy correlation functions using Fourier transforms
NASA Astrophysics Data System (ADS)
Slepian, Zachary; Eisenstein, Daniel J.
2016-01-01
Though Fourier transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle surveys because the line-of-sight direction is not constant on the Cartesian grid. Here we show how FTs can be used to compute the multipole moments of the anisotropic 2PCF. We also show how FTs can be used to accelerate the 3PCF algorithm of Slepian & Eisenstein. In both cases, these FT methods allow one to avoid the computational cost of pair counting, which scales as the square of the number density of objects in the survey. With the upcoming large data sets of Dark Energy Spectroscopic Instrument, Euclid, and Large Synoptic Survey Telescope, FT techniques will therefore offer an important complement to simple pair or triplet counts.
NASA Astrophysics Data System (ADS)
Tieng, S. M.; Lai, W. Z.
Because of the importance of the temperature scalar measurements in combination diagonostics, application of phase shift holographic interferometry to temperature measurement of an axisymmetrically premixed flame was experimentally investigated. The test apparatus is an axisymmetric Bunsen burner. Propane of 99 percent purity is used as the gaseous fuel. A fast Fourier transform, a more efficient and accurate approach for Abel inversion, is used for reconstructed the axisymmetric temperature field from the interferometric data. The temperature distribution is compared with the thermocouple-measured values. The comparison shows that the proposed technique is satisfactory. The result errors are analyzed in detail. It is shown that this technique overcomes most of the earlier problems and limitations detrimental to the conventional holographic interferometry.
NASA Astrophysics Data System (ADS)
Zhang, Xiaoxing; Liu, Heng; Ren, Jiangbo; Li, Jian; Li, Xin
2015-02-01
Gas-insulated switchgear (GIS) internal SF6 gas produces specific decomposition components under partial discharge (PD). By detecting these characteristic decomposition components, such information as the type and level of GIS internal insulation deterioration can be obtained effectively, and the status of GIS internal insulation can be evaluated. SF6 was selected as the background gas for Fourier transform infrared spectroscopy (FTIR) detection in this study. SOF2, SO2F2, SO2, and CO were selected as the characteristic decomposition components for system analysis. The standard infrared absorption spectroscopy of the four characteristic components was measured, the optimal absorption peaks were recorded and the corresponding absorption coefficient was calculated. Quantitative detection experiments on the four characteristic components were conducted. The volume fraction variation trend of four characteristic components at different PD time were analyzed. And under five different PD quantity, the quantitative relationships among gas production rate, PD time, and PD quantity were studied.
Zhang, Xiaoxing; Liu, Heng; Ren, Jiangbo; Li, Jian; Li, Xin
2015-02-01
Gas-insulated switchgear (GIS) internal SF6 gas produces specific decomposition components under partial discharge (PD). By detecting these characteristic decomposition components, such information as the type and level of GIS internal insulation deterioration can be obtained effectively, and the status of GIS internal insulation can be evaluated. SF6 was selected as the background gas for Fourier transform infrared spectroscopy (FTIR) detection in this study. SOF2, SO2F2, SO2, and CO were selected as the characteristic decomposition components for system analysis. The standard infrared absorption spectroscopy of the four characteristic components was measured, the optimal absorption peaks were recorded and the corresponding absorption coefficient was calculated. Quantitative detection experiments on the four characteristic components were conducted. The volume fraction variation trend of four characteristic components at different PD time were analyzed. And under five different PD quantity, the quantitative relationships among gas production rate, PD time, and PD quantity were studied. PMID:25459612
The Fourier transform spectrometer of the Universite? Pierre et Marie Curie QualAir platform.
Té, Y; Jeseck, P; Payan, S; Pépin, I; Camy-Peyret, C
2010-10-01
A Bruker Optics IFS 125HR Fourier transform spectrometer (FTS) and the Laboratoire de Physique Mole?culaire pour l'Atmosphe?re et l'Astrophysique retrieval algorithm were adapted for ground based atmospheric measurements. As one of the major instruments of the experimental research platform QualAir, this FTS is dedicated to study the urban air composition of large megacity such as Paris. The precise concentration measurements of the most important atmospheric pollutants are a key to improve the understanding and modeling of urban air pollution processes. Located in the center of Paris, this remote sensing spectrometer enables to monitor many pollutants. Examples for NO(2) and CO are demonstrating the performances of this new experimental setup. PMID:21034070
Park, Jinsoo; Kim, Wooil; Han, David K.; Ko, Hanseok
2014-01-01
A new voice activity detector for noisy environments is proposed. In conventional algorithms, the endpoint of speech is found by applying an edge detection filter that finds the abrupt changing point in a feature domain. However, since the frame energy feature is unstable in noisy environments, it is difficult to accurately find the endpoint of speech. Therefore, a novel feature extraction algorithm based on the double-combined Fourier transform and envelope line fitting is proposed. It is combined with an edge detection filter for effective detection of endpoints. Effectiveness of the proposed algorithm is evaluated and compared to other VAD algorithms using two different databases, which are AURORA 2.0 database and SITEC database. Experimental results show that the proposed algorithm performs well under a variety of noisy conditions. PMID:25170520
Quantification of DNA in simple eukaryotic cells using Fourier transform infrared spectroscopy.
Whelan, Donna R; Bambery, Keith R; Puskar, Ljiljana; McNaughton, Don; Wood, Bayden R
2013-10-01
A technique capable of detecting and monitoring nucleic acid concentration offers potential in diagnosing cancer and further developing an understanding of the biochemistry of disease. The application of Fourier transform infrared (FTIR) spectroscopy has previously been hindered by the supposed non-Beer-Lambert absorption behavior of DNA in intact cells making elucidation of the DNA bands difficult. We use known composition DNA/hemoglobin standards to successfully estimate the DNA content in avian erythrocyte nuclei (44.2%) and intact erythrocytes (12.8%). Furthermore we demonstrate that the absorption of cellular DNA does follow the Beer-Lambert Law and highlights the role of conformation and hydration in FTIR spectroscopy of biological samples. PMID:22997011
A Novel Application of Fourier Transform Spectroscopy with HEMT Amplifiers at Microwave Frequencies
NASA Technical Reports Server (NTRS)
Wilkinson, David T.; Page, Lyman
1995-01-01
The goal was to develop cryogenic high-electron-mobility transistor (HEMT) based radiometers and use them to measure the anisotropy in the cosmic microwave background (CMB). In particular, a novel Fourier transform spectrometer (FTS) built entirely of waveguide components would be developed. A dual-polarization Ka-band HEMT radiometer and a similar Q-band radiometer were built. In a series of measurements spanning three years made from a ground-based site in Saskatoon, SK, the amplitude, frequency spectrum, and spatial frequency spectrum of the anisotropy were measured. A prototype Ka-band FTS was built and tested, and a simplified version is proposed for the MAP satellite mission. The 1/f characteristics of HEMT amplifiers were quantified using correlation techniques.
Color image encryption using iterative phase retrieve process in quaternion Fourier transform domain
NASA Astrophysics Data System (ADS)
Sui, Liansheng; Duan, Kuaikuai
2015-02-01
A single-channel color image encryption method is proposed based on iterative phase iterative process in quaternion Fourier transform domain. First, three components of the plain color image is confused respectively by using cat map. Second, the confused components are combined into a pure quaternion image, which is encode to the phase only function by using an iterative phase retrieval process. Finally, the phase only function is encrypted into the gray scale ciphertext with stationary white noise distribution based on the chaotic diffusion, which has camouflage property to some extent. The corresponding plain color image can be recovered from the ciphertext only with correct keys in the decryption process. Simulation results verify the feasibility and effectiveness of the proposed method.
Fourier transforms by white-light interferometry: Michelson stellar interferometer fringes
NASA Astrophysics Data System (ADS)
Breckinridge, James B.
2011-10-01
The white-light compensated rotational shear interferometer (coherence interferometer) was developed in an effort to study the spatial frequency content of passively illuminated white-light scenes in real-time and to image sources of astronomical interest at high spatial frequencies through atmospheric turbulence. This work was inspired by Professor Goodman's studies of the image formation properties of coherent (laser) illuminated transparencies. We discovered that real-time image processing is possible using white-light interferometry. The concept of a quasimonoplanatic approximation is introduced as a parallel to the quasimonochromatic approximation needed to describe the theory of Fourier transform spectrometers. This paper describes the coherence interferometer and reviews its image formation properties under the conditions of quasimonoplanacity and describes its development and its applications to physical optics, optical processing and astrophysics including the search for exoplanets.
a Study of 4,4-DIMETHYLAMINOBEZONITRILE by Chirped-Pulsed Fourier Transform Microwave Spectroscopy
NASA Astrophysics Data System (ADS)
Bird, Ryan G.; Alstadt, Valerie J.; Pratt, David W.; Neill, Justin L.; Pate, Brooks H.
2010-06-01
The ground state rotational spectrum of 4,4-dimethylaminobenzonitrile (DMABN) was studied using chirped-pulsed Fourier transform microwave spectroscopy (CP-FTMW). The rotational spectrum from 6.5 to 18 GHz was collected using a compilation of 250 MHz chirped pulses and pieced together. DMABN is widely known as an important model for excited state twisted intramolecular charge transfer dynamics. It has been previously studied in our group using high resolution electronic spectroscopy, in which a strong coupling between methyl group internal rotation and overall rotation was discovered. We have recently determined that these couplings are not present in the ground state spectrum. The ground state structure and nuclear quadrupole coupling terms will also be discussed.
NASA Astrophysics Data System (ADS)
Castilho, Maiara L.; Campos, Claudia B. L.; Matos, Tatiana G. F.; de Abreu, Geraldo M. A.; Martin, Airton A.; Raniero, Leandro
2012-01-01
Paracoccidioides brasiliensis the etiological agent of paracoccidioidomycosis, is a dimorphic fungus existing as mycelia in the environment (or at 25 °C in vitro) and as yeast cells in the human host (or at 37°C in vitro). The most prominent difference between both forms is probably the cell wall polysaccharide, being 1,3-?-glucan usually found in mycelia and 1,3-?-glucan found in yeasts, but a plethora of other differences have already been described. In this work, we performed a Fourier Transform Infrared Spectroscopy analysis to compare the yeast and mycelia forms of P. brasiliensis and found additional biochemical differences. The analysis of the spectra showed that differences were distributed in chemical bonds of proteins, lipids and carbohydrates.
Data reflection algorithm for spectral enhancement in Fourier transform ICR and NMR spectroscopies
Gorshkov, M.V.; Kouzes, R.T.
1995-10-01
The use of a data reflection algorithm in which the signal acquired in real time is juxtaposed with the same signal reflected relatively to zero time axis through exact phase matching is considered. Because of the additional information provided by a knowledge of the exact initial phase of the signal, the resulting Fourier transform (FT) spectra have a higher resolution and signal-to-noise ratio. This algorithm was applied to ion cyclotron resonance and nuclear magnetic resonance time-domain signals. In both cases, the method improved the FT spectra compared with the original ones. It was found that artifacts may result from the time delay between the end of the excitation event and the beginning of the acquisition period, as well as from time-dependent excitation wave forms such as chirp excitation. Possible ways to decrease or eliminate the artifacts are considered. Comparison to other spectral enhancement techniques is made. 18 refs., 11 figs.
Fourier transform ion cyclotron resonance versus time of flight for precision mass measurements
Kouzes, R.T.
1993-02-01
Both Fourier Transform Ion Cyclotron Resonance and ICR Time-of-Flight mass spectroscopy (FTICR-MS and ICR-TOF-MS, respectively) have been applied to precision atomic mass measurements. This paper reviews the status of these approaches and compares their limitations. Comparisons are made of FTICR-MS and ICR-TOF-MS for application to precision atomic mass measurements of stable and unstable nuclei, where the relevant scale is an accuracy of 1 keV and where halflives are longer than 10 milliseconds (optimistically). The atomic mass table is built up from mass chains, and ICR-MS brings a method of producing new types of mass chains to the mass measurement arena.
Fourier transform infrared spectroscopy techniques for the analysis of drugs of abuse
NASA Astrophysics Data System (ADS)
Kalasinsky, Kathryn S.; Levine, Barry K.; Smith, Michael L.; Magluilo, Joseph J.; Schaefer, Teresa
1994-01-01
Cryogenic deposition techniques for Gas Chromatography/Fourier Transform Infrared (GC/FT-IR) can be successfully employed in urinalysis for drugs of abuse with detection limits comparable to those of the established Gas Chromatography/Mass Spectrometry (GC/MS) technique. The additional confidence of the data that infrared analysis can offer has been helpful in identifying ambiguous results, particularly, in the case of amphetamines where drugs of abuse can be confused with over-the-counter medications or naturally occurring amines. Hair analysis has been important in drug testing when adulteration of urine samples has been a question. Functional group mapping can further assist the analysis and track drug use versus time.
Lay, L.T.
1994-12-31
The US Environmental Protection Agency (EPA) published amendments to the Clean Air Act (CAA) November 15, 1990. Title 3 of the CAA amendments included a list of 189 hazardous air pollutants (HAPs) for which emission test procedures must be established. An extractive emission test method, using Fourier Transform Infrared (FTIR) spectroscopy, is being developed for measuring HAP compounds. The FTIR procedure has the potential to detect over 100 of the listed compounds plus additional compounds such as criteria pollutants. This procedure has the ability to detect multiple compounds simultaneously and will provide near real-time data. Since the development of the extractive FTIR procedure, many source categories have been screened for HAP emissions using this technique. Modifications to the procedure have been made and validation testing has been performed. Currently, this technique is being used to collect data for maximum achievable control technology (MACT) standard development.
NASA Astrophysics Data System (ADS)
Hartland, Gregory V.; Henson, Bryan F.; Felker, Peter M.
1989-08-01
A perturbation theory analysis of Fourier transform (interferometric) versions of coherent Raman scattering and ionization-detected (or fluorescence-detected) stimulated Raman scattering is presented. The analysis has the principal aim of examining the information content of these spectroscopies as a function of the temporal characteristics of the excitation fields. The general conclusion of the analysis is that the information content of the techniques does not depend on excitation pulsewidths and, in particular, that spectral resolution is not limited by such pulsewidths. This is an important result because it allows for the use of short-pulse laser systems in implementing the methods. It is also shown, however, that the temporal characteristics of the excitation fields do influence the practical implementations of the spectroscopies significantly in that signal-to-noise ratios, Doppler broadening, etc. can be dependent on these characteristics.
Laser Mode Behavior of the Cassini CIRS Fourier Transform Spectrometer at Saturn
NASA Technical Reports Server (NTRS)
Brasunas, John C.
2012-01-01
The CIRS Fourier transform spectrometer aboard the NASA/ESA/ASI Cassini orbiter has been acquiring spectra of the Saturnian system since 2004. The CIRS reference interferometer employs a laser diode to trigger the interferogram sampling. Although the control of laser diode drive current and operating temperature are stringent enough to restrict laser wavelength variation to a small fraction of CIRS finest resolution element, the CIRS instrument does need to be restarted every year or two, at which time it may start in a new laser mode. By monitoring the Mylar absorption features in uncalibrated spectra due to the beam splitter Mylar substrate, it can be shown that these jumps are to adjacent modes and that most of the eight-year operation so far is restricted to three adjacent modes. For a given mode, the wavelength stability appears consistent with the stability of the laser diode drive curren.t and operating temperature.
Reference Ultraviolet Wavelengths of Cr III Measured by Fourier Transform Spectrometry
NASA Technical Reports Server (NTRS)
Smillie, D.G.; Pickering, J.C.; Smith, P.L.
2008-01-01
We report Cr III ultraviolet (UV) transition wavelengths measured using a high-resolution Fourier transform spectrometer (FTS), for the first time, available for use as wavelength standards. The doubly ionized iron group element spectra dominate the observed opacity of hot B stars in the UV, and improved, accurate, wavelengths are required for the analysis of astronomical spectra. The spectrum was excited using a chromium-neon Penning discharge lamp and measured with the Imperial College vacuum ultraviolet FTS. 140 classified 3d(exp 3)4s- 3d(exp 3)4p Cr III transition lines, in the spectral range 38,000 to 49,000 cm(exp -1) (2632 to 2041 A), the strongest having wavelength uncertainties less than one part in 10(exp 7), are presented.
A carrier removal technique for Fourier transform profilometry based on principal component analysis
NASA Astrophysics Data System (ADS)
Feng, Shijie; Chen, Qian; Zuo, Chao; Sun, Jiasong; Tao, Tianyang; Hu, Yan
2015-11-01
We present a carrier removal method for Fourier transform profilometry using the principal component analysis. The proposed approach is able to decompose the phase map into several principal components, in which the phase of the carrier can be extracted from the first dominant component acquired. It can cope well with the nonlinear carrier problem resulted from the divergent illumination which is commonly adopted in the fringe projection profilometry. It is effective, fully automatic and does not require the estimation for system geometrical parameters or the prior knowledge on the measured object. Further, the influence of the lens distortion is considered thus the carrier can be determined more accurately. The principle of the technique is verified by our experiments, showing that it performs well in both static and dynamic measurements.
NASA Astrophysics Data System (ADS)
Nagler, Peter C.; Fixsen, Dale J.; Kogut, Alan; Tucker, Gregory S.
2015-11-01
The detection of the primordial B-mode polarization signal of the cosmic microwave background (CMB) would provide evidence for inflation. Yet as has become increasingly clear, the detection of a such a faint signal requires an instrument with both wide frequency coverage to reject foregrounds and excellent control over instrumental systematic effects. Using a polarizing Fourier transform spectrometer (FTS) for CMB observations meets both of these requirements. In this work, we present an analysis of instrumental systematic effects in polarizing FTSs, using the Primordial Inflation Explorer (PIXIE) as a worked example. We analytically solve for the most important systematic effects inherent to the FTS—emissive optical components, misaligned optical components, sampling and phase errors, and spin synchronous effects—and demonstrate that residual systematic error terms after corrections will all be at the sub-nK level, well below the predicted 100 nK B-mode signal.
Authentication of canned fish packing oils by means of Fourier transform infrared spectroscopy.
Dominguez-Vidal, Ana; Pantoja-de la Rosa, Jaime; Cuadros-Rodríguez, Luis; Ayora-Cañada, María José
2016-01-01
The authentication of packing oil from commercial canned tuna and other tuna-like fish species was examined by means of attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) and chemometrics. Using partial least squares discriminant analysis (PLS-DA), it was possible to differentiate olive oil from seed oils. Discrimination of olive oil from high-oleic sunflower oil was possible, despite the latter having a degree of unsaturation more similar to olive oil than to sunflower oil. However, in the samples analyzed, sunflower oil could not be differentiated clearly from those labeled with the generic term "vegetable oil". Furthermore, the authentication of extra virgin olive oil, although more difficult, could be achieved using ATR-FTIR spectroscopy. The method could be applied regardless of fish type, without interference from fish lipids. PMID:26212950
The Phase Derivative Around Zeros of the Short-Time Fourier Transform
Balazs, Peter; Jaillet, Florent; Søndergaard, Peter
2011-01-01
The phase of the short-time Fourier transform (STFT) is sometimes considered difficult to interpret. However, the phase information is important for improved analysis and processing. The phase derivative, in particular, is essential for the reassignment method or the phase vocoder algorithm. In order to understand the phase derivative of the STFT more thoroughly, we describe an interesting phenomenon, a recurring pattern in the neighborhood of zeros. Contrary to the possible expectation of an arbitrary behavior, the phase derivative always shows a singularity with the same characteristic shape with a negative and a positive peak of infinite height at these points. We show this behavior in a numerical investigation, present a simple explicit analytic example and then do a complete analytical treatment. For this we present several intermediate results about the regularity of the STFT for Schwartz windows, which are of independent interest.
NASA Astrophysics Data System (ADS)
Montejo, Ludguier D.; Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2013-03-01
We apply the Fourier Transform to absorption and scattering coefficient images of proximal interphalangeal (PIP) joints and evaluate the performance of these coefficients as classifiers using receiver operator characteristic (ROC) curve analysis. We find 25 features that yield a Youden index over 0.7, 3 features that yield a Youden index over 0.8, and 1 feature that yields a Youden index over 0.9 (90.0% sensitivity and 100% specificity). In general, scattering coefficient images yield better one-dimensional classifiers compared to absorption coefficient images. Using features derived from scattering coefficient images we obtain an average Youden index of 0.58 +/- 0.16, and an average Youden index of 0.45 +/- 0.15 when using features from absorption coefficient images.
NASA Technical Reports Server (NTRS)
Tarbell, T. D.; Title, A. M.
1976-01-01
Fourier techniques have been exhaustively calibrated using Unno's (1956) results for the absorption profile of a simple Zeeman triplet. If a simple transformation is applied to the normalized line depths, then magnetic-field strengths and inclination angles can be measured very accurately from noisy saturated line profiles. Systematic errors caused by saturation effects can be estimated and reduced by varying one parameter. When a significant fraction of the line profile is unsplit and unpolarized, large errors may be made in measurements of low fields, unless the line is sufficiently weak. For a weak line, a vertical field of 1600 gauss can be measured to 10% accuracy even when 70% of the line profile is stray light. These stray-light errors are troublesome in measuring fields of gaps and pores but not sunspots. Numerical results of the error analysis are presented graphically.
Use of in situ Fourier transform infrared spectroscopy to study freezing and drying of cells.
Wolkers, Willem F; Oldenhof, Harriëtte
2015-01-01
An infrared spectrum gives information about characteristic molecular vibrations of specific groups in molecules. Fourier transform infrared spectroscopy can be applied to study lipids and proteins in cells or tissues. Spectra can be collected during cooling, heating, or dehydration of a sample using a temperature-controlled sample holder or a sample holder for controlled dehydration. In the current chapter, acquisition and analysis of infrared spectra during cooling, warming, or dehydration is described. Spectra analysis involving assessment of specific band positions, areas, or ratios is described. Special emphasis is given on studying membrane phase behavior and protein denaturation in cells or tissues. In addition, methods are presented to determine the water-to-ice phase change during freezing, dehydration kinetics, and the glass transition temperature of amorphous systems. PMID:25428005
NASA Astrophysics Data System (ADS)
Creux, A.; Morand, A.; Benech, P.; Martin, B.; Grosa, G.; Le Coarer, E.; Kern, P.
2012-01-01
The characterization of a Leaky Loop Integrated Fourier Transform Spectrometer (LLIFTS) in integrated optics is described in the visible and the near infrared spectral domain. The device is realized using ion-exchange technology in a glass substrate. LLIFTS is compact, costless with no moveable parts. Its principle consists in a two beam interferometer in planar design using a leaky loop waveguide structure. The advantage of the design of the LLIFTS structure is to control the shape of the interference pattern in order to measure a high contrast and fringe spacing well sampled by a 2048 pixels camera directly at the output of the component. Spectral resolution of 7nm at 1500nm and 2nm at 633nm are obtained.
NASA Astrophysics Data System (ADS)
Gerdjikov, Vladimir S.; Grahovski, Georgi G.; Mikhailov, Alexander V.; Valchev, Tihomir I.
2011-10-01
A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes of soliton solutions associated with the Lax operator. Next, by using the Wronskian relations, the mapping between the potential and the minimal sets of scattering data is constructed. Furthermore, completeness relations for the 'squared solutions' (generalized exponentials) are derived. Next, expansions of the potential and its variation are obtained. This demonstrates that the interpretation of the inverse scattering method as a generalized Fourier transform holds true. Finally, the Hamiltonian structures of these generalized multi-component Heisenberg ferromagnetic (MHF) type integrable models on A.III-type symmetric spaces are briefly analyzed.
Terahertz time-domain and Fourier-transform infrared spectroscopy of traditional Korean pigments
NASA Astrophysics Data System (ADS)
Hong, Taeyoon; Choi, Kyujin; Ha, Taewoo; Park, Byung Cheol; Sim, Kyung Ik; Kim, Jong Hyeon; Kim, Jae Hoon; Kwon, Jy Eun; Lee, Sanghyun; Kang, Dai Ill; Lee, Han Hyoung
2014-03-01
Representative traditional Korean pigments (oyster shell white [hobun], massicot [miltaseung], indigo [jjok], azurite [seokcheong], malachite [seokrok], and red lead [yeondan]) have been studied with terahertz time-domain spectroscopy (THz-TDS) and Fourier-transform infrared spectroscopy (FTIRS) over the spectral region of 0.1-7.5 THz. Both the refractive index n and the extinction coefficient k were simultaneously and independently determined in the terahertz region without a Kramers-Kronig analysis while the absoprtion coefficient spectra were acquired in the infrared region. All pigments studied in the present work exhibited a set of characteristic absorption peaks unique to the pigment species in addition to a background that increased with increasing frequency. Our study demonstrates that terahertz and infrared techniques can be useful identification and diagnostic tools for the traditional Korean pigments used in heritage buildings and artworks.
Li, Chao; Yang, Sheng-Chao; Guo, Qiao-Sheng; Zheng, Kai-Yan; Wang, Ping-Li; Meng, Zhen-Gui
2016-01-01
A combination of Fourier transform infrared spectroscopy with chemometrics tools provided an approach for studying Marsdenia tenacissima according to its geographical origin. A total of 128 M. tenacissima samples from four provinces in China were analyzed with FTIR spectroscopy. Six pattern recognition methods were used to construct the discrimination models: support vector machine-genetic algorithms, support vector machine-particle swarm optimization, K-nearest neighbors, radial basis function neural network, random forest and support vector machine-grid search. Experimental results showed that K-nearest neighbors was superior to other mathematical algorithms after data were preprocessed with wavelet de-noising, with a discrimination rate of 100% in both the training and prediction sets. This study demonstrated that FTIR spectroscopy coupled with K-nearest neighbors could be successfully applied to determine the geographical origins of M. tenacissima samples, thereby providing reliable authentication in a rapid, cheap and noninvasive way. PMID:26233789
Nagib, Samy; Rau, Jörg; Sammra, Osama; Lämmler, Christoph; Schlez, Karen; Zschöck, Michael; Prenger-Berninghoff, Ellen; Klein, Guenter; Abdulmawjood, Amir
2014-01-01
The present study was designed to investigate the potential of Fourier transform infrared (FT-IR) spectroscopy to identify Trueperella (T.) pyogenes isolated from bovine clinical mastitis. FT-IR spectroscopy was applied to 57 isolates obtained from 55 cows in a period from 2009 to 2012. Prior to FT-IR spectroscopy these isolates were identified by phenotypic and genotypic properties, also including the determination of seven potential virulence factor encoding genes. The FT-IR analysis revealed a reliable identification of all 57 isolates as T. pyogenes and a clear separation of this species from the other species of genus Trueperella and from species of genus Arcanobacterium and Actinomyces. The results showed that all 57 isolates were assigned to the correct species indicating that FT-IR spectroscopy could also be efficiently used for identification of this bacterial pathogen. PMID:25133407
Thompson, Sandra E.; Foster, Nancy S.; Johnson, Timothy J.; Valentine, Nancy B.; Amonette, James E.
2003-08-28
Fourier Transform Infrared Photoacoustic Spectroscopy (FTIR-PAS) has been applied for the first time to the identification and speciation of bacterial spores. With minimal preparation the spores were deposited into the photoacoustic sample cup and their spectra recorded. A total of 40 different samples of 5 different strains of Bacillus spores were analyzed: Bacillus subtilis ATCC 49760, Bacillus atrophaeus ATCC 49337, Bacillus subtilis 6051, Bacillus thuringiensis ssp. kurstaki, and Bacillus globigii Dugway. The statistical methods used included principal-component analysis (PCA), classification and regression trees (CART), and Mahalanobis-distance calculations. Internal cross-validation studies successfully classify the spores according to their bacterial strain in 38 of 40 cases (95%) and 36 of 40 (90%) in cross-validation. Analysis of fifteen blind samples, which included library and other spores, and nonbacterial materials, resulted in correct strain classification the blind samples that were members of the library and correct rejection of the nonbacterial samples.
Behr, Bradford B.; Cenko, Andrew T.; Hajian, Arsen R.; Meade, Jeff; McMillan, Robert S.; Murison, Marc; Hindsley, Robert
2011-07-15
We present orbital parameters for six double-lined spectroscopic binaries ({iota} Pegasi, {omega} Draconis, 12 Booetis, V1143 Cygni, {beta} Aurigae, and Mizar A) and two double-lined triple star systems ({kappa} Pegasi and {eta} Virginis). The orbital fits are based upon high-precision radial velocity (RV) observations made with a dispersed Fourier Transform Spectrograph, or dFTS, a new instrument that combines interferometric and dispersive elements. For some of the double-lined binaries with known inclination angles, the quality of our RV data permits us to determine the masses M{sub 1} and M{sub 2} of the stellar components with relative errors as small as 0.2%.
Nam, Yun Sik; Park, Jin Sook; Kim, Nak-Kyoon; Lee, Yeonhee; Lee, Kang-Bong
2014-07-01
Seals are traditionally used in the Far East Asia to stamp an impression on a document in place of a signature. In this study, an accuser claimed that a personal contract regarding mining development rights acquired by a defendant was devolved to the accuser because the defendant stamped the devolvement contract in the presence of the accuser and a witness. The accuser further stated that the seal ink stamped on the devolvement contract was the same as that stamped on the development rights application document. To verify this, the seals used in two documents were analyzed using micro-attenuated total reflectance Fourier transform infrared spectroscopy and infrared spectra. The findings revealed that the seals originated from different manufacturers. Thus, the accuser's claim on the existence of a devolvement contract was proved to be false. PMID:24844350
Nanowire humidity optical sensor system based on fast Fourier transform technique
NASA Astrophysics Data System (ADS)
Rota-Rodrigo, S.; Pérez-Herrera, R.; Lopez-Aldaba, A.; López Bautista, M. C.; Esteban, O.; López-Amo, M.
2015-09-01
In this paper, a new sensor system for relative humidity measurements based on its interaction with the evanescent field of a nanowire is presented. The interrogation of the sensing head is carried out by monitoring the fast Fourier transform phase variations of one of the nanowire interference frequencies. This method is independent of the signal amplitude and also avoids the necessity of tracking the wavelength evolution in the spectrum, which can be a handicap when there are multiple interference frequency components with different sensitivities. The sensor is operated within a wide humidity range (20%-70% relative humidity) with a maximum sensitivity achieved of 0.14rad/% relative humidity. Finally, due to the system uses an optical interrogator as unique active element, the system presents a cost-effective feature.
Liu, S.; Haigis, J.R.; DiTaranto, M.B.
1995-12-31
A computer algorithm, which matches theoretical to measured infrared reflectance spectra, was successfully employed to determine multiple thin film properties of integrated circuits. Properties, such as film thickness, dielectric constant, and free carrier concentration were determined for a variety of important electronic films both in the laboratory and in process reactors. The latter measurements were accomplished by optically interfacing a Fourier transform infrared (FT-IR) spectrometer to several reactors. Real-time process monitoring allowed determination of deposition rate, free carrier activation temperature, and the influence of reactor conditions on film properties. Finally, these measurements were nondestructive, performed in-situ and within seconds, demonstrating the utility of this method for real-time process monitoring and control.
NASA Astrophysics Data System (ADS)
Yi, Wei-song; Cui, Dian-sheng; Li, Zhi; Wu, Lan-lan; Shen, Ai-guo; Hu, Ji-ming
2013-01-01
The manuscript has investigated the application of near-infrared (NIR) spectroscopy for differentiation gastric cancer. The 90 spectra from cancerous and normal tissues were collected from a total of 30 surgical specimens using Fourier transform near-infrared spectroscopy (FT-NIR) equipped with a fiber-optic probe. Major spectral differences were observed in the CH-stretching second overtone (9000-7000 cm-1), CH-stretching first overtone (6000-5200 cm-1), and CH-stretching combination (4500-4000 cm-1) regions. By use of unsupervised pattern recognition, such as principal component analysis (PCA) and cluster analysis (CA), all spectra were classified into cancerous and normal tissue groups with accuracy up to 81.1%. The sensitivity and specificity was 100% and 68.2%, respectively. These present results indicate that CH-stretching first, combination band and second overtone regions can serve as diagnostic markers for gastric cancer.
Horikawa, Mami; Akai, Nobuyuki; Kawai, Akio; Shibuya, Kazuhiko
2014-05-01
Several protic ionic liquids (PILs) with a wide range of pK(a) differences (?pK(a)) between the parent acid and base molecules were thermally evaporated in vacuum, trapped on a CsI plate by a cryogenic neon matrix-isolation method, and studied by Fourier transform infrared spectroscopy and density functional theory calculations. The parent neutral molecules and proton-transferred cation-anion pair species were identified as chemical components evaporated from the PILs with lower and higher ?pK(a) values, respectively. The ?pK(a)-dependent vaporization mechanism is discussed in terms of thermodynamic equilibrium between acid-base and anion-cation systems in the liquid phase. PMID:24724531
Kelly, Damien P.; Hennelly, Bryan M.; Sheridan, John T
2005-05-01
The optical fractional Fourier transform (OFRT) in combination with speckle photography has previously been used to measure the magnitude of surface tilting and translation. Previous OFRT techniques used to determine motion have not been able to discern the direction of the tilt and translation. A simple new approach involving use of correlation is presented to overcome this limitation. Controlled variation of the minimum resolution and dynamical range of measurement is demonstrated. It is then experimentally confirmed that if a rigid body's motion is captured by two OFRT systems of different orders, the direction and magnitude of both the tilting and the in-plane translation motion of the body can be independently determined without a priori knowledge. The experimental results confirm the validity of previous theoretical predictions.
NASA Astrophysics Data System (ADS)
Pan, Jun-Yang; Xie, Yi
2013-11-01
In the context of the fact that Einstein's general relativity has become an inevitable part of deep space missions, we will extend previous works on relativistic transformation between the proper time ? of a clock onboard a spacecraft orbiting Mars and the Barycentric Coordinate Time (TCB) by taking the clock offset into account and investigate its accessibility by Fourier analysis on the residuals after fitting the ?-TCB curve in terms of n-th order polynomials. We find that if the accuracy of a clock can achieve better than ~ 10-5 s or ~ 10-6 s (depending on the type of clock offset) in one year after calibration, the relativistic effects on the difference between ? and TCB will need to be carefully considered.
NASA Astrophysics Data System (ADS)
Li, Chao; Yang, Sheng-Chao; Guo, Qiao-Sheng; Zheng, Kai-Yan; Wang, Ping-Li; Meng, Zhen-Gui
2016-01-01
A combination of Fourier transform infrared spectroscopy with chemometrics tools provided an approach for studying Marsdenia tenacissima according to its geographical origin. A total of 128 M. tenacissima samples from four provinces in China were analyzed with FTIR spectroscopy. Six pattern recognition methods were used to construct the discrimination models: support vector machine-genetic algorithms, support vector machine-particle swarm optimization, K-nearest neighbors, radial basis function neural network, random forest and support vector machine-grid search. Experimental results showed that K-nearest neighbors was superior to other mathematical algorithms after data were preprocessed with wavelet de-noising, with a discrimination rate of 100% in both the training and prediction sets. This study demonstrated that FTIR spectroscopy coupled with K-nearest neighbors could be successfully applied to determine the geographical origins of M. tenacissima samples, thereby providing reliable authentication in a rapid, cheap and noninvasive way.
Coleman, W. M., III; Gordon, B. M.; Lawrence, B. M.
1989-02-01
Matrix isolation Fourier transform infrared spectra (MI/FT-IR), massspectra (MS), carbon-13 Nuclear Magnetic Resonance (/sup 13/C-NMR) spectra,condensed-phase infrared spectra, and vapor-phase infrared (IR)spectra are presented for a series of terpene compounds. Subtle differencesin positional and configurational isomers commonly found withterpenes could be easily detected by the MI/FT-IR spectra. The resultsare comparable in some aspects to those obtainable from /sup 13/C-NMR andthin-film IR; however, most importantly, they are acquired at the lownanogram level for MI/FT-IR, as compared to the milligram level forthe other techniques. These results represent an advance in the technologyavailable for the analysis of complex mixtures such as essential oilscontaining terpene-like molecules.
Label-free identification of individual bacteria using Fourier transform light scattering
NASA Astrophysics Data System (ADS)
Jo, YoungJu; Jung, JaeHwang; Kim, Min-hyeok; Park, HyunJoo; Kang, Suk-Jo; Park, YongKeun
2015-06-01
Rapid identification of bacterial species is crucial in medicine and food hygiene. In order to achieve rapid and label-free identification of bacterial species at the single bacterium level, we propose and experimentally demonstrate an optical method based on Fourier transform light scattering (FTLS) measurements and statistical classification. For individual rod-shaped bacteria belonging to four bacterial species (Listeria monocytogenes, Escherichia coli, Lactobacillus casei, and Bacillus subtilis), two-dimensional angle-resolved light scattering maps are precisely measured using FTLS technique. The scattering maps are then systematically analyzed, employing statistical classification in order to extract the unique fingerprint patterns for each species, so that a new unidentified bacterium can be identified by a single light scattering measurement. The single-bacterial and label-free nature of our method suggests wide applicability for rapid point-of-care bacterial diagnosis.
Bonnamy, Anthony; Hermsdorf, Dana; Ueberschaer, Roman; Signorell, Ruth
2005-05-15
A new apparatus for the in situ characterization of the rapid expansion of supercritical solutions (RESS) by Fourier transform infrared spectroscopy is presented. The infrared characterization is complemented by particle sizing with a scanning mobility particle sizer, by three-wavelengths-extinction measurements, and by scanning electron microscopy. Several examples show that a wide range of information about particle properties can be obtained with this setup. One new aspect is the possibility to expand into the vacuum which also allows us to investigate the conditions in the collision-free region before the Mach disk. These investigations elucidate that in the free jet region the solvent CO{sub 2} condenses to particles with mean radii >50 nm for pre-expansion pressures between 100-400 bar and temperatures between 298-398 K.
Waveguide Chirped-Pulse Fourier Transform Microwave Spectroscopy of Allyl Bromide
NASA Astrophysics Data System (ADS)
McCabe, Morgan N.; Shipman, Steven
2014-06-01
The rotational spectrum of allyl bromide was recorded from 8.7 to 26.5 GHz at -20 °C with a waveguide chirped-pulse Fourier transform microwave spectrometer. The rotational spectrum of allyl bromide has been previously studied by Niide and coworkers. However, previous assignments of this spectrum only extended to J = 12 and K_a = 1. Newly acquired data from our spectrometer has allowed us to extend the previous work to higher values of J and K_a, leading to significant improvements in the distortion constants in particular. Comparisons between the spectra and conformational preferences of the allyl halides will also be discussed. Y. Niide, M, Takano,T. Satoh, and Y. Sasada J. Mol. Spectrosc., 63, 108(1976) Niide, Yuzuru, J. Sci. Hiroshima Univ., Ser. A, 48, 1(1984)
NASA Astrophysics Data System (ADS)
Irudayaraj, Joseph; Yang, Hong; Sakhamuri, Sivakesava
2002-03-01
Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) was used to differentiate and identify microorganisms on a food (apple) surface. Microorganisms considered include bacteria ( Lactobacillus casei, Bacillus cereus, and Escherichia coli), yeast ( Saccharomyces cerevisiae), and fungi ( Aspergillus niger and Fusarium verticilliodes). Discriminant analysis was used to differentiate apples contaminated with the different microorganisms from uncontaminated apple. Mahalanobis distances were calculated to quantify the differences. The higher the value of the Mahalanobis distance metric between different microorganisms, the greater is their difference. Additionally, pathogenic (O157:H7) E. coli was successfully differentiated from non-pathogenic strains. Results demonstrate that FTIR-PAS spectroscopy has the potential to become a non-destructive analysis tool in food safety related research.
NASA Astrophysics Data System (ADS)
Yang, Hong; Irudayaraj, Joseph
2003-02-01
Fourier transform (FT) Raman spectroscopy was used for non-destructive characterization and differentiation of six different microorganisms including the pathogen Escherichia coli O157:H7 on whole apples. Mahalanobis distance metric was used to evaluate and quantify the statistical differences between the spectra of six different microorganisms. The same procedure was extended to discriminate six different strains of E. coli. The FT-Raman procedure was not only successful in discriminating the different E. coli strain but also accurately differentiated the pathogen from non-pathogens. Results demonstrate that FT-Raman spectroscopy can be an excellent tool for rapid examination of food surfaces for microorganism contamination and for the classification of microbial cultures.
Feng, Ming-Chun; Xu, Liang; Gao, Min-Guang; Jiao, Yang; Wei, Xiu-Li; Jin, Ling; Cheng, Si-Yang; Li, Xiang-Xian; Feng, Shu-Xiang
2012-12-01
The authors measured IR transmission spectra of two different concentrations of Bacillus subtilis spores by using Fourier transform infrared spectroscopy (FTIR) technology. The mass extinction cross section k of Bacillus subtilis spores was calculated according to Lambert-Beer law and the imaginary part n(i) of the complex refractive index was also calculated through k. The real part n(r) of the complex refractive index was derived from the KK (Kramers-Kronig) relationship and the experimental results were also analyzed and discussed with the study of measurement and analysis method of the complex refractive index on Bacillus subtilis spores, it is of great significance to further research the absorption and scattering characteristics, and to broaden the measurement and remote sensing technology method of the biological aerosols. PMID:23427533
Fourier Transform Raman Spectroscopy of Photoactive Proteins with Near-Infrared Excitation
Johnson, Carey K.; Rubinovitz, Ronald
1990-07-01
from pigments other than BPh. Several of the bands observed in Fig. 2B correlate well with previously ob- 1104 Volume 44, Number 7, 1990 0.02 LU I.- Z uJ _> I.- ~ 0.016 0.012 200 I I I I I I I I 400 600 800 1000 WAVENUMBER (cm "1) 0.024 0....10 I J I I I l l i B 0.08 uJ F- z 0.06 ILl _> I,- 0.04 0'02 ~ " - ~ ~ I l I , J l 1000 1200 1400 1600 1800 WAVENUMBER (cm "1) FIG. 2. Fourier transformed Raman spectrum of reaction centers of R. sphaeroides xcited with 1.0 W at 1.06 #m...
NASA Astrophysics Data System (ADS)
Tang, Bin; Jiang, ShengBao; Jiang, Chun; Zhu, Haibin
2014-07-01
A hollow sinh-Gaussian beam (HsG) is an appropriate model to describe the dark-hollow beam. Based on Collins integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of a HsG beam passing through fractional Fourier transform (FRFT) optical systems with and without apertures have been studied in detail by some typical numerical examples. The results obtained using the approximate analytical formula are in good agreement with those obtained using numerical integral calculation. Further, the studies indicate that the normalized intensity distribution of the HsG beam in FRFT plane is closely related with not only the fractional order but also the beam order and the truncation parameter. The FRFT optical systems provide a convenient way for laser beam shaping.
Propagation of a general-type beam through a truncated fractional Fourier transform optical system.
Zhao, Chengliang; Cai, Yangjian
2010-03-01
Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping. PMID:20208958
A Discussion of Using a Reconfigurable Processor to Implement the Discrete Fourier Transform
NASA Technical Reports Server (NTRS)
White, Michael J.
2004-01-01
This paper presents the design and implementation of the Discrete Fourier Transform (DFT) algorithm on a reconfigurable processor system. While highly applicable to many engineering problems, the DFT is an extremely computationally intensive algorithm. Consequently, the eventual goal of this work is to enhance the execution of a floating-point precision DFT algorithm by off loading the algorithm from the computing system. This computing system, within the context of this research, is a typical high performance desktop computer with an may of field programmable gate arrays (FPGAs). FPGAs are hardware devices that are configured by software to execute an algorithm. If it is desired to change the algorithm, the software is changed to reflect the modification, then download to the FPGA, which is then itself modified. This paper will discuss methodology for developing the DFT algorithm to be implemented on the FPGA. We will discuss the algorithm, the FPGA code effort, and the results to date.
Prepreg cure monitoring using diffuse reflectance-FTIR. [Fourier Transform Infrared Technique
NASA Technical Reports Server (NTRS)
Young, P. R.; Chang, A. C.
1984-01-01
An in situ diffuse reflectance-Fourier transform infrared technique was developed to determine infrared spectra of graphite fiber prepregs as they were being cured. A bismaleimide, an epoxy, and addition polyimide matrix resin prepregs were studied. An experimental polyimide adhesive was also examined. Samples were positioned on a small heater at the focal point of diffuse reflectance optics and programmed at 15 F/min while FTIR spectra were being scanned, averaged, and stored. An analysis of the resulting spectra provided basic insights into changes in matrix resin molecular structure which accompanied reactions such as imidization and crosslinking. An endo-exothermal isomerization involving reactive end-caps was confirmed for the addition polyimide prepregs. The results of this study contribute to a fundamental understanding of the processing of composites and adhesives. Such understanding will promote the development of more efficient cure cycles.
Fourier-transform microwave spectroscopy of the vinoxy radical, CH2CHO
NASA Astrophysics Data System (ADS)
Endo, Yasuki; Nakajima, Masakazu
2014-07-01
Pure rotational transitions of the vinoxy radical in the ground vibronic state have been observed by Fourier-transform microwave spectroscopy in the cm-wave region and double resonance spectroscopy in the mm-wave region. Total of 6 rotational transitions are newly observed in the present work, which are least squares fitted together with the mm-wave data observed previously (Endo et al., 1985). The hyperfine coupling constants for the third proton in the -CHO moiety of the vinoxy radical have been determined precisely for the first time. Four b-type transitions, that escaped to be detected in the previous study in the mm-wave region, have provided a more accurate set of molecular constants for the ground vibronic state.
The Ccn (tilde{X}2?1/2) Radical Revisited: New Fourier Transform Microwave Measurements
NASA Astrophysics Data System (ADS)
Anderson, J. K.; Halfen, D. T.; Ziurys, L. M.
2012-06-01
The CCN (tilde{X}2?1/2) radical was first studied by Ohshima & Endo in 1995, who measured the lowest rotational transition, J = 3/2 ? 1/2, in the ? = 1/2 ladder near 35 GHz. No subsequent work has been performed for this species to date. Here we present measurements of the J = 5/2 ? 3/2 rotational transition of CCN (? = 1/2) near 59 GHz, recorded using Fourier transform microwave (FTMW) spectroscopy. CCN was synthesized in a supersonic expansion from a dilute mixture of (CN)2 and CH_4 in argon, in the presence of a DC discharge. Both lambda-doublets were recorded, each consisting of three hyperfine components. These measurements, combined with past data, have been analyzed and refined spectroscopic constants have been established. Studies of additional rotational transitions are currently being conducted.
NASA Astrophysics Data System (ADS)
Kamnev, Alexander A.; Calce, Enrica; Tarantilis, Petros A.; Tugarova, Anna V.; De Luca, Stefania
2015-01-01
Chemically modified pectin derivatives obtained by partial esterification of its hydroxyl moieties with fatty acids (FA; oleic, linoleic and palmitic acids), as well as the initial apple peel pectin were comparatively characterised using diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy. Characteristic changes observed in DRIFT spectra in going from pectin to its FA esters are related to the corresponding chemical modifications. Comparing the DRIFT spectra with some reported data on FTIR spectra of the same materials measured in KBr or NaCl matrices has revealed noticeable shifts of several polar functional groups both in pectin and in its FA-esterified products induced by the halide salts. The results obtained have implications for careful structural analyses of biopolymers with hydrophilic functional groups by means of different FTIR spectroscopic methodologies.
NASA Astrophysics Data System (ADS)
Schindler, Thomas; Berg, Christian; Niedner-Schatteburg, Gereon; Bondybey, Vladimir E.
1996-03-01
High resolution Fourier-transform ion cyclotron resonance (FT-ICR) mass spectroscopy is used to investigate reactions of large ionic water clusters H+(H2O)n and X-(H2O)n (n=1-100, X=O or OH). Reactions of the clusters with chlorine nitrate, important ``reservoir compound'' involved in the stratospheric ozone chemistry, are investigated to evaluate the importance of heterogeneously catalyzed reactions for ozone depletion. It is found that reactions of both cationic and anionic clusters result in effective hydrolysis of chlorine nitrate and return of the more active hypochlorous acid, HOCl into the gas phase. The chemistry of clusters is discussed, and its validity and relevance as a model for ``real life'' processes in the so-called polar stratospheric clouds (PSC's) is assessed.
NASA Astrophysics Data System (ADS)
Ogilvie, Jennifer
2010-03-01
Two-dimensional (2D) Fourier transform electronic spectroscopy has recently emerged as a powerful tool for the study of energy transfer in complex condensed-phase systems. Its experimental implementation is challenging but can be greatly simplified by implementing a pump-probe geometry, where the two phase-stable collinear pump pulses are created with an acousto-optic pulse-shaper. This approach also allows the use of a continuum probe pulse, expanding the available frequency range of the detection axis and allowing studies of energy transfer and electronic coupling over a broad range of frequencies. We discuss several benefits of 2D electronic spectroscopy and present 2D data on the D1-D2 reaction center complex of Photosystem II from spinach. We discuss the ability of 2D spectroscopy to distinguish between current models of energy and charge transfer in this system.
NASA Astrophysics Data System (ADS)
Chen, Cheng; Liang, Jingqiu; Liang, Zhongzhu; Lü, Jinguang; Qin, Yuxin; Tian, Chao; Wang, Weibiao
2015-12-01
A method of "slope splicing" is proposed to build a tall-stepped mirror with high precision in a stepped-mirror-based static Fourier transform infrared spectrometer. The structural parameters were designed, and their errors were analyzed. We present the test results and an analysis of the combined effect of the errors on the recovered spectrum. The spectrum-constructing error of the constructed spectrum, 5.81%, meets the requirements for the system and suitable for realization of a miniaturized spectrometer. We performed experiments with the tall-stepped mirror to obtain the interferogram and spectrum of a silicon carbide light source. Further work is needed to optimize the capability of the system.
Accelerating the 2-point and 3-point galaxy correlation functions using Fourier transforms
Slepian, Zachary
2015-01-01
Though Fourier Transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle surveys because the line-of-sight direction is not constant on the Cartesian grid. Here we show how FTs can be used to compute the multipole moments of the anisotropic 2PCF. We also show how FTs can be used to accelerate the 3PCF algorithm of Slepian & Eisenstein (2015). In both cases, these FT methods allow one to avoid the computational cost of pair counting, which scales as the square of the number density of objects in the survey. With the upcoming large datasets of DESI, Euclid, and LSST, FT techniques will therefore offer an important complement to simple pair or triplet counts.
Pietrzak,L.; Miller, S.
2005-01-01
The distribution of water in soybean seeds during imbibition varies with the chemical composition of the tissue. To understand the dynamics of imbibition, the proteins, lipids, and carbohydrates of the cotyledons and hilum region in mature soybean seeds were mapped using synchrotron Fourier transformed infrared microspectroscopy, based on characteristic peaks for each component: amide I at 1650 cm{sup -1} and amide II at 1550 cm{sup -1} for protein, lipid ester stretch at 1545 cm{sup -1}, and the region from 1200 to 900 cm{sup -1} for carbohydrates. The amount and configuration of the proteins varied across the cotyledon, as well as the amount of lipid and carbohydrate. It was found that protein distribution across the cotyledon is similar to water distribution during imbibition. The chemistry of the hilum region was also studied, as this is the point of water entry, and differences in the chemical composition of the tissues studied were observed.
Fast Fourier transform analysis of sounds made while swallowing various foods.
Taniwaki, Mitsuru; Kohyama, Kaoru
2012-10-01
The cervical auscultation method was applied to investigate sounds generated while swallowing various foods with unique physical properties, including liquid (water), semiliquid (yogurt), and solid (konjac jelly). To study the differences among swallowing sounds for various foods, fast Fourier transform (FFT) analysis was applied to signals that were attributed to the flow of a food bolus, which is a swallowable soft mass of chewed food. An FFT program was developed that enabled the calculation of a spectrum for a specified region of time domain swallowing sound signals. The intensity of spectra in the frequency range between 400 and 1000 Hz significantly differed: liquid > semiliquid > solid. The FFT spectrum in this range was suggested to represent the frequency characteristics of the swallowing sounds of various foods. PMID:23039442
Schnegg, Alexander; Behrends, Jan; Lips, Klaus; Bittl, Robert; Holldack, Karsten
2009-08-21
Frequency domain Fourier transform THz electron paramagnetic resonance (FD-FT THz-EPR) based on coherent synchrotron radiation (CSR) is presented as a novel tool to ascertain very large zero field splittings in transition metal ion complexes. A description of the FD-FT THz-EPR at the BESSY II storage ring providing CSR in a frequency range from 5 cm(-1) up to 40 cm(-1) at external magnetic fields from -10 T to +10 T is given together with first measurements on the single molecule magnet Mn(12)Ac where we studied DeltaM(S) = +/-1 spin transition energies as a function of the external magnetic field and temperature. PMID:19639156
Du, Jian-Hua; Zhang, Ren-Cheng
2008-03-01
CO was chosen as an early fire detection factor through analyzing all kinds of characters in the process of fires, and an experiment system was established based on Fourier transform infrared spectrometer. Through this system, lots of early fire experiments were carried out, and the authors got the CO concentrations of all kinds of materials. Using the concentration of CO, an autoregressive integrated model was established by time series analysis, then the process characters phi1 and phi2 were extracted from them. Through analyzing the phase graph of the process characters, it was found that the real fires and the nuisance fires were distributed in different regions. Plenty of experiments indicate that this detection method can discriminate between real fire sources and nuisance sources quickly when fires occur. PMID:18536412