Quantum Fourier Transform Over Galois Rings
Yong Zhang
2009-04-16
Galois rings are regarded as "building blocks" of a finite commutative ring with identity. There have been many papers on classical error correction codes over Galois rings published. As an important warm-up before exploring quantum algorithms and quantum error correction codes over Galois rings, we study the quantum Fourier transform (QFT) over Galois rings and prove it can be efficiently preformed on a quantum computer. The properties of the QFT over Galois rings lead to the quantum algorithm for hidden linear structures over Galois rings.
Fourier-transforming with quantum annealers
NASA Astrophysics Data System (ADS)
Hen, Itay
2014-07-01
We introduce a set of quantum adiabatic evolutions that we argue may be used as `building blocks', or subroutines, in the onstruction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT) with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.
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.
Purple bacteria and quantum Fourier transform
Lipovaca, S
2007-01-01
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 ...
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.
Cavity QED implementation of the discrete quantum Fourier transform
Scully, Marlan O.; Zubairy, M. Suhail
2002-01-01
We present a scheme for the implementation of the discrete quantum Fourier transform using cavity quantum electrodynamics. In the proposed scheme a series of atoms whose atomic coherence carries the input state passes through a series of cavities...
From fractional Fourier transformation to quantum mechanical fractional squeezing transformation
NASA Astrophysics Data System (ADS)
Lv, Cui-Hong; Fan, Hong-Yi; Li, Dong-Wei
2015-02-01
By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function, i.e., tan ? ? tanh ?, sin ? ? sinh ?, we find the quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within the ordered product of operators (IWOP) we derive the unitary operator responsible for the FrST, which is composite and is made of ei?a†a/2 and exp . The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches. Project supported by the National Natural Science Foundation of China (Grant No. 11304126), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130532), the Natural Science Fund for Colleges and Universities in Jiangsu Province, China (Grant No. 13KJB140003), the Postdoctoral Science Foundation of China (Grant No. 2013M541608), and the Postdoctoral Science Foundation of Jiangsu Province, China (Grant No. 1202012B).
Scaling and Better Approximating Quantum Fourier Transform by Higher Radices
Zilic, Zeljko
the approximation bounds for QFT. Index Terms--Fourier transform, quantum computing, multivalued logic circuits, multivariable systems, Walsh functions. Ã? 1 INTRODUCTION QUANTUM computing [15] has so far been demonstrated, as well as being useful in cryptographic applications. Several working quantum-computing systems have
Quantum Fourier Transform (QFT) over Galois fields
NASA Astrophysics Data System (ADS)
Rodriguez, Sergio
2013-05-01
Galois fields are constantly gaining importance in quantum computing due to their wide usage in quantum error correction algorithms, and so it becomes relevant to define the QFT over Galois fields because of its main role in many of the most important quantum algorithms. The present article illustrates how to generalize the QFT so it can be applied over Galois fields and explains several examples of the application of the QFT over the simplest Galois fields. In particular the QFT will be defined for the Galois fields F2, F4 and GF(9), also the application of the QFT and the operations involved will be made using the Maple mathematical software.
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 wave-packet basis for quantum information in the atom. A change of basis from energy levels to wave
Quantum control in two-dimensional Fourier-transform spectroscopy
Lim, Jongseok; Lee, Han-gyeol; Lee, Sangkyung; Ahn, Jaewook [Department of Physics, KAIST, Daejeon 305-701 (Korea, Republic of)
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.
Discrete quantum Fourier transform in coupled semiconductor double quantum dot molecules
Ping Dong; Ming Yang; Zhuo-Liang Cao
2008-11-28
In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary transformations. The current scheme would be a useful step towards the realization of complex quantum algorithms in the quantum dot system.
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.
On the Fourier Transform Approach to Quantum Error Control
Hari Dilip Kumar
2012-08-24
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. These are analyzed in a framework using the Fourier transform on finite groups, the finite group in question being a subgroup of the quantum error group considered. All the classes of codes that can be obtained in this framework are explored, including codes more general than Clifford codes. The error detection properties of one of these more general classes ("direct sums of translates of Clifford codes") are characterized. Examples codes are constructed, and computer code search results presented and analysed.
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.
Entanglement of periodic states, the quantum Fourier transform, and Shor's factoring algorithm
Most, Yonatan; Biham, Ofer [Racah Institute of Physics, Hebrew University, Jerusalem IL-91904 (Israel); Shimoni, Yishai [Racah Institute of Physics, Hebrew University, Jerusalem IL-91904 (Israel); Department of Neurology, Mount Sinai School of Medicine, New York, New York (United States)
2010-05-15
The preprocessing stage of Shor's algorithm generates a class of quantum states referred to as periodic states, on which the quantum Fourier transform is applied. Such states also play an important role in other quantum algorithms that rely on the quantum Fourier transform. Since entanglement is believed to be a necessary resource for quantum computational speedup, we analyze the entanglement of periodic states and the way it is affected by the quantum Fourier transform. To this end, we derive a formula that evaluates the Groverian entanglement measure for periodic states. Using this formula, we explain the surprising result that the Groverian entanglement of the periodic states built up during the preprocessing stage is only slightly affected by the quantum Fourier transform.
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.
Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics
Wu, Yinghua
Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuit/split-operator Fourier in dynamically adaptive coherent-state representations, generated by an approach that combines the matching
Large quantum Fourier transforms are never exactly realized by braiding conformal blocks
Freedman, Michael H.; Wang, Zhenghan
2007-03-15
Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {l_brace}U(2), controlled-NOT{r_brace}, the discrete Fourier transforms F{sub N}=({omega}{sup ij}){sub NxN}, i,j=0,1,...,N-1, {omega}=e{sup 2{pi}}{sup i} at {sup {approx}}{sup sol{approx}} at {sup N}, can be realized exactly by quantum circuits of size O(n{sup 2}), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F{sub N} and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks.
Ranabir Das; T. S. Mahesh; Anil Kumar
2002-12-19
A new method of quantum state tomography for quantum information processing is described. The method based on two-dimensional Fourier transform technique involves detection of all the off-diagonal elements of the density matrix in a two-dimensional experiment. All the diagonal elements are detected in another one-dimensional experiment. The method is efficient and applicable to a wide range of spin systems. The proposed method is explained using a 2 qubit system and demonstrated by tomographing arbitrary complex density matrices of 2 and 4 qubit systems using simulations.
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.
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
Efficient classical simulation of the semi-classical Quantum Fourier Transform
Daniel E. Browne
2006-12-03
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability of the quantum Fourier transform (QFT). In this note, we show that one can demonstrate a number of simulability results for QFT circuits in a straightforward manner using Griffiths and Niu's semi-classical QFT construction [Phys. Rev. Lett. 76, 3228 (1996)]. We then discuss the consequences of these results in the context of Shor's factorisation algorithm.
Unraveling quantum pathways using optical 3D Fourier-transform spectroscopy
Li, Hebin; Bristow, Alan D.; Siemens, Mark E.; Moody, Galan; Cundiff, Steven T.
2013-01-01
Predicting and controlling quantum mechanical phenomena require knowledge of the system Hamiltonian. A detailed understanding of the quantum pathways used to construct the Hamiltonian is essential for deterministic control and improved performance of coherent control schemes. In complex systems, parameters characterizing the pathways, especially those associated with inter-particle interactions and coupling to the environment, can only be identified experimentally. Quantitative insight can be obtained provided the quantum pathways are isolated and independently analysed. Here we demonstrate this possibility in an atomic vapour using optical three-dimensional Fourier-transform spectroscopy. By unfolding the system’s nonlinear response onto three frequency dimensions, three-dimensional spectra unambiguously reveal transition energies, relaxation rates and dipole moments of each pathway. The results demonstrate the unique capacity of this technique as a powerful tool for resolving the complex nature of quantum systems. This experiment is a critical step in the pursuit of complete experimental characterization of a system’s Hamiltonian. PMID:23340430
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.
Enobio, Eli Christopher I.; Ohtani, Keita; Ohno, Yuzo; Ohno, Hideo, E-mail: ohno@riec.tohoku.ac.jp [Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan)] [Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577 (Japan)
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.
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.
Svetoslav S. Ivanov; Michael Johanning; Christof Wunderlich
2015-09-06
We propose a simplified mathematical construction of the quantum Fourier transform which is suited for systems described by Ising-type Hamiltonians. By contrast to the standard Cooley-Tuckey scheme, which prescribes sequences of CPHASE gates, our implementation is based on one-qubit gates and a free evolution process. We also show how to obtain a quadratic speed-up by applying the conditional interactions simultaneously. Thus rather than O($N^2$) our implementation time scales as O($N$). Finally, we show a realization of our method with homogeneous microwave driven ion traps in a magnetic field with gradient.
Scaling laws for Shor's algorithm with a banded quantum Fourier transform
NASA Astrophysics Data System (ADS)
Nam, Y. S.; Blümel, R.
2013-03-01
We investigate the performance of a streamlined version of Shor's algorithm in which the quantum Fourier transform is replaced by a banded version that, for each qubit, retains only coupling to its b nearest neighbors. Defining the performance P(n,b) of the n-qubit algorithm for bandwidth b as the ratio of the success rates of Shor's algorithm equipped with the banded and the full-bandwidth (b=n-1) versions of the quantum Fourier transform, our numerical simulations show that P(n,b)?exp[-?max2(n,b)/100] for n
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...
The quantum state vector in phase space and Gabor's windowed Fourier transform
NASA Astrophysics Data System (ADS)
Bracken, A. J.; Watson, P.
2010-10-01
Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schrödinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.
NASA Astrophysics Data System (ADS)
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-12-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135° and 165° 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).
NASA Astrophysics Data System (ADS)
Douard, M.; Bacis, R.; Rambaldi, P.; Ross, A.; Wolf, J.-P.; Fabre, G.; Stringat, R.
1995-10-01
We propose a new method based on the differential absorption lidar technique for multipollutant detection. A broadband laser is sent into the atmosphere in a wavelength range in which several pollutants absorb. The backscattered light is analyzed by a Fourier-transform spectrometer with time resolution. This mode of detection provides both spatial and high spectral resolution down to 0.01 cm-1 , allowing range-resolved measurements of several pollutants simultaneously. To demonstrate the feasibility of this method, we have measured water vapor concentration by using more than 10 individual lines in the 720-nm absorption band. The potential and the limitations are discussed critically.
Douard, M; Bacis, R; Rambaldi, P; Ross, A; Wolf, J P; Fabre, G; Stringat, R
1995-10-15
We propose a new method based on the differential absorption lidar technique for multipollutant detection. A broadband laser is sent into the atmosphere in a wavelength range in which several pollutants absorb. The backscattered light is analyzed by a Fourier-transform spectrometer with time resolution. This mode of detection provides both spatial and high spectral resolution down to 0.01 cm(-1), allowing range-resolved measurements of several pollutants simultaneously. To demonstrate the feasibility of this method, we have measured water vapor concentration by using more than 10 individual lines in the 720-nm absorption band. The potential and the limitations are discussed critically. PMID:19862277
Fractional Fourier transform reflectometry
NASA Astrophysics Data System (ADS)
Shiloh, Lihi; Eyal, Avishay
2014-05-01
In some OFDR implementations it is advantageous to use sinusoidal frequency tuning and to work in the linear range of the sinusoid. For a given scan frequency this limits the maximum length of the interrogated fiber. We propose a new method which allows exceedingly large delays while maintaining high scan rates. It is based on the observation that delay of half the scan period yields linearly frequency modulated (LFM) signals at the OFDR receiver. Using Fractional Fourier Transform (FrFT) for processing the raw data enables measurement of the z-dependent reflection at long ranges with high resolution and high scan rates.
NASA Astrophysics Data System (ADS)
Celeghini, E.; del Olmo, M. A.
2015-04-01
Quantum physics and signal processing in the line R are strictly related to Fourier transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and allows to obtain the projective algebra io(2). A rigged Hilbert space is found and a new discrete basis in R obtained. All operators defined on R are shown to belong to the universal enveloping algebra of io(2) allowing, in this way, their algebraic treatment. Introducing in the half-line a Fourier-like transform, the procedure is extended to R+ and can be easily generalized to Rn and to spherical cohordinate systems.
Imaging Fourier Transform Spectrometer
Bennett, C.L.; Carter, M.R.; Fields, D.J.; Hernandez, J.
1993-04-14
The operating principles of an Imaging Fourier Transform Spectrometer (IFTS) are discussed. The advantages and disadvantages of such instruments with respect to alternative imaging spectrometers are discussed. The primary advantages of the IFTS are the capacity to acquire more than an order of magnitude more spectral channels than alternative systems with more than an order of magnitude greater etendue than for alternative systems. The primary disadvantage of IFTS, or FTS in general, is the sensitivity to temporal fluctuations, either random or periodic. Data from the IRIFTS (ir IFTS) prototype instrument, sensitive in the infrared, are presented having a spectral sensitivity of 0.01 absorbance units, a spectral resolution of 6 cm{sup {minus}1} over the range 0 to 7899 cm{sup {minus}1}, and a spatial resolution of 2.5 mr.
Quadratic discrete Fourier transform and mutually unbiased bases
Maurice Robert Kibler
2010-10-28
The present chapter [submitted for publication in "Fourier Transforms, Theory and Applications", G. Nikolic (Ed.), InTech (Open Access Publisher), Vienna, 2011] is concerned with the introduction and study of a quadratic discrete Fourier transform. This Fourier transform can be considered as a two-parameter extension, with a quadratic term, of the usual discrete Fourier transform. In the case where the two parameters are taken to be equal to zero, the quadratic discrete Fourier transform is nothing but the usual discrete Fourier transform. The quantum quadratic discrete Fourier transform plays an important role in the field of quantum information. In particular, such a transformation in prime dimension can be used for obtaining a complete set of mutually unbiased bases.
Fractional Fourier transformers through reflection.
Wolf, Kurt Bernardo; Krötzsch, Guillermo
2002-06-01
We show that an arbitrary paraxial optical system, compounded with its reflection in an appropriately warped mirror, is a pure fractional Fourier transformer between coincident input and output planes. The geometric action of reflection on optical systems is introduced axiomatically and is developed in the paraxial regime. The correction of aberrations by warp of the mirror is briefly addressed. PMID:12049357
Fingerprint Classification using Fast Fourier Transform
Park, Haesun
prespecified classes. Automatic classification can be used as a preprocessing step for fingerprint matchingFingerprint Classification using Fast Fourier Transform and Nonlinear Discriminant Analysis£ Cheong for fingerprint classification based on Discrete Fourier Transform (DFT) and nonlinear discriminant analysis
AIR POLLUTION MEASUREMENT BY FOURIER TRANSFORM SPECTROSCOPY
Fourier transform spectroscopy substantially reduces the limitations on infrared methods of pollution measurement. EPA has used long path cells and Fourier transform spectrometers for pollutant measurement both in the laboratory and in the field. Labile pollutants are best measur...
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…
A More Accurate Fourier Transform
Courtney, Elya
2015-01-01
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals (EI) that define Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric $\\mathrm{CO_2}$ concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT's FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability t...
Spacevariant Fourier Analysis: the Exponential Chirp Transform
Schwartz, Eric L.
during the past two decades. Associated with the logpolar map, we define a new linear integral transform of the usual Fourier transform. We then show that a logpolar coordinate transform in frequency (similar100 Spacevariant Fourier Analysis: the Exponential Chirp Transform Giorgio Bonmassar, Eric L
JPL Fourier transform ultraviolet spectrometer
NASA Technical Reports Server (NTRS)
Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.
1994-01-01
The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.
Glaser, Rainer
on the Internet at http://pubs.acs.org/jpcc. This article describes Fourier transform Raman/infrared spectroscopic are helically annelated, forming a cross- conjugated -system. These helicenes may be viewed as fragments, the enhancement of the Raman-active skeletal (CdC) stretching modes in the 1400-1300-cm-1 region is related
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.
a Parallel Fast Fourier Transform
NASA Astrophysics Data System (ADS)
Morante, Silvia; Rossi, Giancarlo; Salina, Gaetano
In this paper we discuss the general problem of implementing the multidimensional Fast Fourier Transform algorithm on parallel computers. We show that, on a machine with P processors and fully parallel node communications, the optimal asymptotic scaling behavior of the total computational time with the number of data points, N, given in d dimensions by the formula aN/Plog(N/P)+bN/P(d-1)/d, can actually be achieved on realistic platforms. As a concrete realization of our strategy, we have produced codes efficiently running on machines of the APE family and on Cray T3E. On the former for asymptotic values of N our codes attain the above optimal result.
Fast fourier transform on hypercube parallel computers
Chu, C.Y.
1988-01-01
The Fast Fourier Transform appears frequently in scientific computing. Therefore, it is desirable to implement it efficiently on parallel computeres. In this thesis, we investigate several different aspects of parallel Fast Fourier Transform implementation techniques for distributed-memory message-passing systems such as hypercube multiprocessors. Various Fast Fourier Transform algorithms are described using a matrix notation. An error analysis is presented that considers the effect of different methods used in the computation of the Fourier Transform coefficients as well as accumulated roundoff. New implementations of one and two-dimensional Fast Fourier Transforms are presented along with comparisons with existing methods. New algorithms for symmetric transforms are also developed, and the results show excellent speedup when implemented on the Intel iPSC hypercube.
NASA Astrophysics Data System (ADS)
Wu, Weixin; Long, B. E.; Cooke, S. A.
2015-08-01
The three lowest energy conformations of the title compound have been investigated using quantum chemical calculations and the lowest energy conformer has been observed using pure rotational spectroscopy. The lowest energy conformer possesses C2 symmetry, a helical CF2 backbone, with the hydrogens nearly eclipsing one another when looking down the long axis of the molecule. The technique of Fourier transform microwave spectroscopy in conjunction with quantum chemical calculations is demonstrated as a complimentary method to X-ray diffraction for structural determinations of small oligomers for which the location of hydrogen atoms may be important.
The fractional Fourier transform and applications
NASA Technical Reports Server (NTRS)
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
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; 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.
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.
Lagrange-mesh calculations and Fourier transform
Lacroix, Gwendolyn; Semay, Claude
2011-09-15
The Lagrange-mesh method is a very accurate procedure for computing eigenvalues and eigenfunctions of a two-body quantum equation written in the configuration space. Using a Gauss quadrature rule, the method only requires the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions, which vanish at all mesh points except one. Using the peculiarities of the method, it is shown that the Fourier transform of the eigenfunctions, computed in the configuration space, can easily be obtained with good accuracy in the physical domain of the momentum space. Also, observables in this space can easily be computed with good accuracy only using matrix elements and eigenfunctions computed in the configuration space.
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
FOURIER TRANSFORM SPECTROMETER IN ASTRONOMY SOOJONG PAK*
Pak, Soojong
. (apodization) . (inverse Fourier Transform) , = max min )2cos()()( p p FTS dpppFI , FTS IFTS Nyquist , S (over sampling factor). FTS S 5 . 4 FTS (apodization) . (Window Function or Apodization Function) . Hamming Gauss . #12;105 3. FTS 3
FOURIER TRANSFORM INFRARED SPECTROMETRY OF AMBIENT AEROSOLS
Fourier transform infrared (FTIR) spectrometry has been evaluated as a method for determining the concentration of selected species present in ambient aerosols collected on Teflon filters. The filters are analyzed by transmission measurements after collection of the fine fraction...
Miniaturization of Holographic FourierTransform Spectrometers
Nikolay I. Agladze; Albert J. Sievers
2004-01-01
Wave propagation equations in the stationary-phase approximation have been used to identify the theoretical bounds of a miniature holographic Fourier-transform spectrometer HFTS. It is demon- strated that the HFTS throughput can be larger than for a scanning Fourier-transform spectrometer. Given room- or a higher-temperature constraint, a small HFTS has the potential to outperform a small multichannel dispersive spectrograph with the
MONODROMY AT INFINITY AND FOURIER TRANSFORM II
Sabbah, Claude
with some of its properties, has been considered in [3]. A potential application is to produce a category call partial Laplace transform. 2000 Mathematics Subject Classification. -- Primary 32S40; Secondary 14C30, 34Mxx. Key words and phrases. -- Twistor D-module, Fourier-Laplace transform, specialization
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)
Optimal modal fourier-transform wavefront control.
Poyneer, Lisa A; Véran, Jean-Pierre
2005-08-01
Optimal modal Fourier-transform wavefront control combines the speed of Fourier-transform reconstruction (FTR) with real-time optimization of modal gains to form a fast, adaptive wavefront control scheme. Our modal basis is the real Fourier basis, which allows direct control of specific regions of the point-spread function. We formulate FTR as modal control and show how to measure custom filters. Because the Fourier basis is a tight frame, we can use it on a circular aperture for modal control even though it is not an orthonormal basis. The modal coefficients are available during reconstruction, greatly reducing computational overhead for gain optimization. Simulation results show significant improvements in performance in low-signal-to-noise-ratio situations compared with nonadaptive control. This scheme is computationally efficient enough to be implemented with off-the-shelf technology for a 2.5 kHz, 64 x 64 adaptive optics system. PMID:16134846
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.
Fourier Transform and Reflective Imaging Pyrometry
Stevens, G. D.
2011-07-01
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.
Ultrafast Fourier-transform parallel processor
Greenberg, W.L.
1980-04-01
A new, flexible, parallel-processing architecture is developed for a high-speed, high-precision Fourier transform processor. The processor is intended for use in 2-D signal processing including spatial filtering, matched filtering and image reconstruction from projections.
Directional Uncertainty Principle for Quaternion Fourier Transform
Eckhard Hitzer
2013-06-06
This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric algebras with quaternion subalgebras. We demonstrate this with the example of a directional spacetime algebra function uncertainty principle related to multivector wave packets.
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 ...
Livermore Imaging Fourier Transform Infrared Spectrometer (LIFTIRS)
Carter, M.R.; Bennett, C.L.; Fields, D.J.; Lee, F.D.
1995-05-10
Lawrence Livermore National Laboratory is currently operating a hyperspectral imager, the Livermore Imaging Fourier Transform Infrared Spectrometer (LIFTIRS). This instrument is capable of operating throughout the infrared spectrum from 3 to 12.5 {mu}m with controllable spectral resolution. In this presentation we report on it`s operating characteristics, current capabilities, data throughput and calibration issues.
Fourier type transforms on Lie symmetry groups
NASA Astrophysics Data System (ADS)
Craddock, Mark
2015-09-01
In this paper, we construct operators on a Lie symmetry group which may be regarded as Fourier transforms. Essentially, we integrate solutions generated by Lie symmetries against suitable test functions. We show that this idea leads to a powerful method for solving Cauchy problems for parabolic and hyperbolic equations in two and higher dimensions. We also discuss applications to the elliptic case.
Faraggi, A.E. [Univ. of Florida, Gainesville, FL (United States). Institute for Fundamental Theory; Matone, M. [Univ. of Padova (Italy). Dept. of Physics G. Galilei
1998-01-09
We show that the quantum Hamilton-Jacobi equation can be written in the classical form with the spatial derivative {partial_derivative}{sub q} replaced by {partial_derivative}{sub q} with dq = dq/{radical}1{minus}{beta}{sup 2}(q), where {beta}{sup 2}(q) is strictly related to the quantum potential. This can be seen as the opposite of the problem of finding the wave function representation of classical mechanics as formulated by Schiller and Rosen. The structure of the above {open_quotes}quantum transformation{close_quotes}, related to the recently formulated equivalence principle, indicates that the potential deforms space geometry. In particular, a result by Flanders implies that both W(q) = V(q) {minus} E and the quantum potential Q are proportional to the curvatures {kappa}{sub W} and {kappa}{sub Q} which arise as natural invariants in an equivalence problem for curves in the projective line. In this formulation the Schroedinger equation takes the geometrical form ({partial_derivative}{sub q}{sup 2} + {kappa}{sub W}){psi} = 0.
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.
An algorithm for the basis of the finite Fourier transform
NASA Technical Reports Server (NTRS)
Santhanam, Thalanayar S.
1995-01-01
The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.
Fourier transform profilometry based on defocusing
NASA Astrophysics Data System (ADS)
Fu, Yanjun; Wu, Jianfeng; Jiang, Guangyu
2012-06-01
Sinusoidal fringe patterns are popularly used in conventional Fourier transform profilometry. There are numerous harmonics in the Fourier spectrum, so as to avoid spectrum overlapping; the maximum range of measurement is limited. The present paper studies FTP based on properly defocusing a binary square wave. There are only odd harmonics in the Fourier spectrum of a binary square wave, and the maximum range of measurement is expanded 1.5 times. Defocusing has a low-pass filtering effect and higher-order odd harmonics are suppressed. Therefore, the fundamental spectrum is easy to extract. The proposed method overcomes the filtering problem of conventional FTP. Measurement experiments show that the proposed method has a good measurement result and the measurement accuracy is improved.
Fourier Transform Fabry-Perot Interferometer
NASA Technical Reports Server (NTRS)
Snell, Hilary E.; Hays, Paul B.
1992-01-01
We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.
The Unified Discrete Fourier-Hartley Transforms Processor
Oraintara, Soontorn
The Unified Discrete Fourier-Hartley Transforms Processor P. Potipantong1 , S. Oraintara4 , P Fourier-Hartley transform (UDHFT) processor for digital signal processing applications. The proposed architecture uses a UDHFT theory which can calculate the discrete Fourier and Hartley transforms (DFT, DHT
Nonuniqueness of phase retrieval for three fractional Fourier transforms
Claudio Carmeli; Teiko Heinosaari; Jussi Schultz; Alessandro Toigo
2014-11-25
We prove that, regardless of the choice of the angles $\\theta_1,\\theta_2,\\theta_3$, three fractional Fourier transforms $F_{\\theta_1}$, $F_{\\theta_2}$ and $F_{\\theta_3}$ do not solve the phase retrieval problem. That is, there do not exist three angles $\\theta_1$, $\\theta_2$, $\\theta_3$ such that any signal $\\psi\\in L^2(R)$ could be determined up to a constant phase by knowing only the three intensities $|F_{\\theta_1}\\psi|^2$, $|F_{\\theta_2}\\psi|^2$ and $|F_{\\theta_3}\\psi|^2$. This provides a negative argument against a recent speculation by P. Jaming, who stated that three suitably chosen fractional Fourier transforms are good candidates for phase retrieval in infinite dimension. We recast the question in the language of quantum mechanics, where our result shows that any fixed triple of rotated quadrature observables $Q_{\\theta_1}$, $Q_{\\theta_2}$ and $Q_{\\theta_3}$ is not enough to determine all unknown pure quantum states. The sufficiency of four rotated quadrature observables, or equivalently fractional Fourier transforms, remains an open question.
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.
Advanced Techniques for Fourier Transform Wavefront Reconstruction
Poyneer, L A
2002-08-05
The performance of Fourier transform (FT) reconstructors in large adaptive optics systems with Shack-Hartmann sensors and a deformable mirror is analyzed. FT methods, which are derived for point-based geometries, are adapted for use on the continuous systems. Analysis and simulation show how to compensate for effects such as misalignment of the deformable mirror and wavefront sensor gain. Further filtering methods to reduce noise and improve performance are presented. All these modifications can be implemented at the filtering stage, preserving the speed of FT reconstruction. Simulation of a large system shows how compensated FT methods can have equivalent or better performance to slower vector-matrix-multiply reconstructions.
Fourier transform analysis of irradiated Weiss oscillations
NASA Astrophysics Data System (ADS)
Iñarrea, Jesús; Platero, Gloria
2015-03-01
We present a theoretical approach to study the effect of microwave radiation on the magnetoresistance of a one-dimensional superlattice. In our proposal the magnetoresistance of a unidirectional spatial periodic potential (superlattice), is modulated by microwave radiation due to an interference effect between both space- and time-dependent potentials. The final magnetoresistance will mainly depend on the spatial period of the superlattice and the radiation frequency. We consider an approach to study these effects based on the fast Fourier transform of the obtained magnetoresistance profiles in function of the inverse of the magnetic field. Based on this theory we propose the design of a novel radiation sensor for the terahertz band.
NASA Astrophysics Data System (ADS)
Yfantis, E. A.; Borgman, L. E.
Several programs based on the Fast Fourier Transform (FFT) Algorithm developed by Cooley and Tukey are available. The Cooley and Tukey algorithm for the FFT requires the number of data N be a power of 2. Along with a subroutine which implements the Cooley and Tukey algorithm, six other new subroutines which are extensions of the Cooley and Tukey algorithm are given in this paper. Some applications to geoscience, along with some examples where the FFT subroutine based on the Cooley and Tukey algorithm is undesirable also are given.
LWIR and MWIR ultraspectral Fourier transform imager
NASA Astrophysics Data System (ADS)
Meigs, Andrew D.; Otten, Leonard John, III; Cherezova, Tatyana Y.; Rafert, Bruce; Sellar, R. Glenn
1997-12-01
Kestrel Corporation has designed and is now building a dual- band infrared Fourier transform ultraspectral imager for aircraft deployment. Designed for installation in a Cessna 206, this instrument will have a 15 degree FOV, with an IFOV of 1.0 mrad. The target spectral resolution is better than 1.5 cm-1 over 2000 to 3000 cm-1 and 0.4 cm-1 over 850 to 1250 cm(superscript -1$. using 512 spectral channels. The device will use a variety of spectral enhancement techniques to achieve this unprecedented spectral resolution. Computer simulations of the optical systems demonstrates sub-wavenumber resolutions and signal to noise ratios of over 900.
Fourier transform infrared spectroscopy of peptides.
Bakshi, Kunal; Liyanage, Mangala R; Volkin, David B; Middaugh, C Russell
2014-01-01
Fourier transform infrared (FTIR) spectroscopy provides data that are widely used for secondary structure characterization of peptides. A wide array of available sampling methods permits structural analysis of peptides in diverse environments such as aqueous solution (including optically turbid media), powders, detergent micelles, and lipid bilayers. In some cases, side chain vibrations can also be resolved and used for tertiary structure and chemical analysis. Data from several low-resolution spectroscopic techniques, including FTIR, can be combined to generate an empirical phase diagram, an overall picture of peptide structure as a function of environmental conditions that can aid in the global interpretation of large amounts of spectroscopic data. PMID:24146410
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.
Transforming quantum operations: quantum supermaps
G. Chiribella; G. M. D'Ariano; P. Perinotti
2008-10-22
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.
Transforming quantum operations: Quantum supermaps
NASA Astrophysics Data System (ADS)
Chiribella, G.; D'Ariano, G. M.; Perinotti, P.
2008-08-01
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.
On the q-Bessel Fourier transform Lazhar Dhaouadi
Paris-Sud XI, UniversitÃ© de
On the q-Bessel Fourier transform Lazhar Dhaouadi Abstract In this work, we are interested by the q-Bessel Fourier transform with a new approach. Many important results of this q-integral transform are proved with a new constructive demonstrations and we establish in particular the associated q
Fourier 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.
Fourier transform infrared spectroscopic study of truffles
NASA Astrophysics Data System (ADS)
Zhao, Dezhang; Liu, Gang; Song, Dingshan; Liu, Jian-hong; Zhou, Yilan; Ou, Jiaming; Sun, Shizhong
2006-01-01
Truffles are rare wild growing edible mushrooms belonging to Ascomycetes. In this paper, Fourier transform infrared (FTIR) spectroscopy was used to obtain vibrational spectra of truffles. The results show that the mushrooms exhibit characteristic spectra. The two strongest absorption bands appear at about 1077cm -1 and 1040 cm -1, which were described as C-O stretching in carbohydrate. The vibrational spectra indicate that the main compositions of the truffles are polysaccharide and protein. According to the characteristics bands and absorption ratios of spectra, different species of truffles can be discriminated. It is also found the great changes between moldy and healthy truffles, which the major differences are observed in the bands of protein. In addition, FTIR spectral differences are observed between the same species of truffles from different producing areas. It is showed that the FTIR spectroscopic method is valuable tool for rapid and nondestructive analysis of truffles prior to any extraction method used.
Surface Inspection using fourier transform infrared spectroscopy
Powell, G.L.; Smyrl, N.R.; Williams, D.M.; Meyers, H.M. III [Martin Marietta Energy Systems, Inc., TN (United States). Oak Ridge Y-12 Plant; Barber, T.E.; Marrero-Rivera, M. [Oak Ridge Institute for Science and Education, Oak Ridge, TN (United States)
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.
Spectral Analysis of Orbits via Discrete Fourier Transforms
Spectral Analysis of Orbits via Discrete Fourier Transforms C. Hunter (hunter-periodic motion of regular orbits from numerical integrations of those orbits. The algorithms rely entirely on discrete Fourier transforms. We calibrate the algorithms by applying them to some orbits which were studied
Edge detection based on the multiresolution Fourier transform
Chang-Tsun Li; Der-Chyuan Lou
1999-01-01
In this paper, an edge detection technique is proposed by using the multiresolution Fourier transform (MFT) to analyze the local properties in the spatial frequency domain. Five major steps are adopted to implement the detection of edges. First, the Laplacian pyramid method is used to create a high-pass filtered image. Secondly, the Multiresolution Fourier Transform (MFT) is applied to divide
Fourier transform spectroscopy to study planetary atmospheres.
NASA Astrophysics Data System (ADS)
Olsen, Kevin; Walker, Kaley; Strong, Kimberly; Hipkin, Victoria; Toon, Geoff; Conway, Stephanie; Berube, Philippe; Veilleux, James
Motivated by the selection of MATMOS for the ExoMars Trace Gas Orbiter (withdrawn), we have been working on algorithms for retrieving information about the Martian atmosphere using infrared spectroscopy.The Mars Atmospheric Trace Molecule Occultation Spectrometer (MATMOS) was a joint Canadian Space Agency (CSA) and Jet Propulsion Laboratory (JPL) mission to send a high-resolution Fourier transform spectrometer to Mars, similar to the CSA's Atmospheric Chemistry Experiment (ACE) FTS. The ACE-FTS, currently in Earth orbit, is a solar-occultation instrument measuring the solar spectrum between 750-4400 cm (-1) at a spectral resolution of 0.02 cm (-1) . We present an algorithm to retrieve temperatures and pressures from measured spectra, accurate knowledge of which is vital for inferring volume mixing ratios of trace gases. The effects of high dust quantities on spectra have been simulated using synthetic spectra of the Martian atmosphere and a method for mitigating these effects has been tested and will be presented. Work has been done to characterize the interferometer performance of the Engineering Demonstration Unit, constructed by ABB, with a focus on gaining a better understanding of the modulation efficiency of the interferometer.
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.
Implementation of weighted summation type fractional Fourier transform on FPGA
NASA Astrophysics Data System (ADS)
Zou, Qiming; Li, Longlong; Huang, Qian; Wang, Fei
2015-07-01
Recently Fractional Fourier transform (FrFT) has got a variety of applications in digital signal and image processing. This paper presents a novel hardware architecture for real-time computation of Discrete Fractional Fourier Transform (DFrFT), which can easily be extended to other fractional transforms. The proposed architecture has been verified on Xilinx FPGA(XC6VLX240T), which can run at a frequency up to 291MHz while with high accuracy.
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.
Assembled Fourier transform micro-spectrometer
NASA Astrophysics Data System (ADS)
Sin, Jeongsik; Lee, Woo Ho; Popa, Dan; Stephanou, Harry E.
2006-01-01
Microassembly process plays a key role in building 3-dimensional heterogeneous microsystems. This paper presents a miniaturized Fourier transform spectrometer (FTS) implemented by combining silicon micromachining and microassembly techniques. The FTS is based on a Michelson interferometer where a scanning mirror mechanism creates an interferogram, and the recorded interferogram is converted to a spectrum by Fourier transform. The miniaturized Michelson interferometer is integrated on a microoptical bench, which is fabricated using Deep RIE (Reactive Ion Etching) process on a SOI (Silicon On Insulator) wafer. Key components of the FTS optical bench are a linear translation stage, mechanical assembly sockets, a beam splitter, and assembled mirrors. An electrothermal actuator with stroke amplification mechanisms provides the amplified scanning motion of a scanning mirror. The sockets are female mechanical flexure structures that allow a precise snap-fit assembly with micromachined silicon mirrors. The dimension of the FTS optical bench is 1cm2, and its embedded thermal actuator has a couple of V-beam structures whose beam length is 1mm. The mirrors are Deep RIE micromachined structures with reflection area 500x450?m2 and 750?m long flexure structures for pick & place assembly. The flexure structure allows large deflection so that a microgripper can pick up the mirror by inserting the gripper tip into the structure, and snap-fit assembles it into the mechanical socket of the bench. The linear translation stage generates up to 30?m scanning stroke at 22V input, which corresponds to a spectral resolution of 10nm at 775nm wavelength. While this microassembly method is designed to self-align the mirror in the socket, the mirror slightly tilts after assembly due to the slope of side wall of DRIE processed structures. The measured tilting angles of assembled mirrors range from -2.5° to 0.8° from several assembly trials. The tilting angle combined with beam divergence can cause the loss of power and resolution, spectrum shift and phase error. A He-Ne laser was used as a light source to create interferogram with the assembled microspectrometer. Formation of fringe patterns was successfully conducted with a prototype. Mirrors with a large tilting misalignment resulted in stripe pattern fringes, whereas an improved alignment generated circular pattern fringes. A detector was used to measure light power with respect to input voltage, and the displacement of a scanning mirror was measured and curve-fitted. The relationship between light power changes versus the displacement of a scanning mirror represents interferogram. Spectrum profiles showed a peak around 632nm with FWHM (Full Width Half Magnitude) 25nm approximately. While further research is on going to improve spectrum quality and microassembly technique for the integration of various components with heterogeneous materials and shapes, this approach is expected to facilitate the design and manufacturing of MOEMS from the constraints of micromachining processes.
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
2D Fourier-transform Spectroscopy of Potassium Vapor
NASA Astrophysics Data System (ADS)
Dai, Xingcan; Bristow, Alan D.; Karaiskaj, Denis; Cundiff, Steven T.
2010-03-01
2D Fourier-transform (2DFT) spectroscopy is a time-domain technique that measures the coherent optical response in two spectral dimensions. This method has elucidated the structure and electronic dynamics in molecules and semiconductors [1], where many-body interactions are expected. Here we demonstrate how 2DFT spectroscopy isolates specific quantum excitation pathways in a simple quantum system, namely potassium vapor in a thin transmission cell [2]. A femtosecond pulse sequence excites both the D1 and D2 lines simultaneously to reveal coupling between the transitions as a result of quantum interference and Raman-like coherences. Observations agree well with numerical simulations based on the optical Bloch equations. The non-radiative Raman pathways have population-time dependence and are isolated by altering the 2DFT projection. Density-dependent measurements show distortion of the 2DFT spectral features due to pulse propagation effects. Unexpected two-quantum coherences are observed and attributed to interatomic interactions.[4pt] [1] Cundiff et al, Acc. Chem. Res. 42, 1423 (2009).[0pt] [2] Dai et al, arXiv:1001.1955v1
A complex exponential Fourier transform approach to gradient density estimation
Rangarajan, Anand
A complex exponential Fourier transform approach to gradient density estimation Karthik S transformation of a uniformly distributed random variable) defined on a closed, bounded interval R transformation Y = S (X) where X is uniformly distributed] with the normalized power spectrum of exp (i
NASA Technical Reports Server (NTRS)
Marko, H.
1978-01-01
A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.
Boundary values, Fourier-Sato tranform and Laplace transform
Schapira, Pierre
Boundary values, Fourier-Sato tranform and Laplace transform Pierre Schapira Abstract In the first part of this paper we describe the well-known Fourier-Sato, the normal bundle to M in X. When fl is open and convex (i.e. the fibers of fl over M are convex), Sato
Fourier transform ion cyclotron resonance: state of the art.
Marshall, A G; Hendrickson, C L; Emmett, M R; Rodgers, R P; Blakney, G T; Nilsson, C L
2007-01-01
This short review summarizes recent and projected advances in Fourier transform ion cyclotron resonance mass spectrometry instrumentation and applications, ranging from petroleomics to proteomics. More details are available from the cited primary literature and topical reviews. PMID:17878540
Fast Fourier transform on a 3D FPGA
Basha, Elizabeth (Elizabeth Ann)
2005-01-01
Fast Fourier Transforms perform a vital role in many applications from astronomy to cellphones. The complexity of these algorithms results from the many computational steps, including multiplications, they require and, as ...
FT Digital Filtering and Simulating Fourier transform Apodization via Excel
NSDL National Science Digital Library
Overway, Ken
This report presents an excel spreadsheet which simulates Fourier Transform apodization filtering on a noisy signal that contains either white or an environmental noise source. Users may download the report in PDF file format.
Thorwirth, Sven
Fourier transform microwave spectroscopy of vinyldiacetylene, vinyltriacetylene microwave spectroscopy of a supersonic molecular beam. The molecules were observed as products/diacetylene for the pure hydrocarbon molecules and vinylacetylene/cyanoacetylene for vinylcyanodiacetylene
Technique for the metrology calibration of a Fourier transform spectrometer
Spencer, Locke D.; Naylor, David A
2008-11-10
A method is presented for using a Fourier transform spectrometer (FTS) to calibrate the metrology of a second FTS. This technique is particularly useful when the second FTS is inside a cryostat or otherwise inaccessible.
Fourier transform-wavefront reconstruction for the pyramid wavefront sensor
Fernando Quirós-Pacheco; Carlos Correia; Simone Esposito
2010-01-01
The application of Fourier-transform reconstruction techniques to the pyramid wavefront sensor has been investigated. A preliminary study based on end-to-end simulations of an adaptive optics system with ≈40x40 subapertures and actuators shows that the performance of the Fourier-transform reconstructor (FTR) is of the same order of magnitude than the one obtained with a conventional matrix-vector multiply (MVM) method.
Herz spaces and restricted summability of Fourier transforms and Fourier series
NASA Astrophysics Data System (ADS)
Weisz, Ferenc
2008-08-01
A general summability method, the so-called [theta]-summability is considered for multi-dimensional Fourier transforms and Fourier series. A new inequality for the Hardy-Littlewood maximal function is verified. It is proved that if the Fourier transform of [theta] is in a Herz space, then the restricted maximal operator of the [theta]-means of a distribution is of weak type (1,1), provided that the supremum in the maximal operator is taken over a cone-like set. From this it follows that over a cone-like set a.e. for all . Moreover, converges to f(x) over a cone-like set at each Lebesgue point of if and only if the Fourier transform of [theta] is in a suitable Herz space. These theorems are extended to Wiener amalgam spaces as well. The Riesz and Weierstrass summations are investigated as special cases of the [theta]-summation.
Koepf, Wolfram
1 Two Classes of Special Functions Using Fourier Transforms of Generalized Ultraspherical of orthogonal functions, which are respectively Fourier trans- forms of the generalized ultraspherical, Fourier transform, Parseval identity, hypergeometric functions MSC(2010): 33C45 1. Introduction. Let us
Quaternion Fourier Transform on Quaternion Fields and Generalizations
Eckhard Hitzer
2013-06-05
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear ($GL$) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging non-commutative multivector FT generalizations of the QFT. Examples given are new volume-time and spacetime algebra Fourier transformations.
[Analysis of cell arrangements in Biota orientalis using Fourier transformation].
Duo, Hua-Qiong; Wang, Xi-Ming
2009-10-01
Fourier transform image-processing technology is applied for determining the cross section cell arrangement of early-wood in Biota orientalis. In this method, the disc-convoluted dot map from each cell radius with 10 pixels is transformed by Fourier transform, generating the angle distribution function in the power spectral pattern. The maximum value is the arrangement of the cell. The results of Fourier transform image-processing technology indicated that the arrangements of the cell of Biota orientalis are 15 degrees in oblique direction, respectively. This method provides a new basis for the digitized identification of the wood, and also the new theoretical research direction for the digitized identification and examination of the wood species. PMID:20038030
Extending Fourier transformations to Hamilton's quaternions and Clifford's geometric algebras
NASA Astrophysics Data System (ADS)
Hitzer, Eckhard
2013-10-01
We show how Fourier transformations can be extended to Hamilton's algebra of quaternions. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Hamilton's algebra of quaternions is only one example of the larger class of Clifford's geometric algebras, complete algebras encoding a vector space and all its subspace elements. We introduce how Fourier transformations are extended to Clifford algebras and applied in electromagnetism, and in the processing of images, color images, vector field and climate data.
Fourier-transform 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.
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.
Fractional Fourier transform of Lorentz-Gauss beams.
Zhou, Guoquan
2009-02-01
Lorentz-Gauss beams are introduced to describe certain laser sources that produce highly divergent beams. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz-Gauss beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz-Gauss beam passing through an FRFT system has been derived. By using the derived expression, the properties of a Lorentz-Gauss beam in the FRFT plane are graphically illustrated with numerical examples. PMID:19183688
Convolution and Product Theorem for the Special Affine Fourier Transform
Ayush Bhandari; Ahmed Zayed
2015-06-24
The Special Affine Fourier Transform or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Unlike the Fourier transform, the SAFT does not work well with the standard convolution operation. Recently, Q. Xiang and K. Y. Qin introduced a new convolution operation that is more suitable for the SAFT and by which the SAFT of the convolution of two functions is the product of their SAFTs and a phase factor. However, their convolution structure does not work well with the inverse transform in sofar as the inverse transform of the product of two functions is not equal to the convolution of the transforms. In this article we introduce a new convolution operation that works well with both the SAFT and its inverse leading to an analogue of the convolution and product formulas for the Fourier transform. Furthermore, we introduce a second convolution operation that leads to the elimination of the phase factor in the convolution formula obtained by Q. Xiang and K. Y. Qin.
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.
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…
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.
Fourier transform wavefront control with adaptive prediction of the atmosphere.
Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre
2007-09-01
Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s. PMID:17767234
The Power of Quantum Fourier Sampling
Bill Fefferman; Chris Umans
2015-07-20
A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. Aaronson and Arkhipov take this further by considering a distribution that can be sampled efficiently by linear optical quantum computation, that under two feasible conjectures, cannot even be approximately sampled classically within bounded total variation distance, unless the PH collapses. In this work we use Quantum Fourier Sampling to construct a class of distributions that can be sampled by a quantum computer. We then argue that these distributions cannot be approximately sampled classically, unless the PH collapses, under variants of the Aaronson and Arkhipov conjectures. In particular, we show a general class of quantumly sampleable distributions each of which is based on an "Efficiently Specifiable" polynomial, for which a classical approximate sampler implies an average-case approximation. This class of polynomials contains the Permanent but also includes, for example, the Hamiltonian Cycle polynomial, and many other familiar #P-hard polynomials. Although our construction, unlike that proposed by Aaronson and Arkhipov, likely requires a universal quantum computer, we are able to use this additional power to weaken the conjectures needed to prove approximate sampling hardness results.
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
Static Fourier-transform spectrometer with spherical reflectors
NASA Astrophysics Data System (ADS)
Zhan, Gao
2002-01-01
A compact reflection Fourier-transform spectrometer without moving parts is developed. The spectrometer consists of two spherical reflectors: a Sagnac interferometer and a linear detector. The developed system is as small as 202 mm long × 185 mm wide × 100 mm high. The optics and the system configuration are described, and the preliminary experimental results are shown.
Parallel fast Fourier transforms for electronic structure calculations
NASA Astrophysics Data System (ADS)
Haynes, Peter D.; Côté, Michel
2000-07-01
We present a new method for performing fast Fourier transforms for electronic structure calculations on parallel computers which minimizes the latency cost involved in communication between nodes. We compare the new and traditional methods in theory and in practice, and thus suggest the conditions under which the new method will be more efficient than current methods.
Acoustic matching network synthesis using discrete space Fourier transforms
J. Stevenson Kenney; W. D. Hunt
1990-01-01
A method used to analyze and synthesize acoustic plane wave matching structures between a transducer and a medium is described. The analysis is applicable to multilayer structures with periodic discontinuities in characteristic impedance. It is shown that the frequency response of such structures is approximately equal to the discrete-time Fourier transform of the individual-layer reflection coefficients. The synthesis procedure uses
On the abstracted dataflow complexity of Fast Fourier Transforms
A. P. W. Boehm; R. E. Hiromoto; K. A. Kelly; J. M. Ashley
1992-01-01
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
On the abstracted dataflow complexity of Fast Fourier Transforms
A. P. W. Boehm; R. E. Hiromoto; K. A. Kelly; J. M. Ashley
1992-01-01
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
MICROMACHINED FOURIER TRANSFORM SPECTROMETER ON SILICON OPTICAL BENCH PLATFORM
Park, Namkyoo
of a silicon-on-insulator wafer. Our bulk micromachining process combines the flexible definition capability is becoming increasingly important in a number of applications such as environmental monitoring, chemical), and a Fourier transform is subsequently performed to obtain the spectral information from the measured
A fast Fourier transform (FFT) based sonar signal processor
ROBERT C. TRIDER
1978-01-01
The design for a convolution processor is presented, which employs a single highly parallel implementation of the fast Fourier transform (FFT) algorithm. This processor is eminently suited for real-time matched filtering of coded signals encountered in sonar systems. Computer simulations have shown that this processor, which uses fixed point arithmetic and modest word sizes, can efficiently handle signals with multiple
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...
Clutter characterization algorithms for Fourier transform hyperspectral imagers
NASA Astrophysics Data System (ADS)
Sears, Robert D.; Fraser, James C.; Winings, M.; Otten, Leonard John, III; Turner, Theodore S., Jr.; O'Hair, John R.
1997-08-01
Background clutter and target signatures have traditionally been described by parameters derived form measurements of spatial structure and spectral ratios derived from fixed spectral bandpass images. The advent of hyperspectral imagery requires descriptions of background clutter in a mixed wavelength-spatial or Fourier-transformed (FT) spectral - spatial framework because the data stream may contain simultaneous spatial - spectral, or FT spectral - spatial clutter components. We have developed and tested analytical routines for characterizing the background clutter and target signatures observed by Fourier-transform instruments, without requiring production of a hyperspectral data cube having spectra wavelength and 2D spatial image dimensions. The Kestrel Fourier-transform hyper spectral imager, a Sagnac format interferometer produces a data stream consisting of the Fourier spectra of the background in the in-track focal plane dimension and the spatial information int he cross-track dimension. The temporal data stream thus consists of a time series of frames in FT- spectral vs. spatial dimensions. Spectral wavelength filtering and guard-band subtraction can be accomplished in FT space by binary shift and add algorithms without prior transformation of the data into a hyperspectral data cube. Spatial filtering in the cross track dimension can similarly benefit from efficient binary operations. This paper summarizes some of the target and background clutter characterization algorithms developed and their evaluation against an example atmospheric gas detection scenario.
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...
Gas Analysis by Fourier Transform Mm-Wave Spectroscopy
NASA Astrophysics Data System (ADS)
Harris, Brent J.; Steber, Amanda L.; Lehmann, Kevin K.; Pate, Brooks H.
2013-06-01
Molecular rotational spectroscopy of low pressure, room temperature gases offers high chemical selectivity and sensitivity with the potential for a wide range of applications in gas analysis. A strength of the technique is the potential to identify molecules that have not been previously studied by rotational spectroscopy by comparing experimental results to predictions of the spectroscopic parameters from quantum chemistry -6 so called library-free detection. The development of Fourier transform mm-wave spectrometers using high peak power (30 mW) active multiplier chain mm-wave sources brings new measurement capabilities to the analysis of complex gas mixtures. Strategies for gas analysis based on high-throughput mm-wave spectroscopy and arbitrary waveform generator driven mm-wave sources are described. Several new measurement capabilities come from the intrinsic time-domain measurement technique. High-sensitivity double-resonance measurements can be performed to speed the analysis of a complex gas sample containing several species. This technique uses a "pi-pulse" to selectively invert the population of two selected rotational energy levels and the effect of this excitation pulse on all other transitions in the spectrometer operating range is monitored using segmented chirped-pulse Fourier transform spectroscopy. This method can lead to automated determination of the molecular rotational constants. Rapid pulse duration scan experiments can be used to estimate the magnitude and direction of the dipole moment of the molecule from an unknown spectrum. Coherent pulse echo experiments, using the traditional Hahn sequence or two-color population recovery methods, can be used to determine the collisional relaxation rate of the unknown molecule. This rate determination improves the ability to estimate the mass of the unknown molecule from the determination of the Doppler dephasing rate. By performing a suite of automated, high-throughput measurements, there is the potential to determine the shape (via the rotational constant), electric properties (the dipole moments and its direction in the principal axis system), and the mass of the molecule to aid its identification.
Ultrafast ranging lidar based on real-time Fourier transformation.
Xia, Haiyun; Zhang, Chunxi
2009-07-15
Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the time delay between the two signals. The temporal interferograms are transformed from the time domain into the frequency domain using a time-to-frequency conversion function obtained in the calibration process. The Fourier transform is used in the data processing. A range resolution of 334 nm at a sampling rate of 48.6 MHz over a distance of 16 cm is demonstrated in the laboratory. PMID:19823517
Transfer Functions Via Laplace- And Fourier-Borel Transforms
NASA Technical Reports Server (NTRS)
Can, Sumer; Unal, Aynur
1991-01-01
Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.
Recovering missing slices of the discrete Fourier transform using Ghosts.
Chandra, Shekhar S; Svalbe, Imants D; Guédon, Jeanpierre; Kingston, Andrew M; Normand, Nicolas
2012-10-01
The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n log(2) n) (for an n=N×N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT. PMID:22752128
A Student's Guide to Fourier Transforms - 2nd Edition
NASA Astrophysics Data System (ADS)
James, J. F.
2002-09-01
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science. Expanded to include more emphasis on applications An established successful textbook for undergraduate and graduate students Includes worked examples and copious diagrams throughout
Fourier transforms and fractals in the food and agricultural industry
NASA Astrophysics Data System (ADS)
Zwiggelaar, Reyer; Bull, Christine R.
1994-11-01
Links between the fractal Hausdorff-dimension, the Fourier transform of 2D scenes and image segmentation by texture are discussed. It is shown that the fractal Hausdorff-dimension can be derived by integration of the intensity of the spatial frequency domain (i.e. the Fourier plane) over a set of different band-limited spatial filters. The difference between a computational and optical approach to determine the Hausdorff-dimension are shown, with advantages of both methods discussed. Possible future directions of research/improvements are mentioned. Natural and simulated scenes are considered which apply to a wide range of situations in the agricultural and food industry.
Conformations of seven-membered rings: The Fourier transform model
NASA Astrophysics Data System (ADS)
Cano, F. H.; Foces-Foces, C.
A representation of the puckered conformations of seven-membered rings, using the Fourier Fourier Transform model and derived from the torsion angles, is presented in terms of two puckering amplitudes and their corresponding puckering phases. These four parameters are used to describe the main conformational types and to study the planarity of the rings, symmetrical forms, pseudorotation pathways and symmetrical interconversions through the puckering levels. This analysis provides a criterion for characterizing the basic conformations which have already been established by earlier work. A comparison with previous models is also given and the representation applied to some 1,4-benzodiazepine compounds.
The Fourier transform of spline-function approximations to continuous data
L. Ostrander
1971-01-01
The transform of a spline-function approximation to continuous data is called a spline transform. In this correspondence, the spline and the discrete Fourier transforms (DFT) are compared as means for numerical computation of the Fourier integral transform. It is shown how the spline transform reduces errors introduced by the discrete transform and alleviates noise problems when the sampling rate is
Chained Quantum Arnold Transformations
López-Ruiz, Francisco F; Aldaya, Victor
2011-01-01
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.
Omnidirectional shape measurement using reliability evaluation value in Fourier transform
NASA Astrophysics Data System (ADS)
Matui, Toru; Ri, Shien; Fujigaki, Motoharu; Morimoto, Yoshiharu
2005-12-01
Non-contacting shape measurement for 3-D objects is important in automated manufacturing, quality control of components, 3-D solid modeling, etc. Optical measurement of omnidirectional shape has been done by rotating an object and/or measuring it from different directions. We previously proposed a phase-shifting method using Fourier transform (PSM/FT) and a multi-reference-planes method (MRPM) to obtain geometric parameters without influence of lens distortions. Both a measured object and a reference object are simultaneously measured from different directions. All partial point-clouds can be merged into one global coordinate system by a transform matrix calculated from the reference column on a rotary stage. 360-deg 3-D shape can be measured using the above method. In the PSM/FT, since the initial phase information is determined from only the first frequency of the Fourier spectrum of the phase-shifted intensity values at each point of an object and the frequency components higher than the first frequency almost depend on noise, almost experimental noise can eliminated. The phase reliability evaluation value using Fourier transform (PREV/FT) is, therefore, defined as the ratio of the first frequency component of the Fourier spectrum to the average of the frequency components higher then the first frequency of the Fourier spectrum. The PREV/FT is useful to merge data when measurement conditions are changed. In this paper, we propose a method that all partial data can be merged into global coordinates using the PREV/FT on overlapped areas and omnidirectional shape measurement is achieved.
Group Fourier transform and the phase space path integral for finite dimensional Lie groups
Matti Raasakka
2011-12-12
We formulate a notion of group Fourier transform for a finite dimensional Lie group. The transform provides a unitary map from square integrable functions on the group to square integrable functions on a non-commutative dual space. We then derive the first order phase space path integral for quantum mechanics on the group by using a non-commutative dual space representation obtained through the transform. Possible advantages of the formalism include: (1) The transform provides an alternative to the spectral decomposition via representation theory of Lie groups and the use of special functions. (2) The non-commutative dual variables are physically more intuitive, since despite the non-commutativity they are analogous to the corresponding classical variables. The work is expected, among other possible applications, to allow for the metric representation of Lorentzian spin foam models in the context of quantum gravity.
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
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.
Edge effects in chirped-pulse Fourier transform microwave spectra
NASA Astrophysics Data System (ADS)
Park, G. Barratt; Field, Robert W.
2015-06-01
Recent applications of chirped-pulse Fourier transform microwave and millimeter wave spectroscopy have motivated the use of short (10-50 ns) chirped excitation pulses. In this regime, individual transitions within the chirped pulse bandwidth do not all, in effect, experience the same frequency sweep through resonance from far above to far below (or vice versa), and "edge effects" may dominate the relative intensities. We analyze this effect and provide simplifying expressions for the linear fast passage polarization response in the limit of long and short excitation pulses. In the long pulse limit, the polarization response converges to a rectangular function of frequency, and in the short pulse limit, the polarization response morphs into a form proportional to the window function of the Fourier-transform-limited excitation pulse.
A simple scanning mirror mechanism for a Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Brasunas, John C.; Cushman, G. Mark
1998-04-01
We present a simple scanning mirror mechanism for a Fourier transform spectrometer, consisting of a voice coil actuator, a ball-bearing slide, and a single cube corner mirror or retroreflector. The use of a single cube corner reduces significantly the sensitivity of the Fourier transform spectrometer to the tilt of its moving mirror, enabling the simple mechanism. With simple velocity feedback using a linear velocity transducer, we achieve a scan speed stability of 2%-5% (root-mean-square) for scan speeds from 40 to 440 ?m/s for a travel of 2.2 cm, corresponding to a spectral resolution of 0.06 cm-1. Fringe amplitude stability is about 5%. This scan mechanism was operated at standard temperature and pressure, but the relatively minute amount of lubricant in the ball-bearing slide may indicate possible operation under vacuum and/or cryogenic conditions.
Perfect vortex beam: Fourier transformation of a Bessel beam.
Vaity, Pravin; Rusch, Leslie
2015-02-15
We derive a mathematical description of a perfect vortex beam as the Fourier transformation of a Bessel beam. Building on this development, we experimentally generate Bessel-Gauss beams of different orders and Fourier transform them to form perfect vortex beams. By controlling the radial wave vector of a Bessel-Gauss beam, we can control the ring radius of the generated beam. Our theoretical predictions match with the experimental results and also provide an explanation for previous published works. We find the perfect vortex resembles that of an orbital angular momentum (OAM) mode supported in annular profiled waveguides. Our prefect vortex beam generation method can be used to excite OAM modes in an annular core fiber. PMID:25680159
Fourier transform Raman approach to structural correlation in hemoglobin derivatives
B. Venkatesh; S Ramasamy; M Mylrajan; R Asokan; P. T Manoharan; J M. Rifkind
1999-01-01
In order to obtain information on the structural aspects of hemoglobin (Hb), Fourier transform Raman (FT-R) measurements on various ferrous, ferric derivatives and nickel reconstituted Hb (NiHb) has been made. FT-R spectra for these derivatives were obtained by laser excitation in the near infrared region (NIR) (1064 nm) whereby the wave-number region (600–1700 cm?1) related to both porphyrin ring modes
Physics 343 Lecture # 5: Sun, Stars, and Planets; Fourier Transforms
Baker, Andrew J.
Physics 343 Lecture # 5: Sun, Stars, and Planets; Fourier Transforms #12; Schedule 12, 2007 Physics/Astronomy 343 4 Size, mass, and distance of the Sun ---3.74 x 108 s 11.9 years 3.156 x 107 s 1 year Period ---778 x 106 km 483 x 106 mi 150 x 106 km 93 x 106 mi Distance From Sun 2.0 x
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.
Fourier transform profilometry by using digital dc subtraction
NASA Astrophysics Data System (ADS)
Wongjarern, J.; Widjaja, J.; Sangpech, W.; Thongdee, N.; Santisoonthornwat, P.; Traisak, O.; Chuamchaitrakool, P.; Meemon, P.
2014-06-01
A new method for eliminating unwanted background of Fourier transform profilometry (FTP) by using simple dc bias and background eliminations from the deformed grating images is proposed. The proposed method has an advantage over a conventional FTP in that the 3-D object profile can be accurately measured although original fundamental spectra are corrupted by a zeroth-order spectrum. Experimental verifications of the proposed method are presented.
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.
Geosynchronous imaging Fourier transform spectrometer (GIFTS): Imaging and tracking capability
D. K. Zhou; A. M. Larar; Xu Liu; R. A. Reisse; G. E. Bingham; L. J. Zollinger; J. J. Tansock; W. L. Smith; H. E. Revercomb; Ronald J. Huppi
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 mum, 6.0 to 4.4 mum) using two 128times128 detector arrays with a spectral resolution of 0.57 cm-1 with a scan duration of ~11 seconds. From a geosynchronous orbit, the
Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions
Wu, Yinghua
Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions Xin an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch as an extension of the recently developed matching-pursuit/split-operator-Fourier-transform MP/SOFT method1
Ab initio prediction of metabolic networks using Fourier transform mass spectrometry data
Breitling, Rainer
; Nicholson et al., 2004). Fourier transform ion cyclotron resonance mass spec- trometry (FT-ICR MS or simplyAb initio prediction of metabolic networks using Fourier transform mass spectrometry data Rainer8, Canada Received 1 February 2006; accepted 19 May 2006 Fourier transform mass spectrometry has
Cohen, Ronald C.
, the saturated hydrocarbons. In this direction we have begun to apply Fourier transform microwave spectroscopyFourier 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
Wavelength-encoded tomography based on optical temporal Fourier transform
Zhang, Chi; Wong, Kenneth K. Y., E-mail: kywong@eee.hku.hk [Photonic Systems Research Laboratory, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road (Hong Kong)
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.
Fourier transform light scattering angular spectroscopy using digital inline holography.
Kim, Kyoohyun; Park, YongKeun
2012-10-01
A simple and practical method for measuring the angle-resolved light scattering (ARLS) from individual objects is reported. Employing the principle of inline holography and a Fourier transform light scattering technique, both the static and dynamic scattering patterns from individual micrometer-sized objects can be effectively and quantitatively obtained. First, the light scattering measurements were performed on individual polystyrene beads, from which the refractive index and diameter of each bead were retrieved. Also, the measurements of the static and dynamic light scattering from intact human red blood cells are demonstrated. Using the present method, an existing microscope can be directly transformed into a precise instrument for ARLS measurements. PMID:23027312
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
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.
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.
NASA Astrophysics Data System (ADS)
Vdovenko, Sergey I.; Gerus, Igor I.; Zhuk, Yuri I.; Kukhar, Valery P.; Röschenthaler, Gerd-Volker
2014-10-01
IR Fourier spectra of two enaminoketones with general formula F3Csbnd COsbnd CRdbnd CHsbnd N(CH3)2, R = F (DMTFBN); R = CH3, (DMTMBN) were studied in various pure solvents. For comparison results of earlier investigated enaminoketone R = H (DMTBN) was also presented. On the basis of NMR and IR spectra it was shown that enaminoketones DMTBN, DMTFBN and DMTMBN presented in solutions as equilibrium of two conformers, (E-s-Z) ? (E-s-E) (for DMTFBN these conformers are denoted as (Z-s-Z) and (Z-s-E), respectively). DFT calculations were carried out to evaluate relative energy and dipole moment of each spatial form. It was shown that ‘closed-ring' complex formation between (E-s-Z) and (E-s-E) conformers of DMTBN accounts for discrepancies between DFT calculations of conformer relative energies and experimentally evaluated enthalpies of (E-s-Z) ? (E-s-E) equilibrium. In ?-substituted DMTFBN and DMTMBN, where formation of ‘closed-ring' complex was impossible we did not observe such discrepancies. For both (E-s-Z) and (E-s-E) conformers of the DMTBN and DMTMBN the main influence on the ?˜(Cdbnd O) vibrations has the solvent's hydrogen bond donor (HBD) acidity, whereas for the DMTFBN an influence of the solvent's polarity/polarizability dominated.
Desorption-Ionization Techniques and Fourier Transform Mass Spectrometry.
NASA Astrophysics Data System (ADS)
Wang, Binghuang
1990-01-01
Viable ionization techniques are crucial for the structural characterization of involatile and thermally labile compounds by mass spectrometry. To obtain the actual structure of a large ion, especially in the presence of more than one component, tandem mass spectrometry (MS/MS or MS^{rm n}) is a favored approach. Fourier-transform mass spectrometry is a highly promising method for the mass analysis of large ions, with its advantage of ultrahigh resolution, multichannel recording and unique capability for tandem mass spectrometry. In this thesis, a novel SIMS ion source, microMEVVA, introduces multiply-charged primary ions such as Fe ^{2+}, Ta^{(2 -4)+}, W^{(2-6)+} , and Pb^{2+} into a Fourier-transform mass spectrometer to give ~50 muA/cm ^2 current densities at the sample. Maximum ion accelerating potential of 11 kV thus makes possible a maximum ion energy of 66 keV. The efficiency for desorption ionization of crystal violet and gramicidin S is greatly increased by changing from 17 to 38 keV primary ion energy and from 10 to 1 mus ion pulse duration, but is affected less by ion mass. Reactions between tungsten ions and neutral molecules show an increasing cross section for charge exchange with increasing ion charge; only W ^{1+} participates in ion -molecule reactions with chlorotrimethylsilane. Sodium-attached molecular ions, m/z 1164, from gramicidin S can be dissociated in a Fourier-transform mass spectrometer with 65% efficiency using a 50 muA beam of 70 eV electrons for 500 mus, with a high yield of sequence-specific ions. Fragmentation is much more extensive than that from collisionally activated dissociation or 193 nm photodissociation. Also listed are the publications of five other research projects in this area on which the author participated.
Two-dimensional Fourier transform of scaled Dirac delta curves.
Guizar-Sicairos, Manuel; Gutiérrez-Vega, Julio C
2004-09-01
We obtain a Fourier transform scaling relation to find analytically, numerically, or experimentally the spectrum of an arbitrary scaled two-dimensional Dirac delta curve from the spectrum of the nonscaled curve. An amplitude factor is derived and given explicitly in terms of the scaling factors and the angle of the forward tangent at each point of the curve about the positive x axis. With the scaling relation we determine the spectrum of an elliptic curve by a circular geometry instead of an elliptical one. The generalization to N-dimensional Dirac delta curves is also included. PMID:15384434
Parallelisation of a 2-D Fast Fourier Transform Algorithm
NASA Astrophysics Data System (ADS)
Hammersley, Andrew
The calculation of two and higher-dimension Fast Fourier Transforms (FFT’s) are of great importance in many areas of data analysis and computational physics. The two-dimensional FFT is implemented for a parallel network using a master-slave approach. In-place performance is good, but the use of this technique as an “accelerator” is limited by the communications time between the host and the network. The total time is reduced by performing the host-master communications in parallel with the master-slave communications. Results for the calculation of the two-dimensional FFT of real-valued datasets are presented.
Hard X-Ray Fourier Transform Holography with Zone Plates
Watanabe, Norio; Yokosuka, Hiroki; Ohigashi, Takuji; Aoki, Sadao; Takano, Hidekazu; Takeuchi, Akihisa; Suzuki, Yoshio
2004-05-12
Using two zone plates, a hard x-ray lens-less Fourier transform holographic microscope with cone-beam illumination was investigated at SPring-8 BL20XU. One zone plate was placed on the optical axis, and another zone plate was placed 16 mm downstream and 9 {mu}m off the optical axis. The diverging x-rays from the focus of the upstream zone plate illuminated a specimen where the focus of the downstream zone plate was placed. A hologram of a copper mesh of 12.7 {mu}m pitch could be obtained. The intensity and the phase could be successfully reconstructed with sub-micron resolution.
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
NASA Astrophysics Data System (ADS)
Klimyk, A.; Patera, J.
2007-09-01
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms involving the symmetric and antisymmetric multivariate sine and cosine functions.
Fourier Transform Infrared Spectroscopy of Trifluoroiodomethane ICP Discharge
NASA Astrophysics Data System (ADS)
Fagioli, Cassius; Urrabazo, David; Goeckner, Matthew
2012-10-01
Trifluoroiodomethane (CF3I) is an experimental gas that currently is being considered for semiconductor etching. We will report the breakdown characteristics of CF3I in an ICP plasma. In this study, the gas chemistry was examined through the use of Fourier transform infrared (FTIR) spectroscopy. This allowed us to identify the fraction of CF3I remaining in the discharge as well as some of the daughter species produced. Our results indicate that the major multi-atomic species found in the system include Tetrafluoromethane (CF4) and Trifluoromethyl (CF3). Mass balance examination also suggests the creation of atomic and molecular Iodide.
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.
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.
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 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.
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.
Analytical design of curved holographic optical elements for Fourier transform
NASA Astrophysics Data System (ADS)
Talatinian, A.; Pluta, Mieczyslaw
1991-10-01
This paper presents an analytical method for determining the grating vector distribution of holographic Fourier transform lens (FTL) recorded on a curved substrate. The design method is based on analytic ray-tracing procedure that exploits the minimization of the mean-squared difference of the propagation vectors between the actual output and desired output rays. This minimization yields an analytic solution for the optimal grating vector. The simulation of spot diagrams has allowed us to state that the designed grating vector distribution is optimal for a sufficiently wide spatial frequency range.
Laser and Fourier Transform Spectroscopy of Gas Phase Molecules
Leah Christine O'Brien
1987-01-01
Laser and Fourier transform spectroscopy were used to study a variety of gas phase molecules. A series of calcium and strontium monoalkoxides, CaOR and SrOR (R=H, CH_3, CH _2CH_3, CH(CH _3)_2, CH_2CH _2CH_3, CH _2(CH_2)_2 CH_3, CH_2 (CH_3)CH_2 CH_3 and C(CH_3) _3) was studied by laser induced fluorescence and laser excitation techniques. The A - X and B - X
Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform
S. B. WEINSTEIN; PAUL M. EBERT
1971-01-01
The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the bunks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier
On integral and finite Fourier transforms of continuous q-Hermite polynomials
Atakishiyeva, M. K.; Atakishiyev, N. M.
2009-05-15
We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H{sub n}(x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.
Voigt line infrared atmospheric transmittance calculations by Fourier transform
NASA Astrophysics Data System (ADS)
Neuendorffer, A. C.
1980-04-01
The absorption coefficient space of an IR atmospheric path contains the linear superposition of many Voigt spectral lines. This paper discusses the practical application of Karp's method to the simulation of satellite transmittance and radiance observations by using fast Fourier transforms on the recursively generated Voigt transforms. Although the procedure is physically straightforward, it is nonetheless computationally demanding and suited primarily to narrow isolated Q-branch regions. Performing the calculation on a 2.4/cm wide 15-micron CO2 Q-branch region demonstrates that 4% of the total absorption takes place above 0.1 mb. This absorption is in the cold mesopause and results in a 1-2% radiation deficit with its inclusion in a satellite radiation calculation.
Fourier Transform for Fermionic Systems and the Spectral Tensor Network
NASA Astrophysics Data System (ADS)
Ferris, Andrew J.
2014-07-01
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.
Fast Fourier Transform Co-processor (FFTC), towards embedded GFLOPs
NASA Astrophysics Data System (ADS)
Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Witte, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland; Kopp, Nicholas
2012-10-01
Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co-Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment. In frame of the ESA activity "Fast Fourier Transform DSP Co-processor (FFTC)" (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following: • Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP. • The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance. The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10?sec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT-based processing tasks. A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses. The paper will give an overview on the project, including the results of the validation of the FFTC ASIC prototypes.
Distillation protocols for Fourier states in quantum computing
Cody Jones
2013-03-13
Fourier states are multi-qubit registers that facilitate phase rotations in fault-tolerant quantum computing. We propose distillation protocols for constructing the fundamental, $n$-qubit Fourier state with error $O(2^{-n})$ at a cost of $O(n \\log n)$ Toffoli gates and Clifford gates, or any arbitrary Fourier state using $O(n^2)$ gates. We analyze these protocols with methods from digital signal processing. These results suggest that phase kickback, which uses Fourier states, could be the current lowest-overhead method for generating arbitrary phase rotations.
Integrated optics in an electrically scanned imaging Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Breckinridge, James B. (inventor); Ocallaghan, Fred G. (inventor)
1982-01-01
An efficient, lightweight and stable, Fourier transform spectrometer was developed. The mechanical slide mechanism needed to create a path difference was eliminated by the use of retro-reflecting mirrors in a monolithic interferometer assembly in which the mirrors are not at 90 degrees to the propagation vector of the radiation, but rather at a small angle. The resulting plane wave fronts create a double-sided inteferogram of the source irradiance distribution which is detected by a charge-coupled device image sensor array. The position of each CCD pixel in the array is an indication of the path difference between the two retro-reflecting mirrors in the monolithic optical structure. The Fourier transform of the signals generated by the image sensor provide the spectral irradiance distribution of the source. For imaging, the interferometer assembly scans the source of irradiation by moving the entire instrument, such as would occur if it was fixedly mounted to a moving platform, i.e., a spacecraft. During scanning, the entrace slot to the monolithic optical structure sends different pixels to corresponding interferograms detected by adjacent columns of pixels of the image sensor.
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.
The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): noise performance
NASA Astrophysics Data System (ADS)
Taylor, Joe K.; Revercomb, Henry E.; Tobin, David C.; Best, Fred A.; Knuteson, Robert O.; Elwell, John D.; Cantwell, Gregory W.; Scott, Deron K.; Bingham, Gail E.; Smith, William L.; Zhou, Daniel K.; Reisse, Robert A.
2006-12-01
The NASA New Millennium Program (NMP) Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) instrument was designed to demonstrate new and emerging technologies and provide immense improvements in satellite based remote sensing of the atmosphere from a geostationary orbit [1]. Combining a Fourier Transform Spectrometer (FTS) and Large Area Focal Plane Arrays, GIFTS measures incident infrared radiance with an extraordinary combination of spectral, temporal, and spatial resolution and coverage. Thermal vacuum testing of the GIFTS Engineering Development Unit (EDU) was performed at the Space Dynamics Laboratory and completed in May 2006 [2,3]. The GIFTS noise performance measured during EDU thermal vacuum testing indicates that threshold performance has been realized, and that goal performance (or better) has been achieved over much of both the Longwave Infrared (LWIR) and Short/Midwave Infrared (SMWIR) detector bands. An organizational structure for the division of the noise sources and effects for the GIFTS instrument is presented. To comprehensively characterize and predict the effects of measurement noise on expected instrument performance, the noise sources are categorically divided and a method of combining the independent effects is defined. Within this architecture, the total noise is principally decomposed into spectrally correlated noise and random (spectrally uncorrelated) noise. The characterization of the spectrally correlated noise sources specified within the structure is presented in detail.
Use of wavelet and fast Fourier transforms in pharmacodynamics.
Mager, Donald E; Abernethy, Darrell R
2007-05-01
Progress has been made in the development and application of mechanism-based pharmacodynamic models for describing the drug-specific and physiological factors influencing the time course of responses to the diverse actions of drugs. However, the biological variability in biosignals and the complexity of pharmacological systems often complicate or preclude the direct application of traditional structural and nonstructural models. Mathematical transforms may be used to provide measures of drug effects, identify structural and temporal patterns, and visualize multidimensional data from analyses of biomedical signals and images. Fast Fourier transform (FFT) and wavelet analyses are two methodologies that have proven to be useful in this context. FFT converts a signal from the time domain to the frequency domain, whereas wavelet transforms colocalize in both domains and may be utilized effectively for nonstationary signals. Nonstationary drug effects are common but have not been well analyzed and characterized by other methods. In this review, we discuss specific applications of these transforms in pharmacodynamics and their potential role in ascertaining the dynamics of spatiotemporal properties of complex pharmacological systems. PMID:17142645
Image tamper detection algorithm based on Radon and Fourier-Mellin transform
Tao Jing; Xinghua Li; Feifei Zhang
2010-01-01
Copy and Move is a very common way of image tampering. In order to detect images through rotation, scaling and other operations quickly and efficiently, image tamper detection based on Radon and Fourier-Mellin transform is presented. First calculate the testing image blocks through the Radon and Fourier-Mellin transform, and then extract the characteristic value of transformation results, finally obtain the
The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical
Prestin, Jürgen
The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical Inversion Ralf Hielscherdimensional Radon transform on the rotation group SO(3) is an ill posed inverse problem which applies to X inversion of the onedimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete
Two-dimensional Fourier-transform spectroscopy of potassium vapor
Dai, X.; Bristow, A. D.; Karaiskaj, D.; Cundiff, S. T. [JILA, University of Colorado and National Institute of Standards and Technology, Boulder, Colorado 80309-0440 (United States)
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.
Measuring Binary Star Orbits with a Dispersed Fourier Transform Spectrograph
NASA Astrophysics Data System (ADS)
Behr, Bradford B.; Hajian, A. R.; Cenko, A. T.; McMillan, R. S.; Murison, M.; Hindsley, R.; Meade, J.
2010-01-01
The Dispersed Fourier Transform Spectrograph (dFTS) concept combines a Michelson interferometer with a dispersive spectrograph to provide high-resolution optical spectra of stellar targets. An internal laser metrology system calibrates the wavelength scale, yielding radial velocity accuracy as small as 1.5 m/s without a superposed reference spectrum. We deployed our second-generation instrument, dFTS2, to the Steward Observatory 2.3-meter Bok Telescope from June 2007 to June 2008, and undertook an observing program on spectroscopic binary stars, with the goal of constraining the velocity semi-amplitudes K1 and K2 of the binary orbits with unprecedented accuracy. We present orbital parameters for six spectroscopic binary systems and calculate stellar masses with relative uncertainties of 0.2% to 1.1%.
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.
Identification of Amanita mushrooms by fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Zhao, Dezhang; Liu, Gang; Song, Dingshan; Liu, Jian-hong; Zhou, Yilan; Ou, Jiaming; Sun, Shizhong
2006-09-01
Amanita is one of cosmopolitan genera of basidiomycetes. This genus contains some of the most poisonous toadstools, as well as several species of the most favorite edible mushrooms. In this paper, Fourier transform infrared spectroscopy was used for obtaining vibrational spectra of the fruiting bodies of wild growing Amanita mushrooms. The results show that the mushrooms exhibit characteristic spectra, whose strong absorption bands appear at about 1655, 1076, and 1040 cm -1. The vibrational spectra indicate that the main compositions of the Amanita mushrooms are proteins and polysaccharides. The observed spectral differences might be used to discriminate different species of Amanita. It is showed that FTIR spectroscopic method is a valuable tool for rapid and nondestructive identification of Amanita mushrooms.
Optimizing architectures for parallel fast Fourier transform processing
NASA Astrophysics Data System (ADS)
Bardin, R. K.; Sisk, J. D.
1989-12-01
In the design of high-performance embedded processor systems dedicated to a predefined range of tasks, the best designs will result from the simultaneous optimization of the hardware architecture and the algorithms for the required task suite. This paper presents studies in progress of techniques for such optimizations applied to synthetic-aperture radar (S AR) and inverse SAR (ISAR) image processing algorithms. Our approach has been to implement scaled-down model calculations of real test problems on a variable-topology parallel test processor. We present here some initial results on the parallelization of the fast Fourier transform (.1-F1) algorithm from this investigation, and propose an enhancement of the hypercube processor topology which appears advantageous for many applications.
Fourier transform infrared and Raman spectral investigations of 5-aminoindole
NASA Astrophysics Data System (ADS)
Arjunan, V.; Puviarasan, N.; Mohan, S.
2006-05-01
Fourier transform infrared (FT-IR) and Raman (FT-Raman) spectra of 5-aminoindole has been recorded and analysed. The FT-IR spectrum of the compound was recorded in a BrukerIFS 66 V spectrometer in the range 4000-400 cm -1 and the FT-Raman spectrum was also recorded in the same instrument in the region 3500-100 cm -1. Observed frequencies for normal modes are compared with those calculated form normal co-ordinate analysis. The shift in the frequencies of the fundamental modes with the substituent amino group and the mixing of different normal modes are discussed with the help of potential energy distribution (PED) calculated through normal co-ordinate analysis.
Generation of Fourier-transform-limited heralded single photons
U'Ren, Alfred B.; Jeronimo-Moreno, Yasser [Division de Fisica Aplicada, Centro de Investigacion Cientifica y Educacion Superior de Ensenada (CICESE), Baja California, 22860 (Mexico); Garcia-Gracia, Hipolito [Photonics and Mathematical Optics Group, Tecnologico de Monterrey, Nuevo Leon, 64849 (Mexico)
2007-02-15
In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets.
Initial Results from the USNO Dispersed Fourier Transform Spectrograph
Hajian, A R; Cenko, A T; Olling, R P; Mozurkewich, D; Armstrong, J T; Pohl, B; Petrossian, S; Knuth, K H; Hindsley, R B; Murison, M; Efroimsky, M; Dantowitz, R; Kozubal, M; Currie, D G; Nordgren, T E; Tycner, C; McMillan, R S; Hajian, Arsen R.; Behr, Bradford B.; Cenko, Andrew T.; Olling, Robert P.; Mozurkewich, David; Pohl, Brian; Petrossian, Sevan; Knuth, Kevin H.; Hindsley, Robert B.; Murison, Marc; Efroimsky, Michael; Dantowitz, Ronald; Kozubal, Marek; Currie, Douglas G.; Nordgren, Tyler E.; Tycner, Christopher; Millan, Robert S. Mc
2006-01-01
We have designed and constructed a ``dispersed Fourier Transform Spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity disadvantage of a conventional FTS for high resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a simple and inexpensive laser metrology system, which enables very precise calibration of the interferometer wavelength scale. The fusion of interferometric and dispersive technologies with a laser metrology system yields an instrument well-suited to stellar spectroscopy, velocimetry, and extrasolar planet detection, which is competitive with existing high-resolution, high accuracy stellar spectrometers. In this paper, we describe the design of our prototype dFTS, explain the algorithm we use to efficiently reconstruct a broadband spectrum from a sequence of narrowband i...
Sound resonance in pipes with discrete Fourier transform
NASA Astrophysics Data System (ADS)
Aljalal, Abdulaziz M.
2015-09-01
Sound resonance in pipes is investigated using a readily available setup consisting of a pipe, loudspeaker, microphone, and laptop. Discrete Fourier transform is used to extract the amplitude and phase spectra from the recorded sound enabling determination of locations and shapes of resonance peaks accurately. Either white noise signal or sharp pulse signal is used as an excited input sound signal. Both have broad frequency spectra and the difference between them is explored. The shapes of the amplitude and phase spectra are found to be well fitted to the predicted shapes. The pipe is either closed at both ends, closed at only one end, or open at both ends. The speed of sound and the effective location of reflection at the open end are in excellent agreement with theory.
Fourier transform infrared spectroscopy for process monitoring and control
NASA Astrophysics Data System (ADS)
Solomon, Peter R.; Morrison, Philip W., Jr.; Serio, Michael A.; Carangelo, Robert M.; Markham, James R.; Bates, Stephen C.; Cosgrove, Joseph E.
1992-08-01
An important requirement in many industries is the ability to perform on-line monitoring and control of harsh, multi-phase process streams. During the last ten years, significant progress has occurred in the hardware and applications for Fourier Transform Infrared (FT-IR) spectroscopy. Instrumentation is now available which can perform, in harsh environments, continuous unattended and simultaneous measurements of absorbed (or reflected) and emitted radiation. The applications of FT-IR include: (1) concentrations of multiple species and phases (gases, liquid, particles, surfaces) as low as ppb; (2) temperatures of multiple species and phases (gases, liquid, particles, surfaces) with accuracies as good as +/- 1 degree(s)C at any elevated temperature; (3) measurement of particle sizes; (4) measurement of film thickness; (5) in-situ line-of-sight data; (6) in-situ spatially resolved data using tomography; (7) data on extracted samples; and (8) data on time scales as short as a few milliseconds.
Fourier transform infrared spectroscopy for process monitoring and control
NASA Astrophysics Data System (ADS)
Solomon, Peter R.; Morrison, Philip W., Jr.; Serio, Michael A.; Carangelo, Robert M.; Markham, James R.; Bates, Stephen C.; Cosgrove, Joseph E.
1993-03-01
An important requirement in many industries is the ability to perform on-line monitoring and control of harsh, multi-phase process streams. During the last ten years, significant progress has occurred in the hardware and applications for Fourier transform infrared (FT-IR) spectroscopy. Instrumentation is now available which can perform, in harsh environments, continuous unattended and simultaneous measurements of absorbed (or reflected) and emitted radiation. The applications of FT-IR include: (1) concentrations of multiple species and phases (gases, liquid, particles, surfaces) as low as ppb; (2) temperatures of multiple species and phases (gases, liquid, particles, surfaces) with accuracies as good as +/- 1 degree(s)C at any elevated temperature; (3) measurement of particle sizes; (4) measurement of film thickness; (5) in-situ line-of-sight data; (6) in-situ spatially resolved data using tomography; (7) data on extracted samples; and (8) data on time scales as short as a few milliseconds.
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.
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.
Initial Results from the USNO Dispersed Fourier Transform Spectrograph
Arsen R. Hajian; Bradford B. Behr; Andrew T. Cenko; Robert P. Olling; David Mozurkewich; J. Thomas Armstrong; Brian Pohl; Sevan Petrossian; Kevin H. Knuth; Robert B. Hindsley; Marc Murison; Michael Efroimsky; Ronald Dantowitz; Marek Kozubal; Douglas G. Currie; Tyler E. Nordgren; Christopher Tycner; Robert S. McMillan
2007-02-05
We have designed and constructed a ``dispersed Fourier Transform Spectrometer'' (dFTS), consisting of a conventional FTS followed by a grating spectrometer. By combining these two devices, we negate a substantial fraction of the sensitivity disadvantage of a conventional FTS for high resolution, broadband, optical spectroscopy, while preserving many of the advantages inherent to interferometric spectrometers. In addition, we have implemented a simple and inexpensive laser metrology system, which enables very precise calibration of the interferometer wavelength scale. The fusion of interferometric and dispersive technologies with a laser metrology system yields an instrument well-suited to stellar spectroscopy, velocimetry, and extrasolar planet detection, which is competitive with existing high-resolution, high accuracy stellar spectrometers. In this paper, we describe the design of our prototype dFTS, explain the algorithm we use to efficiently reconstruct a broadband spectrum from a sequence of narrowband interferograms, and present initial observations and resulting velocimetry of stellar targets.
How to tickle spins with a fourier transform NMR spectrometer.
Segawa, Takuya F; Carnevale, Diego; Bodenhausen, Geoffrey
2013-02-01
In the long bygone days of continuous-wave nuclear magnetic resonance (NMR) spectroscopy, a selected transition within a multiplet of a high-resolution spectrum could be irradiated by a highly selective continuous-wave (CW) radio-frequency (rf) field with a very weak amplitude ?(2)/(2?)?J. This causes splittings of connected transitions, allowing one to map the connectivities of all transitions within the energy-level diagram of the spin system. Such "tickling" experiments stimulated the invention of two-dimensional spectroscopy, but seem to have been forgotten for nearly 50 years. We show that tickling can readily be achieved in homonuclear systems with Fourier transform spectrometers by applying short pulses in the intervals between the sampling points. Extensions to heteronuclear systems are even more straightforward since they can be carried out using very weak CW rf fields. PMID:23281148
[Identification of musk by Fourier transform infrared spectroscopy].
Zhou, Jian; Jin, Cheng; Luo, Yun; Wu, Yan-wen; Li, Jian-yu; Luo, Yong-ming; Xiao, Xiao-he
2010-09-01
Standard nature musk and false nature musk were identified by Fourier transform infrared spectroscopy (FTIR) combined with derivative spectra in the present article. The main characteristic absorption peaks of musk represented the key components such as macrocyclic ketone (2923, 2851 cm(-1)), polypeptides (1655, 1546 cm(-1)) and steroids (1400, 1038 cm(-1)) respectively. Ensuing from the researches artificial musk and natural musk resemble the exemplar of market nature musk. Particularly, the infrared spectra of samples of natural musk and artificial musk are more similar and hard to be distinguished. In virtue of derivative spectra analysis, the resolution of spectra is advanced; several kinds of standard musk have been differentiated directly and effectively. This method was fast, sensitive, direct and nondestructive, and could be used to identify the source of rare materia medica and distinguish the counterfeits of musk successfully. PMID:21105397
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
Data processing in Fourier transform ion cyclotron resonance mass spectrometry.
Qi, Yulin; O'Connor, Peter B
2014-01-01
The Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer intricately couples advanced physics, instrumentation, and electronics with chemical and particularly biochemical research. However, general understanding of the data processing methodologies used lags instrumentation, and most data processing algorithms we are familiar with in FT-ICR are not well studied; thus, professional skill and training in FT-ICR operation and data analysis is still the key to achieve high performance in FT-ICR. This review article is focused on FT-ICR data processing, and explains the procedures step-by-step for users with the goal of maximizing spectral features, such as mass accuracy, resolving power, dynamic range, and detection limits. PMID:24403247
Fourier transform-second-harmonic generation imaging of biological tissues.
Rao, Raghu Ambekar Ramachandra; Mehta, Monal R; Toussaint, Kimani C
2009-08-17
Fourier transform-second-harmonic generation imaging is employed to obtain quantitative metrics of collagen fibers in biological tissues. In particular, the preferred orientation and maximum spatial frequency of collagen fibers for selected regions of interest in porcine trachea, ear, and cornea are determined. These metrics remain consistent when applied to collagen fibers in the ear, which can be expected from observation. Collagen fibers in the trachea are more random with large standard deviations in orientation, and large variations in maximum spatial frequency. In addition, these metrics are used to investigate structural changes through a 3D stack of the cornea. This technique can be used as a quantitative marker to assess the structure of collagen fibers that may change due to damage from disease or physical injury. PMID:19687932
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
Fourier-transform microwave spectroscopy of the CCCCl radical
NASA Astrophysics Data System (ADS)
Yoshikawa, Takashi; Sumiyoshi, Yoshihiro; Endo, Yasuki
2009-03-01
Pure rotational spectra of the CCCCl radical in a supersonic jet have been observed for the first time by Fourier-transform microwave spectroscopy. The radical was produced by a pulsed electric discharge in a C2H2 and CCl4 mixture diluted to 0.3% and 0.2% with Ne, respectively. Transitions with spin and hyperfine splittings were observed for two isotopologs, CCC35Cl and CCC37Cl, in the region from 11.4 GHz for N =2-1 to 34.2 GHz for N =6-5. The molecular constants including the hyperfine coupling constants due to the Cl nucleus have been determined precisely. From the rotational analyses and high-level ab initio calculations, the molecular structure of the CCCCl radical is concluded to be bent in the ground electronic state.
Fourier domain target transformation analysis in the thermal infrared
NASA Technical Reports Server (NTRS)
Anderson, D. L.
1993-01-01
Remote sensing uses of principal component analysis (PCA) of multispectral images include band selection and optimal color selection for display of information content. PCA has also been used for quantitative determination of mineral types and abundances given end member spectra. The preliminary results of the investigation of target transformation PCA (TTPCA) in the fourier domain to both identify end member spectra in an unknown spectrum, and to then calculate the relative concentrations of these selected end members are presented. Identification of endmember spectra in an unknown sample has previously been performed through bandmatching, expert systems, and binary classifiers. Both bandmatching and expert system techniques require the analyst to select bands or combinations of bands unique to each endmember. Thermal infrared mineral spectra have broad spectral features which vary subtly with composition. This makes identification of unique features difficult. Alternatively, whole spectra can be used in the classification process, in which case there is not need for an expert to identify unique spectra. Use of binary classifiers on whole spectra to identify endmember components has met with some success. These techniques can be used, along with a least squares fit approach on the endmembers identified, to derive compositional information. An alternative to the approach outlined above usese target transformation in conjunction with PCA to both identify and quantify the composition of unknown spectra. Preprocessing of the library and unknown spectra into the fourier domain, and using only a specific number of the components, allows for significant data volume reduction while maintaining a linear relationship in a Beer's Law sense. The approach taken here is to iteratively calculate concentrations, reducing the number of endmember components until only non-negative concentrations remain.
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.
Application of a nonuniform spectral resampling transform in Fourier-transform spectrometry.
Sarkissian, Edwin; Bowman, Kevin W
2003-02-20
We describe a nonuniform spectral resampling transform (NUSRT) that resamples a frequency-scaled spectrum that has been measured by a Fourier-transform spectrometer (FTS). Frequency scaling of a spectrum can arise from measurements made with off-axis detectors and Doppler shift induced by motion of a spaceborne FTS relative to an input radiation source. In addition, a spectrum may need to be rescaled in frequency to match spectral lines for applications such as the retrieval of atmospheric state parameters. The NUSRT is cast as a linear algebraic expression that relates a nonuniformly sampled interferogram to an input spectrum. A polynomial approximation is applied to this expression that reduces the inverse of the NUSRT to a series of Fourier transforms that can be implemented as fast Fourier transforms (FFTs). We show that this NUSRT algorithm requires on the order of 6N log N flops, which reduces the computational cost of rescaling by more than 1 order of magnitude compared with conventional FFT-based Shannon interpolation techniques while comparable accuracy is maintained. PMID:12617230
Fourier transform Raman approach to structural correlation in hemoglobin derivatives
NASA Astrophysics Data System (ADS)
Venkatesh, B.; Ramasamy, S.; Mylrajan, M.; Asokan, R.; Manoharan, P. T.; Rifkind, J. M.
1999-07-01
In order to obtain information on the structural aspects of hemoglobin (Hb), Fourier transform Raman (FT-R) measurements on various ferrous, ferric derivatives and nickel reconstituted Hb (NiHb) has been made. FT-R spectra for these derivatives were obtained by laser excitation in the near infrared region (NIR) (1064 nm) whereby the wave-number region (600-1700 cm -1) related to both porphyrin ring modes and some globin modes were monitored. Comparison of various modes was made based on previous resonance Raman (RR) results. The wave-number shifts with respect to changes in oxidation state and spin state are very similar to those observed by RR. Additional bands at 1654, 1459, and 1003 cm -1 for deoxyHb and at 1656, 1454, and 1004 cm -1 for oxy Hb can be correlated to globin modes. The shift in the position of these bands for the binding of oxygen can be related to changes in conformation during the transformation. The presence of two distinct sites in NiHb could be monitored by the use of FT-R technique.
Fourier transform Raman approach to structural correlation in hemoglobin derivatives.
Venkatesh, B; Ramasamy, S; Mylrajan, M; Asokan, R; Manoharan, P T; Rifkind, J M
1999-07-01
In order to obtain information on the structural aspects of hemoglobin (Hb), Fourier transform Raman (FT-R) measurements on various ferrous, ferric derivatives and nickel reconstituted Hb (NiHb) has been made. FT-R spectra for these derivatives were obtained by laser excitation in the near infrared region (NIR) (1064 nm) whereby the wave-number region (600-1700 cm-1) related to both porphyrin ring modes and some globin modes were monitored. Comparison of various modes was made based on previous resonance Raman (RR) results. The wave-number shifts with respect to changes in oxidation state and spin state are very similar to those observed by RR. Additional bands at 1654, 1459, and 1003 cm-1 for deoxyHb and at 1656, 1454, and 1004 cm-1 for oxy Hb can be correlated to globin modes. The shift in the position of these bands for the binding of oxygen can be related to changes in conformation during the transformation. The presence of two distinct sites in NiHb could be monitored by the use of FT-R technique. PMID:10439514
A Fast Algorithm for Nonequispaced Fourier Transforms on the Rotation Group
Prestin, Jürgen
transforms on the rotation group SO(3) motivated by a variety of applications, like protein-protein-docking [4] or texture analysis [3, 28]. Many of these algorithms are based on discrete Fourier transforms
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.
Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups
NASA Astrophysics Data System (ADS)
Guedes, Carlos; Oriti, Daniele; Raasakka, Matti
2013-08-01
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.
Transformative effects of higher magnetic field in Fourier transform ion cyclotron mass spectrometry
Karabacak, N. Murat; Easterling, Michael L.; Agar, N.Y.R.; Agar, Jeffrey N.
2010-01-01
The relationship of magnetic field strength and Fourier transform ion cyclotron resonance mass spectrometry performance was tested using three instruments with the same designs but different fields of 4.7, 7 and 9.4 tesla. We found that the theoretically predicted “transformative” effects of magnetic field are indeed observed experimentally. The most striking effects were that mass accuracy demonstrated approximately 2nd–3rd-order improvement with the magnetic field, depending upon the charge state of the analyte, and that peak splitting, which prohibited automated data analysis at 4.7 T, was not observed at 9.4 T. PMID:20444622
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.
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.
The rapid differentiation of Streptomyces isolates using Fourier transform infrared spectroscopy
Griffith, Gareth
The rapid differentiation of Streptomyces isolates using Fourier transform infrared spectroscopy putative Streptomyces spp. isolated from soil were selected to be analysed using Fourier transform infrared be used for preliminary differentiation of Streptomyces spp. at sub-species or strain level. # 2005
Hélène H. Nieuwoudt; Isak S. Pretorius; Florian F. Bauer; Daniel G. Nel; Bernard A. Prior
2006-01-01
A rapid screening method for the evaluation of the major fermentation products of Saccharomyces wine yeasts was developed using Fourier transform infrared spectroscopy and principal component factor analysis. Calibration equations for the quantification of volatile acidity, glycerol, ethanol, reducing sugar and glucose concentrations in fermented Chenin blanc and synthetic musts were derived from the Fourier transform infrared spectra of small-scale
Quantitative assessment with improved fast Fourier transform based method by signal mirroring
Andrej Prošek; Matjaž Leskovar; Borut Mavko
2008-01-01
The comparison of calculated results to experimental measurements is very important for thermal-hydraulic code qualification. Recently, it was observed that the fast Fourier transform based method (FFTBM) favors certain trends when an edge (difference) is present in the signal between the first and the last data point of the investigated time signal. Namely, the discrete Fourier transform used for the
Soo-Chang Pei; Jian-Jiun Ding; Ja-Han Chang
2001-01-01
The concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. We develop efficient algorithms for QFT, QCV, and quaternion correlation. The conventional complex two-dimensional (2-D) Fourier transform (FT) is
DISCRETE GAUSS-HERMITE FUNCTIONS AND EIGENVECTORS OF THE CENTERED DISCRETE FOURIER TRANSFORM
Santhanam, Balu
DISCRETE GAUSS-HERMITE FUNCTIONS AND EIGENVECTORS OF THE CENTERED DISCRETE FOURIER TRANSFORM Balu that these eigenvectors in the limit converge to Gauss-Hermite (G-H) functions and that the eigenvalue spectrum. Keywords: Gauss-Hermite functions, eigenvalues, eigen- vectors, discrete Fourier transform, finite
David C. Tobin; Henry E. Revercomb; Joe K. Taylor; Fred A. Best; Robert O. Knuteson; William L. Smith; John Elwell; Greg Cantwell; Gail Bingham; Joe Tansock; Robert A. Reisse; Daniel K. Zhou
2006-01-01
The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) represents a revolutionary step in satellite based remote sensing of atmospheric parameters. Using the combination of a Fourier Transform Spectrometer and Large Area Focal Plane Arrays, GIFTS measures incident infrared radiance with an unprecedented combination of spectral, temporal, and spatial resolution and coverage. In its regional sounding mode, it measures the infrared spectrum
PRIME FACTOR CYCLOTOMIC FOURIER TRANSFORMS WITH REDUCED COMPLEXITY OVER FINITE FIELDS
Wagh, Meghanad
PRIME FACTOR CYCLOTOMIC FOURIER TRANSFORMS WITH REDUCED COMPLEXITY OVER FINITE FIELDS Xuebin Wu- tiveness for long DFTs is limited by their complexities. In this paper, we propose prime factor cyclotomic Fourier transforms (PFCFTs), which use CFFTs as sub-DFTs via the prime fac- tor algorithm. When the length
Exploiting early time response using the half Fourier transform (HFT) for parameter estimation
S. Jang; Tapan K. Sarkar; C. E. Baum
2002-01-01
This paper present a new technique for estimating parameters (frequencies and damping factors) of early time responses. An early time response is composed of damped sinusoids and impulse-like components. Due to the impulse-like components, it is difficult to extract meaningful damped sinusoids. The new technique uses fractional Fourier transforms (FrFT) especially the half Fourier transform (HFT). Unlike the normal Fourier
Pulsed Fourier-transform NQR of sup 14 N with a dc SQUID
Huerlimann, M.D.; Pennington, C.H.; Fan, N.Q.; Clarke, J.; Pines, A.; Hahn, E.L. (Department of Physics, University of California, Berkeley, Berkeley, California 94720 (United States) Department of Chemistry, University of California, Berkeley, Berkeley, California 94720 (United States) Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 (United States))
1992-07-27
The zero-field free induction decay of solid ammonium perchlorate at 1.5 K has been directly detected with a dc superconducting quantum interference device. The Fourier-transform spectrum consists of three sharp lines at 17.4, 38.8, and 56.2 kHz arising from pure {sup 14}N nuclear quadrupole resonance transitions. The absence of splittings and resonance transitions from dipolar-coupled proton spins is attributed to reorientation of the ammonium groups by quantum tunneling in combination with motional averaging in the three proton levels characterized by the irreducible representation {ital T}. The measured {sup 14}N spin-spin relaxation time is 22{plus minus}2 ms and the spin-lattice relaxation time is 63{plus minus}6 ms.
Quantization maps, algebra representation and non-commutative Fourier transform for Lie groups
Guedes, Carlos; Raasakka, Matti
2013-01-01
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-commutati...
Quantum Canonical Transformations: Physical Equivalence of Quantum Theories
Arlen Anderson
1993-02-15
Two quantum theories are physically equivalent if they are related, not by a unitary transformation, but by an isometric transformation. The conditions under which a quantum canonical transformation is an isometric transformation are given.
Fractional Fourier Transform Applied to Digital Images Encryption
NASA Astrophysics Data System (ADS)
Vilardy, Juan M.; Torres, Cesar O.; Mattos, Lorenzo
2008-04-01
In the present paper a digital algorithm was developed to make phase encryption of digital indexed images to color using the fractional Fourier transform (the images in RGB are converted to indexed before to encrypt). The indexed images are represented by a matrix of M×N pixels (where M defines the height and N is the Width of the image) and a color map (it's a matrix of C×3 elements, where C indicates the colors number of the image and the number 3 indicates the three columns associated with the color components: Red, Green and Blue of each pixel of the matrix of M×N) associated to the matrix of pixels to suitably represent the color information of the image. The indexed image (matrix of M×N pixels) to encrypt is placed as the phase of a complex exponential, then is transformed three times and multiplied in intermediate steps by two random phase masks statistically independent thus to obtain the encrypted image, for decrypt the coding image the encryption procedure is applied in the inverse sense to the conjugated complex of the encrypted image, then is taken the negative of the phase of the resulting function of the decryption process and the original image is obtained this way that had been encrypted; For the color map equal procedure is applied in the encryption/decryption process described previously for the matrix of M×N pixels. In the implemented cryptographic algorithm five keys are used, constituted by three fractional orders and two random phase masks, all these keys are necessary for a correct decryption providing a dependability to the transference of images by means of the communications nets.
Fourier transform optical profilometry using fiber optic Lloyd's mirrors.
Kart, Türkay; Köso?lu, Gül?en; Yüksel, Heba; ?nci, Mehmet Naci
2014-12-10
A fiber optic Lloyd's mirror assembly is used to obtain various optical interference patterns for the detection of 3D rigid body shapes. Two types of fiber optic Lloyd's systems are used in this work. The first consists of a single-mode optical fiber and a highly reflecting flat mirror to produce bright and dark strips. The second is constructed by locating a single-mode optical fiber in a v-groove, which is formed by two orthogonal flat mirrors to allow the generation of square-type interference patterns for the desired applications. The structured light patterns formed by these two fiber Lloyd's techniques are projected onto 3D objects. Fringe patterns are deformed due to the object's surface topography, which are captured by a digital CCD camera and processed with a Fourier transform technique to accomplish 3D surface topography of the object. It is demonstrated that the fiber-optic Lloyd's technique proposed in this work is more compact, more stable, and easier to configure than other existing surface profilometry systems, since it does not include any high-cost optical tools such as aligners, couplers, or 3D stages. The fringe patterns are observed to be more robust against environmental disturbances such as ambient temperature and vibrations. PMID:25608057
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.
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.
Fourier transform Raman LIDAR for trace gas detection and quantification
NASA Astrophysics Data System (ADS)
Sentell, James C.
1994-09-01
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 florescence 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(subscript 2)F(subscript 2), are presented. For a one joule laser and a thirty (30) cm aperture operating in darkness, a concentration of 10(superscript 23) molecules/m(superscript 3) can be detected in a 60 km visibility at a range of 3.4 km.
High-resolution wide-band fast Fourier transform spectrometers
NASA Astrophysics Data System (ADS)
Klein, B.; Hochgürtel, S.; Krämer, I.; Bell, A.; Meyer, K.; Güsten, R.
2012-06-01
We describe the performance of our latest generations of sensitive wide-band high-resolution digital fast Fourier transform spectrometer (FFTS). Their design, optimized for a wide range of radio astronomical applications, is presented. Developed for operation with the GREAT far infrared heterodyne spectrometer on-board SOFIA, the eXtended bandwidth FFTS (XFFTS) offers a high instantaneous bandwidth of 2.5 GHz with 88.5 kHz spectral resolution and has been in routine operation during SOFIA's Basic Science since July 2011. We discuss the advanced field programmable gate array (FPGA) signal processing pipeline, with an optimized multi-tap polyphase filter bank algorithm that provides a nearly loss-less time-to-frequency data conversion with significantly reduced frequency scallop and fast sidelobe fall-off. Our digital spectrometers have been proven to be extremely reliable and robust, even under the harsh environmental conditions of an airborne observatory, with Allan-variance stability times of several 1000 s. An enhancement of the present 2.5 GHz XFFTS will duplicate the number of spectral channels (64k), offering spectroscopy with even better resolution during Cycle 1 observations.
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.
Fourier transform spectroscopy of doubly ionised transition elements
NASA Astrophysics Data System (ADS)
Pickering, J. C.; Thorne, A. P.; Smith, P. L.
At Imperial College we are using our unique Fourier Transform (FT) spectrometer to record high resolution spectra of doubly ionised iron group elements down to a record short wavelength of 135 nm. Improvements in the quality of astrophysical spectra observed with the new generation of high resolution spectrographs on ground and space based telescopes have highlighted the inadequacies of the laboratory atomic data base needed to interpret these observations, especially in the VUV region (below 200nm) where the majority of absorption lines from hot stars are found. In these spectra lines from doubly and singly ionised species predominate. We are using a DC Penning discharge source to excite the doubly ionised 3d-group elements. Spectra of Fe III at visible through VUV wavelengthshave been recorded at Imperial College and have been complimented with IR spectra measured at NIST. The improvement in wavelength accuracy is an order of magnitude over previous work. Branching ratios from intensity calibrated spectra will be combined with level lifetimes to yield oscillator strengths. Work on Ni III and Mn III is also underway. This work was supported in part by NASA Grant NAG5-4348 to Harvard University, and by PPARC of the UK. J.C.Pickering is supported as a Royal Society University Research Fellow
Fourier transform infrared Hadamard tomography of sooting flames
Bates, S.C.; Carangelo, R.; Knight, K.; Serio, M. )
1993-05-01
An experimental technique is described that combines tomography, Hadamard signal encodement, and a patented Fourier transform infrared (FT-IR) emission/transmission (E/T) technique to perform simultaneous spatially resolved gas species and soot measurements during combustion. Tomographic analysis of line-of-sight FT-IR data allows spatially resolved measurements to be made. Hadamard encodement of the tomographic sections increases the overall signal throughput, improving the signal to noise (S/N) ratio for each measurement. The Hadamard technique leads to a major simplification in the tomographic apparatus in that the scanning apparatus that would normally be required is eliminated, and focusing of the infrared light is much easier. An experiment demonstrating Hadamard data processing as applied to FT-IR tomography is described. Deconvolution of the encoded data is shown to be accurate and gives the predicted improvement in S/N ratio. The FT-IR Hadamard tomography is performed to measure soot in a fuel-rich diffusion flame. Spatially resolved concentration measurements agree well with previous data, and clearly show striking three-dimensional features that could not normally be measured by simple line-of-sight techniques.
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.
Fourier transform methods applied to an optical heterodyne profilometer
NASA Astrophysics Data System (ADS)
Beltrán-González, A.; García-Torales, G.; Martínez-Ponce, G.
2013-11-01
In this work, theory and experiment describe the performance of a surface profile measurement device based on optical heterodyne interferometry are presented. The object and reference beams propagating through the interferometer are obtained by single-pass through an acousto-optic modulator. The diffraction orders 0 and the Doppler-shifted +1 (object and reference beams, respectively) are manipulated to propagate collinearly towards the interferometer output where a fast photodetector is placed to collect the irradiance. The modulated optical signal is Fourier transformed using a data acquisition card and RF communications software. The peak centered at the acousto-optic frequency in the power spectrum is filtered and averaged. The irregularities on the surface of the reflective sample are proportional to the height of this peak. The profile of a reflective blazed grating has been sketched by translating laterally the sample using a nanopositioning system. Experimental results are compared to the measurement done with a scanning electron microscope. There has been found a good agreement between both methods.
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).
Fourier transform molecular rotational resonance spectroscopy for reprogrammable chemical sensing
NASA Astrophysics Data System (ADS)
Harris, Brent J.; Pulliam, Robin L.; Neill, Justin L.; Muckle, Matt T.; Reynolds, Roger; Pate, Brooks H.
2015-03-01
Molecular rotational resonance (MRR) spectroscopy gives spectral signatures with high chemical selectivity. At room temperature, the peak intensity of the MRR spectrum occurs in the 100 GHz - 1 THz frequency range for volatile species with mass <= 100 amu. Advances in high-power sub-mm-wave light sources has made it possible to implement time-domain Fourier transform (FT) spectroscopy techniques that are similar to FT nuclear magnetic resonance (FT-NMR) measurements. In these measurements, the gas sample is excited by a short (200 ns) excitation pulse that creates a macroscopic sample polarization. The electric field of the subsequent transient molecular emission is detected using a heterodyne receiver and a high-speed digitizer. FT-MRR spectroscopy offers speed and sensitivity improvements over absorption spectroscopy. For chemical analysis, FT-MRR spectrometers combine the benefits of broad chemical coverage typical of gas chromatography - mass spectrometry (GC-MS) instruments and the direct measurement capabilities of infrared gas sensors all in a reprogrammable platform. Pulse sequence measurements can be implemented for advanced spectroscopic analysis. Trace level quantitation of volatile species at ppbv concentration can be performed on the time scale of a minute. In cases where the sample is a complex mixture, a double-resonance pulse sequence can be used to achieve chemical selectivity even in cases where spectral overlap occurs. These measurement capabilities are illustrated using the application of FT-MRR spectroscopy to residual solvent analysis of pharmaceutical products.
Toward a soft x-ray Fourier-transform spectrometer
Howells, M.R.; Frank, K.; Hussain, Z.; Moler, E.J.; Reich, T. |; Moeller, D.; Shirley, D.A.
1993-10-29
The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range {+-}1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330.
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.
Remote detection of organics using Fourier transform infrared spectroscopy
Demirgian, J.C.; Spurgash, S.M.
1990-01-01
Fourier transform infrared (FTIR) spectroscopy is an ideal technique for remote detection of organic emissions. There is an atmospheric window in the 1200 to 800 cm{sup {minus}1} region, which corresponds to the fingerprint'' region for organic molecules. Virtually all organic molecules have a unique absorption/emission pattern in the fingerprint region. A remote-passive FTIR relies on ambient emission of infrared energy from organics to obtain spectra. The instrumentation consists of inlet optics, and interferometer, a mercury cadmium telluride (MCT) detector, and an on-board computer. The transportable unit measures 40 cm by 50 cm and has been used to collect data while mounted on a helicopter or ground vehicle. Through the use of this FTIR combined with least squares software, it is possible to analyze qualitatively and quantitatively for organic vapors from either the air or ground. The data presented will include quantitative releases of common organics present in incinerator stacks, hazardous wastes, and illegal laboratories. Data will be presented for pure compounds, mixtures, and target analytes in the presence of interfering compounds. The sensitivity, reproducibility, and the potential of the technique will be discussed. 1 ref., 8 figs., 6 tabs.
The use of fast Fourier transform techniques in blasting analysis
Rholl, S.A.; Stagg, M.S.
1995-12-31
The US Bureau of Mines has developed computer software which uses fast Fourier transform (FFT) techniques to evaluate blasting data. The software is useful because it allows blasters to evaluate (1) the frequency content of ground vibration time history data; (2) the effects of initiator scatter on the frequency spectra of ground vibrations; and (3) the fragmentation distribution of rock muckpiles from photographs. A one-dimensional version of the software was used in the first two cases. Monte Carlo techniques were used to simulate the scatter of initiators. The results are shown in computer generated three-dimensional color contour plots. To determine the fragment size distribution using photographic and digital image processing techniques a two-dimensional FFT routine was written. The FFT of the digitized muckpile images are filtered to remove lower spatial frequencies. The higher spatial frequencies, which are associated with rock particle edges, are subsequently enhanced. The inverse two-dimensional FFT was used to reconstruct the digital image. Photographic images taken of rock muckpiles resulting from full scale blasts at a limestone quarry were digitized and evaluated using the new FFT techniques. The fragment size distributions determined from the photographs agree with the distributions determined by partial screening.
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.
Cryogenic Fourier transform infrared spectrometer from 4 to 20 micrometers
NASA Astrophysics Data System (ADS)
Kaplan, Simon G.; Woods, Solomon I.; Jung, Timothy M.; Carter, Adriaan C.
2010-07-01
We describe the design and performance of a cryogenic Fourier transform spectrometer (Cryo-FTS) operating at a temperature of approximately 15 K. The instrument is based on a porch-swing scanning mirror design with active alignment stabilization using a fiber-optic coupled diode laser and voice-coil actuator mechanism. It has a KBr beamsplitter and has been integrated into an infrared radiometer containing a calibrated Si:As blocked impurity band (BIB) detector. Due to its low operating temperature, the spectrometer exhibits very small thermal background signal and low drift. Data from tests of basic spectrometer function, such as modulation efficiency, scan jitter, spectral range, and spectral resolution are presented. We also present results from measurements of faint point-like sources in a low background environment, including background, signal offset and gain, and spectral noise equivalent power, and discuss the possible use of the instrument for spectral characterization of ground-based infrared astronomy calibration sources. The Cryo-FTS is presently limited to wavelengths below 25 micrometers but can be in principle extended to longer wavelengths with changes in beamsplitter and detector.
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 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.
Cho, Byungmoon; Yetzbacher, Michael K; Kitney, Katherine A; Smith, Eric R; Jonas, David M
2009-11-26
Four-level two-dimensional (2D) Fourier transform relaxation spectra are simulated with response functions for a chromophore pair in the exponential relaxation (optical Bloch model) limit. The parameters in this study are chosen to model coupled carbonyl stretching vibrations. As long as coherence persists, every peak in the real 2D spectra has a partially mixed absorptive/dispersive ("phase-twisted") shape because the nonlinear signals are not symmetric with respect to interchange of the first two pulses. This asymmetry in 2D relaxation spectra arises from coherence between singly excited states and a red shift of the doubly excited state. Coherence between the singly excited states causes oscillation of the 2D spectra and the associated spectrally resolved pump-probe (SRPP) transients at the quantum beat frequency. Projecting the phase-twisted nature of the 2D peaks onto the detection frequency axis, the SRPP peaks are also asymmetric about their maximum when not at maximum or minimum amplitude. Three-dimensional Fourier transform (3DFT) methods are used to simulate absorption/dispersion and beam geometry distortions of the multilevel 2D spectra with cross peaks. The distortions can be understood by consideration of their effects on individual coherence pathways that contribute to peaks in the 2D spectra. The beam geometry distortion explains some unequal cross peak amplitudes previously observed experimentally by Khalil et al. (J. Chem. Phys. 2004, 121, 362). A representation of 2D spectra that reduces beam geometry distortion is presented. If the transformation to correct for beam geometry distortion is combined with the transformations that correct absorptive/dispersive propagation distortions (J. Chem. Phys. 2007, 126, 044511), the recovered 2D spectrum matches the ideal 2D spectrum after all coherence is destroyed. In the presence of coherence, the new representation reduces the error in the distorted 2D spectrum by a factor of 4 for practical 2D-IR experimental conditions. PMID:19780599
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.
Geostationary Imaging Fourier Transform Spectrometer (GIFTS): science applications
NASA Astrophysics Data System (ADS)
Smith, W. L.; Revercomb, H. E.; Zhou, D. K.; Bingham, G. E.; Feltz, W. F.; Huang, H. L.; Knuteson, R. O.; Larar, A. M.; Liu, X.; Reisse, R.; Tobin, D. C.
2006-12-01
A revolutionary satellite weather forecasting instrument, called the "GIFTS" which stands for the "Geostationary Imaging Fourier Transform Spectrometer", was recently completed and successfully tested in a space chamber at the Utah State University's Space Dynamics Laboratory. The GIFTS was originally proposed by the NASA Langley Research Center, the University of Wisconsin, and the Utah State University and selected for flight demonstration as NASA's New Millennium Program (NMP) Earth Observing-3 (EO-3) mission, which was unfortunately cancelled in 2004. GIFTS is like a digital 3-d movie camera that, when mounted on a geostationary satellite, would provide from space a revolutionary four-dimensional view of the Earth's atmosphere. GIFTS will measure the distribution, change, and movement of atmospheric moisture, temperature, and certain pollutant gases, such as carbon monoxide and ozone. The observation of the convergence of invisible water vapor, and the change of atmospheric temperature, provides meteorologists with the observations needed to predict where, and when, severe thunderstorms, and possibly tornados, would occur, before they are visible on radar or in satellite cloud imagery. The ability of GIFTS to observe the motion of moisture and clouds at different altitudes enables atmospheric winds to be observed over vast, and otherwise data sparse, oceanic regions of the globe. These wind observations would provide the means to greatly improve the forecast of where tropical storms and hurricanes will move and where and when they will come ashore (i.e., their landfall position and time). GIFTS, if flown into geostationary orbit, would provide about 80,000 vertical profiles per minute, each one like a low vertical resolution (1-2km) weather balloon sounding, but with a spacing of 4 km. GIFTS is a revolutionary atmospheric sensing tool. A glimpse of the science measurement capabilities of GIFTS is provided through airborne measurements with the NPOESS Airborne Sounding Testbed - Interferometer (NAST-I).
Fourier Transform Emission Spectroscopy of TaO.
Ram; Bernath
1998-09-01
The emission spectrum of TaO, excited in a tantalum hollow cathode lamp, has been observed at high resolution using a Fourier transform spectrometer. In addition to previously known transitions, a number of new bands have been identified and assigned as belonging to two new electronic transitions: H2Pi1/2-X2Delta3/2 and K2Phi5/2-X2Delta3/2. A rotational analysis ofthe 0-0 and 0-1 bands of the H2Pi1/2-X2Delta3/2 transition and of the 0-1, 1-2, 0-0, 1-0, and 2-1 bands of theK2Phi5/2-X2Delta3/2 transition has been carried out, providing the following equilibrium constants for the ground X2Delta3/2 state:omegae = 1028.9060(15) cm-1, omegaexe = 3.58928(66) cm-1, Be = 0.40289737(139) cm-1, alphae = 0.00185445(83) cm-1, andre = 1.6873430(29) Å. The principal molecular constants for the H2Pi1/2 state are T00 = 20 634.32758 (40) cm-1,B0 = 0.3766867(31) cm-1, and r0 = 1.7450604(72) Å, while the equilibrium constants for the K2Phi5/2 state areomegae = 905.4549(15) cm-1, omegaexe = 3.67601(64) cm-1, Be = 0.37965102(36) cm-1, alphae = 0.00189370(21) cm-1, andre = 1.7382343(8) Å. Although the H2Pi1/2 and K2Phi5/2 states have been observed previously in matrix isolation experiments, our work on these states is the first in the gas phase. Copyright 1998 Academic Press. PMID:9724588
Libyan Desert Glass: New field and Fourier transform infrared data
NASA Astrophysics Data System (ADS)
Fröhlich, F.; Poupeau, G.; Badou, A.; Le Bourdonnec, F. X.; Sacquin, Y.; Dubernet, S.; Bardintzeff, J. M.; Véran, M.; Smith, D. C.; Diemer, E.
2013-12-01
Results are presented of new geological observations and laboratory analyses on Libyan Desert Glass (LDG), a unique kind of impact glass found in Egypt, probably 28.5-29.4 million years in age. A new LDG occurrence has been discovered some 50 km southward of the main LDG occurrences in the Great Sand Sea. From Fourier transform infrared (FTIR) analysis, the molecular structure of LDG is refined and significant differences are shown between LDG specimens and other pure silica glasses (fulgurite, industrial fused quartz, and amorphous biogenic silica) that are related to differences in their structures. The slight variations observed here for the mean Si-O-Si angle between the different glasses are attributed to their thermal histories. With regard to the other glasses analyzed, the LDG infrared spectral parameters point to a higher ratio of discontinuities and defects in the tetrahedral (SiO4) network. The quantitative mineralogical constitutions of sandstones and quartzites from the LDG geological setting were analyzed by FTIR. Cretaceous sandstones have a specific composition (about 90 wt% quartz, 10% dickite), clearly different from the Paleozoic ones (about 90 wt% quartz, but ?7% kaolinite). It is shown that the reddish silts bearing the LDG are constituted mainly of microquartz enriched with dickite, whose particle size distribution is characteristic of fluvio-lacustrine deposits, probably Oligocene to Miocene in age. The target rocks, most probably quartz sand, resulted from the weathering (loss of the cementing microquartz) of the Cretaceous sandstones from the Gilf Khebir Plateau with deposition in a high-energy environment.
A Fourier-transform infrared spectroscopy study of sugar glasses.
Wolkers, Willem F; Oliver, Ann E; Tablin, Fern; Crowe, John H
2004-04-28
Fourier-transform infrared spectroscopy (FTIR) was used to study the hydrogen-bonding interactions that take place in vitrified carbohydrates of different chain lengths. The band position of the OH stretching band (vOH) and the shift in band position as a function of temperature were determined from the FTIR spectra as indicators for the length and strength of intermolecular hydrogen bonds, respectively. Differential scanning calorimetry (DSC) was used to corroborate the FTIR studies and to measure the change in heat capacity (delta C(p)) that is associated with the glass transition. We found that with increasing T(g), the band position of vOH increases, the wavenumber-temperature coefficient of vOH in the glassy state, WTC(g), increases, whereas (delta C(p) decreases. The positive correlation that was found between vOH and the glass transition temperature, T(g), indicates that the length of the hydrogen bonds increases with increasing T(g). The increase in WTC(g) with increasing T(g) indicates that the average strength of hydrogen bonding decreases with increasing T(g). This implies that oligo- and polysaccharides (high T(g)) have a greater degree of freedom to rearrange hydrogen bonds during temperature changes than monosaccharides (low T(g)). Interestingly, WTC(g) and delta C(p) showed a negative linear correlation, indicating that the change in heat capacity during the glass transition is associated with the strength of the hydrogen-bonding network in the glassy state. Furthermore, we report that introduction of poly-L-lysine in glassy sugar matrices decreases the average length of hydrogen bonds, irrespective of the size of the carbohydrate. Palmitoyl-oleoyl-phosphatidylcholine (POPC) vesicles were found to only interact with small sugars and not with dextran. PMID:15063194
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.
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.
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.
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.
Soo-Chang Pei; Chien-Cheng Tseng; Min-Hung Yeh
1999-01-01
This paper is concerned with the definition of the discrete fractional Fourier transform (DFRFT). First, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions, which are eigenfunctions of the continuous Fourier transform and by performing a novel error-removal procedure. Then, the result of the eigendecomposition of the DFT matrix is used to
Barshan, Billur; Ayrulu, Birsel
2002-01-01
This study investigates fractional Fourier transform pre-processing of input signals to neural networks. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a. Judicious choice of this parameter can lead to overall improvement of the neural network performance. As an illustrative example, we consider recognition and position estimation of different types of objects based on their sonar returns. Raw amplitude and time-of-flight patterns acquired from a real sonar system are processed, demonstrating reduced error in both recognition and position estimation of objects. PMID:11958486
Complexation of chitosan with acetic acid according to Fourier transform Raman spectroscopy data
NASA Astrophysics Data System (ADS)
Mikhailov, G. P.; Tuchkov, S. V.; Lazarev, V. V.; Kulish, E. I.
2014-06-01
The results of the interaction between the protonated chitosan (CHI) macromolecule and the acetate ion in dilute acetic acid solutions were studied by Fourier transform Raman spectroscopy and quantum-chemical modeling. The complexation of CHI with the acetate ion showed itself as the 934 cm-1 band in the Raman spectrum, which suggests the formation of [CHI+ · CH3COO-] type ion pairs. It was concluded that a comparative analysis of the integrated intensities of the Raman bands in the range 880-940 cm-1 makes it possible to judge about the relative content of hydrated acetate ions, CHI macromolecules of the [CHI+ · CH3COO-] complex, and acetic acid molecules not involved in CHI protonation.
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
Liouville transformations and quantum reflection
NASA Astrophysics Data System (ADS)
Dufour, G.; Guérout, R.; Lambrecht, A.; Reynaud, S.
2015-08-01
Liouville transformations of Schrödinger 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.
STAT692, Wisconsin Rowe, MCW The Fourier Transform in MRI/fMRI
Rowe, Daniel B.
STAT692, Wisconsin Rowe, MCW The Fourier Transform in MRI/fMRI Daniel B. Rowe, Ph.D. dbrowe/Edge detetection. One Dimensional fMRI Time Series · fMRI time series Fourier spectrum and filtering. FMRI Time Image Processing · Smoothing/Edge detetection. One Dimensional fMRI Time Series · fMRI time series
Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method
Th. A. Rijken
2014-09-19
In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for $p_f \
Winick, Kim
1918 IEEE JOURNAL OF QUANTUM ELECTRONICS. VOL. 26, NO. 11. NOVEMBER 1990 Design of Corrugated Waveguide Filters by Fourier- Transform Abstract-A new, approximate, corrugated waveguide filter design method is developed for thin film optical waveguides. The method de- termines both the corrugation period
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
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,...
[General expression of optic path difference of reflecting rotating Fourier transform spectrometer].
Zhou, Jin-Song; Xiangli, Bin; Wei, Ru-Yi; Jing, Juan-Juan
2011-01-01
The principle of reflecting rotating Fourier transform spectrometer was introduced in the present paper. Based on the Malus law and reflecting characteristic of cube corner, the optic path difference of reflecting rotating Fourier transform spectrometer was analyzed and calculated by choosing the center of rotating mirror as a reference point of the aplanatic surface of incidence beam and return beam. General expression of optic path difference at any time and maximal optic path difference of reflecting rotating Fourier transform spectrometer was presented. The factors that influence the maximal optic path difference and the period of optic path difference were analyzed. The results provide a theoretical guidance for design and manufacture of reflecting rotating Fourier transform spectrometer. PMID:21428102
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).
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 and can cause intermittent operation, system failure, electrical shock hazard, and even fire. Further, arc
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...
The Plancherel Theorem for Fourier-Laplace-Nahm Transform for Connections on the Projective Line
NASA Astrophysics Data System (ADS)
Szabó, Szilárd
2015-09-01
We prove that the Fourier-Laplace-Nahm transform for connections with finitely many logarithmic singularities and a double pole at infinity on the projective line, all with semi-simple singular parts, is a hyper-Kähler isometry.
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...
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...
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
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.
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.
High signal-to-noise Fourier transform spectroscopy with light emitting diode sources
NASA Astrophysics Data System (ADS)
Bhosale, J. S.
2011-09-01
A temperature tuned light emitting diode (LED) has several advantages over conventional sources for Fourier transform spectroscopy. The large radiation density of LEDs, concentrated in a small spectral region, is ideal for high resolution Fourier transform spectroscopy where a high signal-to-noise (S/N) ratio is desired. A simple, inexpensive LED source leads to a superior performance at high resolutions exceeding that of a tungsten halogen lamp, in the visible region of spectrum.
High-Performance Nonscanning Fourier-Transform Spectrometer That Uses a Wollaston Prism Array
NASA Astrophysics Data System (ADS)
Komisarek, Dan; Reichard, Karl; Merdes, Dan; Lysak, Dan; Lam, Philip; Wu, Shudong; Yin, Shizhuo
2004-07-01
A high-performance nonscanning Fourier-transform spectrometer is reported that is composed mainly of a Wollaston prism array and a two-dimensional photodetector array. It is a substantial improvement over existing Wollaston prism based nonscanning Fourier-transform spectrometers because it offers finer spectral resolution and smaller size. Such spectrometers will find important applications in remote chemical and biological sensing, environmental monitoring, medical diagnosis, etc. Experimental results are consistent with theoretical analyses.
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
Discrete Fourier transform in nanostructures using scattering Michael N. Leuenbergera)
Flatte, Michael E.
, but no entanglement is needed for the implementation of quantum algorithms in the unary repre- sentation performs DFTs at the frequency of the computer clock speed. © 2004 American Institute of Physics. DOI: 10.1063/1.1737804 I. INTRODUCTION The fast developing fields of quantum computing and quantum information processing
High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.
1997-01-01
Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.
Robert A. Brown; Hongmei Zhu; J. Ross Mitchell
2005-01-01
The recently developed S-transform (ST) combines features of the Fourier and Wavelet transforms; it reveals frequency variation over both space and time. It is a potentially powerful tool that can be applied to medical image processing including texture analysis and noise filtering. However, calculation of the ST is computationally intensive, making conventional implementations too slow for many medical applications. This
Adapted fourier transform of schwartz spaces for certain nilpotent Lie groups
Hamid Zahir
1989-01-01
In the framework of the deformation program (*-product), initiated in [1], a nilpotent Fourier transform Theta was introducted ([4], [5]). This transformation is defined for f; in S(G) : a dense invariant open subset F of g* is parametrized by F = R2k × V where V is the set of coadjoint orbits in F and: X ? bdg, (p,
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.
Palmer, Paul
Seasonal variation of carbon monoxide in northern Japan: Fourier transform IR measurements 2006; published 10 August 2006. [1] Tropospheric carbon monoxide (CO) was measured throughout 2001. Matsumi, and H. Tanimoto (2006), Seasonal variation of carbon monoxide in northern Japan: Fourier
Locke, Jonathan; White, Paul R
2011-10-01
The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species. PMID:21973352
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.
Paris-Sud XI, Université de
COLOR IMAGE WATERMARKING USING QUATERNION FOURIER TRANSFORM Patrick Bas, Nicolas Le Bihan and Jean and the Quaternion Fourier Transform (QFT). Previous color image watermarking methods are first presented with an unique quaternion number having three imaginary parts. The QFT is presented, this transform depends
Fourier analysis and cortical architectures: the exponential chirp transform
Schwartz, Eric L.
¡ Eric L. Schwartz ¢ £ Dept. Biomedical ¤ Dept. Cognitive and Engineering Neural Systems Boston in the text. 1 #12;transform" (ECT). The method is, however, general for other forms of map- ping, or warp
Fourier analysis and cortical architectures: the exponential chirp transform \\Lambda
Schwartz, Eric L.
Bonmassar y Eric L. Schwartz z yDept. Biomedical zDept. Cognitive and Engineering Neural Systems Boston in the text. 1 #12; transform'' (ECT). The method is, however, general for other forms of map ping, or warp
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.
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
Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions
NASA Technical Reports Server (NTRS)
Holmes, J. J.; Balanis, C. A.
1974-01-01
Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.
Fourier-transform spectroscopy: new methods and applications: introduction by the feature editors
NASA Astrophysics Data System (ADS)
Traub, Wesley A.; Winkel, Raymond J., Jr.; Goldman, Aaron
1996-06-01
We are pleased to introduce this special issue of papers on Fourier-transform spectroscopy, which grew out of a recent topical meeting sponsored by the Optical Society of America. The topical meeting welcomed all researchers who practice the art of Fourier-transform spectroscopy in the laboratory, in the atmosphere, and in space. The power and the wide applicability of Fourier-transform spectroscopy unite these fields with a common mathematical and instrumental bond. The meeting probed each of these areas in depth, bringing out new ideas for instrumentation, analysis, and applications. There was a strong sentiment at the meeting that the quality of papers and posters was exceptionally high and that it would be important for future progress in the field to have the results of this meeting captured in print. This special issue is the fruit of that effort.
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.
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.
The su(2)_{\\alpha} Hahn oscillator and a discrete Hahn-Fourier transform
Jafarov, E I; Van der Jeugt, J
2011-01-01
We define the quadratic algebra su(2)_{\\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can be extended to representations of su(2)_{\\alpha}. We investigate a model of the finite one-dimensional harmonic oscillator based upon this algebra su(2)_{\\alpha}. It turns out that in this model the spectrum of the position and momentum operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials. The operation mapping position wavefunctions into momentum wavefunctions is studied, and this so-called discrete Hahn-Fourier transform is computed explicitly. The matrix of this discrete Hahn-Fourier transform has many interesting properties, similar to those of the traditional discrete Fourier transform.
Understanding colloidal quantum dot excitation with solution photon correlation fourier spectroscopy
Heathcote, S. Leigh (Stephanie Leigh)
2015-01-01
Colloidal quantum dots (CQDs) have useful absorption and emission properties but exist in inhomogenous batches. Solution photon correlation fourier spectroscopy (S-PCFS) combines interferometry with fluorescence correlation ...
NASA Astrophysics Data System (ADS)
Ahadi, Amirhossein; Khoshnevis, Ahmad; Saghir, M. Ziad
2014-04-01
Series of thermodiffusion experiments using optical digital interferometry (ODI) have been conducted onboard the International Space Station. Conventionally, the two-dimensional (2D) fast Fourier transform (FFT) fringe analysis technique has been applied as a fast and reliable technique to extract data. In this study, for the first time, the windowed Fourier transform (WFT) method is used to analyze the same experiments. In this method, a Fourier transformation is applied on the fringes at two different stages: initially, during the filtration of the non-zero peaks and then on the wrapped phase image. We provide a detailed comparison between FFT and WFT results of binary and ternary mixtures for ODI thermodiffusion experiments. The substantial enhancements of this method are presented and discussed for different experiments conducted for both binary and ternary mixtures. We show that while disturbances in the phase fringe pattern can cause significant error in FFT techniques, if the windowed Fourier filtration (WFF) parameters are properly chosen this type of noise can be eliminated during WFF analysis. The importance of replacing the FFT method becomes more pronounced for the ternary system, as this method fails to reconcile reliable concentration profiles. The results of this work can show that the application of the windowed Fourier transform in optical digital interferometry investigations show improved results over the same experiments analyzed using FFT methods, especially for experiments involving very small heat and mass fluxes such as the Soret effect in multicomponent mixtures.
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.
NASA Astrophysics Data System (ADS)
He, Qian; Wang, Guangping; Wu, Jingli; Li, Junwei
2014-11-01
As the impact of the instrument internal error, external interference and other factors, the interferogram measured by Fourier transform spectrometer is asymmetric, result in the complex outcome after Fourier transform. Currently, most radiometric calibration method used for Fourier transform spectrometer is usually based on real spectrums, which is converted from the above complex spectrum by calculating magnitude value or make the phase correction first. Proceed from error sources and mechanisms of the Fourier transform spectrometer, we propose a multi-point radiometric calibration method based on complex spectral data to improve the processing efficiency and accuracy, which is obtained by the original interferogram via Fourier transform. We solving the instrument response function include linear gain and offset by complex spectrum above to calculate complex spectral radiance. Compared with the traditional method based on real spectrum, the present efficient method does not limited to real spectrum and the phase correction is not required. In this paper, we use BOMEM's MR304 Fourier transform infrared spectrometer and the DCN1000N3 blackbody made by HGH Infrared Systems to carry out the radiation calibration experiment in laboratory. The results show that, the amplitude of complex radiance spectrum obtained by this method has a high consistency with the theoretical value, while the extra imaginary spectrum is similar with the difference between results and theoretical value in absolute value and trends. It proved that, this multi-point radiometric calibration method by using the amplitude of complex spectral data is highly reliable; meanwhile, the imaginary spectrum can reflect the calibration error very well and offer a new technical approach for accuracy evaluation research.
Reflections on the q-Fourier transform and the q-Gaussian function
NASA Astrophysics Data System (ADS)
Plastino, A.; Rocca, M. C.
2013-09-01
The standard q-Fourier Transform (qFT) of a constant diverges, which begs for a better treatment. In addition, Hilhorst has conclusively proved that the ordinary qFT is not of a one-to-one character for an infinite set of functions [H.J. Hilhorst, J. Stat. Mech. (2010) P10023]. Generalizing the ordinary qFT analyzed in [S. Umarov, C. Tsallis, S. Steinberg, Milan J. Math. 76 (2008) 307], we appeal here to a complex q-Fourier transform, and show that the problems above mentioned are overcome.
Fast transform from an adaptive multi-wavelet representation to a partial Fourier representation
Jia, Jun [ORNL; Harrison, Robert J [ORNL; Fann, George I [ORNL
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.
Performance of portable high-resolution Fourier transform spectrometer for trace gas remote sensing
NASA Astrophysics Data System (ADS)
Wei, Haoyun; Ren, Libing; Fan, Dongdong; Soucy, Marc-André
2012-12-01
Fourier Transform Spectrometer (FTS), with its throughput, multiplex, and spectra resolution advantages, has become one of the most promising atmospheric remote-sensing instruments for the research on the global climax change and air quality evaluation. In this paper, the instrument concept and performances of a compact, portable, high resolution Fourier transform spectrometer, named B3M-FTS are reported. Sample atmospheric absorption spectra and corresponding retrieval results measured by the FTS are given. The success of atmospheric composition profile retrieval using the FTS measurements provides a useful way to understand the atmospheric chemistry, and validates the feasibility of atmospheric composition remote sensing using high resolution FTS.
[Research on spatially modulated Fourier transform imaging spectrometer data processing method].
Huang, Min; Xiangli, Bin; Lü, Qun-Bo; Zhou, Jin-Song; Jing, Juan-Juan; Cui, Yan
2010-03-01
Fourier transform imaging spectrometer is a new technic, and has been developed very rapidly in nearly ten years. The data catched by Fourier transform imaging spectrometer is indirect data, can not be used by user, and need to be processed by various approaches, including data pretreatment, apodization, phase correction, FFT, and spectral radicalization calibration. No paper so far has been found roundly to introduce this method. In the present paper, the author will give an effective method to process the interfering data to spectral data, and with this method we can obtain good result. PMID:20496726
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.
Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage
NASA Astrophysics Data System (ADS)
Ahmad, Salman; Hussain, Shafqat; Siddiqui, Abuzar Abid; Ali, Asad; Aqeel, Muhammad
2014-06-01
Magneto-Hydrodynamic (MHD) flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-?-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.
Underwood, D.
1986-09-05
Simple examples of finding tracks by Fourier transform with filter or correlation function are presented. Possibilities for using this method in more complicated real situations and the processing times which might be achieved are discussed. The method imitates the simplest examples in the literature on optical pattern recognition and optical processing. The possible benefits of the method are in speed of processing in the optical Fourier transform wherein an entire picture is processed simultaneously. The speed of a computer vector processor may be competitive with present electro-optical devices. 2 refs., 6 figs.
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.
Fourier-transform spectroscopy and potential construction of the (2)1? state in KCs
NASA Astrophysics Data System (ADS)
Birzniece, I.; Nikolayeva, O.; Tamanis, M.; Ferber, R.
2015-04-01
The paper presents an empirical pointwise potential energy curve (PEC) of the (2)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-1 involved in the fit were based on Fourier-Transform spectroscopy data obtained with 0.01 cm-1 accuracy from the laser-induced (2)1? ? X1?+ fluorescence spectra. Buffer gas Ar was used to facilitate the appearance of rotation relaxation lines in the spectra, thus enlarging the (2)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-1. The obtained value of the ?-doubling constant q = + 1.8 × 10-6 cm-1 for J' > 50 and v' ? [0, 6] is in an excellent agreement with q = + 1.84 × 10-6 cm-1 reported in Kim, Lee, and Stolyarov [J. Mol. Spectrosc. 256, 57-67 (2009)].
Development of Scanning-Type X-ray Fourier Transform Holography
NASA Astrophysics Data System (ADS)
Nomura, K.; Awaji, N.; Doi, S.; Isogami, S.; Kodama, K.; Nakamura, T.; Suzuki, M.; Tsunoda, M.
2011-09-01
We developed a scanning-type x-ray Fourier transform holography and applied it to both the soft and hard x-ray regions. For this approach, we prepared the holography mask and the imaging object separately and placed them in contact with each other. In this configuration, the illuminated area can be changed by moving the sample relative to the mask via the translation stage. In this case, an image can be recovered by Fourier inversion of the hologram as in the usual lensless Fourier transform holography. This method also reduces the relative vibration between the mask and sample, and provides good quality images. The method was successfully applied to large-area imaging of magnetic domains in a Co/Pt perpendicular magnetic film with soft x-rays. In addition, cross-sectional imaging of Cu interconnect lines was performed in the hard x-ray region.
Operational Properties of Two Integral Transforms of Fourier Type and their Convolutions
Bui Thi Giang; Nguyen Van Mau; Nguyen Minh Tuan
2009-01-01
. In this paper we present the operational properties of two integral transforms of Fourier type, provide the formulation of\\u000a convolutions, and obtain eight new convolutions for those transforms. Moreover, we consider applications such as the construction\\u000a of normed ring structures on $$L_{1}({\\\\mathbb{R}})$$, further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel.
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.
Green's function of a finite chain and the discrete Fourier transform
S. Cojocaru
2007-04-22
A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered as an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.
Prediction of valid acidity in intact apples with Fourier transform near infrared spectroscopy
LIU Yan-de; YING Yi-bin; FU Xia-ping
To develop nondestructive acidity prediction for intact Fuji apples, the potential of Fourier transform near infrared (FT-NIR) method with fiber optics in interactance mode was investigated. Interactance in the 800 nm to 2619 nm region was measured for intact apples, harvested from early to late maturity stages. Spectral data were analyzed by two multivariate calibra- tion techniques including partial least
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...
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
Donald Francis Smith
2007-01-01
The ultra-high mass resolving power and high mass accuracy of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) have been shown to be well suited for the characterization of highly complex mixtures. Petroleum mixtures, arguably the most complex on the planet, have been extensively characterized by FT-ICR MS. This new field of \\
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...
NASA Astrophysics Data System (ADS)
Qureshi, Kalim; Rashid, Haroon
In this paper, we present the performance analysis of two parallel Fast Fourier Transform algorithms, binary-exchange and transpose algorithms. These two algorithms were implemented and tested on a cluster of PCs using Message Passing Interface (MPI). The binary-exchange algorithm implementation was showing less processing and communication time than transpose algorithm.
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
The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.
ERIC Educational Resources Information Center
Suslick, Kenneth S.; And Others
1987-01-01
Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)
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
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 ...
Trillo, C; Doval, A F; López-Vázquez, J C
2010-07-01
Phase evaluation methods based on the 2D spatial Fourier transform of a speckle interferogram with spatial carrier usually assume that the Fourier spectrum of the interferogram has a trimodal distribution, i. e. that the side lobes corresponding to the interferential terms do not overlap the other two spectral terms, which are related to the intensity of the object and reference beams, respectively. Otherwise, part of the spectrum of the object beam is inside the inverse-transform window of the selected interference lobe and induces an error in the resultant phase map. We present a technique for the acquisition and processing of speckle interferogram sequences that separates the interference lobes from the other spectral terms when the aforementioned assumption does not apply and regardless of the temporal bandwidth of the phase signal. It requires the recording of a sequence of interferograms with spatial and temporal carriers, and their processing with a 3D Fourier transform. In the resultant 3D spectrum, the spatial and temporal carriers separate the conjugate interferential terms from each other and from the term related to the object beam. Experimental corroboration is provided through the measurement of the amplitude of surface acoustic waves in plates with a double-pulsed TV holography setup. The results obtained with the proposed method are compared to those obtained with the processing of individual interferograms with the regular spatial-carrier 2D Fourier transform method. PMID:20639988
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
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...
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
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.
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.
Rohith Reddy; Brynmor Davis; Paul Scott Carney; Rohit Bhargava
2011-01-01
Fourier transform infrared (FT-IR) spectroscopic imaging is an emerging technique that provides both spatially and chemically resolved information. The rich chemical content of data may be utilized for computer-aided determinations of structure and pathologic state (cancer diagnosis) in histological tissue sections for Prostate and Breast Cancer. Recent results show that tissue type (histological) classification can be performed to an accuracy
Quantitative analysis of nitrate ion in ambient aerosols by fourier-transform infrared spectroscopy
James S. Bogard; Stanley A. Johnson; Romesh Kumar; Paul T. Cunningham
1982-01-01
A sensitive, quantitative method has been developed for determining the amount of nitrate ion in atmospheric aerosol samples collected by impaction. This method consists of Fourier-transform infrared absorption spectrophotometry of the sample in a KBr matrix. The nitrate ion can be determined from the absorbance at 1384 and 2430 cmâ»Â¹, the two absorption bands covering different ranges of the amount
Coherent Fourier transform electrical pulse Shijun Xiao and Andrew M. Weiner
Purdue University
Coherent Fourier transform electrical pulse shaping Shijun Xiao and Andrew M. Weiner School and links 1. A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929- 1960 (2000). 2. J. D. McKinney, D. E. Leaird, A. M. Weiner, "Millimeter-wave arbitrary waveform
Fourier transform spectroscopy of the A1?-X1?+ transition of BH and BD
NASA Astrophysics Data System (ADS)
Fernando, W. T. M. L.; Bernath, P. F.
1991-02-01
The A1?-X1?+ transitions of BH and BD were recorded in emission near 4330 Å by Fourier transform spectroscopy. For BH improved line positions and molecular constants were determined from the analysis of the data. New bands of BD were found in our spectra. Alfred P. Sloan Fellow; Camille and Henry Dreyfus Teacher Scholar.
$(p,q)-$deformed Fibonacci and Lucas polynomials: characterization and Fourier integral transforms
Mahouton Norbert Hounkonnou; Sama Arjika
2013-07-09
A full characterization of $(p,q)$-deformed Fibonacci and Lucas polynomials is given. These polynomials obey non-conventional three-term recursion relations. Their generating functions and Fourier integral transforms are explicitly computed and discussed. Relevant results known in the literature are examined as particular cases.
Discrete Fourier Transform Problems with star are just for fun: they ...
Using the polar coordinates in the plane, we can represent every complex. number w = a + bi .... N. We define its (discrete) Fourier Transform as another complex vector. F = (F(0),...,F(N - 1)) .... integral presents no difficulty. It is our purpose to ...
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 ...
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.
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...
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 ...
NASA Astrophysics Data System (ADS)
Clerbaux, Cathy; Chazette, Patrick; Megie, Gerard J.
1995-12-01
Atmospheric spectra to be recorded in the infrared spectral range by a spaceborne Fourier transform spectrometer using a nadir view have been simulated. Relevant spectral domains have been selected for the retrieve of carbon monoxide, methane, ozone and nitrous oxide. A new inversion algorithm using neural networks techniques is proposed to retrieve integrated contents and low resolution vertical profiles.
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)
Effect of Apodization on the Retrieval of Geophysical Parameters from FourierTransform Spectrometers
Umberto Amato; Daniela de Canditiis; Carmine Serio
1998-01-01
The problem of the effect of apodization on the retrieval of geophysical parameters from infrared radiances recorded by Fourier transform spectrometers has been analytically and numerically addressed. Exploiting a matrix representation of apodization, we first derive a general analytical expression for the apodized covariance matrix and then show that apodization, when properly applied, has no effect on retrievals. The methodology
The Use of the Fourier Transform for Solving Linear Elasticity Problems
NASA Astrophysics Data System (ADS)
Kozubek, Tomas; Mocek, Lukas
2011-11-01
This paper deals with solving linear elasticity problems using a modified fictitious domain method and an effective solver based on the discrete Fourier transform and the Schur complement reduction in combination with the null space method. The main goal is to show step by step all ingredients of the numerical solution.
NASA Astrophysics Data System (ADS)
Mocek, Lukas; Kozubek, Tomas
2011-09-01
The paper deals with the numerical solution of elliptic boundary value problems for 2D linear elasticity using the fictitious domain method in combination with the discrete Fourier transform and the FETI domain decomposition. We briefly mention the theoretical background of these methods, introduce resulting solvers, and demonstrate their efficiency on model benchmarks.
Two-dimensional fast Fourier transform and power spectrum for wear particle analysis
Z. Peng; T. B. Kirk
1997-01-01
Statistical parameters, such as Ra and Rq, have been widely used to investigate the roughness of wear particle surfaces in the literature. It has been reported that wear particle analysis based only on numerical characterization is often insufficient to distinguish certain types of wear debris. In this study, two-dimensional fast Fourier transform, power spectrum and angular spectrum analyses are applied
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
Adaptation of a Fast Fourier Transform-Based Docking Algorithm for Protein Design
Love, John J.
Adaptation of a Fast Fourier Transform-Based Docking Algorithm for Protein Design PO-SSU HUANG,1 InterScience (www.interscience.wiley.com). Abstract: Designing proteins with novel protein/protein for protein docking and protein design. We describe here the sequence- independent generation of protein dimer
Sparks, Donald L.
the Surface Chemistry of a Drying Soil. (4172) Authors: C.E. Dowding - Univ. of Stellenbosch, South Africa M chemistry largely overlooked. The present study, involving the examination of a manganese-rich soil on pH changes in real-time at a soil surface. Attenuated total reflectance Fourier transform infrared
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-...
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…
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...
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 ...
Modeled vs. actual performance of the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS)
Gregory W. Cantwell; John D. Elwell; Roy W. Esplin; Mark P. Esplin; Deron K. Scott; Lorin J. Zollinger; Gail E. Bingham; Henry E. Revercomb; William L. Smith; Robert A. Reisse
2006-01-01
The NASA Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) has been completed as an Engineering Demonstration Unit (EDU) and has recently finished thermal vacuum testing and calibration. The GIFTS EDU was designed to demonstrate new and emerging sensor and data processing technologies with the goal of making revolutionary improvements in meteorological observational capability and forecasting accuracy. The GIFTS EDU includes a
On-orbit calibration of the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS)
Robert O. Knuteson; Fred A. Best; Gail E. Bingham; John D. Elwell; Henry E. Revercomb; David C. Tobin; Deron K. Scott; Joseph K. Taylor; William L. Smith Sr.
2005-01-01
The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) sensor has been designed to provide highly accurate radiometric and spectral radiances in order to meet the requirements of remote sensing of atmospheric motion from a geostationary orbit. The GIFTS sensor was developed under NASA New Millenium Program funding to demonstrate the tracking of infrared water vapor features in the atmosphere with high
G. E. Bingham; R. E. Anderson; G. W. Cantwell; D. K. Zhou; D. K. Scott; R. W. Esplin; G. B. Hansen; S. M. Jensen; M. D. Jensen; S. B. Brown; L. J. Zollinger; V. A. Thurgood; M. P. Esplin; R. J. Huppi; H. E. Revercomb; F. A. Best; D. C. Tobin; J. K. Taylor; R. O. Knuteson; W. L. Smith; R. A. Reisse; R. Hooker
2006-01-01
The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS), developed for the NASA New Millennium Program (NMP) Earth Observing-3 (EO-3) mission, has recently completed a series of uplooking atmospheric measurements. The GIFTS development demonstrates a series of new sensor and data processing technologies that can significantly expand geostationary meteorological observational capability. The resulting increase in forecasting accuracy and atmospheric model development utilizing
On-orbit calibration of the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS)
F. A. Best; G. E. Bingham; J. D. Elwell; D. C. Tobin; D. K. Scott; W. L. Smith
The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) sensor has been designed to provide highly accurate radiometric and spectral radiances in order to meet the requirements of remote sensing of atmospheric motion from a geostationary orbit. The GIFTS sensor was developed under NASA New Millenium Program funding to demonstrate the tracking of infrared water vapor features in the atmosphere with high
Fred A. Best; Henry E. Revercomb; David C. Tobin; Robert O. Knuteson; Joseph K. Taylor; Donald J. Thielman; Douglas P. Adler; Mark W. Werner; Scott D. Ellington; John D. Elwell; Deron K. Scott; Gregory W. Cantwell; Gail E. Bingham; William L. Smith
2006-01-01
The NASA New Millennium Program's Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) instrument was designed to provide enormous advances in water vapor, wind, temperature, and trace gas profiling from geostationary orbit. The top-level instrument calibration requirement is to measure brightness temperature to better than 1 K (3 sigma) over a broad range of atmospheric brightness temperatures, with a reproducibility of +\\/-0.2
NASA Astrophysics Data System (ADS)
Mandon, Julien; Guelachvili, Guy; Picqué, Nathalie
2007-08-01
A new method, FM-FTS, combining frequency modulation heterodyne laser spectroscopy and Fourier transform spectroscopy is presented. It provides simultaneous sensitive measurement of absorption and dispersion profiles with broadband spectral coverage capabilities. Experimental demonstration of the overtone spectrum of C2H2 in the 1.5 ?m region is presented.
APDE2 2012 Problems 7 Fourier Transforms Hand in at lecture on Tuesday 20th March: Q. 1, 2.
Dettmann, Carl
APDE2 2012 Problems 7 Fourier Transforms Hand in at lecture on Tuesday 20th March: Q. 1, 2. 1 and is to be downloaded or copied for your private study only. #12;APDE2 2012 Problems 7 Fourier Transforms (b) Now
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.
Fourier transforms with rotations on circles or ellipses in signal and image processing
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.
2015-03-01
Fast unitary transforms are widely used in different areas such as data compression, pattern recognition and image reconstruction, interpolation, linear filtering, and spectral analysis. In this paper, we analyze the general concept of rotation and processing of data around not only circles but ellipses, in general. For that, we describe and analyze the general concept of the elliptic Fourier transform which was developed by Grigoryan in 2009. The block-wise representation of the discrete Fourier transform is considered in the real space, which is effective and that can be generalized to obtain new methods in spectral analysis. The N-point Elliptic discrete Fourier transform (EDFT) uses as a basic 2 × 2 transformation the rotations around ellipses. The EDFT distinguishes well from the carrying frequencies of the signal in both real and imaginary parts. It also has a simple inverse matrix. It is parameterized and includes also the DFT. Our preliminary results show that by using different parameters, the EDFT can be used effectively for solving many problems in signal and image processing field, in which includes problems such as image enhancement, filtration, encryption and many others.
Efficient method for localized functions using domain transformation and Fourier sine series
Jovanovic, Raka; Alharbi, Fahhad H
2014-01-01
An efficient approach to handle localized states by using spectral methods (SM) in one and three dimensions is presented. The method consists of transformation of the infinite domain to the bounded domain in $(0, \\pi)$ and using the Fourier sine series as a set of basis functions for the SM. It is shown that with an appropriate choice of transformation functions, this method manages to preserve the good properties of original SMs; more precisely, superb computational efficiency when high level of accuracy is necessary. This is made possible by analytically exploiting the properties of the transformation function and the Fourier sine series. An especially important property of this approach is the possibility of calculating the Hartree energy very efficiently. This is done by exploiting the positive properties of the sine series as a basis set and conducting an extinctive part of the calculations analytically. We illustrate the efficiency of this method and implement it to solve the Poisson's and Helmholtz equ...
Detecting of copy-move forgery in digital images using fractional Fourier transform
NASA Astrophysics Data System (ADS)
Yang, Renqing; Bai, Zhengyao; Yin, Liguo; Gao, Hao
2015-07-01
Copy-move forgery is one of the most simple and commonly used forging methods, where a part of image itself is copied and pasted on another part of the same image. This paper presents a new approach for copy-move forgery detection where fractional Fourier transform (FRFT) is used. First, the 1-level discrete wavelet transform (DWT) of the forged image is to reduce its dimension. Next, the low frequency the sub-band is divided into overlapped blocks of equal size. The fractional Fourier transform of each block is calculated and the vector of the coefficients is constructed. All feature vectors are sorted using lexicographical order. Finally, the difference of adjacent feature vectors is evaluated and employed to locate the duplicated regions which have the same feature vectors. Experimental results show that the proposed method is effective in detection of the copy-move forgery regions.
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.
A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis
NASA Technical Reports Server (NTRS)
Ioup, G. E.
1980-01-01
Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.
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.
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.
Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform.
Poyneer, Lisa A; Gavel, Donald T; Brase, James M
2002-10-01
Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack-Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector-matrix-multiply reconstructors. The boundary problem that prevented the accurate reconstruction of phase in circular apertures by means of square-grid Fourier transforms (FTs) is identified and solved. The methods are adapted for use on the Fried geometry. Detailed performance analysis of mean squared error and noise propagation for FT methods is presented with the use of both theory and simulation. PMID:12365629
[The calculation of the dose from a 60Co source using 3-dimensional Fourier transform].
Vasil'ev, V N
1999-01-01
The distribution of a dose in tissue-equivalent phantoms was calculated through convolution of scattered photon flux by using three-dimensional Fourier transform. A simplified model of a scattering kernel is presented, wherein multiple scattering radiation is taken into account by a water point source accumulation factor. A 64 x 64 x 64 grid calculation lasts about 2 sec on a routine personal computer (three-dimensional Fourier transform and convolution). The dose were calculated in the cube, 32 x 32 x 32 cm in size and in the cylinder, 12 cm in diameter for 4 x 4-to-20 x 20-cm radiation fields. The results are in good agreement with the reference data and Monte Carlo simulation results. PMID:10560089
Simulation of micromechanical behavior of polycrystals: finite elements vs. fast Fourier transforms
Lebensohn, Ricardo A [Los Alamos National Laboratory; Prakash, Arun [IWM FREIBURG
2009-01-01
In this work, we compare finite element and fast Fourier transform approaches for the prediction of micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular, stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases - rolling of aluminium and wire drawing of tungsten - are used to evaluate the predictions of the two mode1s. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison to the fast Fourier transform simulations.
NASA Astrophysics Data System (ADS)
Zhang, Xinya; Jackson, Ted; Lafond, Emmanuel
2005-02-01
A laboratory instrument that utilizes broadband laser ultrasonics and two-dimensional Fourier transformation for signal processing has been developed to characterize the properties of various foils and plates. Laser ultrasonics generation is achieved by using a pulsed laser which deposits pulsed laser energy on the surface of the specimen. The displacement of the resulting broadband ultrasonic modes is monitored using a two-wave mixing photorefractive interferometer. By means of the two-dimensional Fourier transformation of the detected spatial and temporal displacement wave forms, the image of density of state (DOS) for the excited ultrasound is obtained, and from it the materials properties are extracted. Results are presented for a 150?m thick paper sample, a 50?m stainless steel foil, and a 1.27mm thick aluminum plate. The DOS image demonstrates the ability to measure the properties of each generated ultrasonic modes and provides a direct, nondestructive, measure of elastic moduli of the tested specimens.
Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer
Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.
1993-10-01
We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.
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
Stress wave calculations in composite plates using the fast Fourier transform.
NASA Technical Reports Server (NTRS)
Moon, F. C.
1973-01-01
The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.
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.
Surpassing the Path-Limited Resolution of a Fourier Transform Spectrometer with Frequency Combs
Maslowski, Piotr; Johansson, Alexandra C; Khodabakhsh, Amir; Kowzan, Grzegorz; Rutkowski, Lucile; Mills, Andrew A; Mohr, Christian; Jiang, Jie; Fermann, Martin E; Foltynowicz, Aleksandra
2015-01-01
Fourier transform spectroscopy based on incoherent light sources is a well-established tool in research fields from molecular spectroscopy and atmospheric monitoring to material science and biophysics. It provides broadband molecular spectra and information about the molecular structure and composition of absorptive media. However, the spectral resolution is fundamentally limited by the maximum delay range ({\\Delta}$_{max}$) of the interferometer, so acquisition of high-resolution spectra implies long measurement times and large instrument size. We overcome this limit by combining the Fourier transform spectrometer with an optical frequency comb and measuring the intensities of individual comb lines by precisely matching the {\\Delta}$_{max}$ to the comb line spacing. This allows measurements of absorption lines narrower than the nominal (optical path-limited) resolution without ringing effects from the instrumental lineshape and reduces the acquisition time and interferometer length by orders of magnitude.
The X1? +g ground state of Mg2 studied by Fourier-transform spectroscopy
NASA Astrophysics Data System (ADS)
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.
Laude, D.A. Jr.; Pentoney, S.L. Jr.; Griffiths, P.R.; Wilkins, C.L.
1987-09-15
A Fourier transform mass spectrometer used as a detector and identifier for supercritical fluid chromatography demonstrates low nanogram detection limits and a pressure-limited resolution in excess of 10,000 at m/z 128 for the molecular ion of naphthalene. Supercritical carbon dioxide is introduced directly into the source of a dual differential pumped trapped ion cell generating pressures in the low 10/sup -4/ Torr range with sample detection occurring in the analyzer cell at pressures a factor of 100 lower. Ionization is accomplished by charge exchange with carbon dioxide to yield spectra exhibiting 70-eV-like fragmentation patterns. Supercritical fluid chromatography/Fourier transform mass spectrometry data for three test samples, a six-component mixture of substituted aromatic compounds and polyaromatic hydrocarbons, a five-component barbiturate mixture, and a seven-component pesticide mixture, are presented.
Nicholas C. Hill; Patrick A. Limbach; Ronald E. Shomo; Alan G. Marshall; Anthony D. Appelhans; James E. Delmore
1991-01-01
The coupling of an autoneutralizing SF?6 fast ion-beam gun to a Fourier transform ion cyclotron resonance (FT\\/ICR) mass spectrometer is described. The fast neutral beam provides for secondary-ion-type FT\\/ICR mass analysis [e.g., production of abundant pseudomolecular (M+H)+ ions] of involatile samples without the need for external ion injection, since ions are formed at the entrance to the ICR ion trap.
Huggins Z. Msimanga; Robert J. Ollis Jr.
2010-01-01
Principal component anal. (PCA) and partial least squares discriminant anal. (PLS-DA) were used to classify acetaminophen-contg. medicines using their attenuated total reflection Fourier transform IR (ATR-FT-IR) spectra. Four formulations of Tylenol (Arthritis Pain Relief, Extra Strength Pain Relief, 8 H Pain Relief, and Extra Strength Pain Relief Rapid Release) along with 98% pure acetaminophen were selected for this study because
Nicholas C. Hill; Patrick A. Limbach; Ronald E. Shomo II; Alan G. Marshall; Anthony D. Appelhans; James E. Delmore
1991-01-01
The coupling of an autoneutralizing SFâ»â fast ion-beam gun to a Fourier transform ion cyclotron resonance (FT\\/ICR) mass spectrometer is described. The fast neutral beam provides for secondary-ion-type FT\\/ICR mass analysis (e.g., production of abundant pseudomolecular (M+H){sup +} ions) of involatile samples without the need for external ion injection, since ions are formed at the entrance to the ICR ion
(Astro)Physics 343 Lecture # 5: Sun, Stars, and Planets; Fourier Transforms
Baker, Andrew J.
(Astro)Physics 343 Lecture # 5: Sun, Stars, and Planets; Fourier Transforms #12; Schedule, without getting stung. #12;February 12, 2007 Physics/Astronomy 343 6 Size, mass, and distance of the Sun 106 mi Distance From Sun 2.0 x 1030 kg1.9 x 1027 kg6.0 x 1024 kgMass 1,400,00 km 865,000 mi 140,000 km
(Astro)Physics 343 Lecture # 5: Sun, Stars, and Planets; Fourier Transforms
Baker, Andrew J.
(Astro)Physics 343 Lecture # 5: Sun, Stars, and Planets; Fourier Transforms #12; Schedule # 5: running now #12;February 12, 2007 Physics/Astronomy 343 5 Size, mass, and distance of the Sun 106 mi Distance From Sun 2.0 x 1030 kg1.9 x 1027 kg6.0 x 1024 kgMass 1,400,00 km 865,000 mi 140,000 km
Using single buffers and data reorganization to implement a multi-megasample fast Fourier transform
NASA Technical Reports Server (NTRS)
Brown, R. D.
1992-01-01
Data ordering in large fast Fourier transforms (FFT's) is both conceptually and implementationally difficult. Discribed here is a method of visualizing data orderings as vectors of address bits, which enables the engineer to use more efficient data orderings and reduce double-buffer memory designs. Also detailed are the difficulties and algorithmic solutions involved in FFT lengths up to 4 megasamples (Msamples) and sample rates up to 80 MHz.
Y. B. Che Man; M. E. S. Mirghani
2000-01-01
A simple, rapid, and direct Fourier transform infrared (FTIR) spectroscopic method was developed for the determination of\\u000a moisture content of crude palm oil (CPO). The calibration set was prepared by adding double-distilled water to dried CPO in\\u000a ratios (w\\/w) between 0 and 13% moisture. A partial least squares (PLS) regression technique was employed to construct a calibration\\u000a model followed by
Yongli Zhao; Fan Gu; Jing Xu; Jing Jin
2010-01-01
The aging mechanism of SBS modified asphalt during its aging process was studied. The characterizations of base asphalt, SBS\\u000a polymer and its modified asphalt were determined in different aging time by Fourier transform infrared spectrum (FTIR). FTIR\\u000a shows that oxidative dehydrogenation reaction occurs in asphalt, and unsaturated carbon bond is generated under short-term\\u000a thermal aging condition. Additionally, SBS polymer was
Fourier transform infrared emission spectra of atomic rubidium: g- and h-states
S Civiš; M Ferus; P Kubelík; V E Chernov; E M Zanozina
2012-01-01
Time-resolved Fourier transform infrared spectroscopy has been used to observe the rubidium atomic emission spectrum in a vacuum (10?2 Torr). We observe 31 Rb I lines in the 800–8000 cm?1 range with a resolution of 0.02 cm?1, including 21 previously unmeasured lines. From the measured spectra, we identify the energy values of the previously unknown 6g, 6h, 7g and 7h
$(q,?)$ and $(p,q,?)-$exponential functions: Rogers-Szeg? polynomials and Fourier-Gauss transform
M. N. Hounkonnou; E. B. Ngompe Nkouankam
2010-08-07
From the realization of $q-$oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szeg\\H{o} polynomials as well as their relevant properties. We also compute the matrix elements associated to the $(p,q)-$oscillator algebra (a generalization of the $q-$one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.
Thompson, Christopher J.; Riley, Robert G.; Amonette, James E.; Gassman, Paul L.
2006-06-01
Soil aging may have a significant influence on the success of environmental remediation strategies and the accuracy of numerical models that estimate contaminant transport. The focus of this study was to define the ability of online Fourier transform infrared (FT-IR) spectroscopy to monitor the concentration of halogenated volatile organic compounds in a process that simulates long-term slow accumulation of contaminants in soils.
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
Stephan J. Hug
1997-01-01
Anin situattenuated total reflection (ATR)–Fourier transform infrared (FTIR) method, in which the ATR element is coated with hematite particle layers in direct contact with the aqueous phase, was used to measure sulfate adsorption as a function of aqueous sulfate concentration and pH. Between pH 3 and 6, monitoring the spectral region 900–1300 cm?1, an IR spectrum with three bands between
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.
IUP MAI3 -TD M54 FFT : transforme de Fourier Rapide sur Hypercube
Dumas, Jean-Guillaume
IUP MAI3 - TD M54 FFT : transformÃ©e de Fourier Rapide sur Hypercube Soit n N, nous notons N = 2n_Comm_rank(MPI_COMM_WORLD,&rank);). On dÃ©nit une topologie d'hypercube de dimension n sur un rÃ©seau de taille 2n par : soit jn-1, jn-2, . . . , n - 1}, jl0 = kl0 (et l = 0, . . . , n - 1, l = l0 jl = kl) 1. Dessinez les hypercubes de dimension
IUP MAI3 -M54 Mini-projet : FFT (transforme de Fourier Rapide) sur Hypercube
Dumas, Jean-Guillaume
IUP MAI3 - M54 Mini-projet : FFT (transformÃ©e de Fourier Rapide) sur Hypercube L'objectif premier l'hypercube. Soit rang le numÃ©ro d'un pro- cessus (ou processeur). On dÃ©nit une topologie d'hypercube (et l = 0, . . . , n - 1, l = l0 jl = kl) 1. A l'aide de MPI_Graph_create, construisez un hypercube
Hong Yang; Joseph Irudayaraj
2003-01-01
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
[A novel spatial modulation Fourier transform spectrometer with adjustable spectral resolution].
Lian, Yu-Sheng; Liao, Ning-Fang; Lü, Hang; Wu, Wen-Min; Dong, Zhi-Gang
2014-11-01
In the premise of fulfilling the application requirement, the adjustment of spectral resolution can improve efficiency of data acquisition, data processing and data saving. So, by adjusting the spectral resolution, the performance of spectrometer can be improved, and its application range can be extended. To avoid the problems of the fixed spectral resolution of classical Fourier transform spectrometer, a novel type of spatial modulation Fourier transform spectrometer with adjustable spectral resolution is proposed in this paper. The principle of the novel spectrometer and its interferometer is described. The general expressions of the optical path difference and the lateral shear are induced by a ray tracing procedure. The equivalent model of the novel interferometer is analyzed. Meanwhile, the principle of the adjustment of spectral resolution is analyzed. The result shows that the novel spectrometer has the merits of adjustable spectral resolution, high stability, easy assemblage and adjustment etc. This theoretical study will provide the theoretical basis for the design of the spectrometer with adjustable spectral resolution and expand the application range of Fourier transform spectrometer. PMID:25752074
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.
[The principle and analysis of micro-Fourier transform spectrometer based on MEMS micro-mirror].
Chen, Jian-Jun; Zhu, Yong; Liu, Bo; Wei, Wei; Zhang, Jie; Wang, Ning
2012-11-01
The present paper puts forward a novel micro-Fourier transform infrared spectrometer based on programmable MEMS micro-mirror. This design uses a MEMS micro-mirror and a slantwise reflector to replace the moving mirror system on traditional spectrometer. This paper analyzes the operating principle of this spectrometer and gives the simulation result to prove the feasibility of this method. The results show that the spectral resolution is less than 5 nm in near-infrared wave band, the wave-length accuracy is approximately 1 nm and the sampling period of this spectrometer is approximately 50 ms. This method can use Hadamard transform to improve the SNR. PMID:23387198
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, E-mail: endo@bunshi.c.u-tokyo.ac.jp [Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902 (Japan)] [Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902 (Japan); Sumiyoshi, Yoshihiro [Division of Pure and Applied Science, Faculty of Science and Technology, Gunma University, Aramaki 4-2, Maebashi, Gunma 371-8510 (Japan)] [Division of Pure and Applied Science, Faculty of Science and Technology, Gunma University, Aramaki 4-2, Maebashi, Gunma 371-8510 (Japan); Ohshima, Yasuhiro [Department of Photo-Molecular Science, Institute for Molecular Science, Okazaki 444-8585 (Japan)] [Department of Photo-Molecular Science, Institute for Molecular Science, Okazaki 444-8585 (Japan); Kohguchi, Hiroshi [Department of Chemistry, Graduate School of Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526 (Japan)] [Department of Chemistry, Graduate School of Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-Hiroshima 739-8526 (Japan)
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.
Motional averaging of ions for control of magnetron motion in Fourier transform ion cyclotron resonance open-geometry trapped-ion cells Victor H. Vartanian1 , David A. Laude* Department of Chemistry Abstract Open trapped-ion cell geometries have been utilized extensively in external source Fourier
Hsu, Wei-Chun
A measurement platform is introduced that combines a bilayer cantilever probe with a Fourier transform infrared spectrometer to measure absolute spectral absorptance between wavelengths of 3??m and 18??m directly and ...
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 ...
-Fourier transform infrared (ATR-FTIR) spectroscopy along with site-directed isotope labeling to probe the local of the protein, including the peptide groups of Leu-39 and Leu-42, appear inaccessible to exchange, indicating
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 ...
Beck, Travis W; Housh, Terry J; Johnson, Glen O; Cramer, Joel T; Weir, Joseph P; Coburn, Jared W; Malek, Moh H
2006-01-15
The purpose of this study was to compare the eccentric torque-related patterns for mechanomyographic (MMG) center frequencies (mean power frequency (MPF), median frequency (MDF), and average instantaneous mean power frequency (AIMPF)) determined by the fast Fourier transform (FFT) and continuous wavelet transform (CWT). Eight adults (mean+/-S.D. age=22.5+/-2.4 years) performed submaximal to maximal, eccentric isokinetic muscle actions of the biceps brachii on a Cybex 6,000 dynamometer. The mean MMG MPF, MDF, and AIMPF values for both the absolute and normalized data from 10 to 100% eccentric peak torque (PT) were highly intercorrelated at r=0.908-0.985. Linear models provided the best fit for the absolute MMG MPF (r=0.873), MDF (r=0.831), and AIMPF (r=0.924), as well as normalized MMG MPF (r=0.869), MDF (r=0.816), and AIMPF (r=0.920) versus percentage eccentric PT relationships. There were no significant differences (p>0.05) among the linear slope coefficients for the MMG MPF, MDF, and AIMPF versus percentage eccentric PT relationships for either the absolute or normalized data. These results suggested that Fourier or wavelet transform procedures can be used to examine the patterns of MMG responses during eccentric muscle actions of the biceps brachii. PMID:16051373
Discrimination of Unitary Transformations and Quantum Algorithms
David Collins
2008-11-09
Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the sequence with others remaining fixed. For oracle query algorithms, the input determines the oracle unitary transformation. Such algorithms can be regarded as devices for discriminating amongst a set of unitary transformations. The question arises: "Given a set of known oracle unitary transformations, to what extent is it possible to discriminate amongst them?" We investigate this for the Deutsch-Jozsa problem. The task of discriminating amongst the admissible oracle unitary transformations results in an exhaustive collection of algorithms which can solve the problem with certainty.
A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws
Levenhagen, R. S., E-mail: ronaldo.levenhagen@gmail.com [Universidade Federal de São Paulo, Depto. Ciências Exatas e da Terra, Rua Prof. Arthur Riedel, 275, Jd. Eldorado, CEP 09972-270 Diadema, SP (Brazil)
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).
A Fourier Transform Method for Vsin i Estimations under Nonlinear Limb-darkening Laws
NASA Astrophysics Data System (ADS)
Levenhagen, R. S.
2014-12-01
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).
[Study on the method to adjust optical fiber's spectrum attenuation with the Fourier transform].
Meng, Xian-jiang; Zhang, Tie-qiang; Shi, Wei-jie; Shen, Xuan-guo
2005-04-01
A method based on Fourier transform to compensate the non-linear attenuation of optical fiber used as a probe in a spectrum-collecting system was proposed. First the output electric currents of photoelectric tube with and without fiber were transformed to the frequency field. So an adjustable function in frequency field was obtained, and the adjustable function was transformed to the spectrum field, so the final adjustable function was obtained. A photoelectric system was designed for testing. With visible light, this method can make the error rate of fiber transmission as low as less than 1.54%. It is proved that the method is fit for adjusting some optical fiber spectrum attenuation. PMID:16097680
PC-based two-dimensional discrete fourier transform programs for terrain analysis
NASA Astrophysics Data System (ADS)
Harrison, John Michael; Lo, Chor-Pang
1996-05-01
A two-dimensional Fast Fourier Transform (2D-FFT) program written in C language was developed for the personal computer with the specific purpose of extracting periodicities from digital elevation model (DEM) data. The program generates the individual frequency pairs, the coefficients representing the amplitudes of the cosine and sine waves, the angle the wavefront makes in the terrain, the wavelength, the power of the wave, the percent contribution the wave makes to the overall landscape, and finally the overall percentage of variance accounted for by the model. The landscape can be reconstructed based on the number of significant waveforms extracted. Generalizations on the spatial trends of the terrain therefore can be made. The Fourier analysis provides insight to the nature and complexity of the terrain. An application of the program to the karst landscape of Manati, Puerto Rico is illustrated.
Asymmetric multiple-image encryption based on the cascaded fractional Fourier transform
NASA Astrophysics Data System (ADS)
Li, Yanbin; Zhang, Feng; Li, Yuanchao; Tao, Ran
2015-09-01
A multiple-image cryptosystem is proposed based on the cascaded fractional Fourier transform. During an encryption procedure, each of the original images is directly separated into two phase masks. A portion of the masks is subsequently modulated into an interim mask, which is encrypted into the ciphertext image; the others are used as the encryption keys. Using phase truncation in the fractional Fourier domain, one can use an asymmetric cryptosystem to produce a real-valued noise-like ciphertext, while a legal user can reconstruct all of the original images using a different group of phase masks. The encryption key is an indivisible part of the corresponding original image and is still useful during decryption. The proposed system has high resistance to various potential attacks, including the chosen-plaintext attack. Numerical simulations also demonstrate the security and feasibility of the proposed scheme.
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.
Synthesis of Arbitrary Unitary Transformations in Quantum Systems by Householder Reflections
Ivanov, P. A.; Vitanov, N. V. [Department of Physics, Sofia University, James Bourchier 5 blvd, 1164 Sofia (Bulgaria)
2007-12-26
We demonstrate that Householder reflections emerge naturally in the propagator of a coherently driven degenerate two-level system. Such reflections are a very powerful tool for constructing arbitrary unitary transformations of an N-state quantum system. We present examples for construction of discrete Fourier transforms, superposition-to-superposition navigation between pure states, engineering of arbitrary mixed states, and entanglement of trapped ions.
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.
NASA Astrophysics Data System (ADS)
Mc Leod, Roger David; Mc Leod, David M.
2007-10-01
Vision, via transform space: ``Nature behaves in a reciprocal way;' also, Rect x pressure-input sense-reports as Sinc p, indicating brain interprets reciprocal ``p'' space as object space. Use Mott's and Sneddon's Wave Mechanics and Its Applications. Wave transformation functions are strings of positron, electron, proton, and neutron; uncertainty is a semantic artifact. Neutrino-string de Broglie-Schr"odinger wave-function models for electron, positron, suggest three-quark models for protons, neutrons. Variably vibrating neutrino-quills of this model, with appropriate mass-energy, can be a vertical proton string, quills leftward; thread string circumferentially, forming three interlinked circles with ``overpasses''. Diameters are 2:1:2, center circle has quills radially outward; call it a down quark, charge --1/3, charge 2/3 for outward quills, the up quarks of outer circles. String overlap summations are nodes; nodes also far left and right. Strong nuclear forces may be --px. ``Dislodging" positron with neutrino switches quark-circle configuration to 1:2:1, `downers' outside. Unstable neutron charge is 0. Atoms build. With scale factors, retinal/vision's, and quantum mechanics,' spatial Fourier transforms/inverses are equivalent.
NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS
BAJAJ, CHANDRAJIT; BAUER, BENEDIKT; BETTADAPURA, RADHAKRISHNA; VOLLRATH, ANTJE
2013-01-01
The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ? SO(3), t ? ?3 that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup either with respect to the sought translation or rotation. We present PFcorr, a new exhaustive solution, based on the non-equispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PFcorr can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogs of the above problems in which the flexibility of the protein is relevant. PMID:24379643
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.
Fourier Transform-Raman spectroscopic study of natural resins of archaeological interest.
Brody, Rachel H; Edwards, Howell G M; Pollard, A Mark
2002-01-01
Resins from several different genera are studied using Fourier transform (FT)-Raman spectroscopy. Tree resins can be broadly divided into those that contain diterpenoid components and those that contain triterpenoid components. The diterpenoid resins analyzed are from the genera Pinus, Cedrus, and Agathis (kauri resin) and the triterpenoid resins examined are samples from Pistacia, Boswellia (frankincense), and Commiphora (myrrh) genera. A protocol is developed to nondestructively distinguish diterpenoid and triterpenoid resins and to differentiate the genera within the two types. The effects of oxidation on the discrimination of the FT-Raman spectra are considered. PMID:12073935
Analysis of high-explosive samples by Fourier transform Raman spectroscopy
NASA Astrophysics Data System (ADS)
Akhavan, Jacqueline
The application of spectroscopic techniques to the detection and identification of explosive materials is of considerable importance in forensic investigations. However, forensic scientists do not routinely use conventional Raman spectroscopy in their analysis. This is due to the problems of high background scatter and time-consuming sample alignment. The development of Fourier transform Raman spectroscopy has overcome these problems. Using this technique three samples of different batches of Semtex labelled Semtex A, Semtex B and Semtex C were analysed. Semtex A was found to contain the explosive cyclotrimethylenetrinitramine (RDX), Semtex B contained pentaerythritol tetranitrate (PETN) and Semtex C contained a mixture of RDX and PETN.
Pulse propagation effects in optical 2D Fourier-transform spectroscopy: experiment.
Li, Hebin; Spencer, Austin P; Kortyna, Andrew; Moody, Galan; Jonas, David M; Cundiff, Steven T
2013-07-25
In optical two-dimensional Fourier-transform (2DFT) spectroscopy, understanding how the spectral line shape is affected by pulse propagation in the sample is crucial for an accurate interpretation of spectra. We report an experimental study of pulse propagation effects in 2DFT spectroscopy performed in a dense atomic vapor. The spectral line shape can be dramatically distorted due to high optical density as well as the physical thickness of a sample. The spectral distortion can be partially corrected by using a reference pulse copropagating with the signal combined with appropriate data processing. PMID:23565590
Room temperature chirped-pulse Fourier transform microwave spectroscopy of anisole
NASA Astrophysics Data System (ADS)
Reinhold, B.; Finneran, I. A.; Shipman, S. T.
2011-12-01
The room-temperature rotational spectrum of anisole from 8.7 to 18.3 GHz was collected with a waveguide-based chirped-pulse Fourier transform microwave spectrometer whose operating principles are described. Three spectra were assigned, corresponding to the vibrational ground state and the first and second excited states of the lowest frequency torsional mode. Results for the ground state and first excited state are in agreement with prior millimeter wave studies of this molecule. Microwave-microwave double resonance measurements also confirm these assignments.
NASA Astrophysics Data System (ADS)
Behr, Bradford B.; Cenko, Andrew T.; Hajian, Arsen R.; McMillan, Robert S.; Murison, Marc; Meade, Jeff; Hindsley, Robert
2011-07-01
We present orbital parameters for six double-lined spectroscopic binaries (? Pegasi, ? Draconis, 12 Boötis, V1143 Cygni, ? Aurigae, and Mizar A) and two double-lined triple star systems (? Pegasi and ? 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 1 and M 2 of the stellar components with relative errors as small as 0.2%.
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.
NASA Astrophysics Data System (ADS)
Vuotto, J. L.; Huong, P. V.; Meaudre, R.
1986-03-01
The structure of amorphous hydrogenated silicon-nitrogen alloys, potential materials for photovoltaic conversion and for micro-electronics, was studied in sight of their Fourier transform infrared spectra. The presence of NH vibration and the appearance of Si?N stretching band with progressive decreasing of SiH 2 vibrational bands suggest that the incorporation of nitrogen is realized at the expense of SiH 2 groups leading to Si?N bonds in structures of different local environments. A relationship has been established between the ?(Si?H) frequency and the amount of nitrogen : ? and offers an easy method for quantitative analyses.
Range-invariant anomaly detection applied to imaging Fourier transform spectrometry data
NASA Astrophysics Data System (ADS)
Borel, Christoph; Rosario, Dalton; Romano, Joao
2012-09-01
This paper describes the end-to-end processing of image Fourier transform spectrometry data taken of surrogate tank targets at Picatinny Arsenal in New Jersey with the long-wave hyper-spectral camera HyperCam from Telops. The first part of the paper discusses the processing from raw data to calibrated radiance and emissivity data. The second part discusses the application of a range-invariant anomaly detection approach to calibrated radiance, emissivity and brightness temperature data for different spatial resolutions and compares it to the Reed-Xiaoli detector.
Determination of doubly labeled water by gas-phase Fourier transform infrared spectroscopy.
Khaled, M A; Krumdieck, C L; Ong, J L
1995-01-01
Both 2H (deuterium) and 18O (oxygen 18) in isotopically enriched water have been detected by gas-phase Fourier transform infrared (FTIR) spectroscopy at 2,720 and 3,661.8 cm-1, respectively. A linear relationship between varying concentrations of each of these isotopes and their absorbance at the above frequencies indicates that gas-phase FTIR may provide a rapid and potentially less expensive approach to measure doubly labeled water in biological fluids for the estimation of energy expenditure and total body water. PMID:7854152
Fast parallel complex discrete fourier transforms using a multichannel optical correlator
NASA Astrophysics Data System (ADS)
Huang, Hong Xin; Liu, Li Ren; Yin, Yao Zu; Zhao, Li Ying
1988-11-01
Based on a multichannel incoherent optical correlator, a new simple scheme is proposed for performing a complex discrete Fourier transform. A complex value is represented by using three nonnegative reals, and every real is encoded with the area of a rectangular aperture. A 3 N×3 N-element kernel mask together with a 3 N-element 1D-pin-hole-array illuminated with an extended source is used to calculate an 1D-DFT of an N-point input. Some properties of DFT are demonstrated in experiments.
NASA Astrophysics Data System (ADS)
Li, YaSheng; Chen, Yan; Liao, Ningfang; Lyu, Hang; He, Shufang; Wan, Lifang
2015-08-01
A new calibration method for infrared hyperspectral imaging Fourier transform spectrometer is presented. Two kinds of common materials as Polypropylene (PP) and Polyethylene Terephthalate (PET) films which have special absorption peaks in the infrared band were used in the calibration experiment. As the wavelengths at the sharp absorption peaks of the films are known, an infrared imaging spectrometer can be calibrated on spectra with two or three peaks. With high precision and stability, this method simplifies the calibration work. It is especially appropriate for the measuring condition with a lack of calibration equipment or with inconvenience to calibrate the multiple light sources outdoors.
Fast Wavefront Reconstruction in Large Adaptive Optics Systems Using the Fourier Transform
Poyneer, L; Gravel, D T; Brase, J M
2002-01-13
Wavefront Reconstruction using the Fast Fourier Transform and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster and can have lower noise propagation than traditional VMM reconstructors. The boundary problem which prevented the accurate reconstruction of phase in circular apertures using square-grid FTs is identified and solved. The methods are adapted for use on the Fried-geometry. Detailed performance analysis of mean squared error and noise propagation for FT methods is presented, using both theory and simulation.
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).
Niece, Krista L; Akers, Kevin S
2015-09-01
Colistin use has increased in response to the advent of infections caused by multidrug-resistant organisms. It is administered parenterally as an inactive prodrug, colistin methanesulfonate (CMS). Various formulations of CMS and labeling conventions can lead to confusion about colistin dosing, and questions remain about the pharmacokinetics of CMS. Since CMS does not have strong UV absorbance, current methods employ a laborious process of chemical conversion to colistin followed by precolumn derivatization to detect formed colistin by high-performance liquid chromatography. Here, we report a method for direct quantification of colistin methanesulfonate by attenuated total reflectance Fourier transform infrared spectroscopy (ATR FTIR). PMID:26124160
Shen, Fabin; Wang, Anbo
2006-02-20
The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method. PMID:16523770
NASA Astrophysics Data System (ADS)
Shen, Fabin; Wang, Anbo
2006-02-01
The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method.
MTI Thermal Bands Calibration at Ivanpah Playa with a Fourier Transform Infrared Spectrometer
Villa-Aleman, E.
2001-06-27
The Savannah River Technology Center (SRTC) is currently calibrating the Multispectral Thermal Imager (MTI) satellite sponsored by the Department of Energy. The reflective bands of the MTI satellite are calibrated in desert playas such as Ivanpah Playa in the Nevada/California border. The five MTI thermal bands are calibrated with targets of known emissivity and temperature such as power plant heated lakes. In order to accomplish a full calibration at the desert playas, a Fourier transform infrared spectrometer was used to measure soil surface radiance and temperature during the satellite overpass. The results obtained with the mobile FTIR during the ground truth campaign at Ivanpah Playa will be presented.
Mao, Zhuoxiong; McIntosh, M.J.; Demirgian, J.C.
1992-01-01
Incineration of chlorobenzene in a small laboratory incinerator was monitored by using Fourier transform infrared spectroscopy (FTIR) coupled with a heated long-path cell (LPC) to analyze and quantify flue gas emissions in near real time. The effects of operating conditions under stable and decreasing incineration temperatures on the destruction of chlorobenzene were studied. The results from the decreasing temperature experiments were found to be consistent with those from experiments at stable temperatures. This finding demonstrates that the FTIR/LPC, as a continuous emissions monitor, can effectively detect dynamic changes in the incinerator emissions and can contribute significantly to the safety of incinerators.
Mao, Zhuoxiong; McIntosh, M.J.; Demirgian, J.C.
1992-06-01
Incineration of chlorobenzene in a small laboratory incinerator was monitored by using Fourier transform infrared spectroscopy (FTIR) coupled with a heated long-path cell (LPC) to analyze and quantify flue gas emissions in near real time. The effects of operating conditions under stable and decreasing incineration temperatures on the destruction of chlorobenzene were studied. The results from the decreasing temperature experiments were found to be consistent with those from experiments at stable temperatures. This finding demonstrates that the FTIR/LPC, as a continuous emissions monitor, can effectively detect dynamic changes in the incinerator emissions and can contribute significantly to the safety of incinerators.
J. Dubois; F. R. van de Voort; J. Sedman; A. A. Ismail; H. R. Ramaswamy
1996-01-01
A Fourier transform infrared (FTIR) transmission-based spectroscopic method was investigated for the simultaneous monitoring\\u000a of aldehyde formation and the determination of anisidine value (AV) in thermally stressed oils. Synthetic calibration standards\\u000a were prepared by adding known amounts of hexanal,t-2-hexenal andt,t-2,4-decadienal to canola oil (these compounds considered representative of aldehydic compounds formed during oxidation) plus\\u000a random amounts of other compounds representative
Fourier transform spectroscopy of chemiluminescence from the A ?1?– X 1? + system of SrO
Randall H. Skelton; Hongzhi Li; Chris D. Boone; Robert J. Le Roy; Peter F. Bernath; Cristian Focsa; Bernard Pinchemel
2003-01-01
The A?1?–X1?+ near infrared system of strontium oxide (SrO) was observed at high spectral resolution by measuring the chemiluminescence from a Broida flow reactor using a Fourier transform spectrometer. In total, 32 bands from 88SrO, 87SrO, 86SrO were measured within the 4000–10000cm?1 spectral region at a resolution of 0.03cm?1. Vibrational levels of the upper state were observed up to vA?=4,
Fourier Transform Spectroscopy of Chemiluminescence from the SrO A 1? +– X 1? + Transition
Hongzhi Li; Randall Skelton; Cristian Focsa; Bernard Pinchemel; Peter F. Bernath
2000-01-01
The A1?+–X1?+ chemiluminescence spectrum of SrO was observed using a Fourier transform spectrometer. SrO was produced in a Broida-type oven from the Sr + N2O reaction. A total of 75 bands from 88SrO, 87SrO, and 86SrO were measured in the range of 7600–13 600 cm?1 at a resolution of 0.04 cm?1. The vibrational levels of the ground state were observed
Fourier transform emission spectroscopy of the A2?-X2?+ transition of ZnD
NASA Astrophysics Data System (ADS)
O'Brien, L. C.; Fernando, W. T. M. L.; Bernath, P. F.
1990-02-01
The 0-0 band of zinc deuteride A2?-X2?+ transition was recorded in emission by Fourier transform spectroscopy. Compared with previous work on ZnD, improved line positions and molecular constants were determined from the analysis of the data. Rotational structure from the three zinc isotopes in zinc deuteride, 64ZnD, 66ZnD, and 68ZnD, were resolved in many of the branches. Alfred P. Sloan fellow; Camille and Henry Dreyfus teacher-scholar.
Vibration-rotation spectrum of BH X1?+ by Fourier transform emission spectroscopy
NASA Astrophysics Data System (ADS)
Pianalto, F. S.; O'Brien, L. C.; Keller, P. C.; Bernath, P. F.
1988-06-01
The vibration-rotation emission spectrum of the BH X1?+ state was observed with the McMath Fourier transform spectrometer at Kitt Peak. The 1-0, 2-1, and 3-2 bands were observed in a microwave discharge of B2H6 in He. Spectroscopic constants of the individual vibrational levels and equilibrium molecular constants were determined. An RKR potential curve was calculated from the equilibrium constants. Alfred P. Sloan Fellow; Camille and Henry Dreyfus Teacher-Scholar.
Webb, J.D.; Schissel, P.; Thomas, T.M.; Pitts, J.R.; Czanderna, A.W.
1983-07-01
The technique of Fourier transform infrared reflection-absorption (FTIR-RA) spectroscopy has been successfully adapted to studying bulk and interfacially activated photodegradation of several types of polymers on various metallic substrates. The technique enables qualitative and quantitative study of photochemical reaction mechanisms and rates. A Controlled Environmental Exposure Chamber (CEEC), which permits collection of IR-RA spectra of the polymer/metal samples during their exposure to controlled spectral distributions of uv, temperatures, and gas mixtures, was built into the sample compartment of a Nicolet 7199 FTIR spectrophotometer. Surface analysis, gel permeation chromatography (GPC), uv spectroscopy, and uv spectroradiometry were used to complement the FTIR-RA results.
Okino, Tomoya; Yamanouchi, Kaoru [Department of Chemistry, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Extreme Photonics Research Group, RIKEN Advanced Science Institute, 2-1 Hirosawa, Wako-shi, Saitama 351-0198 (Japan); Shimizu, Toshihiko; Ma, Ri; Nabekawa, Yasuo; Midorikawa, Katsumi [Extreme Photonics Research Group, RIKEN Advanced Science Institute, 2-1 Hirosawa, Wako-shi, Saitama 351-0198 (Japan)
2008-10-28
The interferometric autocorrelation functions of attosecond pulse trains in the time domain were measured by detecting CO{sub 2}{sup 2+} as well as the atomic and molecular fragment ions generated via two-photon absorption of intense vacuum ultraviolet-extreme ultraviolet light by CO{sub 2}. It was demonstrated that the Fourier transformation of the interferometric autocorrelation functions of the respective fragment ions appearing in a time-of-flight mass spectrum exhibit spectroscopic information in the frequency domain corresponding to the two-photon photofragment excitation spectra of CO{sub 2} and the double ionization excitation spectrum to form CO{sub 2}{sup 2+}.
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.
NASA Astrophysics Data System (ADS)
Levin, Ira W.; Bhargava, Rohit
2005-05-01
The recent development of Fourier transform infrared (FTIR) spectroscopic imaging has enhanced our capability to examine, on a microscopic scale, the spatial distribution of vibrational spectroscopic signatures of materials spanning the physical and biomedical disciplines. Recent activity in this emerging area has concentrated on instrumentation development, theoretical analyses to provide guidelines for imaging practice, novel data processing algorithms, and the introduction of the technique to new fields. To illustrate the impact and promise of this spectroscopic imaging methodology, we present fundamental principles of the technique in the context of FTIR spectroscopy and review new applications in various venues ranging from the physical chemistry of macromolecular systems to the detection of human disease.
NASA Astrophysics Data System (ADS)
Hanafi, Abdelmalek; Gharbi, Tijani; Cornu, Jean-Yves
2005-07-01
We explore the potential use of the Fourier-transform profilometry technique in in vivo studies of muscular contractions through the variation of muscle-group cross sections. Thanks to a tensorial analysis of the technique, a general expression of its sensitivity vector is established. It allows derivation of the expression of the resolution and the limit condition imposed by the spatial sampling of the fringe pattern. Key parameters that maximize the sensitivity are then simulated. A measurement system is accordingly built up and characterized. It is then successfully applied to the evaluation of the deformation of the forearm muscles during grasping exertions.
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.
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).
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.
Sample switching interface for Fourier transform infrared spectroscopy of electrode surfaces
NASA Astrophysics Data System (ADS)
Faguy, Peter W.; Fawcett, W. Ronald; Quach, James; Rieg, Ron A.
1990-10-01
A simple electronic system that enables an FTIR spectrometer to control sample state parameters through its sample switching ability is described. Up to sixteen different logic states can be assigned through the software, automating the applied FTIR experiment. The operation of the device is demonstrated for the collection of subtractively normalized interfacial Fourier transform infrared spectroscopy (SNIFTIRS) using a custom designed potentiostat. One of the most important advantages of this interface is its flexibility towards various timing/sampling schemes found for different in situ spectroelectrochemical experiments. The suitability of this device for other than electrochemical switching applications is also described.
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
Quantum Simulation of Noncausal Kinematic Transformations
NASA Astrophysics Data System (ADS)
Alvarez-Rodriguez, U.; Casanova, J.; Lamata, L.; Solano, E.
2013-08-01
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.
A Borel transform method for locating singularities of Taylor and Fourier series
W. Pauls; U. Frisch
2007-02-09
Given a Taylor series with a finite radius of convergence, its Borel transform defines an entire function. A theorem of P\\'olya relates the large d istance behavior of the Borel transform in different directions to singularities of the original function. With the help of the new asymptotic interpolation method of van der Hoeven, we show that from the knowledge of a large number of Taylor coefficients we can identify precisely the location of such singularities, as well as their type when they are isolated. There is no risk of getting artefacts with this method, which also gives us access to some of the singularities beyond the convergence disk. The method can also be applied to Fourier series of analytic periodic functions and is here tested on various instances constructed from solutions to the Burgers equation. Large precision on scaling exponents (up to twenty accurate digits) can be achieved.
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
NASA Astrophysics Data System (ADS)
Steber, Amanda L.; Harris, Brent J.; Neill, Justin L.; Pate, Brooks H.
2012-10-01
The performance of a chirped-pulse Fourier transform millimeter-wave spectrometer operating from 260 to 295 GHz is described. The spectrometer uses a high-speed arbitrary waveform generator (AWG) to create both a chirped excitation pulse and the single-frequency local oscillator (LO) used for the final down conversion detection stage. The mm-wave excitation source is an active multiplier chain (factor of 24 frequency multiplication) with power output of greater than 10 mW across the 260-295 GHz frequency range. The LO, produced by a separate active multiplier chain (factor of 12 frequency multiplication), drives a subharmonic mixer which downconverts the molecular emission to the microwave region for digitization on a 100 GS/s digital oscilloscope. All frequency sources in the experiment are locked to a 10 MHz Rb-disciplined oscillator providing direct frequency calibration for molecular transitions in the Fourier transform frequency-domain spectrum. Benchmark measurements are presented on ethyl cyanide and 1-butyne and are used to illustrate advantages and tradeoffs compared with direct absorption millimeter-wave spectroscopy.
NASA Astrophysics Data System (ADS)
Sato, Yusuke; Sakamoto, Yuji
2012-03-01
A computer-generated hologram (CGH) is generated by simulating light waves propagated from virtual objects, and we are able to observe natural 3-D images without feeling tired. However, the resolution of current output devices, liquid crystal displays, is not high enough to display CGH data, so the size of reconstructed images are restricted. To increase image size, a method by using the Fourier transform optical system has been proposed. The Fourier transform optical system converges reconstructed light by arranging a lens between an observer and hologram and reconstructs floating images near the observer. In the system, a reconstruction position is confined around a focal point of the lens because a CGH calculation method had not yet been developed . To solve this problem, this describes a CGH calculation method using a unified formula to reconstruct images at arbitrary depth. This formula is derived by considering image formation of a lens and hologram. Moreover, process for eliminating unnecessary light elimination processing is described in this paper. By changing the elimination process according to the reconstruction position, images are reconstructed without overlapping unnecessary light at arbitrary depth. To confirm the effectiveness of the proposed method, we conducted optical reconstruction experiments. The results show that correctly sized images are reconstructed at correct depth, and unnecessary light is eliminated. It is possible to observe large and free-depth 3-D images with the proposed method.
NASA Astrophysics Data System (ADS)
Rossbach, P. C.
1985-12-01
The calculation of the Discrete Fourier Transform has long been a significant bottleneck in many Digital Signal Processing applications. With the arrival of Very Large Scale Integration and new DFT algorithms, system architectures that significantly reduce the DFT bottleneck are possible. This thesis addresses the design, simulation, implementation, and testing of the control circuitry for a high speed, VLSI Winograd Fourier Transform (WFT) processor. Three WFT processors are combined into a pipelined architecture that is capable of computing a 4080-point DFT on complex input data approximately every 120 microseconds when operating with 70 MHz clock signals. The chip control architecture features a special Programmable Logic Array (PLA) to control the on-chip arithmetic circuitry, and a dense, 54K ROM to generate data addresses for the external RAM. The PLA controller was fabricated in 3 micron CMOS and functioned properly for clock rates of over 60 MHz. The address generator ROM was designed and submitted for fabrication in 3 micron CMOS, and SPICE simulations predict an access time of 60 nanoseconds. Software that automatically generates a ROM layout description from a data file was developed to ensure the correctness of the final design. The transistor minimization procedure i s based on a graph partitioning heuristic, and the drain removal procedure is based on an algorithm that near-optimally solves the Traveling Salesman Problem.
Gorzsás, András; Sundberg, Björn
2014-01-01
Fourier transform infrared (FT-IR) spectroscopy is a fast, sensitive, inexpensive, and nondestructive technique for chemical profiling of plant materials. In this chapter we discuss the instrumental setup, the basic principles of analysis, and the possibilities for and limitations of obtaining qualitative and semiquantitative information by FT-IR spectroscopy. We provide detailed protocols for four fully customizable techniques: (1) Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS): a sensitive and high-throughput technique for powders; (2) attenuated total reflectance (ATR) spectroscopy: a technique that requires no sample preparation and can be used for solid samples as well as for cell cultures; (3) microspectroscopy using a single element (SE) detector: a technique used for analyzing sections at low spatial resolution; and (4) microspectroscopy using a focal plane array (FPA) detector: a technique for rapid chemical profiling of plant sections at cellular resolution. Sample preparation, measurement, and data analysis steps are listed for each of the techniques to help the user collect the best quality spectra and prepare them for subsequent multivariate analysis. PMID:24057375
3D-printed slit nozzles for Fourier transform microwave spectroscopy.
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. PMID:26133873
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
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
State-of-the-art imaging Fourier-transform spectrometer with CCD camera
NASA Astrophysics Data System (ADS)
Genest, Jérôme E.; Roy, Simon A.; Dubois, Patrick; Potvin, Simon
2007-09-01
Imaging Fourier-transform spectrometers can quickly produce massive amounts of raw data, especially when paired with large focal plane arrays. As the spatial resolution is increased, overwhelming amounts of data must be managed properly. A suitable design of the data processing chain is thus required to minimize the dataload and deliver processed information in real-time. This paper reviews the work being done to tailor data processing pipelines for Fourier-transform spectrometers (FTS) coupled with externally triggered CCD cameras. Various sampling techniques as well as spectral calibration and line shape correction approaches will be reviewed. Since traditional sampling techniques are not well suited for an FTS operating with a CCD camera, a hybrid time-position sampling approach is presented to reduce the number of samples per pixel. Furthermore, the approach enables a sampling jitter correction algorithm that can account for velocity fluctuations and channel delays, such as the CCD integration time. A fast spectral calibration approach is also demonstrated, based on a rapid line shape integration scheme. The calibration algorithm brings all pixel spectra on the same spectral grid and allows the user to directly compare spectral features between pixels. Moreover, the correction method offers software field-widening capabilities by binning pixels after spectral calibration. A large single-pixel detector can thus be emulated from the CCD array, allowing the user to broaden the field of view and to increase the SNR.
Fourier transform infrared evanescent wave (FTIR-FEW) spectroscopy of tissue
NASA Astrophysics Data System (ADS)
Bruch, Reinhard F.; Sukuta, Sydney; Afanasyeva, Natalia I.; Kolyakov, Sergei F.; Butvina, Leonid N.
1997-05-01
A new Fourier transform infrared fiberoptic evanescent wave (FTIR-FEW) spectroscopy method has been developed for tissue diagnostics in the middle infrared (MIR) wavelength range (3 to 20 micrometers). Specific novel fiberoptical chemical and biological sensors have been studied and used for spectroscopic diagnostic purposes. These nontoxic and nonhygroscopic fiber sensors are characterized by (1) low optical losses (0.05 to 0.2 dB/m at about 10 micrometer) and (2) high flexibility. Our new fiber optical devices can be utilized with standard commercially available Fourier transform spectrometers including attenuated total reflection (ATR) techniques. They are in particular ideally suited for noninvasive, fast, direct, sensitive investigations of in vivo and ex vivo medical diagnostics applications. Here we present data on IR spectra of skin tissue in vivo for various cases of melanoma and nevus in the range of 1480 - 1800 cm-1. The interpretation of the spectra of healthy and different stages of tumor and cancer skin tissue clearly indicates that this technique can be used for precancer and cancer diagnostics. This technique can be designed for real-time and on-line computer modeling and analysis of tissue changes.
Ground-based high resolution Fourier transform spectrometer and its application in Beijing
NASA Astrophysics Data System (ADS)
Fan, Dongdong
2013-10-01
The B3M-FTS instrument, inherited from ACE-FTS and PARIS, is built by Canadian ABB and Beijing Vision Sky Aerospace Co., Ltd. The B3M is a complete stand-alone spectrometer designed to operate from the ground in moderate environment. It can acquire atmospheric spectra with the Sun as back illumination. This instrument is an adapted version of the classical Michelson interferometer using an optimized optical layout, and it is a high-resolution infrared Fourier transform spectrometer operating in the 750 to 4100cm-1 spectral range. In this paper, the instrument concept of a compact, portable, high-resolution Fourier transform spectrometer is introduced. Some test results of the instrument such as ILS and SNR are presented, and the spectral resolution of 0.028cm-1 @ 750cm-1 and SNR over 100:1 are achieved. Sample atmospheric absorption spectra and corresponding retrieval results measured by the FTS are given. The B3M-FTS, with its high performance, provides the capability to monitor the atmospheric composition changes by measuring the atmospheric absorption spectra of solar radiance. Lots of measurements have been acquired at the Olympics atmospheric observation super-station. Up to now, the VMRs of near 10 trace gases have been retrieved. The success of atmospheric composition profile retrieval using the FTS measurements makes the further application of FTS type payload possible in China.
Rebagay, T.V.; Dodd, D.A.
1989-07-01
The effective immobilization of low-level radioactive liquid wastes in the form of grout depends on the quality of the dry cementitious blends used in the grout formulation. Variation in the mix ratios of the components of the blend can cause detrimental effects on the processing behavior of the grout slurry and the final properties of the cured grout. Thus the blends require thorough chemical characterization and monitoring by strict quality control protocols. In an earlier work at our laboratories, Fourier transform infrared- transmission method has been successfully applied in the analysis of blends of cement, fly ash, and clays. However, this method involved time-consuming sample preparation resulting in slow turnaround for repetitive sampling. A practical approach to quality control required a fast and simple method for the analysis of the blends. This paper describes a diffuse reflectance infrared Fourier transform (DRIFT) spectrometric procedure for the routine examination of neat blends consisting of cement, fly ash, clays and/or blast furnace slags. (1 ref., 10 figs., 4 tabs.)
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.
An Intelligent Dynamic Alignment System for Interferometer of Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Yang, Kun; Zeng, Libo
An intelligent dynamic alignment system for a Michelson interferometer which is applied to a Mid-infrared band Fourier transform spectrometer (FTS) is presented. Three photodiodes are used to detect the tilt of moving mirror opposite to fixed mirror with the assistance of the interfered signal of a reference He-Ne laser. This technique is based on detecting the phase difference of laser signal between every two diodes in two perpendicular directions. And four magnetic actuators behind the mounting brace of fixed mirror are used to change the pose of fixed mirror. The system is controlled by a digital signal processor (DSP) in real-time. A feedback algorithm is used to tilt fixed mirror following the action of moving mirror so as to keep both mirror planes in perpendicular. Experiment result shows that the relative tilt between two reflecting mirrors can be restricted in a range no more than ±1.5×10-6rad. This system is effective and reliable to be applied to scanning interferometer of Fourier transform spectrometer.
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.
NASA Astrophysics Data System (ADS)
Cao, Min; Fu, Yaowen; Jiang, Weidong; Li, Xiang; Zhuang, Zhaowen
2007-11-01
Due to high speed moving of the target, the wideband radar echoes after dechirping is a multi-component LFM signal. Directly using the fast Fourier transform (FFT) to implement pulse compression, the high resolution range profile (HRRP) will be broadened and distorted. To improve the quality of the HRRP, considering the fractional Fourier transform (FRFT) is the generalization of the FFT with good concentration for the LFM signal and without cross-term interference, we substitute the optimal FRFT for the FFT in the conventional HRRP imaging method and propose a new imaging method. For the proposed method, selecting the optimal order of the FRFT is important and a fast search algorithm based on fractional autocorrelation is employed in this paper. Compared with other HRRP imaging methods with the motion compensation, the proposed method not only is easy to perform without involvement of complex motion compensation, but also can correct the phase distortion, which is important for the following ISAR imaging process. Furthermore the method has low computational cost and good robust property for additive noises. Experimental results show the effectiveness of the proposed method.
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.
Seismological observations with a Fourier transform spectrometer - Detection of Jovian oscillations
NASA Astrophysics Data System (ADS)
Mosser, B.; Mekarnia, D.; Maillard, J. P.; Gay, J.; Gautier, D.; Delache, P.
1993-01-01
This paper describes a new method to search for giant-planet oscillations based on the detection of small Doppler shifts of tropospheric absorption lines. By using the multiplex properties of a Fourier Transform Spectrometer (FTS) the Doppler information in the whole bandpass of a planetary spectrum dominated by strong but non saturated atmospheric absorptions can be retrieved from the resulting amplitude modulation of the output signal recorded continuously at a fixed path difference. Hence, the Fourier transform of this signal will yield the frequency spectrum of the planetary oscillations. After presenting the principle of this interferometric method, the paper describes its application to Jupiter by observing the planet with the CFHT-FTS in the region of the 3 nu3 band of CH4 at 1.1 micron. The analysis of the recorded signal led to the positive detection of low-degree pressure oscillations through the identification of the l = 1 and l = 2 p-modes and a measure of their equidistance. The deduced value of the characteristic frequency of Jovian oscillations does not agree with theoretical determinations and calls for revision of the standard model of Jupiter's interior.
NASA Astrophysics Data System (ADS)
Tobin, David C.; Revercomb, Henry E.; Taylor, Joe K.; Best, Fred A.; Knuteson, Robert O.; Smith, William L.; Elwell, John; Cantwell, Greg; Bingham, Gail; Tansock, Joe; Reisse, Robert A.; Zhou, Daniel K.
2006-12-01
The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) represents a revolutionary step in satellite based remote sensing of atmospheric parameters. Using the combination of a Fourier Transform Spectrometer and Large Area Focal Plane Arrays, GIFTS measures incident infrared radiance with an unprecedented combination of spectral, temporal, and spatial resolution and coverage. In its regional sounding mode, it measures the infrared spectrum every 11 seconds at a spectral resolution of ~0.6 cm-1 in two spectral bands (14.6 to 8.8 ?m, 6.0 to 4.4 ?m) using two 128 × 128 detector arrays. 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 thermal and gaseous concentration profiles, cloud properties, wind field profiles, and other derived products can be retrieved. Thermal vacuum testing of the GIFTS Engineering Development Unit (EDU) was performed at the Space Dynamics Laboratory in Logan Utah and completed in September 2006. With a focus on spectral characterization of the sensor, analyses of selected thermal vacuum tests are presented here.
[Application of Fourier transform infrared spectroscopy in identification of wine spoilage].
Zhao, Xian-De; Dong, Da-Ming; Zheng, Wen-Gang; Jiao, Lei-Zi; Lang, Yun
2014-10-01
In the present work, fresh and spoiled wine samples from three wines produced by different companies were studied u- sing Fourier transform infrared (FTIR) spectroscopy. We analyzed the physicochemical property change in the process of spoil- age, and then, gave out the attribution of some main FTIR absorption peaks. A novel determination method was explored based on the comparisons of some absorbance ratios at different wavebands although the absorbance ratios in this method were relative. Through the compare of the wine spectra before and after spoiled, the authors found that they were informative at the bands of 3,020~2,790, 1,760~1,620 and 1,550~800 cm(-1). In order to find the relation between these informative spectral bands and the wine deterioration and achieve the discriminant analysis, chemometrics methods were introduced. Principal compounds analysis (PCA) and soft independent modeling of class analogy (SIMCA) were used for classifying different-quality wines. And partial least squares discriminant analysis (PLS-DA) was applied to identify spoiled wines and good wines. Results showed that FTIR technique combined with chemometrics methods could effectively distinguish spoiled wines from fresh samples. The effect of classification at the wave band of 1 550-800 cm(-1) was the best. The recognition rate of SIMCA and PLSDA were respectively 94% and 100%. This study demonstrates that Fourier transform infrared spectroscopy is an effective tool for monitoring red wine's spoilage and provides theoretical support for developing early-warning equipments. PMID:25739205
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
Real-time 2D floating-point fast Fourier transforms for seeker simulation
NASA Astrophysics Data System (ADS)
Chamberlain, Richard; Lord, Eric; Shand, David J.
2002-07-01
The floating point Fast Fourier Transform (FFT) is one of the most useful basic functions available to the image and signal processing engineer allowing many complex and detailed special functions to be implemented more simply in the frequency domain. In the Hardware-in-the-Loop field an image transformed using FFT would allow the designer to think about accurate frequency based simulation of seeker lens effects, motion blur, detector transfer functions and much more. Unfortunately, the transform requires many hundreds of thousands or millions of floating point operations on a single modest sized image making it impractical for realtime Hardware-in-the-Loop systems. .until now. This paper outlines the development, by Nallatech, of an FPGA based IEEE floating point core. It traces the subsequent use of this core to develop a full 256 X 256 FFT and filter process implemented on COTS hardware at frame rates up to 150Hz. This transform can be demonstrated to model optical transfer functions at a far greater accuracy than the current spatial models. Other applications and extensions of this technique will be discussed such as filtering for image tracking algorithms and in the simulation of radar processing in the frequency domain.
Ma, Q. [NASA/Goddard Institute for Space Studies and Department of Applied Physics and Applied Mathematics, Columbia University, 2880 Broadway, New York, New York 10025 (United States)] [NASA/Goddard Institute for Space Studies and Department of Applied Physics and Applied Mathematics, Columbia University, 2880 Broadway, New York, New York 10025 (United States); Boulet, C. [Institut des Sciences Moléculaires d'Orsay (ISMO), CNRS (UMR8214) et Université Paris-Sud Bât 350, Campus d'Orsay F-91405 (France)] [Institut des Sciences Moléculaires d'Orsay (ISMO), CNRS (UMR8214) et Université Paris-Sud Bât 350, Campus d'Orsay F-91405 (France); Tipping, R. H. [Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487-0324 (United States)] [Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487-0324 (United States)
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.
Ma, Q; Boulet, C; 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 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 ? 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. PMID:24628166
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)
Ma, Q.; Boulet, C.; Tipping, R. H.
2014-03-01
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 {hat 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 Technical Reports Server (NTRS)
Klimas, A. J.
1983-01-01
A numerical method is presented for studying one-dimensional electron plasma evolution under typical interplanetary conditions. The method applies the Fourier-Fourier transform approach to a plasma model that is a generalization of the electrostatic Vlasov-Poisson system of equations. Conservation laws that are modified to include the plasma model generalization and also the boundary effects of nonperiodic solutions are given. A new conservation law for entropy in the transformed space is then introduced. These conservation laws are used to verify the numerical solutions. A discretization error analysis is presented. Two numerical instabilities and the methods used for their suppression are treated. It is shown that in interplanetary plasma conditions, the bump-on-tail instability produces significant excitation of plasma oscillations at the Bohm-Gross frequency and its second harmonic. An explanation of the second harmonic excitation is given in terms of wave-wave coupling during the growth phase of the instability.
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.
NASA Astrophysics Data System (ADS)
Yen, K. S.; Ratnam, M. M.
2012-05-01
The analysis of moiré patterns generated by a pair of circular gratings requires complex computation, especially for high resolution in-plane displacement measurements. In this paper, the Fourier transformation method developed by previous researchers for analyzing the moiré patterns was applied to digitally generated and real moiré patterns. The real moiré patterns were formed by low-frequency gratings, typically used in crack growth monitoring. Due to the failure of the Fourier transformation method when applied to moiré patterns generated by low-frequency gratings, the performance of the recently proposed graphical analysis method that determines the displacement values accurately from the moiré patterns was compared with the Fourier transformation approach. In this method, the moiré patterns were spatially transformed from Cartesian-to-polar coordinate system. The morphological grayscale dilation operation was used to eliminate the residual grating in the transformed pattern and preserve only the moiré fringes. The centerline of each moiré fringe was fitted with a sine function, and the eccentricity magnitude and directions between the two gratings were determined directly from the amplitude and the phase shift of the fitted function. The comparison shows that the proposed graphical analysis method is able to give high in-plane displacement accuracy with a mean error of -0.002 mm and 0.451° in the eccentricity magnitude and direction, respectively, without the need for complex computation using Fourier transformation.
A two-phase approach to fourier transform ion mobility time-of-flight mass spectrometry.
Clowers, Brian H; Siems, William F; Yu, Zhihao; Davis, Austen L
2015-09-28
It is well known that the duty cycle of common drift-tube ion mobility experiments is often below 1%. However, multiplexing approaches such as Fourier and Hadamard pulsing schemes have been shown to independently enhance the throughput of ion mobility spectrometry (IMS) experiments to levels that approach 50%. While challenges remain to their broad scale implementation we describe a new Fourier transform (FT) IMS experiment that is directly compatible with standard drift tube ion mobility mass spectrometers (DT-IMMS). Compared to previous FT-IMS experiments, our new approach requires only a single gate and circumvents the need for signal apodization by combining data from two frequency pulsing sequences 180° out of phase. Assessment of our initial results highlights an increase in signal-to-noise (SNR) relative to both previous implementations FT-IMS experiments and signal averaged (SA) experiments. For select tetraalkylammonium salts SNR improvements of more than one order of magnitude are routinely possible. To explore the performance metrics associated with the technique a number of experimental variables were systematically altered including frequency sweep range, sweep time, and data acquisition time. Using this experimental design we present the key aspects, considerations, and minimum resources necessary for other IMS researchers to incorporate this operational mode into their research. The two-phase FT-IMMS technique offers a tractable mechanism to enhance sensitivity for IMMS measurements and its broad-scale adoption by IMMS researchers promises to enhance the acquisition speed for mobility measurements using hybrid instrumentation. PMID:26275009
Liu, Derek, E-mail: dmliu@ualberta.ca; Sloboda, Ron S. [Department of Medical Physics, Cross Cancer Institute, Edmonton, Alberta T6G 1Z2, Canada and Department of Oncology, University of Alberta, Edmonton, Alberta T6G 2R3 (Canada)] [Department of Medical Physics, Cross Cancer Institute, Edmonton, Alberta T6G 1Z2, Canada and Department of Oncology, University of Alberta, Edmonton, Alberta T6G 2R3 (Canada)
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.