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.
Quantum Fourier Transform in a Decoherence-Free Subspace
Jian-wu Wu; Chun-wen Li; Re-bing Wu
2004-09-19
Quantum Fourier transform is of primary importance in many quantum algorithms. In order to eliminate the destructive effects of decoherence induced by couplings between the quantum system and its environment, we propose a robust scheme for quantum Fourier transform over the intrinsic decoherence-free subspaces. The scheme is then applied to the circuit design of quantum Fourier transform over quantum networks under collective decoherence. The encoding efficiency and possible improvements are also discussed.
Secret sharing based on quantum Fourier transform
NASA Astrophysics Data System (ADS)
Yang, Wei; Huang, Liusheng; Shi, Runhua; He, Libao
2013-07-01
Secret sharing plays a fundamental role in both secure multi-party computation and modern cryptography. We present a new quantum secret sharing scheme based on quantum Fourier transform. This scheme enjoys the property that each share of a secret is disguised with true randomness, rather than classical pseudorandomness. Moreover, under the only assumption that a top priority for all participants (secret sharers and recovers) is to obtain the right result, our scheme is able to achieve provable security against a computationally unbounded attacker.
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...
Exploration of Quantum Fourier Transform Algorithms in Wireless Communication Networks
Khalil F. Dajani; Robert S. Owor; D. Zephyrinus Okonkwo; D. John Hamilton
This paper describes a new class of Quantum Fourier Transform (QFT) algorithms which can be used to secure advanced future wireless distributed networks. QFT algorithms provide two main advantages over existing cryptographic algorithms which are based purely on complex and challenging mathematical formulations. The combination of the dual and probabilistic nature of quantum behavior with discrete wave patterns using Fourier
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).
An approximate Fourier transform useful in quantum factoring
D. Coppersmith
2002-01-16
We define an approximate version of the Fourier transform on $2^L$ elements, which is computationally attractive in a certain setting, and which may find application to the problem of factoring integers with a quantum computer as is currently under investigation by Peter Shor. (1994 IBM Internal Report)
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.
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.
Fast parallel circuits for the quantum Fourier transform
Richard Cleve; John Watrous
2000-06-01
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n with error bounded by epsilon. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations with constant error. Moreover, our circuits have size O(n log (n/epsilon)). We also give an upper bound of O(n (log n)^2 log log n) on the circuit size of the exact QFT modulo 2^n, for which the best previous bound was O(n^2). As an application of the above depth bound, we show that Shor's factoring algorithm may be based on quantum circuits with depth only O(log n) and polynomial-size, in combination with classical polynomial-time pre- and post-processing. In the language of computational complexity, this implies that factoring is in the complexity class ZPP^BQNC, where BQNC is the class of problems computable with bounded-error probability by quantum circuits with poly-logarithmic depth and polynomial size. Finally, we prove an Omega(log n) lower bound on the depth complexity of approximations of the QFT with constant error. This implies that the above upper bound is asymptotically optimal (for a reasonable range of values of epsilon).
Entanglement of Periodic States, the Quantum Fourier Transform and Shor's Factoring Algorithm
Most, Yonatan; Biham, Ofer
2010-01-01
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.
Entanglement of periodic states, the quantum Fourier transform, and Shor's factoring algorithm
NASA Astrophysics Data System (ADS)
Most, Yonatan; Shimoni, Yishai; Biham, Ofer
2010-05-01
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.
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.
Entanglement of Periodic States, the Quantum Fourier Transform and Shor's Factoring Algorithm
Yonatan Most; Yishai Shimoni; Ofer Biham
2010-05-20
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.
Fast parallel circuits for the quantum Fourier transform
Richard Cleve; John Watrous
2000-01-01
We give new bounds on the circuit complexity of the quan- tum Fourier transform (QFT). We give an upper bound of on the circuit depth for comput- ing an approximation of the QFT with respect to the mod- ulus with error bounded by . Thus, even for exponen- tially small error, our circuits have depth . The best previous depth
NASA Astrophysics Data System (ADS)
Krovi, Hari; Russell, Alexander
2015-03-01
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups [denoted , for a group G]. These induce a rich family of knot invariants and, additionally, are directly related to topological quantum computation. Regarding algorithms for these invariants, we develop quantum circuits for the quantum Fourier transform over ; in general, we show that when one can uniformly and efficiently carry out the quantum Fourier transform over the centralizers Z( g) of the elements of G, one can efficiently carry out the quantum Fourier transform over . We apply these results to the symmetric groups to yield efficient circuits for the quantum Fourier transform over . With such a Fourier transform, it is straightforward to obtain additive approximation algorithms for the related link invariant. As for hardness results, first we note that in contrast to those concerning the Jones polynomial—where the images of the braid group representations are dense in the unitary group—the images of the representations arising from are finite. This important difference appears to be directly reflected in the complexity of these invariants. While additively approximating "dense" invariants is -complete and multiplicatively approximating them is -complete, we show that certain invariants (such as invariants) are -hard to additively approximate, -hard to multiplicatively approximate, and -hard to exactly evaluate. To show this, we prove that, for groups (such as A n ) which satisfy certain properties, the probability of success of any randomized computation can be approximated to within any by the plat closure. Finally, we make partial progress on the question of simulating anyonic computation in groups uniformly as a function of the group size. In this direction, we provide efficient quantum circuits for the Clebsch-Gordan transform over for "fluxon" irreps, i.e., irreps of characterized by a conjugacy class of G. For general irreps, i.e., those which are associated with a conjugacy class of G and an irrep of a centralizer, we present an efficient implementation under certain conditions, such as when there is an efficient Clebsch-Gordan transform over the centralizers (this could be a hard problem for some groups). We remark that this also provides a simulation of certain anyonic models of quantum computation, even in circumstances where the group may have size exponential in the size of the circuit.
Large quantum Fourier transforms are never exactly realized by braiding conformal blocks
Freedman, Michael H. [Microsoft Project Q, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States); Wang, Zhenghan [Microsoft Project Q, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030 (United States); Department of Mathematics, Indiana University, Bloomington, Indiana 47405 (United States)
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.
The fractional order Fourier transform and its application to quantum mechanics
VICTOR NAMIAS
1980-01-01
The concept of Fourier transforms of fractional order is introduced, the ordinary Fourier transform being of order 1. The integral representation of this transform can be used to construct a table of fractional order Fourier transforms. A generalized operational calculus is developed, paralleling the familiar one for the ordinary transform. Its application provides a convenient technique for solving certain classes
Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells.
Cundiff, Steven T; Zhang, Tianhao; Bristow, Alan D; Karaiskaj, Denis; Dai, Xingcan
2009-09-15
Coherent light-matter interactions of direct-gap semiconductor nanostructures provide a great test system for fundamental research into quantum electronics and many-body physics. The understanding gained from studying these interactions can facilitate the design of optoelectronic devices. Recently, we have used optical two-dimensional Fourier-transform spectroscopy to explore coherent light-matter interactions in semiconductor quantum wells. Using three laser pulses to generate a four-wave-mixing signal, we acquire spectra by tracking the phase of the signal with respect to two time axes and then Fourier transforming them. In this Account, we show several two-dimensional projections and demonstrate techniques to isolate different contributions to the coherent response of semiconductors. The low-temperature spectrum of semiconductor quantum wells is dominated by excitons, which are electron-hole pairs bound through Coulombic interactions. Excitons are sensitive to their electronic and structural environment, which influences their optical resonance energies and line widths. In near perfect quantum wells, a small fluctuation of the quantum well thickness leads to spatial localization of the center-of-mass wave function of the excitons and inhomogeneous broadening of the optical resonance. The inhomogeneous broadening often masks the homogeneous line widths associated with the scattering of the excitons. In addition to forming excitons, Coulombic correlations also form excitonic molecules, called biexcitons. Therefore, the coherent response of the quantum wells encompasses the intra-action and interaction of both excitons and biexcitons in the presence of inhomogeneous broadening. Transient four-wave-mixing studies combined with microscopic theories have determined that many-body interactions dominate the strong coherent response from quantum wells. Although the numerous competing interactions cannot be easily separated in either the spectral or temporal domains, they can be separated using two-dimensional Fourier transform spectroscopy. The most common two-dimensional Fourier spectra are S(I)(omega(tau),T,omega(t)) in which the second time period is held fixed. The result is a spectrum that unfolds congested one-dimensional spectra, separates excitonic pathways, and shows which excitons are coherently coupled. This method also separates the biexciton contributions and isolates the homogeneous and inhomogeneous line widths. For semiconductor excitons, the line shape in the real part of the spectrum is sensitive to the many-body interactions, which we can suppress by exploiting polarization selection rules. In an alternative two-dimensional projection, S(I)(tau,omega(Tau),omega(t)), the nonradiative Raman coherent interactions are isolated. Finally, we show S(III)(tau,omega(Tau),omega(t)) spectra that isolate the two-quantum coherences associated with the biexciton. These spectra reveal previously unobserved many-body correlations. PMID:19555068
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
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
Fourier transform digital holography
Dan Apostol; Adrian Sima; Petre C. Logofatu; Florin Garoi; Victor Damian; Victor Nascov; Iuliana Iordache
2007-01-01
In this paper a Fourier transform digital holography experimental arrangement is presented. It is actually a hybrid arrangement, half digital half analog. The Fourier hologram was constructed using the analogous means of the so called lensless configuration. The hologram was recorded digitally by a camera with a large CCD array in stead of the recording medium. The recording of the
Migration by Fourier transform
R. H. Stolt
1978-01-01
Wave equation migration is known to be simpler in principle when the horizontal coordinate or coordinates are replaced by their Fourier conjugates. Two practical migration schemes utilizing this concept are developed. One scheme extends the Claerbout finite difference method, greatly reducing dispersion problems usually associated with this method at higher dips and frequencies. The second scheme effects a Fourier transform
Fourier transform mass spectrometry.
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-07-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802
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.
Svetoslav S. Ivanov; Michael Johanning; Christof Wunderlich
2015-03-30
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 scheme, which prescribes concatenated sequences of control phase gates, our implementation is based on one-qubit gates and a free evolution process. We show a realization of our method with homogeneous microwave driven ion traps in a magnetic field with gradient. In this setup our implementation presents a series of microwave $\\pi$ or $\\pi/2$ pulses applied at certain times.
NASA Astrophysics Data System (ADS)
Naruse, Nobuyasu; Mera, Yutaka; Nakamura, Yoshiaki; Ichikawa, Masakazu; Maeda, Koji
2009-03-01
Spatially resolved Fourier-transform photoabsorption spectra of individual Ge1-xSnx nanodots, obtained by a technique based on scanning tunneling microscopy, exhibited a distinct peak far below the absorption edge of the Si substrate, which showed a clear blue shift with decreasing dot size. The energy position of the peak measured in high accuracy was in good agreement with the optical transition energy between discrete levels theoretically predicted by the size dependence due to a quantum-confinement effect, which was previously observed in scanning tunneling spectroscopic measurements.
Fourier Transforms, Fourier Series and the FFT
NSDL National Science Digital Library
Lisette de Pillis
The goal of this module is to give students an understanding of the one-dimensional Fourier Transform, both mathematically and computationally, with a focus on finding periodicity in data. To motivate the study of the Fourier Transform, the students will be presented with certain application areas, such as searching for periodic patterns in CO2 data and differentiating between two sound signals using their power spectra. Students will explore some computational issues and challenges of the Discrete and Fast Fourier Transforms.
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
Stone, Katherine W; Turner, Daniel B; Gundogdu, Kenan; Cundiff, Steven T; Nelson, Keith A
2009-09-15
The Coulomb correlations between photoexcited charged particles in materials such as photosynthetic complexes, conjugated polymer systems, J-aggregates, and bulk or nanostructured semiconductors produce a hierarchy of collective electronic excitations, for example, excitons, and biexcitons, which may be harnessed for applications in quantum optics, light-harvesting, or quantum information technologies. These excitations represent correlations among successively greater numbers of electrons and holes, and their associated multiple-quantum coherences could reveal detailed information about complex many-body interactions and dynamics. However, unlike single-quantum coherences involving excitons, multiple-quantum coherences do not radiate; consequently, they have largely eluded direct observation and characterization. In this Account, we present a novel optical technique, two-quantum, two-dimensional Fourier transform optical spectroscopy (2Q 2D FTOPT), which allows direct observation of the dynamics of multiple exciton states that reflect the correlations of their constituent electrons and holes. The approach is based on closely analogous methods in NMR, in which multiple phase-coherent fields are used to drive successive transitions such that multiple-quantum coherences can be accessed and probed. In 2Q 2D FTOPT, a spatiotemporal femtosecond pulse-shaping technique has been used to overcome the challenge of control over multiple, noncollinear, phase-coherent optical fields in experimental geometries used to isolate selected signal contributions through wavevector matching. We present results from a prototype GaAs quantum well system, which reveal distinct coherences of biexcitons that are formed from two identical excitons or from two excitons that have holes in different spin sublevels ("heavy-hole" and "light-hole" excitons). The biexciton binding energies and dephasing dynamics are determined, and changes in the dephasing rates as a function of the excitation density are observed, revealing still higher order correlations due to exciton-biexciton interactions. Two-quantum coherences due to four-particle correlations that do not involve bound biexciton states but that influence the exciton properties are also observed and characterized. The 2Q 2D FTOPT technique allows many-body interactions that cannot be treated with a mean-field approximation to be studied in detail; the pulse-shaping approach simplifies greatly what would have otherwise been daunting measurements. This spectroscopic tool might soon offer insight into specific applications, for example, in detailing the interactions that affect how electronic energy moves within the strata of organic photovoltaic cells. PMID:19691277
Enabling two-dimensional fourier transform electronic spectroscopy on quantum dots
NASA Astrophysics Data System (ADS)
Hill, Robert John, Jr.
Colloidal semiconductor nanocrystals exhibit unique properties not seen in their bulk counterparts. Quantum confinement of carriers causes a size-tunable bandgap, making them attractive candidates for solar cells. Fundamental understanding of their spectra and carrier dynamics is obscured by inhomogeneous broadening arising from the size distribution. Because quantum dots have long excited state lifetimes and are sensitive to both air and moisture, there are many potential artifacts in femtosecond experiments. Two-dimensional electronic spectroscopy promises insight into the photo-physics, but required key instrumental advances. Optics that can process a broad bandwidth without distortion are required for a two-dimensional optical spectrometer. To control pathlength differences for femtosecond time delays, hollow retro-reflectors are used on actively stabilized delay lines in interferometers. The fabrication of rigid, lightweight, precision hollow rooftop retroreflectors that allow beams to be stacked while preserving polarization is described. The rigidity and low mass enable active stabilization of an interferometer to within 0.6 nm rms displacement, while the return beam deviation is sufficient for Fourier transform spectroscopy with a frequency precision of better than 1 cm -1. Keeping samples oxygen and moisture free while providing fresh sample between laser shots is challenging in an interferometer. A low-vibration spinning sample cell was designed and built to keep samples oxygen free for days while allowing active stabilization of interferometer displacement to ˜1 nm. Combining these technologies has enabled 2D short-wave infrared spectroscopy on colloidal PbSe nanocrystals. 2D spectra demonstrate the advantages of this key instrumentation while providing valuable insight into the low-lying electronic states of colloidal quantum dots.
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 Technical Reports Server (NTRS)
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Optical transformation from chirplet to fractional Fourier transformation kernel
Hong-yi Fan; Li-yun Hu
2009-02-11
We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship between a phase space function and its Weyl-Wigner quantum correspondence operator is revealed.
Fast quantum efficiency measurement of solar cells by Fourier transform photocurrent spectroscopy
L. Hod’áková; A. Poruba; R. Kravets; M. Vanecek
2006-01-01
Fourier Transform Photocurrent Spectroscopy (FTPS) was introduced four years ago as a method providing fast and highly sensitive evaluation of the spectral dependence of the photoconductive thin film optical absorption coefficient. Recently the method was also applied to the quality assessment of thin film silicon solar cells. In this contribution, we present the FTPS characterization of various thin film solar
Karaiskaj, Denis; Bristow, Alan D; Yang, Lijun; Dai, Xingcan; Mirin, Richard P; Mukamel, Shaul; Cundiff, Steven T
2010-03-19
We present experimental coherent two-dimensional Fourier-transform spectra of Wannier exciton resonances in semiconductor quantum wells generated by a pulse sequence that isolates two-quantum coherences. By measuring the real part of the signals, we determine that the spectra are dominated by two-quantum coherences due to mean-field many-body interactions, rather than bound biexcitons. Simulations performed using dynamics controlled truncation agree with the experiments. PMID:20366499
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.
Multiple fractional Fourier transform holography
NASA Astrophysics Data System (ADS)
Zeng, Yangsu; Zhang, Yixiao; Gao, Feng; Gao, Fuhua; Huang, Xiaoyang; Guo, Yongkang
2002-04-01
In this paper, we introduce the recording and reconstruction theories of the multiple fractional Fourier transform hologram (M-FRTH). We fabricated a multiple fractional Fourier transform hologram, and obtained satisfying reconstruction results. The experimental result shows that the M-FRTH has a high anti-counterfeiting capacity and can be used in the fabrication of the trademark, ID, and the notes.
On the braided Fourier transform on the n-dimensional quantum space
NASA Astrophysics Data System (ADS)
Carnovale, Giovanna
1999-11-01
We work out in detail a theory of integrability on the braided covector Hopf algebra and the braided vector Hopf algebra of type An introduced by Majid. Using a braided Fourier transform very similar to the one defined by Kempf and Majid we obtain n-dimensional analogs of results by Koornwinder expressing the correspondence between products of the q2-Gaussian gq2(x_) times monomials, and products of the q2-Gaussian Gq2(?_) times q2-Hermite polynomials under the transform. We invert the correspondence by finding a suitable inversion, different from the one of Kempf and Majid. We show that with this transforms, whenever n?2, the Plancherel measure will depend on the parity of the power series that we are transforming.
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…
Fractional Fourier transform and geometric quantization
NASA Astrophysics Data System (ADS)
Chmielowiec, Witold; Kijowski, Jerzy
2012-06-01
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of the phase-space: no linear structure is necessary. It is shown that the “fractional Fourier transform” provides a simple example of this construction. As an application of this technique we show that for any linear Hamiltonian system, its quantum dynamics can be obtained exactly as the lift of the corresponding classical dynamics by means of the above transformation. Moreover, it can be deduced from the free quantum evolution. This way new, unknown symmetries of the Schrödinger equation can be constructed. It is also argued that the above construction defines in a natural way a connection in the bundle of quantum states, with the base space describing all their possible representations. The non-flatness of this connection would be responsible for the non-existence of a quantum representation of the complete algebra of classical observables.
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...
Discrete integer Fourier transform in real space: elliptic Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Grigoryan, Merughan M.
2009-02-01
The concept of the N-point DFT is generalized, by considering it in the real space (not complex). The multiplication by twiddle coefficients is considered in matrix form; as the Givens transformation. Such block-wise representation of the matrix of the DFT is effective. The transformation which is called the T-generated N-block discrete transform, or N-block T-GDT is introduced. For each N-block T-GDT, the inner product is defined, with respect to which the rows (and columns) of the matrices X are orthogonal. By using different parameterized matrices T, we define metrics in the real space of vectors. The selection of the parameters can be done among only the integer numbers, which leads to integer-valued metric. We also propose a new representation of the discrete Fourier transform in the real space R2N. This representation is not integer, and is based on the matrix C (2x2) which is not a rotation, but a root of the unit matrix. The point (1, 0) is not moving around the unite circle by the group of motion generated by C, but along the perimeter of an ellipse. The N-block C-GDT is therefore called the N-block elliptic FT (EFT). These orthogonal transformations are parameterized; their properties are described and examples are given.
FPGA FFT(Fast Fourier Transform) 1 FPGA FFT(Fast Fourier Transform)
Jang, Ju-Wook
FPGA FFT(Fast Fourier Transform) 1 FPGA FFT(Fast Fourier Transform) Gokul Govindu Viktor K. Prasanna FPGA (FFT) . FPGA FFT a set storage types as parameters, on Xilinx Vertex-II FPGA to verify the estimates. Our designs
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 [Campus Saint-Jean, University of Alberta, 8406 Rue Marie-Anne Gaboury, 91 Street, Edmonton, Alta., T6C 4G9 (Canada)]. E-mail: hassan.safouhi@ualberta.ca; Berlu, Lilian [Laboratoire SEESIB, UMR 6504, Universite Blaise Pascal, 63177 Aubiere Cedex (France)
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.
Hypercomplex Fourier transforms of color images.
Ell, Todd A; Sangwine, Stephen J
2007-01-01
Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed. PMID:17283762
Fourier transform zero field NMR and NQR
Zax, D.B.
1985-01-01
In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive, or the information contained in the dipole-dipole couplings is more important. In these cases, Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subject of this thesis. Chapter I presents the quantum mechanical background and notational formalism for what follows. Chapter II gives a brief review of high resolution magnetic resonance methods, with particular emphasis on techniques applicable to dipole-dipole and quadrupolar couplings. Level crossings between spin-1/2 and quadrupolar spins during demagnetization transfer polarization from high to low lambda nuclei. This is the basis of very high sensitivity zero field NQR measurements by field cycling. Chapter III provides a formal presentation of the high resolution Fourier transform zero field NMR method. Theoretical signal functions are calculated for common spin systems, and examples of typical spectra are presented. Chapters IV and V review the experimental progress in zero field NMR of dipole-dipole coupled spin-1/2 nuclei and for quadrupolar spin systems. Variations of the simple experiment describe in earlier chapters that use pulsed dc fields are presented in Chapter VI.
The Geostationary Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Key, Richard; Sander, Stanley; Eldering, Annmarie; Miller, Charles; Frankenberg, Christian; Natra, Vijay; Rider, David; Blavier, Jean-Francois; Bekker, Dmitriy; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for an earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. The GeoFTS instrument is a half meter cube size instrument designed to operate in geostationary orbit as a secondary "hosted" payload on a commercial geostationary satellite mission. The advantage of GEO is the ability to continuously stare at a region of the earth, enabling frequent sampling to capture the diurnal variability of biogenic fluxes and anthropogenic emissions from city to continental scales. The science goal is to obtain a process-based understanding of the carbon cycle from simultaneous high spatial resolution measurements of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) many times per day in the near infrared spectral region to capture their spatial and temporal variations on diurnal, synoptic, seasonal and interannual time scales. The GeoFTS instrument is based on a Michelson interferometer design with a number of advanced features incorporated. Two of the most important advanced features are the focal plane arrays and the optical path difference mechanism. A breadboard GeoFTS instrument has demonstrated functionality for simultaneous measurements in the visible and IR in the laboratory and subsequently in the field at the California Laboratory for Atmospheric Remote Sensing (CLARS) observatory on Mt. Wilson overlooking the Los Angeles basin. A GeoFTS engineering model instrument is being developed which will make simultaneous visible and IR measurements under space flight like environmental conditions (thermal-vacuum at 180 K). This will demonstrate critical instrument capabilities such as optical alignment stability, interferometer modulation efficiency, and high throughput FPA signal processing. This will reduce flight instrument development risk and show that the GeoFTS design is mature and flight ready.
The Geostationary Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
FOURIER TRANSFORM 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...
SAR vibrometry using fractional Fourier transform processing
Qi Wang; Majeed M. Hayat; Balu Santhanam; Tom Atwood
2009-01-01
A novel signal-processing approach is reported for vibrometry in synthetic aperture radar (SAR) imaging systems. The approach exploits the conventional deramp process; however, in place of Fourier-transform processing we utilize the fractional Fourier transform (FRFT) as a processing tool. The FRFT is geared toward non-stationary signals and chirped sinusoids particularly. A simplified mathematical expression is developed to describe the reflectivity
Replica Fourier Transform: Properties and applications
NASA Astrophysics Data System (ADS)
Crisanti, A.; De Dominicis, C.
2015-02-01
The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically.
Quantifying momenta through the Fourier transform
Rodr\\'\\iguez-Lara, B M
2011-01-01
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be calculated using only Fourier transforms. This result is used to evaluate the mean value of momenta associated to the symmetries of the reduced wave equation. As an explicit example, the orbital angular momenta of plane and elliptic-cylindrical waves is presented.
Fractional discrete q-Fourier transforms
NASA Astrophysics Data System (ADS)
Muñoz, Carlos A.; Rueda-Paz, J.; Wolf, Kurt Bernardo
2009-09-01
The discrete Fourier transform (DFT) matrix has a manifold of fractionalizations that depend on the choice of its eigenbases. One prominent basis is that of Mehta functions; here we examine a family of fractionalizations of the DFT stemming from q-extensions of this basis. Although closed expressions are given, many results of our analysis derive from numerical computation and display. Thus we suggest that the account of fractional Fourier transformations applied on signals as presented by other authors—typically of a centred rectangle function—may be biased because the support of the function lies in the central part of the domain only. The phase and amplitude of the whole fractional DFT matrices reveal the location of departures from the continuous kernel of the fractional Fourier integral transform, whose phase and constant amplitude are well known.
Interferogram analysis using Fourier transform techniques
NASA Technical Reports Server (NTRS)
Roddier, Claude; Roddier, Francois
1987-01-01
A method of interferogram analysis is described in which Fourier transform techniques are used to map the complex fringe visibility in several types of interferograms. Algorithms are developed for estimation of both the amplitude and the phase of the fringes (yielding the modulus and the phase of the holographically recorded object Fourier transform). The algorithms were applied to the reduction of interferometric seeing measurements (i.e., the estimation of the fringe amplitude only), and the reduction of interferometric tests (i.e., estimation of the fringe phase only). The method was used to analyze scatter-plate interferograms obtained at NOAO.
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.
ON FOURIER TRANSFORMS OF RADIAL FUNCTIONS AND DISTRIBUTIONS
Grafakos, Loukas
ON FOURIER TRANSFORMS OF RADIAL FUNCTIONS AND DISTRIBUTIONS LOUKAS GRAFAKOS AND GERALD TESCHL analogous results for radial tempered distributions. 1. Introduction The Fourier transform of a function Abstract. We find a formula that relates the Fourier transform of a radial function on Rn with the Fourier
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space. PMID:16138556
Abel inversion using fast Fourier transforms.
Kalal, M; Nugent, K A
1988-05-15
A fast Fourier transform based Abel inversion technique is proposed. The method is faster than previously used techniques, potentially very accurate (even for a relatively small number of points), and capable of handling large data sets. The technique is discussed in the context of its use with 2-D digital interferogram analysis algorithms. Several examples are given. PMID:20531689
Fourier transform resampling: theory and application
William G. Hawkins
1997-01-01
One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. The standard geometry is the parallel ray geometry of the conventional Radon transform. This work focuses on the resampling of a nonstandard geometry to obtain a data set in standard geometry. The approach is guided by the application of Fourier analysis to
Fast Fourier Transform Spectral Analysis Program
NASA Technical Reports Server (NTRS)
Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.
1969-01-01
Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.
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.
Imaging Fourier transform spectrometry of chemical plumes
Kenneth C. Bradley; Kevin C. Gross; Glen P. Perram
2009-01-01
A midwave infrared (MWIR) imaging Fourier transform spectrometer (FTS), the Telops FIRST-MWE (Field-portable Imaging Radiometric Spectrometer Technology - Midwave Extended) has been utilized for the standoff detection and characterization of chemical plumes. Successful collection and analysis of MWIR hyperspectral imagery of jet engine exhaust has allowed us to produce spatial profiles of both temperature and chemical constituent concentrations of exhaust
Multiple imaging by lensless Fourier transform holography
P. C. Mehta; C. Bhan; R. Hradaynath
1979-01-01
A simple method for producing multiple images is reported by recording a lensless Fourier transform hologram of the master object using a holographic grating. Relations for optimizing reference-to-object beam intensity ratio are derived in order to retain linearity and efficiency of the hologram. One of the advantages of the technique is that the same grating can be used for the
Color Image Watermarking Using Multidimensional Fourier Transforms
Tsz Kin Tsui; Xiao-ping Zhang; Dimitrios Androutsos
2008-01-01
Abstract—This paper presents two vector watermarking schemes that are based on the use of complex and quaternion Fourier transforms and demonstrates, for the first time, how to embed watermarks into the frequency domain that is consistent with our human visual system. Watermark casting is performed by estimating the just-noticeable distortion of the images, to ensure watermark invisibility. The first method
REMOTE FOURIER TRANSFORM INFRARED AIR POLLUTION STUDIES
A commercial Fourier transform infrared interferometer system has been installed in a van and used to make longpath absorption and single-ended emission measurements of gaseous pollutant concentrations at a variety of pollutant sources. The interferometer system is described and ...
Fourier Transform and Reflective Imaging Pyrometry
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.
Fourier Transform Spectroscopy, Eleventh International Conference. Proceedings
de Haseth, J.A. [Department of Chemistry, University of Georgia, Atlanta, GA 30602-2556 (United States)
1998-05-01
These proceedings represent the papers presented at the Eleventh International Conference on Fourier Transform Spectroscopy held in August, 1997 in Athens, Georgia, USA. The Conference provided an atmosphere for people of diverse backgrounds to congregate and exchange information. The topics discussed included applications of Fourier transform spectroscopy to surface science, biological systems, atmospheric science, forensics and textiles, etc. Biochemical and biomedical studies utilizing Fourier Transform infrared spectroscopy formed a large section of the Conference Applications to semiconductor industry, namely monitoring of CVD processes and photoresists were also discussed. Most of the applications were in the near and mid infrared, with a few extending to the far infrared and visible regions of the electromagnetic spectrum. In the Keynote Address, Fourier Transform Ion Cyloctron Resonance Spectroscopy was reviewed by Professor Alan G. Marshall of the National High Magnetic Field Laboratory in Florida. Altogether 152 papers were presented at the Conference and out of these, 15 have been abstracted for the Energy, Science and Technology database. (AIP)
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.
Pseudochromatic encoding fractional Fourier transform rainbow hologram
NASA Astrophysics Data System (ADS)
Guo, Yongkang; Huang, Qizhong; Du, Jinglei
1998-08-01
The FRTH is presented in this paper and its properties are discussed. Then we make a pseudo chromatic encoding fractional Fourier transform rainbow hologram, based on its specialty in its reconstruction and that the encoding color has relationship with the order of the reconstruction FRT system, a new type of anti-counterfeiting hologram is introduced.
MATH 890 FOURIER ANALYSIS F13 HW 3. More about the Fourier Transform
Torres, Rodolfo
MATH 890 Â FOURIER ANALYSIS Â F13 HW 3. More about the Fourier Transform 1. Compute the Fourier the Fourier coefficients of the left hand side.) 4. Compute the Fourier transform of p.v. 1 x . (Hint: write f if and only if supp f = {0}. b) Let S0(Rn ) be the subspace of S(Rn ) consisting of functions whose Fourier
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.
Holographic image projection using fractional Fourier transformation
NASA Astrophysics Data System (ADS)
Chang, Chenliang; Xia, Jun; Lei, Wei
2012-01-01
A new method of image projection based on fractional Fourier transformation is presented. This method can project an image at any distance after a lens plane. We use a modified Gerschberg-Saxton (GS) iteration algorithm to compute a phase-only hologram. The amplitude distributions both on the hologram plane and image plane are restricted while allowing their phase distributions to drift into an optimum value. The quality of the image projected by fractional Fourier hologram is close to the image projected by Fourier hologram. The RMS error between the projected image and the constrained image is computed in our experiment. A comparison in flexibility of the two projection methods is also discussed.
Improved Fourier transform for multicarrier processing
NASA Astrophysics Data System (ADS)
Shattil, Steve J.; Nassar, Carl R.
2002-11-01
We present a simplified Fourier-transform process, called the orthogonal frequency Fourier transform (OFFT). Conventional divide-and-conquer techniques, such as the fast Fourier transform (FFT), reduce the number of operations in a Fourier transform and simplify at least some of the complex-valued terms (i.e. twiddle factors). The FFT reduces the number of multipliers, which account for much of the chip area and power consumption in digital VLSI design. The OFFT and inverse OFFT exploit orthogonal frequency relationships to replace multiplications with simpler sampling and adding operations. Specifically, the OFFT replaces twiddle factors with step functions, which are superpositions of harmonic sinusoids. The resulting transform is adapted to add samples that are selected relative to at least one periodic step function, thus eliminating all complex multiplications. In phase and quadrature phase OFFT processing may be performed. OFFTs can be combined with pass-band sampling to simultaneously perform filtering, down conversion, and demodulation. Inverse OFFTs combined with pass-band filters can be used to provide up conversion of multi-carrier signals. Since OFFTs are substantially less complex than FFTs, OFFT processing is applicable to digital radio systems where there are considerable constraints on power consumption and chip size. The OFFT is particularly useful for processing multi-carrier transmission protocols in wireless communications, such as Carrier Interferometry, Orthogonal Frequency Division Multiplexing, and Multi-carrier Code Division Multiple Access, which are quickly gaining favor over single-carrier protocols. OFFT algorithms can process a greater number of carriers and provide lower complexity compared to FFTs.
Design of high-resolution Fourier transform lens
Lei Zhang; Xing Zhong; Guang Jin
2007-01-01
With the development of optical information processing, high-resolution Fourier transform lens has often been used in holographic data storage system, spatial filtering and observation of particles. This paper studies the optical design method of high-resolution Fourier transform optical lenses system, which could be used in particles observation and holographic data storage system. According to Fourier transform relation between object and
Fourier transform electrospray ion mobility spectrometry
Yong Hong Chen; William F. Siems; Herbert H. Hill
1996-01-01
The analytical merit of Fourier transform electrospray ionization ion mobility spectrometry (FT-ESI-IMS) was investigated. When compared with signal-averaged electrospray ionization ion mobility spectrometry (SA-ESI-IMS) an increase in both signal\\/noise ratio (SN) and ion mobility resolving power was observed for the FT mode of operation. Using angiotensin II, glucosamine, n-tetradecylamine and gramicidin s as test compounds, electrospray ion mobility spectra were
Pulse FourierTransform Optical Spectroscopy
Stephen B. Grossman; A. Schenzle; Richard G. Brewer
1977-01-01
The optical analog of pulse Fourier-transform NMR spectroscopy is demonstrated. Doppler-free infrared spectra are obtained for a set of closely spaced 13CH3F transitions at 9.66 mum from two-pulse echo and free-induction decay transients. The effects of elastic or inelastic collisions on the decay rate are obtained for each transition, and the long-range force laws are deduced from the dependence of
Fourier transform particle flow for nonlinear filters
NASA Astrophysics Data System (ADS)
Daum, Fred; Huang, Jim
2013-05-01
We derive five new algorithms to design particle flow for nonlinear filters using the Fourier transform of the PDE that determines the flow of particles corresponding to Bayes' rule. This exploits the fact that our PDE is linear with constant coefficients. We also use variance reduction and explicit stabilization to enhance robustness of the filter. Our new filter works for arbitrary smooth nowhere vanishing probability densities.
SAR vibrometry using fractional Fourier transform processing
NASA Astrophysics Data System (ADS)
Wang, Qi; Hayat, Majeed M.; Santhanam, Balu; Atwood, Tom
2009-05-01
A novel signal-processing approach is reported for vibrometry in synthetic aperture radar (SAR) imaging systems. The approach exploits the conventional deramp process; however, in place of Fourier-transform processing we utilize the fractional Fourier transform (FRFT) as a processing tool. The FRFT is geared toward non-stationary signals and chirped sinusoids particularly. A simplified mathematical expression is developed to describe the reflectivity of the aimed patch of ground containing vibrating targets as a function of space and time. Under the approximation that the velocities of vibrating point targets are constant during each probing chirped pulse, it is shown that the returned echo after the deramp process is a superposition of sinusoids that are chirped according to the Doppler effects induced by the vibrating point targets. By applying the multiangle centered discrete fractional Fourier transform (MA-CDFRFT) to the demodulated echoes, the instantaneous velocities of the vibrating point targets are estimated from the two coordinates of each peak in the MA-CDFRFT's frequency-angle plane. By repeating this process where a sequence of successive pulses are used to interrogate the vibrating targets, the velocities of the targets are estimated in each pulse, thereby generating a piecewise-linear estimate of the history of the vibration velocity in time. Theoretical performance evaluation of the proposed technique is carried out using real SAR-system parameters and simulated vibrating targets. The interplay amongst minimum detectable velocity, maximum detectable vibration frequency, pulse duration and chirp rate is determined analytically.
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.
Comparison Analysis of HHT and Fourier Transformation in Network Fault
Ming-ling Song; Li-xing Zhou; Jing-tao Hu; Xiao-long Li
2012-01-01
The paper presented the fundamental of HHT and Fourier transformation through elaborating the theory and simulation experiments on matlab. Giving specific signal, the two transformations were used in application of partial discharge, voltage dip, and harmonic wave. Visualized spectrogram were obtained to compare the two transformations from each other, therefore, HHT and Fourier transformation can be respectively used in different
Mario Serna; Dustin McCauley
At previous SPIE meetings, we reported on an optoelectronic device that measures the complete polarization state of incident infrared light in a single pixel and in a single frame for a narrow wavelength band ( ?? <0.05 µm). Using at least four quantum-well stacks and four linear gratings, each stacked alternating above the other, the device uses the interference among
The PROSAIC Laplace and Fourier Transform
Smith, G.A.
1994-11-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today`s emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting.
The prosaic Laplace and Fourier transform
Smith, G.A. [Brookhaven National Laboratory, Upton, New York (United States)
1995-05-05
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today`s emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
OPTI 512R-Linear Systems, Fourier Transforms Course Description
Arizona, University of
, Fresnel zone plates #12;Imaging Systems and Fourier Optics 18. Fresnel diffraction from Lenses and Fourier transforming properties of lenses 19. Diffraction limited imaging systems 20. Performance of optical imaging. Linear Systems, Fourier Transforms, and Optics. Wiley Interscience Goodman, Joseph W. Introduction
Fourier Transform Spectroscopy of Selected Transient Species
NASA Astrophysics Data System (ADS)
Li, Gang
The procedures and results of experimental and/or theoretical studies of four transient molecules, GeO, WO, BeH, and MgH are reported in the thesis. Two of them, GeO and WO, are diatomic molecules composed of relatively heavy atoms, and the other two are diatomic molecules with hydrogen as one of their component atoms. The GeO species was generated using a high temperature furnace. The rovibrational spectrum of five isotopomers were detected in emission using a Bruker IFS 120 HR Fourier transform spectrometer. Combined-isotopomer Dunham-type molecular constants have been derived for GeO using the DSParFit computer program. Analysis shows that the Born-Oppenheimer approximation is valid, as expected, for a molecule containing heavy atoms. The WO molecule was generated using a microwave discharge cell, and the spectra of electronic transitions of various systems were detected in emission using both the Bruker IFS 120 HR Fourier transform spectrometer at Waterloo and the McMath Pierce One-Meter Fourier transform spectrometer at the National Solar Observatory in Arizona. The ground electronic state has been confirmed to be X??- based on the analysis of seven 0-0 bands. BeH and MgH are typical molecules with hydrogen as one of their component atoms, and the effects of Born-Oppenheimer breakdown were expected. Both of these molecules have rotational perturbations in their excited electronic states. A 'new' method of data processing was used, i. e. , treating the electronic data as if they were from fluorescence series. Thus the harmful influence of the perturbed upper electronic states on the ground electronic state molecular constants is eliminated. By using the DSParFit computer program, accurate sets of combined-isotopomer Dunham-type molecular constants have been derived for the ground electronic states of the two molecules, and Born-Oppenheimer breakdown correction terms have been obtained.
Analysis method for Fourier transform spectroscopy
NASA Technical Reports Server (NTRS)
Park, J. H.
1983-01-01
A fast Fourier transform technique is given for the simulation of those distortion effects in the instrument line shape of the interferometric spectrum that are due to errors in the measured interferogram. The technique is applied to analyses of atmospheric absorption spectra and laboratory spectra. It is shown that the nonlinear least squares method can retrieve the correct information from the distorted spectrum. Analyses of HF absorption spectra obtained in a laboratory and solar CO absorption spectra gathered by a balloon-borne interferometer indicate that the retrieved amount of absorbing gas is less than the correct value in most cases, if the interferogram distortion effects are not included in the analysis.
Fourier transform zero field NMR and NQR
Zax, D.B.
1984-09-01
The characterization of the structural and chemical properties of matter, particularly in disordered condensed phases, is a difficult process. Few analytical methods work effectively on polycrystalline or amorphous solids. In many systems the chemical shifts measured by traditional high resolution solid state NMR methods are insufficiently sensitive or the information contained in the dipole-dipole couplings is more important. In these cases Fourier transform zero field magnetic resonance may make an important contribution. Zero field NMR and NQR is the subjecti of this thesis.
Mario A. Serna; Dustin W. McCauley
2004-01-01
At previous SPIE meetings, we reported on an optoelectronic device that measures the complete polarization state of incident infrared light in a single pixel and in a single frame for a narrow wavelength band (deltalambda<0.05 mum). Using at least four quantum-well stacks and four linear gratings, each stacked alternating above the other, the device uses the interference among light paths
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.
Color Object Recognition Based On Clifford Fourier Transform
Paris-Sud XI, Université de
(Scale-Invariant Feature Transform) descriptors are a popular choice giving very good results [11Color Object Recognition Based On Clifford Fourier Transform Jose Mennesson, Christophe Saint recognition, both using the recently defined color Clifford Fourier transform. The first one deals with so
On the q-Bessel Fourier transform Lazhar Dhaouadi
Paris-Sud XI, Université 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 use the crucial properties namely the positivity of the q-Bessel translation operator to prove some
Discrete fractional Fourier transform based on orthogonal projections
Soo-Chang Pei; Min-Hung Yeh; Chien-Cheng Tseng
1999-01-01
The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time-frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been developed by Santhanam and McClellan (see ibid., vol.42, p.994-98, 1996) but its results do not match those of the corresponding continuous fractional Fourier transforms. We propose a
Fourier transform spectrometer controller for partitioned architectures
NASA Astrophysics Data System (ADS)
Tamas-Selicean, D.; Keymeulen, D.; Berisford, D.; Carlson, R.; Hand, K.; Pop, P.; Wadsworth, W.; Levy, R.
The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Researchers at ESA and NASA advocated for the use of partitioned architecture to reduce this complexity. Partitioned architectures rely on platform mechanisms to provide robust temporal and spatial separation between applications. Such architectures have been successfully implemented in several industries, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture.
Theory of amplified dispersive Fourier transformation
Goda, Keisuke; Solli, Daniel R.; Jalali, Bahram [Department of Electrical Engineering, University of California, Los Angeles, California 90095 (United States); Tsia, Kevin K. [Deparment of Electrical and Electronic Engineering, University of Hong Kong, Pokfulam Road (Hong Kong)
2009-10-15
Amplified dispersive Fourier transformation (ADFT) is a powerful technique that maps the spectrum of an optical pulse into a time-domain waveform using group-velocity dispersion (GVD) and simultaneously amplifies it in the optical domain. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector, greatly simplifying the system and, more importantly, enabling ultrafast real-time spectroscopic measurements. Here we present a theory of ADFT by deriving the general equation and spectral resolution for ADFT and studying the evolution of the pulse spectrum into time, the effect of GVD coefficients on ADFT, and the requirement for dispersion. This theory is expected to lend valuable insights into the process and implementation of ADFT.
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.
Metaphase Selection By Analysis Of The Fourier Transformed Image
NASA Astrophysics Data System (ADS)
Hutzler, P.; Stettmaier, K.; Brettel, H.
1982-11-01
Automatic metaphase finding may be done by analysing the images of the chromosomes in the image plane or by investigation of their Fourier spectrum. We found that both digital Fourier transformation and optical Fourier processing of these objects give results which are in good agreement.
Spectral Analysis of Orbits via Discrete Fourier Transforms
Aluffi, Paolo
Spectral Analysis of Orbits via Discrete Fourier Transforms C. Hunter (hunter. Keywords: Hamiltonian Dynamics, Orbits, Fourier Analysis 1. Introduction This work develops e of galaxies, and this work is relevant to them at least. The methods to be described use Fourier analysis
Identification of stratigraphic formation interfaces using wavelet and Fourier transforms
Shih-Yu Pan; Bieng-Zih Hsieh; Ming-Tar Lu; Zsay-Shing Lina
2008-01-01
The purpose of this study was to identify the formation interfaces from geophysical well log data using the wavelet transform, and a combination of the wavelet transform and the Fourier transform methods. In the wavelet transform method, the identification of formation interfaces is based on the wavelet coefficients from the wavelet transform of spontaneous potential (SP) log and gamma ray
New 2D discrete Fourier transforms in image processing
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, the concept of the two-dimensional discrete Fourier transformation (2-D DFT) is defined in the general case, when the form of relation between the spatial-points (x, y) and frequency-points (?1, ?2) is defined in the exponential kernel of the transformation by a nonlinear form L(x, y; ?1, ?2). The traditional concept of the 2-D DFT uses the Diaphanous form x?1 +y?2 and this 2-D DFT is the particular case of the Fourier transform described by the form L(x, y; ?1, ?2). Properties of the general 2-D discrete Fourier transform are described and examples are given. The special case of the N × N-point 2-D Fourier transforms, when N = 2r, r > 1, is analyzed and effective representation of these transforms is proposed. The proposed concept of nonlinear forms can be also applied for other transformations such as Hartley, Hadamard, and cosine transformations.
Numerical Projection Method For Inverse Fourier Transform And Its Application
Andrey S. Krylov; Anton V. Liakishev
2000-01-01
Numerical projection method of the Fourier transform inversion from data given on a finite interval is proposed. It is based on an expansion of the solution into a series of eigenfunctions of the Fourier transform. The number of terms of the expansion depends on the length of the data interval. Convergence of the solution of the method is proved. The
The application of finite fourier transforms to analog computer simulations
Eric Liban
1962-01-01
An Analog Computer technique for the solution of certain classes of boundary-value problems of partial differential equation based on Finite Fourier Transforms is presented, which requires considerably less computer components than conventional finite difference methods. The derivation of the Finite Fourier Transform method is briefly stated and then applied to analog computer simulations of heat transfer equations with linear and
Computer-generated hologram of asymmetry fractional Fourier transform
Zhaoxuan Sheng; Hongxia Wang; Junfa He; Youjie Zhou; Jun Wang; Cairong Mao
2005-01-01
A new optical encryption technique based on computer-generated hologram (CGH) and fractional Fourier transform (FRT) is presented. And the algorithm of making asymmetry FRT CGH is provided in this paper. In this method, the fractional Fourier transform of the input image is performed by two one-dimensional FRT with different orders in the x and y directions in cascade. With Lohmann
Euler-Bessel and Euler-Fourier Transforms Robert Ghrist
Ghrist, Robert W.
Euler-Bessel and Euler-Fourier Transforms Robert Ghrist Departments of Mathematics and Electrical;Euler Transforms 2 Abstract. We consider a topological integral transform of Bessel (concentric Rn . Core contributions include: the definition of the topological Bessel transform; a relationship
Imaging Fourier transform spectrometry of chemical plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.; Gross, Kevin C.; Perram, Glen P.
2009-05-01
A midwave infrared (MWIR) imaging Fourier transform spectrometer (FTS), the Telops FIRST-MWE (Field-portable Imaging Radiometric Spectrometer Technology - Midwave Extended) has been utilized for the standoff detection and characterization of chemical plumes. Successful collection and analysis of MWIR hyperspectral imagery of jet engine exhaust has allowed us to produce spatial profiles of both temperature and chemical constituent concentrations of exhaust plumes. Successful characterization of this high temperature combustion event has led to the collection and analysis of hyperspectral imagery of lower temperature emissions from industrial smokestacks. This paper presents MWIR data from remote collection of hyperspectral imagery of methyl salicilate (MeS), a chemical warfare agent simulant, during the Chemical Biological Distributed Early Warning System (CBDEWS) test at Dugway Proving Grounds, UT in 2008. The data did not contain spectral lines associated with emission of MeS. However, a few broad spectral features were present in the background-subtracted plume spectra. Further analysis will be required to assign these features, and determine the utility of MWIR hyperspectral imagery for analysis of chemical warfare agent plumes.
Fourier transform infrared spectroscopy in cancer detection.
Sahu, R K; Mordechai, S
2005-10-01
The rapid developments in the field of infrared spectroscopy in the past decade have demonstrated a potential for disease diagnosis using noninvasive technologies. Several earlier studies have highlighted the advantage of using infrared spectroscopy both in the near- and mid-infrared regions for diagnostic purposes at clinical levels. The areas of focus have been the distinction of premalignant and malignant cells and tissues from their normal state using specific parameters obtained from Fourier transform infrared spectra, making it a rapid and reagent-free method. While it still requires pilot studies and designed clinical trials to ensure the applicability of such systems for cancer diagnosis, substantial progress has been made in incorporating advances in computational methods into the system to increase the sensitivity of the entire setup, making it an objective and sensitive technique suitable for automation to suit the demands of the medical community. The development of fiber-optics systems for infrared spectroscopy have further opened up new and modern avenues in medical diagnosis at various levels of cells, tissues and organs under laboratory and clinical conditions. PMID:16556041
Stepwise Iterative Fourier Transform: The SIFT
NASA Technical Reports Server (NTRS)
Benignus, V. A.; Benignus, G.
1975-01-01
A program, designed specifically to study the respective effects of some common data problems on results obtained through stepwise iterative Fourier transformation of synthetic data with known waveform composition, was outlined. Included in this group were the problems of gaps in the data, different time-series lengths, periodic but nonsinusoidal waveforms, and noisy (low signal-to-noise) data. Results on sinusoidal data were also compared with results obtained on narrow band noise with similar characteristics. The findings showed that the analytic procedure under study can reliably reduce data in the nature of (1) sinusoids in noise, (2) asymmetric but periodic waves in noise, and (3) sinusoids in noise with substantial gaps in the data. The program was also able to analyze narrow-band noise well, but with increased interpretational problems. The procedure was shown to be a powerful technique for analysis of periodicities, in comparison with classical spectrum analysis techniques. However, informed use of the stepwise procedure nevertheless requires some background of knowledge concerning characteristics of the biological processes under study.
A discrete Fourier transform for virtual memory machines
NASA Technical Reports Server (NTRS)
Galant, David C.
1992-01-01
An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.
Principle and application of multiple fractional Fourier transform holography
NASA Astrophysics Data System (ADS)
Zeng, Yangsu; Guo, Yongkang; Gao, Fuhua; Zhu, Jianhua
2003-01-01
In this paper, the principle of multiple fractional Fourier transform hologram (FRTH) is presented, and its characteristics based on the particularity in recording and reconstruction are analyzed. With this method, a multiple FRTH of several objects with different fractional transform orders is fabricated on one holographic plate. It requires a matched multiple fractional Fourier transform system to reconstruct the recorded images correctly. The potential application of multiple FRTH in optical security or anti-counterfeiting system is also discussed.
NASA Astrophysics Data System (ADS)
Thorwirth, S.; McCarthy, M. C.; Dudek, J. B.; Thaddeus, P.
2005-05-01
The rotational spectra of the three carbon chain molecules vinyldiacetylene (hex-1-ene-3,5-diyne, C6H4), vinyltriacetylene (oct-1-ene-3,5,7-triyne, C8H4), and its cyano analog vinylcyanodiacetylene (1-cyanohex-5-ene-1,3-diyne, C7H3N) have been observed for the first time by Fourier transform microwave spectroscopy of a supersonic molecular beam. The molecules were observed as products of an electrical discharge through selected precursor mixtures: ethylene/diacetylene and vinylacetylene/diacetylene for the pure hydrocarbon molecules and vinylacetylene/cyanoacetylene for vinylcyanodiacetylene. The measurements yield precise sets of rotational constants that compare very well with theoretical constants obtained by quantum chemical calculations at the B3LYP/cc-pVTZ level of theory. Since these three carbon chains are similar in structure and composition to known astronomical molecules and because of their significant polarity, all three are candidates for radio astronomical detection.
Estimates of Lebesgue constants via Fourier transforms. Many dimensions
Elijah Liflyand
1995-01-01
This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function generating such a method. Only few proofs are given in order to illustrate a general idea of techniques applied. Among the
Matrix probing, skeleton decompositions, and sparse Fourier transform
Chiu, Jiawei
2013-01-01
In this thesis, we present three different randomized algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with ...
Surface Fourier-transform lens using a metasurface
NASA Astrophysics Data System (ADS)
Li, Yun Bo; Cai, Ben Geng; Cheng, Qiang; Cui, Tie Jun
2015-01-01
We propose a surface (or 2D) Fourier-transform lens using a gradient refractive index (GRIN) metasurface in the microwave band, which is composed of sub-wavelength quasi-periodical metallic patches on a grounded dielectric substrate. Such a metasurface supports the transverse magnetic (TM) modes of surface waves. To gradually change the size of textures, we obtain different surface refractive indices, which can be tailored to fit the required refractive-index profile of a surface Fourier-transform lens. According to the theory of spatial Fourier transformation, we make use of the proposed lens to realize surface plane-wave scanning under different feeding locations. The simulation and experimental results jointly confirm the validity of the surface Fourier-transform lens. The proposed method can also be extended to the terahertz frequency.
Fourier Transform Infrared Spectroscopy for Process Monitoring and Control
Solomon, P. R.; Carangelo, M. D.; Carangelo, R. M.
1994-01-01
FOURIER TRANSFORM INFRARED SPECl'ROSCOPY FOR PROCESS MONITORING AND CONTROL Peter R. Solomon Martin D. Carangelo Robert M. Carangelo President Software Engineer Vice-President On-Line Technologies, Inc. On-Line Technologies, Inc. On... years, significant progress has been made in the applications and hardware for Fourier Transform Infrared (Ff?IR) spectroscopy. The applications of Fr-IR include: i) concentrations of multiple species and phases (gases, liquid, particles, surfaces...
Quasi-Fourier transform hologram format for data storage
NASA Astrophysics Data System (ADS)
Ramenah, H.; Bertrand, P.; Soubari, E. H.; Meyrueis, P.
1996-11-01
For a recording medium such as dichromated gelatin, a quasi-Fourier transform holographic memory is preferred over the exact Fourier transform. We proceed here with angular multiplexing and consider undesired reconstructed waves such as cross-talk noise, and show that the signal-to-noise ratio is 33 dB for 20 angular multiplexed elements in 25 ?m thickness of the recording medium. We also study the energy coupling between gratings to standardize the diffraction efficiency of each multiplexed grating.
The APEX digital Fast Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Klein, B.; Philipp, S. D.; Krämer, I.; Kasemann, C.; Güsten, R.; Menten, K. M.
2006-08-01
Context: . We present the technology and first scientific results of a new generation of very flexible and sensitive spectrometers, well-suited for the needs of spectral-line radio and (sub)millimeter astronomy: Fast Fourier Transform Spectrometers (FFTS), which are in operation at the Atacama Pathfinder EXperiment (APEX) telescope. Aims: . The FFTS for APEX is a novel high-resolution 2× 1 GHz bandwidth digital spectrometer backend. Due to its high frequency resolution, and the demonstrated capability of operating at high altitude, the FFTS became the facility spectrometer for spectral line observations at APEX. Methods: . The FFTS is based on one of the currently most powerful digitizer/analyzer boards available from Acqiris, Switzerland. The board incorporates two 1 Gsamples/s analog-to-digital converters (ADCs) with 8-bit resolution which feed an on-board complex field programmable gate array (FPGA) chip. The enormous processing power by today's FPGAs allow for a complete real-time FFT signal processing pipeline to decompose a 1 GHz band into 16 384 spectral channels in just one chip. Results: . Since May 2005 an MPIfR FFTS has been extensively used in all regular spectroscopic science observations. The performance at APEX was demonstrated to be very reliable and as good as measured in the first laboratory tests which finally led to the request to provide a second, facility type FFTS for APEX. The unit was delivered and commissioned in March this year. Conclusions: . Using a commercially available digitizer board, it was possible to develop a complete FFTS in only a few months. Successful observations at APEX demonstrate that this new generation of FPGA-based spectrometers easily matching and superseding the performance of older technology spectrometers and can built up much more easily. Furthermore, the by now available class of new high-speed ADCs and the continuous increase of FPGA processing power makes it very likely that FFTS can be pushed to broader bandwidth and even more spectral channels in the near future.
Roland G. Wilson; Andrew D. Calway; Edward R. S. Pearson
1992-01-01
A wavelet transform specifically designed for Fourier analysis at multiple scales is described and shown to be capable of providing a local representation which is particularly well suited to segmentation problems. It is shown that, by an appropriate choice of analysis window and sampling intervals, it is possible to obtain a Fourier representation which can be computed efficiently and overcomes
A comparative image analysis of discrete radial Fourier transforms
Guojun Zhang; Bo Li; Bo Fu; Li Li; Gaoxiang Liu
2010-01-01
Fourier transform is not often applied to pattern and object recognition, because of its inefficiency in image description and calculation. In order to solve this problem, a bi-discrete radial cosine transform is proposed. This new transform has two superior properties. Firstly, by using Mukundan’s square-to-circular transformation, it projects images in square to images in discrete circle girds. Secondly, different from
Computer-generated hologram of asymmetry fractional Fourier transform
NASA Astrophysics Data System (ADS)
Sheng, Zhaoxuan; Wang, Hongxia; He, Junfa; Zhou, Youjie; Wang, Jun; Mao, Cairong
2005-02-01
A new optical encryption technique based on computer-generated hologram (CGH) and fractional Fourier transform (FRT) is presented. And the algorithm of making asymmetry FRT CGH is provided in this paper. In this method, the fractional Fourier transform of the input image is performed by two one-dimensional FRT with different orders in the x and y directions in cascade. With Lohmann III detour phase encoding method and computer plotting program, the transformed image is encoded and fabricated into CGH on the computer. Then a piece of asymmetry fractional Fourier transform CGH (AFRTCGH) of original input image is obtained. In order to reconstruct the encoded image, a special fractional Fourier transform systems with two special cylinder lens" are needed. Namely, only when the transform order in each direction is respectively matched with that of the asymmetry fractional Fourier transform CGH, can the encoded image be reconstructed exactly. Because of its particularity of image reconstruction, it is regarded as a new optical security system and can be used in anti-counterfeiting. When it is used to encrypt image or to anti-Counterfeit, anti-counterfeiting intensity can be improved greatly. So it has very high applying value.
Dynamic measurement of deformation using Fourier transform digital holographic interferometry
NASA Astrophysics Data System (ADS)
Gao, Xinya; Wu, Sijin; Yang, Lianxiang
2013-10-01
Digital holographic interferometry (DHI) is a well-established optical technique for measurement of nano-scale deformations. It has become more and more important due to the rapid development of applications in aerospace engineering and biomedicine. Traditionally, phase shift technique is used to quantitatively measure the deformations in DHI. However, it cannot be applied in dynamic measurement. Fourier transform phase extraction method, which can determine the phase distribution from only a single hologram, becomes a promising method to extract transient phases in DHI. This paper introduces a digital holographic interferometric system based on 2D Fourier transform phase extraction method, with which deformations of objects can be measured quickly. In the optical setup, the object beam strikes a CCD via a lens and aperture, and the reference beam is projected on the CCD through a single-mode fiber. A small inclination angle between the diverging reference beam and optical axial is introduced in order to physically separate the Fourier components in frequency domain. Phase maps are then obtained by the utilization of Fourier transform and windowed inverse Fourier transform. The capability of the Fourier transform DHI is discussed by theoretical discussion as well as experiments.
Aperture scattering models based on mode matching and Fourier transform
Hyo J. Eom
2004-01-01
In this paper, three theoretical aperture scattering models for rectangular, circular, and circumferential apertures are presented. The techniques of Fourier transform, integral transform, and mode matching are used to form sets of simultaneous equations for the discrete modal coefficients. The presented scattering models are amenable to computation and are useful for various antenna and EMI\\/EMC applications.
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.
On q-extended eigenvectors of the integral and finite Fourier transforms
NASA Astrophysics Data System (ADS)
Atakishiyev, N. M.; Rueda, J. P.; Wolf, K. B.
2007-10-01
Mehta has shown that eigenvectors of the N × N finite Fourier transform can be written in terms of the standard Hermite eigenfunctions of the quantum harmonic oscillator (1987 J. Math. Phys. 28 781). Here, we construct a one-parameter family of q-extensions of these eigenvectors, based on the continuous q-Hermite polynomials of Rogers. In the limit when q ? 1 these q-extensions coincide with Mehta's eigenvectors, and in the continuum limit as N ? ? they give rise to q-extensions of eigenfunctions of the Fourier integral transform.
J. Twamley; G. J. Milburn
2007-02-12
We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.
Fixed-point error analysis of Winograd Fourier transform algorithms
NASA Technical Reports Server (NTRS)
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Parallel fast Fourier transforms for non power of two data
Semeraro, B.D.
1994-09-01
This report deals with parallel algorithms for computing discrete Fourier transforms of real sequences of length N not equal to a power of two. The method described is an extension of existing power of two transforms to sequences with N a product of small primes. In particular, this implementation requires N = 2{sup p}3{sup q}5{sup r}. The communication required is the same as for a transform of length N = 2{sup p}. The algorithm presented is intended for use in the solution of partial differential equations, or in any situation in which a large number of forward and backward transforms must be performed and in which the Fourier Coefficients need not be ordered. This implementation is a one dimensional FFT but the techniques are applicable to multidimensional transforms as well. The algorithm has been implemented on a 128 node Intel Ipsc/860.
The Fourier transform for certain hyperKähler fourfolds
Shen, Mingmin; Vial, Charles
2014-01-01
THE FOURIER TRANSFORM FOR CERTAIN HYPERKA¨HLER FOURFOLDS MINGMIN SHEN AND CHARLES VIAL Abstract. Using a codimension-1 algebraic cycle obtained from the Poincare´ line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian... . The second author is supported by EPSRC Early Career Fellowship number EP/K005545/1. 1 2 MINGMIN SHEN AND CHARLES VIAL Introduction A. Abelian varieties. Let A be an abelian variety of dimension d over a field k. Let Aˆ = Pic0(A) be its dual and let L...
Modulated Fourier Transform Raman Fiber-Optic Spectroscopy
NASA Technical Reports Server (NTRS)
Jensen, Brian J. (Inventor); Cooper, John B. (Inventor); Wise, Kent L. (Inventor)
2000-01-01
A modification to a commercial Fourier Transform (FT) Raman spectrometer is presented for the elimination of thermal backgrounds in the FT Raman spectra. The modification involves the use of a mechanical optical chopper to modulate the continuous wave laser, remote collection of the signal via fiber optics, and connection of a dual-phase digital-signal-processor (DSP) lock-in amplifier between the detector and the spectrometer's collection electronics to demodulate and filter the optical signals. The resulting Modulated Fourier Transform Raman Fiber-Optic Spectrometer is capable of completely eliminating thermal backgrounds at temperatures exceeding 300 C.
Resonance lineshapes in two-dimensional Fourier transform spectroscopy.
Siemens, Mark E; Moody, Galan; Li, Hebin; Bristow, Alan D; Cundiff, Steven T
2010-08-16
We derive an analytical form for resonance lineshapes in two-dimensional (2D) Fourier transform spectroscopy. Our starting point is the solution of the optical Bloch equations for a two-level system in the 2D time domain. Application of the projection-slice theorem of 2D Fourier transforms reveals the form of diagonal and cross-diagonal slices in the 2D frequency data for arbitrary inhomogeneity. The results are applied in quantitative measurements of homogeneous and inhomogeneous broadening of multiple resonances in experimental data. PMID:20721156
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.
D. L. Mathine; S. Krishnan Myjak; G.N. Maracas
1995-01-01
A new technique for solving the BenDaniel-Duke Hamiltonian using a Fourier series method is discussed. This method Fourier transforms the effective mass and potential profiles to calculate the eigenenergies and probability densities in transform space. Numerical solutions of the eigenenergies of a rectangular quantum well are compared to the finite difference, finite element, and transfer matrix methods. The eigenenergies of
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.
Fourier transform spectroscopy of six stars
NASA Astrophysics Data System (ADS)
Mendoza V., E. E.
1981-12-01
This paper outlines results from a digital analysis of the lourier transform spectroscopy of six stars: ? Aur, ? Ori, ? Lyr, ? Aql, ? Aql and ? Cyg. Nearly 1200 different spectral lines have been identified in the spectra of these six stars in the wavelength interval 4800-10200 A where the spectra are of very high quality, less than the one per cent level of noise versus signal. ? Lyr and ? Cyg show spectral line and profile variations easily seen in their spectra.
Data analysis of continuous gravitational wave: Fourier transform-II
D. C. Srivastava; S. K. Sahay
2002-07-30
In this paper we obtain the Fourier Transform of a continuous gravitational wave. We have analysed the data set for (i) one year observation time and (ii) arbitrary observation time, for arbitrary location of detector and source taking into account the effects arising due to rotational as well as orbital motion of the earth. As an application of the transform we considered spin down and N-component signal analysis.
Data analysis of continuous gravitational wave: Fourier transform-I
D. C. Srivastava; S. K. Sahay
2002-09-03
We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for one day observation time and our analysis is applicable for arbitrary location of detector and source. We have taken into account the effects arising due to rotational as well as orbital motions of the earth.
A fixed-point fast Fourier transform error analysis
PETER D. WELCH
1969-01-01
This paper contains an analysis of the fixed-point accuracy of the power of two, fast Fourier transform algorithm. This analysis leads to approximate upper and lower bounds on the root-mean-square error. Also included are the results of some accuracy experiments on a simulated fixed-point machine and their comparison with the error upper bound.
Communication Interlaced Fourier transformation of ultrafast 2D NMR data
Frydman, Lucio
; Interlaced Fourier transformation; Signal-to-noise ratio; Sensitivity enhancement; Spectral resolution Two-dimensional is capable of dealing in a single, combined fashion, with the two mirror-imaged interferograms aris- ing the NMR pulse sequence, monitoring its effects requires the collection of several independent scans
Signal reconstruction from short-time Fourier transform magnitude
S. Nawab; THOMAS F. QUATIERI; JAE S. LIM
1983-01-01
In this paper, a signal is shown to be uniquely represented by the magnitude of its short-time Fourier transform (STFT) under mild restrictions on the signal and the analysis window of the STFT. Furthermore, various algorithms are developed which reconstruct signal from appropriate samples of the STFT magnitude. Several of the algorithms can also be used to obtain signal estimates
Fourier Transform Light Scattering of Biological Structure and Dynamics
Huafeng Ding; Ethan Berl; Zhuo Wang; Larry J. Millet; Martha U. Gillette; Jianming Liu; Marni Boppart; Gabriel Popescu
2010-01-01
We review the principle and application of Fourier transform light scattering (FTLS), a new technique developed in our laboratory to study static and dynamic light scattering (DLS) from the biological tissues and live cells. The results demonstrate that FTLS has significant benefits over existing light scattering techniques in terms of sensitivity and resolution. We anticipate that FTLS will set the
Wavelength-compensated Fourier and Fresnel transformers: a unified approach
J. Lancis; G. Minguez-Vega; E. Tajahuerce; M. Fernandez-Alonso; V. Climent; P. Andres
2002-01-01
We recognize that one can adapt any dispersion-compensated broadband optical Fourier transformer to achieve wavelength compensation in the Fresnel diffraction region just by inserting a diffractive lens at the input plane and vice versa. This unification procedure is employed in a second stage in the design of a novel hybrid (diffractive-refractive) optical setup that provides, in a sequential way, nearly
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...
Information reduction using lensless Fourier transform digital composite holography
Dalip Singh Mehta; Chandra Shakher
2008-01-01
An optical hologram contains substantially more information than necessary for some specific applications. Practical methodology of handling huge information contents in these holograms for such applications is cumbersome. In this paper, a method of information reduction, which aims at efficient storage and transmission of holograms, is investigated using digital composite holography in lensless Fourier transform configuration. The maximum information reduction
A lensless Fourier transform recording method for atom holography
Hongyi Gao; Jianwen Chen; Honglan Xie; Zhizhan Xu
2002-01-01
A novel lensless Fourier transform method for atomic beam holography is proposed. The basic set-up and the effect of coherence on the hologram resolution are discussed. Finally, the possibility of reconstructing the atomic hologram by visible light is analysed.
Lens less zooming fourier-transform digital holography
Ángel F. Doval; Cristina Trillo; Oscar Lopez; Daniel Cernadas; Carlos Lopez; Benito V. Dorrio; Jose L. Fernandez; Mariano Perez-Amor
2003-01-01
Lensless Fourier-Transform Digital Holography through an aperture has been demonstrated some years ago. This technique allows to record and reconstruct images of large objects placed at short distances from the camera. In this paper we show that the distance between the aperture plane and the camera can be used to control the field of view and, therefore, moving the camera
Multiple reference Fourier transform holography with soft x rays
W. F. Schlotter; R. Rick; K. Chen; A. Scherz; J. Stoehr; J. Luening; S. Eisebitt; Ch. Guenther; W. Eberhardt; O. Hellwig; I. McNulty
2006-01-01
The authors demonstrate multiple reference source Fourier transform holography with soft x rays. This technique extends the detection limit of high resolution lensless imaging by introducing spatial multiplexing to coherent x-ray scattering. In this way, image quality is improved without increasing the radiation exposure to the sample. This technique is especially relevant for recording static images of radiation sensitive samples
Rainbow Fourier transform Mikhail D. Alexandrov a,b,n
Rainbow Fourier transform Mikhail D. Alexandrov a,b,n , Brian Cairns b , Michael I. Mishchenko b Rainbow Optical particle characterization Remote sensing a b s t r a c t We present a novel technique between 1351 and 1651 exhibit a sharply defined rainbow structure, the shape of which is determined mostly
Rainbow Fourier transform Mikhail D. Alexandrov a,b,n
71 73 75 77 79 81 Rainbow Fourier transform Mikhail D. Alexandrov a,b,n , Brian Cairns b , Michael I, USAQ3 a r t i c l e i n f o Keywords: ElectromagneticQ4 scattering Polarization Mie theory Rainbow angle range between 1351 and 1651 exhibit a sharply defined rainbow structure, the shape of which
Reflection optical two-dimensional Fourier-transform spectroscopy.
Li, Hebin; Moody, Galan; Cundiff, Steven T
2013-01-28
We have developed a technique to perform optical two-dimensional Fourier-transform (2DFT) spectroscopy in a reflection geometry. Various reflection 2DFT spectra are obtained for an atomic vapor. The technique is useful for the cases where optical 2DFT spectroscopy cannot be performed in the transmission geometry. PMID:23389154
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
Compression imaging based on Fourier transform optical system
NASA Astrophysics Data System (ADS)
Lv, Jinfeng; Zhao, Huaici; Zhao, Chunyang
2014-11-01
Shannon / Nyquist sampling theorem indicates that during the sampling process the minimum sample rate must be more than the double of the band of the signal so that we can achieve images without distortion. High-frequency sampling leads to mass data and results in high cost of storage and transmission procedure. Compressed sensing indicates that we can sample data at far below the Nyquist frequency when the signals are sparse or can be represented as sparse on some orthogonal basis, and the signals can be recovered without distortion after some certain recovery algorithms. By this means the cost of storage and transmission can be reduced significantly. Unlike conventional optical imaging process, this paper presents a new imaging method using a Fourier transform lens system, which enables single-exposure and single-aperture compressed imaging. First, the Fourier transformation of image signals is accomplished after they pass through a Fourier transform optical system. Second, sparse sample data can be obtained after the spectrum signals pass the sensor array. The process mentioned above can be interpreted as that using a Fourier matrix and a sparse matrix to complete the measurement of the image signals. Third, we make use of fast iterative threshold recovery algorithm to compute the sampling values and obtain the target image signals. Compared with the conventional imaging methods, in the case of ensuring the image quality, our method can significantly reduce the number of samples, thus greatly reduce the data redundancy. Simulation results indicate that the imaging method proposed can be prospective.
A VLSI architecture for simplified arithmetic Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.
1992-01-01
The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.
Achieving Efficient Polynomial Multiplication in Fermat Fields Using the Fast Fourier Transform
Achieving Efficient Polynomial Multiplication in Fermat Fields Using the Fast Fourier Transform domain. The Fast Fourier Transform (FFT) based frequency domain multiplication technique, originally proposed for in- teger multiplication, provides an extremely efficient method for multiplication
Multiple reference Fourier Transform holography using coherent high-harmonic soft-x-rays
D. A. Raymondson; R. L. Sandberg; C. La-o-vorakiat; A. Paul; M. M. Murnane; H. C. Kapteyn; W. F. Schlotter
2008-01-01
We demonstrate multiple reference Fourier transform holography with coherent soft X-rays from a tabletop high harmonic source for the first time. Simple reconstruction using a two dimensional Fourier transform shows a 90 nm resolution.
Novel fringe scanning/Fourier transform method of synthetic imaging
Crawford, T.M.; Albano, R.K.
1993-08-01
We have developed a one-dimensional theory and a computer model for synthetically imaging scenes using a novel fringe scanning/Fourier transform technique. Our method probes a scene using two interfering beams of slightly different frequency. These beams form a moving fringe pattern which scans the scene and resonates with any spatial frequency components having the same spatial frequency as the scanning fringe pattern. A simple, non-imaging detector above the scene observes any scattered radiation from the scene falling onto it. If a resonance occurs between the scanning fringe pattern and the scene, then the scattered radiation will be modulated at the difference frequency between the two probing beams. By changing the spatial period of the fringe pattern and then measuring the amplitude and phase of the modulated radiation that is scattered from the scene, the Fourier amplitudes and phases of the different spatial frequency components making up the scene can be measured. A synthetic image of the scene being probed can be generated from this Fourier amplitude and phase data by taking the inverse Fourier transform of this information. This technique could be used to image objects using light, ultrasonic, or other electromagnetic or acoustic waves.
Near-infrared Fourier transform imaging spectrometer for remote sensing
NASA Astrophysics Data System (ADS)
Li, Jianxin; Meng, Xin; Xu, Donglei; Song, Huaqing; Wang, Liu; Zhu, Rihong
2014-11-01
Fourier transform spectrometer without input slit is an emerging technology for spectral imaging. It has the advantages of high spatial resolution and high radiation throughput compared to the similar device with input slit. A near-infrared (NIR) Fourier transform spectrometer using Sagnac interferometer is presented and discussed in this paper. This system is composed of a Sagnac interferometer used as a lateral shearing splitter, an objective and a NIR camera. The principle of the system is presented including the discuss of its main characteristics and the optical layout of the Sagnac interferometer. Then the main technical features are discussed, such as the sample of the optical path difference (OPD). A experimental device is set up and presented that is used for two proven experiments. Some spectral images are reconstructed from 1050nm to 1720nm and proves the feasibility of the proposed system for NIR spectral imaging.
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
Fractional Fourier transforms of electromagnetic rectangular Gaussian Schell model beams
NASA Astrophysics Data System (ADS)
Liu, Xiayin; Zhao, Daomu
2015-06-01
We extend the scalar rectangular Gaussian Schell model (RGSM) beams to the electromagnetic domain and obtain the analytical expression for the propagation of the electromagnetic RGSM (EM RGSM) beams through an ABCD optical system. As a practical application, we illustrate how the spectral density, the spectral degree of polarization and the spectral degree of coherence of the EM RGSM beams through the fractional Fourier transform (FRFT) optical system depend on the FRFT order p and the value of beam profile M. It is found that the periods of the on-axis spectral density, the on-axis degree of polarization and the transverse degree of coherence for the FRFT order are all 2. In addition, it is of interest that the profiles of the transverse spectral intensity and the degree of polarization in the standard Fourier transform plane (i.e., p=1) are shown to form flat rectangular region which is wider for larger values of M.
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.
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.
Target Image Enhancement in Radar Imaging Using Fractional Fourier Transform
NASA Astrophysics Data System (ADS)
El-Mashed, M. G.; Dessouky, M. I.; El-Kordy, M.; Zahran, O.; Abd El-Samie, F. E.
2012-03-01
This paper presents a new Range-Doppler Algorithm based on Fractional Fourier Transform (RDA-FrFT) to obtain High-Resolution (HR) images for targets in radar imaging. The performance of the proposed RDA-FrFT is compared with the classical RDA algorithm, which is based on the Fast Fourier Transform (FFT). A closed-form expression for the range and azimuth compression of the proposed RDA-FrFT is mathematically derived and analyzed from the HR Synthetic Aperture Radar (SAR) imaging point of view. The proposed RDA-FrFT takes its advantage of the property of the FrFT to resolve chirp signals with high precision. Results show that the proposed RDA-FrFT gives low Peak Side-Lobe (PSL) and Integrated Side-Lobe (ISL) levels in range and azimuth directions for detected targets. HR images are obtained using the proposed RDA-FrFT algorithm.
Project Summary MRI: Development of a Chirped-Pulse, Fourier-Transform mm-Wave Pulsed
Baskaran, Mark
Project Summary MRI: Development of a Chirped-Pulse, Fourier-Transform mm-Wave Pulsed Uniform technologies: chirped-pulse Fourier-transform mm-wave spectroscopy and pulsed uniform supersonic flows: The instrument will leverage the ultra-broadband Chirped-pulse Fourier-transform Microwave (CP
Heterodyne-assisted pulsed spectroscopy with a nearly Fourier-transform limited,
Kono, Mitsu
Heterodyne-assisted pulsed spectroscopy with a nearly Fourier-transform limited, injection. The measured TPE linewidth approaches the ultimate limit imposed by the Fourier transform of the pulse light sources can be no better than the Fourier-transform (FT) limit associated with the FWHM of pulse
Apparatus and methods for continuous beam fourier transform mass spectrometry
McLuckey, Scott A. (Oak Ridge, TN); Goeringer, Douglas E. (Oak Ridge, TN)
2002-01-01
A continuous beam Fourier transform mass spectrometer in which a sample of ions to be analyzed is trapped in a trapping field, and the ions in the range of the mass-to-charge ratios to be analyzed are excited at their characteristic frequencies of motion by a continuous excitation signal. The excited ions in resonant motions generate real or image currents continuously which can be detected and processed to provide a mass spectrum.
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.
High-resolution lensless Fourier transform holography for microstructure imaging
Jie Zhao; Dayong Wang; Huaying Wang; Jianjun Xie
2007-01-01
Digital holography combines the advantages of the optical holography and the computers. It can implement an all-digital processing and has the quasi real-time property. With lensless Fourier transform recording architecture, the limited bandwidth of CCD camera can be utilized sufficiently, and the sampling theorem is satisfied easily. Therefore, high-resolution can be achieved. So it is preferred in the microstructure imaging.
Hybrid optonumerical quasi Fourier transform digital holographic camera
NASA Astrophysics Data System (ADS)
Doval, Ángel F.; Trillo, Cristina
2006-08-01
We present a novel hybrid digital holographic camera which shares most of the advantages of image-plane Fourier transform TV holography (TVH) and quasi-Fourier transform digital holography (QFTDH), whilst avoiding many of the drawbacks of both of them. As in TVH, it has a compact head where an objective lens is attached to accommodate objects of different sizes or placed at different distances; it is also free from aliasing artifacts produced by objects out of the field of view. As in QFTDH, the reconstruction of the object field (amplitude and phase) is accomplished by calculating just one fast Fourier transform (FFT) per hologram; light is spread over the sensor rather than being focused to produce an image, thus enabling the measurement in objects with very large radiance ranges. An optical imaging system (typically a zoom lens) selects the field of view and the working distance by projecting a reduced image of the object on the plane of a rectangular aperture. This image becomes the object for a lensless quasi-Fourier transform digital hologram, which is formed by making the light passing through the aperture to interfere with a reference beam diverging from its edge. This hologram is recorded with a video camera, digitized and numerically reconstructed by means of a single FFT. The function of the aperture is to crop the field of view to make the effective object size suitable to be recorded without aliasing on a sensor with a given pixel spacing; therefore, its size is determined by this spacing, the distance between the aperture and the sensor as well as by the wavelength of light.
Fast Gabor-like windowed Fourier and continuous wavelet transforms
M. Unser
1994-01-01
Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented. The analysis functions approximate complex-modulated Gaussians as closely as desired and may be optimally localized in time and frequency. The Gabor filtering is performed indirectly by convolving a premodulated signal with a Gaussian-like window and demodulating the output. The window functions are either B-splines dilated
Compensating optical systems. Part 3: achromatic fourier transformation.
Katyl, R H
1972-05-01
This paper shows the requirements for the achromatization of an irradiance distribution which is a function of a space coordinate multiplied by wavelength raised to a power. The particular requirements for achromatic Fourier transformation are then presented. The theory is applied to the following problems: achromatization of Newton's ring patterns and Fraunhofer diffraction patterns and frequency plane. filtering of an object illuminated with a broadband light source. Experimental systems that perform these functions are presented. PMID:20119125
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.
Pulsed Nozzle Fourier Transform Microwave Spectrometer: Advances and Applications
E. Arunan; Sagarika Dev; Pankaj K. Mandal
2004-01-01
The pulsed nozzle Fourier transform microwave (PNFTMW) spectrometer was developed by Balle and Flygare [A new method for observing the rotational spectra of weak molecular complexes: KrHCl. J. Chem. Phys. 1979, 71 (6), 2723–2724 and 1980, 72 (2), 922–932] in 1979. The design, fabrication, and operation of this spectrometer are complicated and it has largely remained a research laboratory tool
Field Desorption Ionization Fourier Transform Ion Cyclotron Resonance Mass Spectrometry
Tanner M. Schaub
2004-01-01
This, the 30th year of Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (FT-ICR MS),1 has marked a milestone for incredible growth in the field of high-resolution mass spectrometry. The most notable realizations of this fact being the successful installation of the highest field FT-ICR MS system assembled to date (14.5 Tesla) and the recent release of the most advanced commercial
The determination of peroxide value by fourier transform infrared spectroscopy
F. R. van de Voort; A. A. Ismail; J. Sedman; J. Dubois; T. Nicodemo
1994-01-01
A rapid method for the quantitative determination of peroxide value (PV) of vegetable oils by Fourier transform infrared (FTIR)\\u000a transmission spectroscopy is described. Calibration standards were prepared by the addition oft-butyl hydroperoxide to a series of vegetable oils, along with random amounts of oleic acid and water. Additional standards\\u000a were derived through the addition of mono- and diglyceride spectral contributions,
Properties of the Multidimensional Generalized Discrete Fourier Transform
Paolo Corsini; Graziano Frosini
1979-01-01
In this work the generalized discrete Fourier transform (GFT), which includes the DFT as a particular case, is considered. Two pairs of fast algorithms for evaluating a multidimensional GFT are given (T-algorithm, F-algorithm, and T?-algorithm, F?-algorithm). It is shown that in the case of the DFT of a vector, the T-algorithm represents a form of the classical FFT algorithm based
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.
Fast Fourier transform based direct integration algorithm for the linear canonical transform
NASA Astrophysics Data System (ADS)
Wang, Dayong; Liu, Changgeng; Wang, Yunxin; Zhao, Jie
2010-07-01
The linear canonical transform(LCT) is a parameterized linear integral transform, which is the general case of many well-known transforms such as the Fourier transform(FT), the fractional Fourier transform(FRT) and the Fresnel transform(FST). These integral transforms are of great importance in wave propagation problems because they are the solutions of the wave equation under a variety of circumstances. In optics, the LCT can be used to model paraxial free space propagation and other quadratic phase systems such as lens and graded-index media. A number of algorithms have been presented to fast compute the LCT. When they are used to compute the LCT, the sampling period in the transform domain is dependent on that in the signal domain. This drawback limits their applicability in some cases such as color digital holography. In this paper, a Fast-Fourier-Transform-based Direct Integration algorithm(FFT-DI) for the LCT is presented. The FFT-DI is a fast computational method of the Direct Integration(DI) for the LCT. It removes the dependency of the sampling period in the transform domain on that in the signal domain. Simulations and experimental results are presented to validate this idea.
Fast Fourier transform based direct integration algorithm for the linear canonical transform
NASA Astrophysics Data System (ADS)
Wang, Dayong; Liu, Changgeng; Wang, Yunxin; Zhao, Jie
2011-03-01
The linear canonical transform(LCT) is a parameterized linear integral transform, which is the general case of many well-known transforms such as the Fourier transform(FT), the fractional Fourier transform(FRT) and the Fresnel transform(FST). These integral transforms are of great importance in wave propagation problems because they are the solutions of the wave equation under a variety of circumstances. In optics, the LCT can be used to model paraxial free space propagation and other quadratic phase systems such as lens and graded-index media. A number of algorithms have been presented to fast compute the LCT. When they are used to compute the LCT, the sampling period in the transform domain is dependent on that in the signal domain. This drawback limits their applicability in some cases such as color digital holography. In this paper, a Fast-Fourier-Transform-based Direct Integration algorithm(FFT-DI) for the LCT is presented. The FFT-DI is a fast computational method of the Direct Integration(DI) for the LCT. It removes the dependency of the sampling period in the transform domain on that in the signal domain. Simulations and experimental results are presented to validate this idea.
Partial differential equation transform — Variational formulation and Fourier analysis
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-01-01
Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904
Versatile and Sensitive Dual Comb Fourier Transform Spectroscopy
NASA Astrophysics Data System (ADS)
Jacquey, M.; Jacquet, P.; Mandon, J.; Thon, R.; Guelachvili, G.; Hänsch, T. W.; Picqué, N.
2010-06-01
Fourier transform spectroscopy based on time-domain interferences between two slightly detuned frequency comb sources holds much promise for the real-time diagnostic of gaseous, liquid or solid-state samples. In one very recent example, cavity-enhanced absorption spectroscopy with two infrared frequency combs has demonstrated a dramatically enhanced sensitivity, compared to conventional Fourier spectroscopy, with intriguing implications for instantaneous trace gas analysis. It however remains challenging to match continuously the comb and cavity modes across a broad spectral bandwidth during the time of a measurement. An obvious alternative for reaching a long interaction path is a conventional multipass cell. Additionally, differential detection schemes may be devised to increase the dynamic range of the interferometric measurements, thus providing enhanced signal to noise ratio. Experimental demonstrations will be given in the 1.5 ?m region with a dual comb set-up based on two Er-doped fiber femtosecond lasers. The versatility and performances of these solutions will be compared to the cavity-enhanced dual comb technique and other state-of-the-art alternatives. P. Jacquet, J. Mandon, B. Bernhardt, R. Holzwarth, G. Guelachvili, T. W. Hänsch, N. Picqué, Frequency Comb Fourier Transform Spectroscopy with kHz Optical Resolution, The Optical Society of America, Washington, DC 2009, paper FMB2 (2009). B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T.W. Hänsch, N. Picqué, Cavity-enhanced dual-comb spectroscopy, Nature Photonics 4, 55-57 (2010),
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. [Los Alamos National Lab., NM (United States); Galbraith, A.E. [Los Alamos National Lab., NM (United States)]|[Univ. of Arizona, Tucson, AZ (United States). Electrical and Computer Engineering Dept.; Grubler, A.C. [Los Alamos National Lab., NM (United States)]|[Naval Academy, Annapolis, MD (United States)
1998-12-31
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and if desired, Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LIDAR systems, Fourier Transform Heterodyne (FTH) incorporates transverse spatial encoding of the local oscillator for image capture. Appropriate selection of spatial encoding functions, or basis set, allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging is accomplished on a single element detector requiring no additional scanning or moving components, and (2) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection. In this paper, they introduce the underlying principles governing FTH imaging, followed by demonstration of concept via a simple experimental setup based on a HeNe laser and a 69 element spatial phase modulator.
A generalized Fourier transform approach to risk measures
NASA Astrophysics Data System (ADS)
Bormetti, Giacomo; Cazzola, Valentina; Livan, Giacomo; Montagna, Guido; Nicrosini, Oreste
2010-01-01
We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework in which to efficiently compute the most popular risk measures, value-at-risk and expected shortfall (also known as conditional value-at-risk). The only ingredient required by our approach is the knowledge of the characteristic function describing the financial data in use. This allows us to extend risk analysis to those non-Gaussian models defined in the Fourier space, such as Lévy noise driven processes and stochastic volatility models. We test our analytical results on data sets coming from various financial indexes, finding that our predictions outperform those provided by the standard log-normal dynamics and are in remarkable agreement with those of the benchmark historical approach.
Spectroscopy, dynamics, and c aos of the CS, molecule: Fourier transform and phase-space analysis
Spectroscopy, dynamics, and c aos of the CS, molecule: Fourier transform and phase-space analysis J sevenparameters.Analysis of the spectraby the statistical Fourier transform technique. P. Pique@ and M. Joyeux Laboratoire de Spectromktrie Physique, Universitt Joseph Fourier de Grenoble
hal-00258693,version1-24Feb2008 Wide-field Fourier transform spectral imaging
source in the object plane. This configuration constitutes a lensless Fourier holographic setup [9hal-00258693,version1-24Feb2008 Wide-field Fourier transform spectral imaging Michael Atlan). A numerical Fourier transform of the time-domain recording enables wide-field coherent spectral imaging
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
Chirped-Pulse Fourier Transform Microwave Spectroscopy of 3-VINYLBENZALDEHYDE
NASA Astrophysics Data System (ADS)
Smith, Miranda; Brown, Gordon G.
2013-06-01
The pure rotational spectrum of 3-vinylbenzaldehyde (3VBA) has been measured and assigned. Coker College's chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer was used to measure the rotational spectrum of 3VBA in the 7.5 - 18.5 GHz region of the microwave spectrum. The results have been analyzed to discover the rotational constants and centrifugal distortion constants of four distinct conformations of 3VBA: cis,cis-, cis,trans-, trans,cis-, and trans,trans-3VBA. The experimental rotational constants have been compared to the results of ab initio calculations. The performance of Coker's CP-FTMW spectrometer will also be discussed.
SCUBA-2 Fourier transform spectrometer (FTS-2) commissioning results
NASA Astrophysics Data System (ADS)
Gom, Brad G.; Naylor, David A.; Friberg, Per; Bell, Graham S.; Bintley, Daniel; Abdelazim, Sherif; Sherwood, Matt
2014-07-01
We present the latest commissioning results and instrument performance for the SCUBA-2 imaging Fourier Transform Spectrometer (FTS-2) installed at the James Clerk Maxwell Telescope (JCMT). This ancillary instrument provides intermediate spectral resolution (R ~10 to 5000) across both the 450 and 850 ?m atmospheric transmission windows with a FOV of ~5 arcmin2. The superconducting TES sensors and SQUID readout of SCUBA-2 present unique challenges for operation of an FTS; the sensitivity requirements demand high detector linearity and stability in addition to control of systematic atmospheric and optical spillover effects. We discuss the challenges encountered during commissioning and ongoing efforts to mitigate their effects.
Multiple reference Fourier transform holography with soft x rays
Schlotter, W. F.; Rick, R.; Chen, K.; Scherz, A.; Stoehr, J.; Luening, J.; Eisebitt, S.; Guenther, Ch.; Eberhardt, W.; Hellwig, O.; McNulty, I. [Department of Applied Physics, 316 Via Pueblo Mall, Stanford University, Stanford, California 94305 (United States) and Stanford Synchrotron Radiation Laboratory, SLAC, Menlo Park, California 94025 (United States); Stanford Synchrotron Radiation Laboratory, SLAC, Menlo Park, California 94025 (United States); BESSY mbH, Albert-Einstein-Strasse 15, 12489 Berlin (Germany); San Jose Research Center, Hitachi Global Storage Technologies, 650 Harry Road, San Jose, California 95120 (United States) and BESSY mbH, Albert-Einstein-Strasse 15, 12489 Berlin (Germany); Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439 (United States) and BESSY mbH, Albert-Einstein-Strasse 15, 12489 Berlin (Germany)
2006-10-16
The authors demonstrate multiple reference source Fourier transform holography with soft x rays. This technique extends the detection limit of high resolution lensless imaging by introducing spatial multiplexing to coherent x-ray scattering. In this way, image quality is improved without increasing the radiation exposure to the sample. This technique is especially relevant for recording static images of radiation sensitive samples and for studying spatial dynamics with pulsed light sources. Applying their technique in the weak illumination limit they image a nanoscale test object by detecting {approx}2500 photons. The observed enhancement in the signal-to-noise ratio of the image follows the square root of the number of reference sources.
Quantification of Collagen Organization Using Fractal Dimensions and Fourier Transforms
Frisch, Kayt E.; Duenwald-Kuehl, Sarah E.; Lakes, Roderic S.; Vanderby, Ray
2011-01-01
Summary The structure of the collagen fibers that composes tendon and ligament are disrupted or damaged during injury and healing. Quantification of these changes is traditionally a laborious and subjective task. In this work we apply two automated techniques, Fourier transformation (FFT) and fractal dimension analysis (FA) to quantify the organization of collagen fibrils. Using multi-photon images we show that for healing ligament FA differentiates more clearly between the different time-points during healing. Using scanning electron microcopy images of overstretched tendon we show that combining FFT and FA measures separates the damaged and undamaged groups more clearly than either method individually. PMID:21529898
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 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.
Comparison of Fourier transform methods for calculating MTF
NASA Astrophysics Data System (ADS)
LaVeigne, Joseph D.; Burks, Stephen D.; Nehring, Brian
2008-04-01
Fourier transform methods common in infrared spectroscopy were applied to the problem of calculating the modulation transfer function (MTF) from a system's measured line spread function (LSF). Algorithms, including apodization and phase correction, are discussed in their application to remove unwanted noise from the higher frequency portion of the MTF curve. In general, these methods were found to significantly improve the calculated MTF. Apodization reduces the proportion of noise by discarding areas of the LSF where there is no appreciable signal. Phase correction significantly reduces the rectification of noise that occurs when the MTF is calculated by taking the power spectrum of the complex optical transfer function (OTF).
Particle field holography data reduction by Fourier transform analysis
NASA Technical Reports Server (NTRS)
Hess, Cecil F.; Trolinger, James D.
1987-01-01
The size distribution of a particle field hologram is obtained with a Fourier transformation of the Fraunhofer diffraction pattern of the reconstructed hologram. Off-axis absorption holograms of particle fields with known characteristics were obtained and analyzed with a commercially available instrument. The mean particle size of the reconstructed hologram was measured with an error of + or - 5 percent, while the distribution broadening was estimated within + or - 15 percent. Small sections of a pulsed laser hologram of a synthetic fuel spray were analyzed with this method thus yielding a spatially resolved size distribution. The method yields fast and accurate automated analysis of particle field holograms.
The Quantum Schur Transform: I. Efficient Qudit Circuits
Dave Bacon; Isaac L. Chuang; Aram W. Harrow
2005-12-30
We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis to a labelling related to the representation theory of the symmetric and unitary groups. If we desire to implement the Schur transform to an accuracy of epsilon, then our circuit construction uses a number of gates which is polynomial in n, d and log(1/epsilon). The important insights we use to perform this construction are the selection of the appropriate subgroup adapted basis and the Wigner-Eckart theorem. Our efficient circuit construction renders numerous protocols in quantum information theory computationally tractable and is an important new efficient quantum circuit family which goes significantly beyond the standard paradigm of the quantum Fourier transform.
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.
Debrup Das; N. K. Singh; A. K. Sinha
2006-01-01
This paper presents a comparative study of the performance of Fourier transform and wavelet transform based methods for detection, classification and location of faults on high voltage transmission lines. The algorithms devised are based on Fourier transform analysis of transient current signals recorded in the event of a short circuit on a transmission line. Similar analysis is performed using multi-resolution
Ordered fast fourier transforms on a massively parallel hypercube multiprocessor
NASA Technical Reports Server (NTRS)
Tong, Charles; Swarztrauber, Paul N.
1989-01-01
Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine.
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.
A high-resolution Fourier Transform Spectrometer for planetary spectroscopy
NASA Technical Reports Server (NTRS)
Cruikshank, D. P.; Sinton, W. M.
1973-01-01
The employment of a high-resolution Fourier Transform Spectrometer (FTS) is described for planetary and other astronomical spectroscopy in conjunction with the 88-inch telescope at Mauna Kea Observatory. The FTS system is designed for a broad range of uses, including double-beam laboratory spectroscopy, infrared gas chromatography, and nuclear magnetic resonance spectroscopy. The data system is well-suited to astronomical applications because of its great speed in acquiring and transforming data, and because of the enormous storage capability of the magnetic tape unit supplied with the system. The basic instrument is outlined 2nd some of the initial results from the first attempted use on the Mauna Kea 88-inch telescope are reported.
A versatile ultrastable platform for optical multidimensional Fourier-transform spectroscopy.
Bristow, A D; Karaiskaj, D; Dai, X; Zhang, T; Carlsson, C; Hagen, K R; Jimenez, R; Cundiff, S T
2009-07-01
The JILA multidimensional optical nonlinear spectrometer (JILA-MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delay between them while maintaining phase stability. The JILA-MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy, which records the phase of the nonlinear signal as a function of the time delay between several of the excitation pulses. The resulting multidimensional spectrum is obtained from a Fourier transform. This spectrum can resolve, separate, and isolate coherent contributions to the light-matter interactions associated with electronic excitation at optical frequencies. To show the versatility of the JILA-MONSTR, several demonstrations of two-dimensional Fourier-transform spectroscopy are presented, including an example of a phase-cycling scheme that reduces noise. Also shown is a spectrum that accesses two-quantum coherences, where all excitation pulses require phase locking for detection of the signal. PMID:19655944
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.
Soft x-ray microscope using Fourier transform holography
McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H. (State Univ. of New York, Stony Brook, NY (USA). Dept. of Physics; Lawrence Berkeley Lab., CA (USA); Brookhaven National Lab., Upton, NY (USA))
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.
Microscopy based on digital lensless Fourier transforms holography
NASA Astrophysics Data System (ADS)
Chen, Zhaoji; Liu, Feifei; Gong, Wendi; Wang, Huaying
2010-11-01
With the recent technological advances, there is an increasing need for testing the microstructure of objects. We show here Digital Holographic Microscopy (DHM) that implements digitally the principle of holography. It is particularly well suited for recording and reconstructing three-dimensional objects. In this paper, we present an off-axis digital holographic configuration and address some basic issues of the off-axis lensless Fourier transform digital holography including the recording conditions and the methods to improve the imaging performance. Following the theoretical analysis, the simple imaging system with the off-axis arrangement is built. Through using the resolution test target as microscopic object, the recorded holograms are reconstructed digitally based on the principle of Fresnel diffraction. The experimental results are consistent with the theoretical analysis. In addition, from the experimental operations and the design of reconstruction procedure we can see that the off-axis lensless Fourier-transform digital holographic setup is simple and suitable for real-time applications in microscopy.
Ultrafast and versatile spectroscopy by temporal Fourier transform
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.
2014-01-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system – the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges. PMID:24939667
Ultrafast and versatile spectroscopy by temporal Fourier transform
NASA Astrophysics Data System (ADS)
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.
2014-06-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system - the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges.
Radial Hilbert Transform in terms of the Fourier Transform applied to Image Encryption
NASA Astrophysics Data System (ADS)
Morales, Y.; Díaz, L.; Torres, C.
2015-01-01
In the present investigation, a mathematical algorithm under Matlab platform using Radial Hilbert Transform and Random Phase Mask for encrypting digital images is implemented. The algorithm is based on the use of the conventional Fourier transform and two random phase masks, which provide security and robustness to the system implemented. Random phase masks used during encryption and decryption are the keys to improve security and make the system immune to attacks by program generation phase masks.
Michela Svaluto Moreolo; Gabriella Cincotti; Alessandro Neri
We design all-optical architectures to perform the Discrete Wavelet Transform (DWT), the Wavelet Packet (WP) decomposition and the Discrete Fourier Transform (DFT) of optical digital signals. We give the design guidelines to synthesize optical wavelet filters as two - port lattice-form planar devices. The all-optical signal processing has the advantage of being able to process broad-band signals and by combining
Munther A. Gdeisat; David R. Burton; Michael J. Lalor
2006-01-01
In this paper, a filtering technique based upon two-dimensional continuous wavelet transform (2D-CWT) is used to eliminate the low frequency components of fringe patterns. The filtered fringe patterns are subsequently demodulated using a standard Fourier transform profilometry (FTP) algorithm. This image pre-filtering stage improves the noise performance of the FTP algorithm and enables the FTP method to demodulate fringe patterns
Ma, Shuiliang; Gao, Hongming; Wu, Lin
2008-03-20
Errors in discrete Abel inversion methods using Fourier transform techniques have been analyzed. The Fourier expansion method is very accurate but sensitive to noise. The Fourier-Hankel method has a significant systematic negative deviation, which increases with the radius; inversion error of the method can be reduced by adjusting the value of a factor. With a decrease of the factor both methods show a noise filtering property. Based on the analysis, a modified Fourier-Hankel method that is accurate, computationally efficient, and has the ability to filter noise in the inversion process is proposed for applying to experimental data. PMID:18709083
The Radon Transform on SO(3): A Fourier Slice Theorem and
Hielscher, Ralf
The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical Inversion R. Hielscher1 , D.Hielscher@helmholz-muenchen.de The inversion of the onedimensional Radon transform on the rotation group SO(3) is an ill posed inverse problem approach to the numerical inversion of the onedimensional Radon transform on SO(3). Based on a Fourier
The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical
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
Polarization-dependent optical 2D Fourier transform spectroscopy of semiconductors
Zhang, Tianhao; Kuznetsova, Irina; Meier, Torsten; Li, Xiaoqin; Mirin, Richard P.; Thomas, Peter; Cundiff, Steven T.
2007-01-01
Optical 2D Fourier transform spectroscopy (2DFTS) provides insight into the many-body interactions in direct gap semiconductors by separating the contributions to the coherent nonlinear optical response. We demonstrate these features of optical 2DFTS by studying the heavy-hole and light-hole excitonic resonances in a gallium arsenide quantum well at low temperature. Varying the polarization of the incident beams exploits selection rules to achieve further separation. Calculations using a full many-body theory agree well with experimental results and unambiguously demonstrate the dominance of many-body physics. PMID:17630286
Multiresolution graph Fourier transform for compression of piecewise smooth images.
Hu, Wei; Cheung, Gene; Ortega, Antonio; Au, Oscar C
2015-01-01
Piecewise smooth (PWS) images (e.g., depth maps or animation images) contain unique signal characteristics such as sharp object boundaries and slowly varying interior surfaces. Leveraging on recent advances in graph signal processing, in this paper, we propose to compress the PWS images using suitable graph Fourier transforms (GFTs) to minimize the total signal representation cost of each pixel block, considering both the sparsity of the signal's transform coefficients and the compactness of transform description. Unlike fixed transforms, such as the discrete cosine transform, we can adapt GFT to a particular class of pixel blocks. In particular, we select one among a defined search space of GFTs to minimize total representation cost via our proposed algorithms, leveraging on graph optimization techniques, such as spectral clustering and minimum graph cuts. Furthermore, for practical implementation of GFT, we introduce two techniques to reduce computation complexity. First, at the encoder, we low-pass filter and downsample a high-resolution (HR) pixel block to obtain a low-resolution (LR) one, so that a LR-GFT can be employed. At the decoder, upsampling and interpolation are performed adaptively along HR boundaries coded using arithmetic edge coding, so that sharp object boundaries can be well preserved. Second, instead of computing GFT from a graph in real-time via eigen-decomposition, the most popular LR-GFTs are pre-computed and stored in a table for lookup during encoding and decoding. Using depth maps and computer-graphics images as examples of the PWS images, experimental results show that our proposed multiresolution-GFT scheme outperforms H.264 intra by 6.8 dB on average in peak signal-to-noise ratio at the same bit rate. PMID:25494508
Structural Characterization of Carbohydrates by Fourier Transform Tandem Mass Spectrometry
Zhou, Wen; Håkansson, Kristina
2012-01-01
Fourier transform tandem mass spectrometry (MS/MS) provides high mass accuracy, high sensitivity, and analytical versatility and has therefore emerged as an indispensable tool for structural elucidation of biomolecules. Glycosylation is one of the most common posttranslational modifications, occurring in ~50% of proteins. However, due to the structural diversity of carbohydrates, arising from non-template driven biosynthesis, achievement of detailed structural insight is highly challenging. This review briefly discusses carbohydrate sample preparation and ionization methods, and highlights recent developments in alternative high-resolution MS/MS strategies, including infrared multiphoton dissociation (IRMPD), electron capture dissociation (ECD), and electron detachment dissociation (EDD), for carbohydrates with a focus on glycans and proteoglycans from mammalian glycoproteins. PMID:22389641
Analysis of far-infrared emission Fourier transform spectra
NASA Technical Reports Server (NTRS)
Park, J. H.; Carli, B.
1986-01-01
An analysis method that uses the nonlinear least-squares fit technique has been developed for emission spectra obtained with a Fourier transform spectrometer. This method is used for the analysis of submillimeter-region atmospheric emission spectra obtained with a balloon-borne FT spectrometer that was carried out as a correlative measurement for the Limb IR Monitor of the Stratosphere (LIMS) satellite experiment. The retrieved mixing ratios of H2O and O3 in the stratosphere from four spectral intervals have standard deviations of about 10 percent, and the average values agree to within 10 percent of corresponding results from the LIMS satellite experiment which used a broadband emission radiometer in the IR region.
Single pulse pressure wave analysis by fast Fourier transformation.
Christensen, L; Børgesen, S E
1989-12-01
Pressure recordings from 16 patients with normal pressure by hydrocephalus were analysed during controlled intracranial hypertension. Single pulse pressure wave (PPW) analyses were performed on a computer system with programs for automatic computation of mean intracranial pressure (MICP), pulse amplitude (PA), rise time coefficients (RT) and fast Fourier transformation (FFT). We found good correlation between the first harmony, MICP and PA, and between the fifth harmony and RT. The PPW is mainly composed of low-frequency components, but with increasing RT more high-frequency components are present. RT changes as compliance of the brain changes. Therefore the high-frequency components of the FFT may predict changes in the cerebral compliance, although there was no correlation between any of the harmonies and the pressure volume index (PVI). In this investigation PVI was found difficult to perform and evaluate. PMID:2576101
Universal calculation formula and calibration method in Fourier transform profilometry
Wen Yongfu; Li Sikun; Cheng Haobo; Su Xianyu; Zhang Qican
2010-12-01
We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.
Surface analysis by Fourier-transform infrared (FTIR) spectroscopy
Powell, G.L.; Smyrl, N.R.; Fuller, E.L.
1981-08-12
A diffuse-reflectance capability for the Fourier transform infrared spectrometer at the Y-12 Plant Laboratory has been implemented. A sample cell with a 25 to 400/sup 0/C temperature-controlled sample stage and an ultrahigh-vacuum-to-atmospheric pressure gas-handling capability has been developed. Absorbance of light from the spectrometer beam, resulting from the beam being scattered from a powder sample, can be measured. This capability of detecting molecular species on and in powders is to be used to study chemisorption on actinide and rare-earth metals, alloys, and compounds. Cell design is described along with experiments demonstrating its performance in detecting moisture absorption on uranium oxide, moisture and carbon dioxide absorption on the lithium hydride/hydroxide system, and carbon dioxide absorption on potassium borohydride. 13 figures.
Extreme-ultraviolet lensless Fourier-transform holography.
Lee, S H; Naulleau, P; Goldberg, K A; Cho, C H; Jeong, S; Bokor, J
2001-06-01
We demonstrate 100-nm-resolution holographic aerial image monitoring based on lensless Fourier-transform holography at extreme-UV (EUV) wavelengths, using synchrotron-based illumination. This method can be used to monitor the coherent imaging performance of EUV lithographic optical systems. The system has been implemented in the EUV phase-shifting point-diffraction interferometer recently developed at Lawrence Berkeley National Laboratory. Here we introduce the idea of the holographic aerial image-recording technique and present imaging performance characterization results for a 10x Schwarzschild objective, a prototype EUV lithographic optic. The results are compared with simulations, and good agreement is obtained. Various object patterns, including phase-shift-enhanced patterns, have been studied. Finally, the application of the holographic aerial image-recording technique to EUV multilayer mask-blank defect characterization is discussed. PMID:18357280
Solar radiometry at millimeter wavelengths. [Fast Fourier Transformation solutions
NASA Technical Reports Server (NTRS)
Henze, W.
1974-01-01
In the area of resolution enhancement, the use of Fast Fourier Transform programs was investigated for possible application to millimeter wavelength maps of the sun. A difficulty arises with the La Posta maps in that they are limited to 35 arc-minutes square while the smeared out solar image is larger than that. A list of possible cometary emission lines near 13 millimeters is presented. Although preparation of the list was inspired by the appearance of Comet Kohoutek, the results are applicable to any future comet. The brightness temperature of the sun at 8.6 millimeters was measured using the moon as a calibration source. The result does not confirm a deep absorption feature as apparently observed by earlier workers.
Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform
Hausel, Tamás
2006-01-01
A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski–Dancer and Hausel–Sturmfels), Poincaré polynomials of Hilbert schemes of points and twisted Atiyah–Drinfeld–Hitchin–Manin (ADHM) spaces of instantons on ?2 (recovering results of Nakajima–Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced. PMID:16606857
Polyurethane monitoring by mid-infrared fiber Fourier transform spectrometry
NASA Astrophysics Data System (ADS)
de Haseth, James A.; Andrews, Jennifer E.
1992-03-01
Chalcogenide fibers that transmit radiation in the mid-infrared region have been coupled to a Fourier transform infrared spectrometer. The fibers are used to measure attenuated total reflectance spectra of samples that are remote, or do not lend themselves to conventional sampling methods. The samples used in this study are polyurethane foams and spectra are collected while the foams are forming. The reaction intermediates can be monitored, as well as the reaction kinetics. Spectra can be collected rapidly; faster than one spectrum per second, however, the reaction rates in this study do not require temporal resolutions of faster than 10 seconds. The collected spectra are subjected to factor analysis to identify the reactants, intermediates and products.
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.
Detecting hypovolemia in postoperative patients using a discrete Fourier transform.
Szabó, Viktor; Halász, Gábor; Gondos, Tibor
2015-04-01
In the present paper, an attempt was made to find waveform-derived variables that would be useful for a more precise diagnosis of hypovolemia. In attempting this, arterial blood pressure graphs of 18 hypovolemic postoperative patients were analysed using a discrete Fourier transform. Using a paired samples t-test, the amplitude of the first harmonic (A1) is shown to be significantly higher in normovolemic cases than in hypovolemic ones (p < 0.001). Based on the values of A1, a preliminary study was performed in which an additional group of 14 hypovolemic and 14 normovolemic patients were categorized into hypovolemic and normovolemic groups using logistic regression. The method proved to be successful in identifying hypovolemic patients: the prediction was correct in 80% and wrong only in 20%, indicating that A1 is potentially a useful parameter in detecting hypovolemia. PMID:25665937
Development of an Imaging Fourier Transform Spectrometer for Astronomy
NASA Astrophysics Data System (ADS)
Grandmont, Frederic; Drissen, Laurent; Joncas, Gilles
2003-02-01
We present an overview of the past and current development of the Imaging Fourier Transform Spectrometer (IFTS) concept for ground telescopes produced in collaboration between ABB Bomem and Université Laval. This instrument intends to produce spectra of variable resolutions up to R = ?/?? = 10 000 from the near UV to the near IR (350 nm to 900 nm). It is designed to fit the f/8 focus of the Mont Mégantic 1.6m optical telescope in Québec. The large number of spatial elements (> 1 million pixels) is the novel aspect of this FTS design along with innovative metrology system. Heritage from Next Generation Space Telescope (NGST) IFTS concept, Lawrence Livermore National Laboratory (LLNL)- ABB Bomem instrument and commercial ABB Bomem DA series FTS are reviewed. Techniques for accurately servoing the moving mirror alignment to a value smaller than 0.1 arc second and position to sub nanometer value are discussed. Also presented are results from the assembled interferometer sub-system.
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.
2011-01-01
using discriminant analysis of Fourier transform infraredcompositional analysis of cornstover fractions using Fourieranalysis and monosaccharide composition modeling to identify plant cell wall variations by Fourier
Strauss, Martin J.
Theoretical and experimental analysis of a randomized algorithm for Sparse Fourier transform Abstract We analyze a sublinear RA`SFA (randomized algorithm for Sparse Fourier analysis) that finds a near coefficients of a signal that describe most of the signal trends, is a fun- damental task in Fourier analysis
The Fractional Fourier Transform and Its Application to Fault Signal Analysis
Duan, Xiao
2012-07-16
Fourier Transform (FT), which decomposes a stationary signal into different frequency components. However, a major drawback of the conventional transform is that it does not easily render itself to the analysis of non-stationary signals such as a frequency...
The data processing pipeline for the Herschel/SPIRE Imaging Fourier Transform Spectrometer
Naylor, David A.
The data processing pipeline for the Herschel/SPIRE Imaging Fourier Transform Spectrometer Trevor R the data processing pipeline to generate calibrated data products from the Spectral and Photometric Imaging Receiver (SPIRE) imaging Fourier Transform Spectrometer. The pipeline processes telemetry from SPIRE point
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
An Architectural Performance Study of the Fast Fourier Transform on Vector IRAM
California at Berkeley, University of
Performance Study of the Fast Fourier Transform on Vector IRAM by Randi Thomas Research Project Submitted Architectural Performance Study of the Fast Fourier Transform on Vector IRAM Randi Thomas Master of Science Projects Agency of the Department of Defense under contract DABT63-96-C- 0056, the National Science
An Architectural Performance Study of the Fast Fourier Transform on Vector IRAM
California at Berkeley, University of
Performance Study of the Fast Fourier Transform on Vector IRAM by Randi Thomas Research Project Submitted; An Architectural Performance Study of the Fast Fourier Transform on Vector IRAM Randi Thomas #3; Master of Science Projects Agency of the Department of Defense under contract DABT6396C 0056, the National Science
An Incremental Algorithm for Signal Reconstruction from Short-Time Fourier Transform Magnitude
Poggio, Tomaso
An Incremental Algorithm for Signal Reconstruction from Short-Time Fourier Transform Magnitude Jake@mit.edu Abstract We present an algorithm for reconstructing a time-domain signal from the magnitude of a short-domain signal from only the magnitude of the short-time Fourier transform (STFT) is a common prob- lem in speech
Fourier Transform Light Scattering of Inhomogeneous and Dynamic Structures Huafeng Ding,1
Boppart, Stephen
Fourier Transform Light Scattering of Inhomogeneous and Dynamic Structures Huafeng Ding,1 Zhuo Wang manuscript received 21 October 2008; published 3 December 2008) Fourier transform light scattering (FTLS) is a novel experimental approach that combines optical microscopy, holography, and light scattering
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
Achromatic optical Fourier transformer with planar-integrated free-space optics
Jahns, Jürgen
Achromatic optical Fourier transformer with planar-integrated free-space optics Gladys Mi´nguez-Vega an integrated optical Fourier transformation module that was achromatized for the visible spectrum by means selectivity of the first G. Mi´nguez-Vega (gminguez@exp.uji.es) and J. Lancis are with the Departament de
Causes of the reconstructed cross appearing in lensless Fourier transform digital holography
Xiaoxu Lu; Liyun Zhong; Hongzhan Liu; Zhun Zhang
2010-01-01
Causes of the bright cross appearing in the reconstructed field of lensless Fourier transform digital hologram (LFDH) are presented. Firstly, as LFDH's reconstruction was directly performed by Fourier transform algorithm, the intensity distribution of reconstructed image plane was just LFDH's spectrum, and three parts of the reconstructed field are imaged in the spectral plane. Meanwhile their intensities were almost the
Application of fourier and wavelet transforms to the identification of EMI noise sources in SMPSs
Luisa Coppola; Simone Buso; Qian Liu; Dushan Boroyevich; Amy Bell
2005-01-01
The Fourier and wavelet transform are applied to analyze the signals in a power electronics converter. The wavelet transform makes it possible to have important information about the time evolution of the frequency spectrum. Thank to this post-processing, the source of the harmonic peaks found in the Fourier spectrum can be identified in the time evolution of the signals of
Contributed article Fractional Fourier transform pre-processing for neural networks
Barshan, Billur
Contributed article Fractional Fourier transform pre-processing for neural networks and its This study investigates fractional Fourier transform pre-processing of input signals to neural networks. Judicious choice of this parameter can lead to overall improvement of the neural network performance
Min Cao; Yaowen Fu; Weidong Jiang; Xiang Li; Zhaowen Zhuang
2007-01-01
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
The use of Fourier reverse transforms in crystallographic phase refinement
Ringrose, S.
1997-10-08
Often a crystallographer obtains an electron density map which shows only part of the structure. In such cases, the phasing of the trial model is poor enough that the electron density map may show peaks in some of the atomic positions, but other atomic positions are not visible. There may also be extraneous peaks present which are not due to atomic positions. A method for determination of crystal structures that have resisted solution through normal crystallographic methods has been developed. PHASER is a series of FORTRAN programs which aids in the structure solution of poorly phased electron density maps by refining the crystallographic phases. It facilitates the refinement of such poorly phased electron density maps for difficult structures which might otherwise not be solvable. The trial model, which serves as the starting point for the phase refinement, may be acquired by several routes such as direct methods or Patterson methods. Modifications are made to the reverse transform process based on several assumptions. First, the starting electron density map is modified based on the fact that physically the electron density map must be non-negative at all points. In practice a small positive cutoff is used. A reverse Fourier transform is computed based on the modified electron density map. Secondly, the authors assume that a better electron density map will result by using the observed magnitudes of the structure factors combined with the phases calculated in the reverse transform. After convergence has been reached, more atomic positions and less extraneous peaks are observed in the refined electron density map. The starting model need not be very large to achieve success with PHASER; successful phase refinement has been achieved with a starting model that consists of only 5% of the total scattering power of the full molecule. The second part of the thesis discusses three crystal structure determinations.
[Using Fourier transform to calculate gas concentration in DOAS].
Liu, Qian-lin; Wang, Li-shi; Huang, Xin-jian; Wu, Yan-dan; Xiao, Ming-wei
2008-12-01
Being an analysis tool of high sensitivity, high resolution, multicomponents, real-time and fast monitoring, the differential optical absorption spectrometry (DOAS) is becoming a new method in atmosphere pollution monitoring. In the DOAS technique, many gases spectra have periodicity evidently, such as those from SO2, NO, NH3 and NO2. Aiming at three kinds of main air-polluted gases, i.e., SO2, NO and NO2 in atmosphere, the DOAS technique is used to monitor them, and Fourier transform is used to analyse the above-mentioned absorption spectra. Under the condition of Hanning Windows, Fourier transforma is used to process various gases spectra which have periodicity. In the process, the value of the characteristic frequency has a linearity relation to the gas concentration. So a new analysis method of DOAS is proposed, which is utilizing the relation between the value of the characteristic frequency and the gas concentration to deduce a linearity formula to calculate the gas concentration. So the value of the characteristic frequency can be used to get the gas concentration. For the gases with evident spectrum periodicity, such as SO2 and NO, this method is good. But for some gases with periodicity not evident, the error in the calculated concentration is beyond the allowable value. So in this method, the important process is frequency separation. It is also the main part in the future study. In a word, this method frees itself from the basic theory in the DOAS technique, cuts down on the process of the concentration calculation and the spectral analysis, and deserves further study. PMID:19248493
Fast Registration of Tabular Document Images Using the Fourier-Mellin Transform
Luke A. D. Hutchison; William A. Barrett
2004-01-01
A new technique is presented for quickly identifying global affine transformations applied to tabular document images, and to correct for those transformations. This technique, based on the Fourier-Mellin transform, is used to register (align) a set of tabular documents to each other. Each component of the affine transform is handled separately, which dramatically reduces the total parameter space of the
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.
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.
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.
Picolinic and isonicotinic acids: a Fourier transform microwave spectroscopy study.
Peña, Isabel; Varela, Marcelino; Franco, Vanina G; López, Juan C; Cabezas, Carlos; Alonso, José L
2014-12-01
The rotational spectra of laser ablated picolinic and isonicotinic acids have been studied using broadband chirped pulse (CP-FTMW) and narrowband molecular beam (MB-FTMW) Fourier transform microwave spectroscopies. Two conformers of picolinic acid, s-cis-I and s-cis-II, and one conformer of isonicotinic acid have been identified through the analysis of their rotational spectra. The values of the inertial defect and the quadrupole coupling constants obtained for the most stable s-cis-I conformer of picolinic acid, evidence the formation of an O-H···N hydrogen bond between the acid group and the endocyclic N atom. The stabilization provided by this hydrogen bond compensates the destabilization energy due to the adoption of a -COOH trans configuration in this conformer. Its rs structure has been derived from the rotational spectra of several (13)C, (15)N, and (18)O species observed in their natural abundances. Mesomeric effects have been revealed by comparing the experimental values of the (14)N nuclear quadrupole coupling constants in the isomeric series of picolinic, isonicotinic, and nicotinic acids. PMID:25382020
Computing Fast Fourier Transforms On Boolean Cubes And Related Networks
NASA Astrophysics Data System (ADS)
Johnsson, S. Lennart; Ho, Ching-Tien; Jacquemin, Michel; Ruttenberg, Alan
1988-01-01
High performance architectures are using an ever increasing number of processors. The Boolean cube network has many independent paths between any pair of processors. It provides both a high communications bandwidth as well as the ability to emulate many other networks without contention for communication channels. Of particular interest for the Fast Fourier Transform (FFT) is the ability to emulate butterfly networks, which defines the communication pattern of the FFT. Each node of a Boolean cube network of N nodes has a degree of log2N . For a large number of nodes the number of channels required at the chip boundary may be unfeasibly large with several nodes to a chip, and a network with slightly lower connectivity, such as Cube Connected Cycles networks, may be preferable. The communication system is the most critical resource in many high performance architectures, and its effective use imperative. We describe FFT algorithms that use both the storage bandwidth and the communication sys-tem optimally for an architecture such as the Connection Machine that has 65536 processors interconnected in a Boolean cube related network. We also describe the necessary data allocation, and the allocation and use of the twiddle factors.
Fourier transform infrared and physicochemical analyses of roasted coffee.
Wang, Niya; Lim, Loong-Tak
2012-05-30
In this study, Brazilian coffee beans processed to different stages of roast at 210, 220, 230, and 240 °C were analyzed for pH value, titratable acidity, moisture content, and color lightness. Fourier transform infrared (FTIR) spectroscopy, in conjunction with principal component analysis, was conducted to study the effects of process time and temperature on the IR-active components of the acetyl acetate extract of the roasted coffee. The results showed that high-temperature-short-time resulted in higher moisture content, higher pH value, and higher titratable acidity when the beans were roasted beyond the start-of-second-crack stage, as compare to low-temperature-long-time process (LTLT). The LTLT process also resulted in greater IR absorbance for aldehydes, ketones, aliphatic acids, aromatic acids, and caffeine carbonyl bands on the FTIR spectra. Clusters for principal component score plots were well separated, indicating that the changes IR-active components in the coffee extracts, due to the different roasting treatments, can be discriminated by the FTIR technique. On the basis of the loading plots of principal components, changes of IR-active compounds in the coffee extract at various stages of roasting were discussed. PMID:22563854
Compliant MEMS mechanism to extend resolution in Fourier transform spectroscopy
NASA Astrophysics Data System (ADS)
Sauceda-Carvajal, A.; Kennedy-Cabrera, H. D.; Hernández-Torres, J.; Herrera-May, A. L.; Mireles, José
2014-03-01
A complaint mechanism to extend resolution in the Fourier Transform Spectroscopy (FTS) technique has been designed, fabricated and tested. The mechanism based on the complaint mechanical design strategy has not mobile parts and was fabricated in MEMS technology in a Bosch Process. When this mechanism is used to displacing the mobile mirror in a FTS setup, an extended range travel for the reference mirror is achieved; thus, the optical path difference and hence the resolving power of the FTS system is increased. The fabricated device has dimensions of 5400x4200x400 Microns at the large, width and thickness respectively, with an aspect ratio about 10. Numerical simulations with ANSYS Software were developed to get the Stress limits and the input and output displacements, the mechanical gain and the resonance frequency of the device. Experimental results in both the forced and dynamical regime are presented. It is found that in the dynamical regime when the device is operated at its resonance frequency it exhibits a higher mechanical gain several times its gain in the forced regime.
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.
Fourier transform infrared spectroscopy (FTIR) of laser-irradiated cementum
NASA Astrophysics Data System (ADS)
Rechmann, Peter; White, Joel M.; Cecchini, Silvia C. M.; Hennig, Thomas
2003-06-01
Utilizing Fourier Transform Infrared Spectroscopy (FTIR) in specular reflectance mode chemical changes of root cement surfaces due to laser radiation were investigated. A total of 18 samples of root cement were analyzed, six served as controls. In this study laser energies were set to those known for removal of calculus or for disinfection of periodontal pockets. Major changes in organic as well as inorganic components of the cementum were observed following Nd:YAG laser irradiation (wavelength 1064 nm, pulse duration 250 ?s, free running, pulse repetition rate 20 Hz, fiber diameter 320 ?m, contact mode; Iskra Twinlight, Fontona, Slovenia). Er:YAG laser irradiation (wavelength 2.94 ?m, pulse duration 250 ?s, free running, pulse repetition rate 6 Hz, focus diameter 620 ?m, air water cooling 30 ml/min; Iskra Twinlight, Fontona, Slovenia) significantly reduced the Amid bands due to changes in the organic components. After irradiation with a frequency doubled Alexandrite laser (wavelength 377 nm, pulse duration 200 ns, q-switched, pulse repetition rate 20 Hz, beam diameter 800 ?m, contact mode, water cooling 30 ml/min; laboratory prototype) only minimal reductions in the peak intensity of the Amide-II band were detected.
Ivory and simulated ivory artefacts: Fourier transform Raman diagnostic study
NASA Astrophysics Data System (ADS)
Edwards, H. G. M.; Farwell, D. W.
1995-11-01
The Fourier transform Raman spectrum of ivory is reported and assignments are proposed for the major spectroscopic features. Application of the FT Raman technique to the non-destructive diagnostic identification of ivory and simulated ivory artefacts is illustrated with reference to several specimens, both modern and aged. Although the FT Raman spectrum of ivory is similar to that of other bone samples, the characteristic vibrational modes are identified and it is suggested that the relative intensity ratio of the ?(CH) stretching bands near 2930 cm -1 and the hydroxyapatite ?(PO) stretching band at 960 cm -1 is a good diagnostic parameter for ivory. Other modes, such as ?(NH) near 3300 cm -1, the ?(CH 2) profile near 1250 cm -1 and ?(CC) symmetric ring stretching intensity at 1002 cm -1 are also good confirming indicators to distinguish ivory from bone and synthetic specimens. Modern specimens of "ivory" using synthetic polymers and polymer-inorganic composites are easily distinguished spectroscopically from genuine ivory, particularly close textural specimens, which involved a synthetic blending of poly(methylmethacrylate), polystyrene and calcite.
Xiao-Jun Yang
2011-07-23
It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.
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.
NASA Astrophysics Data System (ADS)
Zhang, Y. G.; Gu, Y.; Wang, K.; Fang, X.; Li, A. Z.; Liu, K. H.
2012-05-01
An improved Fourier transform infrared spectroscopy approach adapting to photoluminescence and electroluminescence measurements in mid-infrared has been developed, in which diode-pumped solid-state excitation lasers were adopted for photoluminescence excitation. In this approach, three different Fourier transform infrared modes of rapid scan, double modulation, and step scan were software switchable without changing the hardware or connections. The advantages and limitations of each mode were analyzed in detail. Using this approach a group of III-V and II-VI samples from near-infrared extending to mid-infrared with photoluminescence intensities in a wider range have been characterized at room temperature to demonstrate the validity and overall performances of the system. The weaker electroluminescence of quantum cascade lasers in mid-infrared band was also surveyed at different resolutions. Results show that for samples with relatively strong photoluminescence or electroluminescence out off the background, rapid scan mode is the most preferable. For weaker photoluminescence or electroluminescence overlapped with background, double modulation is the most effective mode. To get a better signal noise ratio when weaker photoluminescence or electroluminescence signal has been observed in double modulation mode, switching to step scan mode should be an advisable option despite the long data acquiring time and limited resolution.
Quantum transition probabilities and classical Fourier harmonics
NASA Astrophysics Data System (ADS)
Fedak, William
2002-03-01
A quantum dot is an atomic-like system consisting of a semiconductor nanoparticle surrounded by an insulator. When an electron in the valence band of the semiconductor becomes excited, the electron-hole pair that is created (called an exiton) acts much like a hydrogen atom. Investigations have demonstrated the potential application of quantum dots for optical switching and optical memory. A model of a truncated pyramidal InAs quantum dot in an InP matrix will be presented and described. The model uses a single band envelope theory that accurately describes the truncated pyramidal shape of the dot. The matrix representation of the Hamiltonian is calculated in a basis consisting of kinetic energy eigenfunctions that vanish on the surface of a cube containing the dot. The eigenvalues of this matrix are the energy levels. These results will then be compared with photoluminescence measurements of energy levels conducted at the Microelectronics-Photonics Center at the University of Arkansas - Fayetteville
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.
Liouville transformations and quantum reflection
Gabriel Dufour; Romain Guérout; Astrid Lambrecht; Serge Reynaud
2015-02-21
Liouville transformations of Schr\\"odinger equations preserve the scattering amplitudes while changing the effective potential. We discuss the properties of these gauge transformations and introduce a special Liouville gauge which allows one to map the problem of quantum reflection of an atom on an attractive Casimir-Polder well into that of reflection on a repulsive wall. We deduce a quantitative evaluation of quantum reflection probabilities in terms of the universal probability which corresponds to the solution of the $V_4=-C_4/z^4$ far-end Casimir-Polder potential.
Yao, Jianping
, and Jianping Yao, Senior Member, IEEE Abstract--Fourier transform ultrashort optical pulse shaping using response of the entire pulse shaping system is equal to the Fourier transform of the square of the grating. INTRODUCTION F OURIER synthesis, also known as Fourier transform pulse shaping, is one of the most commonly
Bokor, Jeffrey
Extreme-ultraviolet lensless Fourier-transform holography Sang Hun Lee, Patrick Naulleau, Kenneth A aerial image monitoring based on lensless Fourier- transform holography at extreme-UV EUV wavelengths can be predicted from the coherent image. In this study, lensless Fourier-transform hologra- phy3
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
Fourier transform Raman lidar for trace gas detection and quantification
Sentell, J.C. [Coleman Research Corp., Huntsville, AL (United States)
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.
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.
SPICA/SAFARI Fourier transform spectrometer mechanism evolutionary design
NASA Astrophysics Data System (ADS)
van den Dool, Teun C.; Kruizinga, Bob; Braam, Ben C.; Hamelinck, Roger F. M. M.; Loix, Nicolas; Van Loon, Dennis; Dams, Johan
2012-09-01
TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI1 Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme2 in 2022. JAXA3 leads the development of the SPICA satellite and SRON is the prime investigator of the Safari instrument. The FTS scanning mechanism (FTSM) has to meet a 35 mm stroke requirement with an Optical Path Difference resolution of less then 15 nm and must fit in a small volume. It consists of two back-to-back roof-top mirrors mounted on a small carriage, which is moved using a magnetic bearing linear guiding system in combination with a magnetic linear motor serving as the OPD actuator. The FTSM will be used at cryogenic temperatures of 4 Kelvin inducing challenging requirements on the thermal power dissipation and heat leak. The magnetic bearing enables movements over a scanning stroke of 35.5 mm in a small volume. It supports the optics in a free-floating way with no friction, or other non-linearities, with sub-nanometer accuracy. This solution is based on the design of the breadboard ODL (Optical Delay Line) developed for the ESA Darwin mission4 and the MABE mechanism developed by Micromega Dynamics. During the last couple of years the initial design of the SAFARI instrument, as described in an earlier SPIE 2010 paper5, was adapted by the SAFARI team in an evolutionary way to meet the changing requirements of the SPICA payload module. This presentation will focus on the evolution of the FTSM to meet these changing requirements. This work is supported by the Netherlands Space Office (NSO).
Fractal surface synthesis based on two dimensional discrete Fourier transform
NASA Astrophysics Data System (ADS)
Zhou, Chao; Gao, Chenghui; Huang, Jianmeng
2013-11-01
The discrete Fourier transform(DFT) is used for fractional Brownian motion(FBM) surface synthesis in tribology(i.e., contact, sliding, and sealing, etc). However, the relationship between fractal parameters(fractal dimension and scale factor) and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface ( Sq) is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height( Sz), the skewness( Ssk) and the kurtosis( Sku) are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy.
Paul, J; Dey, P; Tokumoto, T; Reno, J L; Hilton, D J; Karaiskaj, D
2014-10-01
The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ?4 × 10(11) cm(-2) was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent "rephasing" (S1) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S1 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The "two-quantum coherence" (S3) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations. PMID:25296819
The Fourier-series method for inverting transforms of probability distributions
Joseph Abate; Ward Whitt
1992-01-01
This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourier-series method are remarkably easy to use, requiring programs of less than fifty lines. The Fourier-series method can be interpreted as numerically integrating a standard inversion integral by means
Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
Dave Bacon; Isaac Chuang; Aram Harrow
2004-08-05
The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/\\epsilon)) for accuracy \\epsilon) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.
A Study of Two Dimensional Electron Gas Using 2D Fourier Transform Spectroscopy
NASA Astrophysics Data System (ADS)
McIntyre, Carl; Paul, Jagannath; Karaiskaj, Denis
2015-03-01
The dephasing of FES was measured in a symmetrically modulation doped 12 nm single quantum well GaAs/AlGaAs two dimensional electron gas system using time integrated four wave mixing (TIFWM) and a two dimensional Fourier transform spectroscopy (2DFTS). At high in-well carrier densities of ~4 x 1011 cm-2, many body effects that are prevalent and measurable with non-linear optical spectroscopy. Effects of exciton-exciton and exciton-phonon scattering events, exciton populations, and biexciton formation are detectable at these carrier concentrations. Homogeneous linewidths obtained from 2DFT and TIFWM yield a zero Kelvin linewidth of 1.42 meV and an acoustic phonon scattering coefficient of 158 ? eV/K. These observations indicate a rapid increase in homogeneous linewidth with increased temperature. NSF REU Grant # DMR-1263066: REU Site in Applied Physics at USF.
The Radon Transform on SO(3): A Fourier Slice Theorem and
Potts, Daniel
The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical Inversion R. Hielscher 1 , D: Ralf.Hielscher@gsf.de The inversion of the one--dimensional Radon transform on the rotation group SO(3. This communication presents a novel approach to the numerical inversion of the one--dimensional Radon transform on SO
The Radon Transform on SO(3): A Fourier Slice Theorem and
Potts, Daniel
The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical Inversion R. Hielscher1 , D: Ralf.Hielscher@gsf.de The inversion of the onedimensional Radon transform on the rotation group SO(3. This communication presents a novel approach to the numerical inversion of the onedimensional Radon transform on SO
Fourier transform spectroscopy of BaO: New ground-state constants from the A 1
Le Roy, Robert J.
¿ chemiluminescence Hongzhi Li, Cristian Focsa,a) Bernard Pinchemel,a) Robert J. Le Roy,b) and P. F. Bernathc) Guelph in a Broida-type oven was revisited using a Fourier transform spectrometer. Chemiluminescence was observed
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
Calcium floride, magnesium fluoride, sulfur, silver bromide, silver chloride, and five different particle sizes of diamond powder were studied for use as matrix materials for diffuse reflectance Fourier transform infrared spectrometry. Potassium chloride was used as a reference b...
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: • The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms. • The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform. • The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.
Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing
NASA Technical Reports Server (NTRS)
Park, J. H.
1984-01-01
An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.
Donald F. Gurka; Jimmie W. Brasch; Russell H. Barnes; Charles J. Riggle; Sidney Bourne
1986-01-01
Micro-diffuse reflectance Fourier transform infrared (DRIFT) and matrix isolation (MI) Fourier transform infrared spectra of the 22 tetrachlorodibenzodioxin (TCDD) isomers have been recorded. The DRIFT and MI techniques required about four minutes and one-half minute, respectively, of signal averaging to produce high signal-to-noise (S\\/N) spectra on low-nanogram-level samples. Spectral subtraction was employed to remove DRIFT solvent impurity interferences. The validity
Comparison of reconstruction algorithms in lens-less Fourier transform digital holography
Jie Zhao; Dayong Wang; Jianjun Xie; Huaying Wang
2008-01-01
The different reconstruction algorithms are investigated and the reconstructed images are presented in lensless Fourier transform digital holography. The most employed three algorithms, all based on the fast-Fourier-transform, are: the convolution algorithm, the angular spectrum algorithm, and the Fresnel algorithm. With the convolution algorithm and angular spectrum algorithm, there is an optimal reconstruction distance where the pass-band range of the
Implementation of a 2-D Fast Fourier Transform on an FPGA-Based Custom Computing Machine
Nabeel Shirazi; Peter M. Athanas; A. Lynn Abbott
1995-01-01
The two dimensional fast Fourier transform (2-D FFT) is an indispensable operation in many digital signal processing applications but yet is deemed computationally expensive when performed on a conventional general purpose processors. This paper presents the implementation and performance figures for the Fourier transform on a FPGA-based custom computer. The computation of a 2-D FFT requires O(N2log2N) floating point arithmetic
Midwave infrared imaging Fourier transform spectrometry of combustion plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.
A midwave infrared (MWIR) imaging Fourier transform spectrometer (IFTS) was used to successfully capture and analyze hyperspectral imagery of combustion plumes. Jet engine exhaust data from a small turbojet engine burning diesel fuel at a low rate of 300 cm3/min was collected at 1 cm -1 resolution from a side-plume vantage point on a 200x64 pixel window at a range of 11.2 meters. Spectral features of H2O, CO, and CO2 were present, and showed spatial variability within the plume structure. An array of thermocouple probes was positioned within the plume to aid in temperature analysis. A single-temperature plume model was implemented to obtain spatially-varying temperatures and plume concentrations. Model-fitted temperatures of 811 +/- 1.5 K and 543 +/- 1.6 K were obtained from plume regions in close proximity to thermocouple probes measuring temperatures of 719 K and 522 K, respectively. Industrial smokestack plume data from a coal-burning stack collected at 0.25 cm-1 resolution at a range of 600 meters featured strong emission from NO, CO, CO2, SO 2, and HCl in the spectral region 1800-3000 cm-1. A simplified radiative transfer model was employed to derive temperature and concentrations for clustered regions of the 128x64 pixel scene, with corresponding statistical error bounds. The hottest region (closest to stack centerline) was 401 +/- 0.36 K, compared to an in-stack measurement of 406 K, and model-derived concentration values of NO, CO2, and SO2 were 140 +/- 1 ppmV, 110,400 +/- 950 ppmV, and 382 +/- 4 ppmV compared to in-stack measurements of 120 ppmV (NOx), 94,000 ppmV, and 382 ppmV, respectively. In-stack measurements of CO and HCl were not provided by the stack operator, but model-derived values of 19 +/- 0.2 ppmV and 111 +/- 1 ppmV are reported near stack centerline. A deployment to Dugway Proving Grounds, UT to collect hyperspectral imagery of chemical and biological threat agent simulants resulted in weak spectral signatures from several species. Plume detection of methyl salicilate was achieved from both a stack release and explosive detonation, although spectral identification was not accomplished due to weak signal strength.
Broadband Mid-Infrared Comb-Resolved Fourier Transform Spectroscopy
NASA Astrophysics Data System (ADS)
Lee, Kevin; Mills, Andrew; Mohr, Christian; Jiang, Jie; Fermann, Martin; Maslowski, Piotr
2014-06-01
We report on a comb-resolved, broadband, direct-comb spectroscopy system in the mid-IR and its application to the detection of trace gases and molecular line shape analysis. By coupling an optical parametric oscillator (OPO), a 100 m multipass cell, and a high-resolution Fourier transform spectrometer (FTS), sensitive, comb-resolved broadband spectroscopy of dilute gases is possible. The OPO has radiation output at 3.1-3.7 and 4.5-5.5 ?m. The laser repetition rate is scanned to arbitrary values with 1 Hz accuracy around 417 MHz. The comb-resolved spectrum is produced with an absolute frequency axis depending only on the RF reference (in this case a GPS disciplined oscillator), stable to 1 part in 10^9. The minimum detectable absorption is 1.6x10-6 wn Hz-1/2. The operating range of the experimental setup enables access to strong fundamental transitions of numerous molecular species for applications based on trace gas detection such as environmental monitoring, industrial gas calibration or medical application of human breath analysis. In addition to these capabilities, we show the application for careful line shape analysis of argon-broadened CO band spectra around 4.7 ?m. Fits of the obtained spectra clearly illustrate the discrepancy between the measured spectra and the Voigt profile (VP), indicating the need to include effects such as Dicke narrowing and the speed-dependence of the collisional width and shift in the line shape model, as was shown in previous cw-laser studies. In contrast to cw-laser based experiments, in this case the entire spectrum (˜ 250 wn) covering the whole P and R branches can be measured in 16 s with 417 MHz resolution, decreasing the acquisition time by orders of magnitude. The parallel acquisition allows collection of multiple lines simultaneously, removing the correlation of possible temperature and pressure drifts. While cw-systems are capable of measuring spectra with higher precision, this demonstration opens the door for fast, massively parallel line shape parameters retrieval combined with analysis reaching beyond the VP and with absolute frequency calibration delivered by frequency combs. R. Wehr et al. J. Mol. Spec. 235 54-68 (2003) A. Cygan, et al. Eur. Phys. J. Special Topics 222 2119-2142 (2013)
Rapid Bacterial Identification Using Fourier Transform Infrared Spectroscopy
Valentine, Nancy B.; Johnson, Timothy J.; Su, Yin-Fong; Forrester, Joel B.
2007-02-01
Recent studies at Pacific Northwest National Laboratory (PNNL) using infrared spectroscopy combined with statistical analysis have shown the ability to identify and discriminate vegetative bacteria, bacterial spores and background interferents from one another. Since the anthrax releases in 2001, rapid identification of unknown powders has become a necessity. Bacterial endospores are formed by some Bacillus species as a result of the vegetative bacteria undergoing environmental stress, e.g. a lack of nutrients. Endospores are formed as a survival mechanism and are extremely resistant to heat, cold, sunlight and some chemicals. They become airborne easily and are thus readily dispersed which was demonstrated in the Hart building. Fourier Transform Infrared (FTIR) spectroscopy is one of several rapid analytical methods used for bacterial endospore identification. The most common means of bacterial identification is culturing, but this is a time-consuming process, taking hours to days. It is difficult to rapidly identify potentially harmful bacterial agents in a highly reproducible way. Various analytical methods, including FTIR, Raman, photoacoustic FTIR and Matrix Assisted Laser Desorption/Ionization (MALDI) have been used to identify vegetative bacteria and bacterial endospores. Each has shown certain areas of promise, but each has shortcomings in terms of sensitivity, measurement time or portability. IR spectroscopy has been successfully used to distinguish between the sporulated and vegetative state. [1,2] It has also shown its utility at distinguishing between the spores of different species. [2-4] There are several Bacillus species that occur commonly in nature, so it is important to be able to distinguish between the many different species versus those that present an imminent health threat. The spectra of the different sporulated species are all quite similar, though there are some subtle yet reproducible spectroscopic differences. Thus, a more robust and reliable method is needed for differentiation. Using chemometrics, a classification scheme was developed and performed on samples sporulated in glucose broth. PNNL has demonstrated that vegetative bacteria and endospores have unique infrared (IR) signatures that can be used to identify to the species-, and in some cases, even to the strain-level. We have shown that the IR spectra of spores of different species tend to be quite similar, yet the small but reproducible differences in the spectra allow for a certain degree of differentiation. Further studies have shown that the culture medium can also have an effect on the spectra. For the distinction between vegetative and endospores, we have consistently observed a series of four peaks at 766, 725, 702, and a fairly sharp peak (FWHM 7 cm-1) at 660 cm-1, present only in the endospore spectra.
Sparse Fourier Transform via Butterfly Algorithm Lexing Ying
Li, Tiejun
. This problem appears naturally in several important applications of wave scattering, digital signal processing is optimal up to a logarithmic factor from the information-theoretical viewpoint. The discussion of our geometric low rank property of the Fourier kernel e2ix·/N . Let A X and B be two square boxes
Carbon nanotube probe resolution: a quantitative analysis using Fourier Transform
H. R. Gutiérrez; D. Nakabayashi; P. C. Silva; J. R. R. Bortoleto; V. Rodrigues; J. H. Clerici; M. A. Cotta; D. Ugarte
2004-01-01
A method to quantify the resolution of atomic force microscopy (AFM) probes using Fourier analysis of the AFM images is proposed. The maximum detectable spatial frequency obtained from the power spectrum was used to estimate the lateral resolution. Carbon nanotube tips were successfully used to study very dense arrays of semiconductor nanostructures. In particular, accurate measurements of shallow facet angles
Fourier-Transform Raman Spectroscopy Of Biological Assemblies
NASA Astrophysics Data System (ADS)
Levin, Ira W.; Lewis, E. Neil
1989-12-01
Although the successful coupling of Raman scattered near-infrared radiation to a Michelson interferometer has recently created an outburst of intense interest in Fourier-transform (FT) Raman spectrometry," extended applications of the technique to macromolecular assemblies of biochemical and biophysical relevance have not progressed as rapidly as studies directed primarily at more conventional chemical characterizations. Since biological materials sampled with visible laser excitation sources typically emit a dominant fluorescence signal originating either from the intrinsic fluorescence of the molecular scatterer or from unrelenting contaminants, the use of near-infrared Nd:YAG laser excitation offers a convenient approach for avoiding this frequently overwhelming effect. In addition, the FT-Raman instrumentation provides a means of eliminating the deleterious resonance and decomposition effects often observed with the more accessible green and blue laser emissions. However, in choosing the incident near-infrared wavelength at, for example, 1064nm, the Raman scattered intensity decreases by factors of eighteen to forty from the Raman emissions induced by the shorter, visible excitations. Depending upon the experiment, this disadvantage is offset by the throughput and multiplex advantages afforded by the interferometric design. Thus, for most chemical systems, near-infrared FT-Raman spectroscopy, clearly provides a means for obtaining vibrational Raman spectra from samples intractable to the use of visible laser sources. In particular, for neat liquids, dilute solutions or polycrystalline materials, the ability to achieve high quality, reproducible spectra is, with moderate experience and perhaps relatively high laser powers, as straightforward as the conventional methods used to obtain Raman spectra with visible excitation and dispersive monochromators. In using near-infrared FT techniques to determine the Raman spectra of biological samples, one encounters new sets of experimental problems that may entail an initial, relatively steep learning curve. These difficulties originate particularly from the fragility of the weakly scattering aggregate paired with the dilute nature of the biochemical or cellular dispersion. Often, the Raman scattered intensity from these samples can be increased by carefully peileting the biological suspension using ultracentrifugation techniques. Since the overtone region of water, the usual medium for biological samples, absorbs radiation from both the Rayleigh signal at the exciting wavelength of the Nd:YAG laser and the longer wavelength Raman scattering from the sample, reproducible temperature measurements and temperature control become significant concerns. In these cases one appeals to internal temperature calibrations, use of deuterium oxide (D20) as a solvent (since absorptions of the laser exciting wavelength and Raman scattered photons are minimized), manipulation of incident laser spot size and the use of fiber optic bundles to carry the exciting and scattered radiation. In the present discussion we briefly cite some of the experimental approaches we have developed and experiences we have encountered in adapting near-infrared FT-Raman spectroscopy to the more challenging biophysical and biochemical systems amenable to vibrational analysis. We emphasize here the determination of the spectra of membrane assemblies and membrane related materials; in particular, we elucidate the interaction of several polyene antibiotics, including amphotericin A, amphotericin B and nystatin, with a model membrane system composed of dipalmitoylphosphatidylcholine bilayers.
A Discrete Fourier-CosineTransform Chip MARTIN VE7TERLIAND ADRIAAN LIGTENBERG
Vetterli, Martin
design-time possible. I. INTRODUCTION HIGH-SPEED computation of the discrete cosine transform(DCT) [l on the In parallelto the design of the actual chip, a software image in a high-level language (C) wasmade. This imageA Discrete Fourier-CosineTransform Chip MARTIN VE7TERLIAND ADRIAAN LIGTENBERG Abstract -An 8-point
A Likelihood Ratio Distance Measure for the Similarity Between the Fourier Transform of Time Series
Gareth J. Janacek; Anthony J. Bagnall; M. Powell
2005-01-01
Discrete Fourier Transforms (DFTs) have been a popular transformation and compression technique in time series data mining since rst being proposed for use in this context in (1). The Euclidean distance between coecien ts has been the most popular distance metric used in conjunction with FFTs in time series data mining. However, on many problems it is not the best
The Numerical Analysis of Soliton Propagation with Plit-Step Fourier Transform Method
Z B Wang; H Y Yang; Z Q Li
2006-01-01
It is very important for practicability and system designing to study on the optical soliton transform and evolution with numerical simulation. In this paper, the split-step Fourier transform method (SSFM) is particularly introduced and the simulation is also given. The Matlab language is used to simulate the soliton propagation in the optical fiber. The influence of optical fiber waste is
On a Pseudo-Subspace Framework for Discrete Fractional Fourier Transform Based Chirp
Santhanam, Balu
On a Pseudo-Subspace Framework for Discrete Fractional Fourier Transform Based Chirp Parameter to develop a pseudo-subspace approach towards chirp parameter estimation. Keywords: Discrete Fractional to the pseudo signal subspace and small values corresponding to the pseudo noise subspace. transform based chirp
q-Extension of Mehta's eigenvectors of the finite Fourier transform for q, a root of unity
NASA Astrophysics Data System (ADS)
Atakishiyeva, Mesuma K.; Atakishiyev, Natig M.; Koornwinder, Tom H.
2009-10-01
It is shown that the continuous q-Hermite polynomials for q, a root of unity, have simple transformation properties with respect to the classical Fourier transform. This result is then used to construct q-extended eigenvectors of the finite Fourier transform in terms of these polynomials.
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.
NASA Astrophysics Data System (ADS)
Fan, Hong-yi; Hu, Li-yun
2012-06-01
By virtue of the new technique of performing integration over Dirac's ket-bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel-Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac's assertion: "...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory".
Fast Fourier and Wavelet Transforms for Wavefront Reconstruction in Adaptive Optics
Dowla, F U; Brase, J M; Olivier, S S
2000-07-28
Wavefront reconstruction techniques using the least-squares estimators are computationally quite expensive. We compare wavelet and Fourier transforms techniques in addressing the computation issues of wavefront reconstruction in adaptive optics. It is shown that because the Fourier approach is not simply a numerical approximation technique unlike the wavelet method, the Fourier approach might have advantages in terms of numerical accuracy. However, strictly from a numerical computations viewpoint, the wavelet approximation method might have advantage in terms of speed. To optimize the wavelet method, a statistical study might be necessary to use the best basis functions or ''approximation tree.''
Study on sampling of continuous linear system based on generalized Fourier transform
NASA Astrophysics Data System (ADS)
Li, Huiguang
2003-09-01
In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.
Sun, Zhiwei; Hou, Peipei; Zhi, Ya'nan; Sun, Jianfeng; Zhou, Yu; Xu, Qian; Lu, Zhiyong; Liu, Liren
2014-03-20
A two-dimensional (2D) Fourier transform algorithm for the image reconstruction of synthetic-aperture imaging ladar (SAIL) collected data is suggested. This algorithm consists of quadratic phase compensation in azimuth direction and 2D fast Fourier transform. Based on this algorithm and the parallel 2D Fourier transform capability of spherical lens, an optical principle scheme that processes the SAIL data is proposed. The basic principle, design equations, and necessary analysis are presented. To verify this principle scheme, an experimental optical SAIL processor setup is constructed. The imaging results of SAIL data obtained by our SAIL demonstrator are presented. The optical processor is compact, lightweight, and consumes low power. This optical processor can also provide inherent parallel and speed-of-light computing capability, and thus has potential applications in on-board and satellite-borne SAIL systems. PMID:24663462
NASA Technical Reports Server (NTRS)
Munoz, R. M. (inventor)
1974-01-01
An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. The original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications.
System design of Fourier transform imaging spectrometer using tunable lateral shearing splitter
NASA Astrophysics Data System (ADS)
Meng, Xin; Li, Jianxin; Bai, Caixun; Zhu, Rihong
2015-04-01
The Fourier transform spectrometer without slit has the advantages of high radiation throughput and high spatial resolution. It can be used for detecting more details of the spectral and spatial information. We present the initial structure of the collimator and objective based on the analysis of the principle of the Fourier transform spectrometer. Then the collimator and objective are optimized by Zemax. The MTF of the cut-off frequency is great than 0.7. The tunable lateral shearing splitter is used as the interferometer, which makes the system more compact compared with the system using Sagnac lateral shearing splitter. The method to calculate the geometric dimension of the splitter is presented. Then the complete Fourier transform spectrometer is designed. The MTF of the cut-off frequency is great than 0.6. And the largest RMS of the spot is less than 6?m.
NASA Astrophysics Data System (ADS)
Merenda, F.; Bühler, S.; Farah, H.; Boer, G.; Scharf, T.
2010-04-01
We present a recently developed miniature scanning Fourier-Transform spectrometer (ARCspectro ANIR), which is based on a lamellar grating interferometer and uses a micro-mechanical actuator. The small dimensions of the interferometer (35 mm x 35 mm x 65 mm) and its low weight makes this device a truly portable Fourier-Transform spectrometer. Two different versions of this new spectrometer are presented: one version uses an InGaAs photodiode (0.9?m to 2.6 ?m) and the other a MCT detector (2 to 4.5 ?m). Their performances are discussed and also illustrated with measurement and application examples.
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.
NASA Astrophysics Data System (ADS)
Kulkarni, Rishikesh; Rastogi, Pramod
2015-07-01
This paper proposes a novel method for the simultaneous estimation of multiple interference phases from a single recording of the interference field in a multi-wave digital holographic interferometry set-up. The method involves the separation of signal components from the recorded interference field based on windowed Fourier transform based filtering and amplitude discrimination criteria. The proposed method possesses the advantages offered by windowed Fourier transform based filtering such as noise robustness and a high quality reconstruction of the signal components. The performance of the method is validated with numerical and experimental examples.
Detecting landscape forms using Fourier transformation and singular value decomposition (SVD)
NASA Astrophysics Data System (ADS)
Wieland, Ralf; Dalchow, Claus
2009-07-01
Landscape structure is a main determinant of ecological landscape potentials. The basic differentiation of relief into depressions and elevations at deliberately chosen scales can be managed comfortably by the Fourier transformation. The automated extraction of these structures from an elevation map using Fourier transformation or singular value decomposition can help to overcome complicated and errorprone procedures based on the determination of numerical structure parameters such as slope and aspect. The combination of automated extraction methods and moving window technology can lead to further, more integrated insights related to complex landscape patterns.
NASA Astrophysics Data System (ADS)
Wang, Qu; Chen, Li; Zhou, Jinyun; Lin, Qinghua
2011-11-01
The morphological joint fractional Fourier transform correlator (MJFTC), as a modified nonlinear joint fractional Fourier transform correlator (JFTC), is introduced in this paper. An optoelectronic setup that can implement such a nonlinear JFTC is advised and constructed. We investigate the correlation properties of the MJFTC using computer simulation and optical experiments. Numerical and experimental results show that the MJFTC exhibits remarkable improvement in terms of discriminability and peak sharpness compared with the classic JFTC. Moreover, the MJFTC provides better noise tolerance to the salt-and-pepper noise or normally distributed white additive noise than the JFTC and the other nonlinear processing or fractional-order filtering JFTC.
[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
Simple geometry to record fractional Fourier transform hologram with holographic lens
NASA Astrophysics Data System (ADS)
Gao, Feng; Zhang, Yixiao; Zeng, Yangsu; Yang, Jing; Xie, Shiwei; Gao, Fuhua; Huang, Xiaoyang; Yao, Jun; Du, Jinglei; Guo, Yongkang
2002-06-01
FRTH is a new kind of hologram, which is different form common Fresnel holograms and Fourier transform holograms. It can be applied for fractional Fourier transform filtering and anti-counterfeiting, etc. Due to the flexibility of holographic lens, we present a method that uses the -1 diffraction wave of holographic lens as the object wave and the 0 diffraction wave as the reference wave to record FRTH. It provides a new simple way to record FRTH. In this paper, the theory of achieving FRT and recording FRTH with holographic lens has been discussed, and the experimental results are also presented.
Applying fast Fourier transform (FFT) to statistic quality control
Cui You-xiang; You Jian-xin; Luo Feng
2010-01-01
This article presents a FFT method in statistic quality control. Most previous statistic quality control tools can not analysis the quality data in both time and frequency. In this paper, the FFT method is used to transforming our view of the quality signal from time-based to frequency-based, to provide a basis for current decision during production as to when to
Fourier-transform spectroscopy and potential construction of the (2)(1)? state in KCs.
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)? ? X(1)?(+) 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)]. PMID:25854245
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)].
Adaptive motion mapping in pancreatic SBRT patients using Fourier transforms
Jones, Bernard L; Miften, Moyed
2015-01-01
Recent studies suggest that 4DCT is unable to accurately measure respiratory-induced pancreatic tumor motion. In this work, we assessed the daily motion of pancreatic tumors treated with SBRT, and developed adaptive strategies to predict and account for this motion. The daily motion trajectory of pancreatic tumors during CBCT acquisition was calculated using a model which reconstructs the instantaneous 3D position in each 2D CBCT projection image. We developed a metric (termed "Spectral Coherence," SC) based on the Fourier frequency spectrum of motion in the SI direction, and analyzed the ability of SC to predict motion-based errors and classify patients according to motion characteristics. The amplitude of daily motion exceeded the predictions of pre-treatment 4DCT imaging by an average of 3.0 mm, 2.3 mm, and 3.5 mm in the AP, LR, and SI directions. SC was correlated with daily motion differences and tumor dose coverage. In a simulated adaptive protocol, target margins were adjusted based on SC, resulting in...
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.
Nabin Ghoshal; J. K. Mandal
2011-01-01
T his paper presents a novel steganographic schemes based on Discrete Fourier Transformation (DFT) and demonstrates the multimedia colour image authentication process in frequency domain for wireless communication(DFTMCIAWC). Authentication is done through embedding secrete message\\/image into the transformed frequency components of the source image at message originating node. The DFT is applied on sub-image block called mask of size 2
Potential-Field Forward Modeling and Inversion Using 3D Fast Fourier Transforms
J. D. Phillips; F. Caratori Tontini; L. Cocchi
2008-01-01
Although 1D and 2D fast Fourier transforms (FFTs) have long been used for the filtering, interpretation, and modeling of potential-field data, 3D FFTs have not enjoyed similar popularity. This may change with the recent discovery (Caratori Tontini et al., in press, JGR) that simple 3D FFT filters can be used to transform distributions of density (or magnetization) within a box-shaped
B. Sporkmann; H. Bross
1994-01-01
A method is described for the calculation of generalized symmetry-adapted Wannier functions by Fourier transformation of Bloch functions obtained by standard first-principles techniques. An additional unitary transformation derived from a Slater-Koster-model Hamiltonian is introduced in order to deal with the nonanalytical behavior of the Bloch functions. The parameters of the Hamiltonian, which are the energy matrix elements of the Wannier
Waveguide Chirped-Pulse Fourier Transform Microwave Spectroscopy of 2-ETHOXYETHANOL
NASA Astrophysics Data System (ADS)
Phillips, Maria A.; Shipman, Steven T.
2013-06-01
The pure rotational spectrum of 2-ethoxyethanol was recorded from 8.7 to 26.5 GHz at 250 K with a waveguide chirped-pulse Fourier transform microwave spectrometer. The full spectrum contains contributions from multiple vibrational states. Preliminary assignments have been made with a combination of ab initio calculations and an automated spectral fitting program that accelerates the initial fitting process.
Pulsed nozzle Fourier transform microwave spectrometer: Ideal to define hydrogen bond radius
E. Arunan; A. P. Tiwari; P. K. Mandal; P. C. Mathias
A pulsed nozzle Fourier transform microwave (PNFTMW) spectrometer has been recently fabri- cated at the Indian Institute of Science. The basic design is the same as that of Balle and Flygare. How - ever, recent advances in microwave and computer technologies have helped in designing a state -of-the- art PNFTMW spectrometer. The range of the spectro- meter is from 2
Fourier and wavelet transformations for the fault detection of induction motor with stator current
Sang-Hyuk Lee; Sungshin Kim; Jang Mok Kim; Man Hyung Lee
2004-01-01
In this literature, fault detection of an induction motor is carried out using the information of stator current. After preprocessing actual data, Fourier and wavelet transforms are applied to detect characteristics under the healthy and various faulted conditions. The most reliable phase current among 3-phase currents is selected by the fuzzy entropy. Data are trained with a neural network system,
Fourier transform spectroscopy of chemiluminescence from system of SrOq
Le Roy, Robert J.
Fourier transform spectroscopy of chemiluminescence from the A01 PX1 Rþ system of SrOq Randall H of strontium oxide (SrO) was observed at high spectral resolution by measuring the chemiluminescence from, many of which involved low reso- lution spectra and examined chemiluminescence of me- tal vapour plus
D. A. Naylor; T. A. Clark; G. R. Davis; W. D. Duncan; G. J. Tompkins
1993-01-01
We report the first use of a polarizing Fourier transform spectrometer on the James Clerk Maxwell Telescope. Solar spectra have been measured through four of the submillimeter and millimeter atmospheric windows. The repeatability is shown to be excellent, with signal-to-noise ratios exceeding 100 per spectral element per scan. The spectra also show good agreement with synthetic atmospheric transmission spectra over
Fourier transform infrared analyses of NTA interaction with the ?-alumina support
NASA Astrophysics Data System (ADS)
Ryczkowski, Janusz
1994-01-01
The current impetus for examining the interaction of nitrilotriacetic acid (NTA or H3X, where X equals N(CH2COO)33-) molecules with (gamma) -alumina support by Fourier transform infrared (FTIR) spectroscopy is chiefly related to the preparation of new heterogeneous dispersed catalysts.
I. Kitamura; S. Kanai; T. Kishinami
2001-01-01
In this paper, a new digital watermarking method for vector maps is proposed, where the watermark can be embedded in a set of polylines by using the discrete Fourier transform (DFT). The robustness against external attacks and visual degradation caused by embedding were evaluated, and the effectiveness of the watermarking was confirmed. Our watermarking method is especially robust against vertex
Camilla Ricci; K. L. Andrew Chan; Sergei G. Kazarian
2006-01-01
Conventional FTIR spectroscopy and microscopy has been widely used in forensic science. New opportunities exist to obtain rapid chemical images and to enhance the sensitivity of detection of trace materials using attenuated total reflection (ATR) Fourier transform infrared (FTIR) spectroscopy coupled with a focal-plane array (FPA) detector. In this work, the sensitivity of ATR-FTIR spectroscopic imaging using three different kinds
A practical implementation of de-Pake-ing via weighted Fourier transformation
Sani, Marc-Antoine; Weber, Daniel K.; Delaglio, Frank; Separovic, Frances
2013-01-01
We provide an NMRPipe macro to meet an increasing need in membrane biophysics for facile de-Pake-ing of axially symmetric deuterium, and to an extent phosphorous, static lineshapes. The macro implements the development of McCabe & Wassall (1997), and is run as a simple replacement for the usual Fourier transform step in an NMRPipe processing procedure. PMID:23638366
Land-Surface Phenologies from AVHRR Using the Discrete Fourier Transform
Aaron Moody; David M. Johnson
2001-01-01
The first and second harmonics of the discrete Fourier transform (DFT) concisely summarize the amplitude and phase of annual and biannual signals embedded in time-series of Advanced Very High Resolution Radiometer (AVHRR) Normalized Difference Vegetation Index (NDVI) data. We applied and evaluated the DFT using monthly composited NDVI data over a 7-year period for a 150 × 150-km study area
Iterative reconstruction of speech from short-time Fourier transform phase and magnitude spectra
Iterative reconstruction of speech from short-time Fourier transform phase and magnitude spectra dimensional, signal reconstruction (specifically speech signals) from the magnitude spectrum and the phase magnitude spectrum, and (iii) a signal can be reconstructed to within a scale factor from its magnitude
M. Hayes
1982-01-01
This paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its Fourier transform. The first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude. Although phase or magnitude information alone is not sufficient, in general, to uniquely specify a sequence, a large
Gallery of datacubes obtained with the Livermore imaging Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Wurtz, Ronald E.; Wishnow, Edward H.; Blais-Ouellette, Sebastien; Cook, Kem H.; Holden, Bradford P.; Carr, Dennis J.; Stubbs, Christopher W.
2003-02-01
We have acquired spatial-spectral datacubes of astronomical objects using the Livermore visible-band imaging Fourier transform spectrometer at Apache Point Observatory. Each raw datacube contains hundreds of thousands of spectral interferograms. We present in-progress demonstrations of these observations.
Tooth-Caries Early Diagnosis and Mapping by Fourier Transform Spectral Imaging Fluorescence
Michal Fisher; Liviu Feller; Israel Schechter
2002-01-01
A new method for fast diagnosis and mapping of tooth caries is suggested. The method is based on autofluorescence and application of Fourier transform imaging microscopy. This device provides simultaneous fluorescence spectra at all pixels of the examined sample. A cooled CCD detector, directly connected to the spectrometer, collects the imaging interferograms and allows for spectral mapping. The feasibility of
Measurement of integrated tuning elements for SIS mixes with a Fourier transform spectrometer
Qing Hu; C. A. Mears; P. L. Richards; F. L. Lloyd
1988-01-01
Planar lithographed quasioptical mixers can profit from the use of integrated tuning elements to improve the coupling between the antenna and the SIS mixer junctions. We have used a Fourier transform spectrometer with an Hg-arc lamp source as an RF sweeper to measure the frequency response of such integrated tuning elements. The SIS junction connected to the tuning element served
Characteristic Length Scale of Bicontinuous Nanoporous Structure by Fast Fourier Transform
Takeshi Fujita; Ming Wei Chen
2008-01-01
We propose a method derived from fast Fourier transform (FFT) process to measure the characteristic length scale of bicontinuous nanoporous structures. By rotationally averaging the FFT power spectrum of a nanoporous micrograph from scanning electron microscope (SEM) or transmission electron microscope (TEM), a significant peak in the power spectrum can be obtained, which reflects the characteristic length scale of the
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 \\
Real-time sampling electronics for double modulation experiments with Fourier transform infrared for publication 13 February 1991) A novel synchronous real-time analog sampling method for obtaining the sum the difference interferogram. The demodulation of a test waveform with the real-time sampling electronics reveals
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 ...
Gabor and lensless Fourier transform X-ray holograms: a comparison
Tiqiao Xiao; Jianwen Chen; Zhizhan Xu; Peiping Zhu
1996-01-01
A comparison between Gabor X-ray holography and lensless Fourier transform X-ray holography is made. Three aspects are considered: recording distance, aberrations in optical reconstructions and digital reconstructions of these two kinds of holograms by theoretical analysis and digital simulations. Some new results are given.
Huakun Cui; Dayong Wang; Yunxin Wang; Changgeng Liu; Jie Zhao; Yan Li
2010-01-01
As the lensless Fourier transform digital holography is applied into the microscopic phase-contrast imaging on the live cells, the motion of the cells will lead to the non-coplanarity phenomena between the object and the reference source. This could result in the imaging aberration. An effective and robust autofocus procedure based on the phase distribution is presented in the paper. With
Study on the depth of focus of lensless Fourier transform digital holographic imaging system
Huaying Wang; Aili Qin; Yi Wang
2009-01-01
Based on the principle of digital holography and the criterion of the depth of focus of coherent lens imaging system, the depth of focus (DOF) of off-axis lensless Fourier transform digital holographic system is analyzed. The DOF expressions of digital holographic systems with symmetrical and unsymmetrical offset of reference point sources are deduced and presented. By using a minute vertical
Jie Zhao; Dayong Wang; Yunxin Wang; Changgeng Liu; Yan Li; Huakun Cui; Yuhong Wan
2010-01-01
The lensless Fourier transform digital holography has been widely employed in microscopic imaging. It enables quantitative phase analysis for both reflection and transmission objects. The phase image is obtained in the numerical reconstruction procedure. The in-focus reconstruction distance could be determined according to the extremum of the autofocusing criterion function, which is commonly applied in finding the in-focus amplitude image
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.
Glenn Dietrich Collins
1983-01-01
This thesis describes the development, analysis, and verification of techniques for constructing Fourier transform holograms in light of reduced coherence. The techniques developed are coherent in the sense that they preserve linearity in the complex amplitude associated with the object. Two complementary techniques are developed; one for use in temporally broadband, spatially coherent illumination, and the other for use in
Faster GPS via the Sparse Fourier Transform Haitham Hassanieh Fadel Adib Dina Katabi Piotr Indyk
Faster GPS via the Sparse Fourier Transform Haitham Hassanieh Fadel Adib Dina Katabi Piotr Indyk, fadel, dk, indyk}@mit.edu ABSTRACT GPS is one of the most widely used wireless systems. A GPS re- ceiver the fastest GPS locking algorithm to date. The algorithm reduces the locking complexity to O(n log n). Fur
Filip Govaert; Magali Bernard
2004-01-01
Red spray paints from different European suppliers were characterised to determine the discriminating power of a sequence of analysing techniques. A total of 51 red spray paints were analysed with the help of three techniques: (1) optical microscopy, (2) Fourier transform infrared spectrometry and (3) X-ray fluorescence. Infrared spectra were classified according to binder type, filler and pigment composition and
Mustafa Kansiz; Philip Heraud; Bayden Wood; Frank Burden; John Beardall; Don McNaughton
1999-01-01
Fourier Transform Infrared (FTIR) microspectroscopy, in combination with chemometrics, was investigated as a novel method to discriminate between cyanobacterial strains. In total, 810 absorbance spectra were recorded from one eukaryotic and five cyanobacterial taxa spanning three genera and including two strains of one species, Microcystis aeruginosa. Principal Component Analysis (PCA) based classification techniques such as Soft Independent Modelling of Class
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 ...
P. A. Evans; K. Hawkins; P. R. Williams; R. L. Williams
2008-01-01
We report a study of the coagulation of whole blood by oscillatory shear Fourier transform mechanical spectroscopy. The results include the first identification of the Gel Point of coagulating blood in terms of the Chambon–Winter Gel Point criterion and we show how this may be used as an appropriate basis for detecting the establishment of an incipient clot in samples
Anal. Chem. 1001, 63,55-60 55 Polarization Modulation Fourier Transform Infrared Reflectance
Anal. Chem. 1001, 63,55-60 55 Polarization Modulation Fourier Transform Infrared Reflectance infrared (PM-FTIR) spectroscopy is applied to the reflectance spectra of thin polymer films, and spectral regions. I. INTRODUCTION Infrared reflectance spectroscopy has developed into one of the primary
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
On the use of windows for harmonic analysis with the discrete Fourier transform
FREDRIC J. HARRIS
1978-01-01
This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a
Computer Generation of Fast Fourier Transforms for the Cell Broadband Engine
Franchetti, Franz
Computer Generation of Fast Fourier Transforms for the Cell Broadband Engine Srinivas Chellappa schellap@ece.cmu.edu Franz Franchetti franzf@ece.cmu.edu Markus Püschel pueschel@ece.cmu.edu Department of Electrical and Computer Engineering Carnegie Mellon University Pittsburgh, PA 15213, USA ABSTRACT The Cell
Michael C. Parker; Stuart D. Walker
2002-01-01
The authors present a new Fourier transform theory which provides analytic results for both strongly coupled fiber Bragg grating and photonic crystal filter structures. Trigonometric and hyperbolic descriptions of these important passive optical devices are well known for the regular grating case. However, the unified approach presented here, which is based upon a modified Debye-Waller approach to the analytical solution
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...
Direct monitoring of lipid oxidation in edible oils by Fourier transform Raman spectroscopy
Barbara Muik; Bernhard Lendl; Antonio Molina-Díaz
2005-01-01
Fourier transform Raman spectroscopy has been used to investigate the chemical changes taking place during lipid oxidation in several edible oils. Oxidative degradation of six vegetable oils was accelerated by heating at 160°C. Formation of aldehydes was detected, and saturated as well as ?,?-unsaturated aldehydes could be identified with the help of pure component spectra. The formation of conjugated double
Ahmed Mahgoub; Thanh Nguyen; Raphaël Desbiens; André Zaccarin
2009-01-01
This paper presents an algorithm to align the frames obtained with a non-stationary imaging Fourier transform spectrometer (IFTS). These frames contain both relative motion and intensity variation due to the interference pattern of the IFTS called interferogram. Two motion estimation techniques are combined to register the frames with a sub-pixel precision. An approach based on mutual information is first used
The United States Environmental Protection Agency (U.S. EPA) requires reference spectra to support its gas chromatography/Fourier transform infrared (GC/FT-IR) routine environmental monitoring program. Although on-the-fly (OTF) techniques are needed to satisfy the Agency's high s...
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...
L. E. Rodriguez-Saona; N. Koca; W. J. Harper; V. B. Alvarez
2006-01-01
There is a need for rapid and simple techniques that can be used to predict the quality of cheese. The aim of this research was to develop a simple and rapid screening tool for monitoring Swiss cheese composition by using Fourier transform infrared spectroscopy. Twenty Swiss cheese samples from different manufac- turers and degree of maturity were evaluated. Direct measurements
Use of fast-Fourier-transform computational methods in radiation transport
Burke Ritchie; Pieter G. Dykema; Dennis Braddy
1997-01-01
Fast-Fourier-transform computational methods are used to solve the radiation-transport equation. Results are presented in nondiffusive and diffusive regimes. In the latter regime the method is benchmarked against the Schrödinger equation, which has the form of a diffusion equation in imaginary time. The method is further tested against prototypical problems in radiation transport.
Diomaris Padilla
2008-01-01
The Fourier transform infrared examination of the combustion products of a selection of forest materials has been undertaken in order to guide future detection of biomass burning using satellite remote sensing. Combustion of conifer Pinus strobus (white pine) and deciduous Prunus serotina (cherry), Acer rubrum (red maple), Friglans nigra (walnut), Fraxinus americana (ash), Betula papyrifera (birch), Querus alba (white oak)
A High Precision Scanning Control System For A VUV Fourier Transform Spectrometer
N. de Oliveira; D. Joyeux; D. Phalippou; J. C. Rodier; L. Nahon; F. Polack; M. Vervloeet
2007-01-01
A VUV Fourier transform spectrometer based on a wavefront division interferometer has been built. Our ultimate goal is to provide a high resolution absorption spectrometer in the 140 - 40 nm range using the new third generation French synchrotron source Soleil as the background continuum. Here, we present the design and latest performance of the instrument scanning control system. It
Transmission line fault location estimation by Fourier & wavelet transforms using ANN
A. Abdollahi; S. Seyedtabaii
2010-01-01
Nowadays, power supply has become a business commodity. The quality and reliability of power needs to be maintained in order to obtain optimum performance. Therefore, it is extremely important that transmission line faults from various sources be identified accurately, reliably and be corrected as soon as possible. In this paper, a comparative study of the performance of Fourier transform and
Detection of exposure damage in composite materials using Fourier transform infrared technology
Dennis Patrick Roach; Randy L. Duvall
2010-01-01
Goal: to detect the subtle changes in laminate composite structures brought about by thermal, chemical, ultraviolet, and moisture exposure. Compare sensitivity of an array of NDI methods, including Fourier Transform Infrared Spectroscopy (FTIR), to detect subtle differences in composite materials due to deterioration. Inspection methods applied: ultrasonic pulse echo, through transmission ultrasonics, thermography, resonance testing, mechanical impedance analysis, eddy current,
Applications of Fourier transform infrared spectroscopy to quality control of the epoxy matrix
NASA Technical Reports Server (NTRS)
Antoon, M. K.; Starkey, K. M.; Koenig, J. L.
1979-01-01
The object of the paper is to demonstrate the utility of Fourier transform infrared (FT-IR) difference spectra for investigating the composition of a neat epoxy resin, hardener, and catalysts. The composition and degree of cross-linking of the cured matrix is also considered.
Fourier transform spectroscopy around 3 microns with a broad difference frequency comb
Meek, Samuel A; Guelachvili, Guy; Hänsch, Theodor W; Picqué, Nathalie
2013-01-01
We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.2 microns. High power per comb mode (>10-7 W/mode) is obtained over a broad spectral span (>700 nm). The source is used for direct absorption spectroscopy with a Michelson-based Fourier transform interferometer.
Eng Teo Ong; Heow Pueh Lee; Kian Meng Lim
2004-01-01
A fast algorithm, called the fast Fourier transform on multipoles (FFTM) method, is developed for efficient solution of the integral equation in the boundary element method (BEM). This method employs the multipole and local expansions to approximate far field potentials, and uses the fast Fourier transform (FFT) to accelerate the multipole to local translation operator based on its convolution nature.
Estimation of motions in color image sequences using hypercomplex fourier transforms.
Alexiadis, Dimitrios S; Sergiadis, George D
2009-01-01
Although the motion estimation problem has been extensively studied, most of the proposed estimation approaches deal mainly with monochrome videos. The most usual way to apply them also in color image sequences is to process each color channel separately. A different, more sophisticated approach is to process the color channels in a "holistic" manner using quaternions, as proposed by Ell and Sangwine. In this paper, we extend standard spatiotemporal Fourier-based approaches to handle color image sequences, using the hypercomplex Fourier transform. We show that translational motions are manifested as energy concentration along planes in the hypercomplex 3-D Fourier domain and we describe a methodology to estimate the motions, based on this property. Furthermore, we compare the three-channels-separately approach with our approach and we show that the computational effort can be reduced by a factor of 1/3, using the hypercomplex Fourier transform. Also, we propose a simple, accompanying method to extract the moving objects in the hypercomplex Fourier domain. Our experimental results on synthetic and natural images verify our arguments throughout the paper. PMID:19095528
Truncated sampling for the Fourier-Mellin transform with applications to wideband WVD computation
NASA Astrophysics Data System (ADS)
Allen, Jeffrey
1990-11-01
The Fourier-Mellin transform (FMT) of an input function is defined as and is the magnitude squared of the Mellin transform of the magnitude squared of the Fourier transform of the input function [1]. As such the FMT is unchanged by translations and dilations of the input function. While the FMT has found applications in optical pattern recognition [3] [5] ship classification by sonar and radar [15] and image processing [10] only cursory attention has been paid to the truncation error incurred by using a finite number of samples of the input function. This paper establishes truncation bounds for computing the FMT for band-limited functions from a finite number of samples of the input function. These bounds naturally suggest an implementation of the FMT by the method of direct expansions [4] [14]. This approach readily generalizes to a direct expansion for the Wigner-Ville distribution [13] and the Q distribution [2]. 1 Principal Notation u(x) fff00 e_2tu(t)dt Fourier transform of u M(u s) fD X_i2r8() Mellin transform of u . FM(u s) M(lI(x)I2 s)________ Fourier-Mellin transform of u Q(U V f002rt U(wft)_V(w/fr) Q distribution of U and V W(U V t w) fe_i2ntY U(w + y/2) V(w y/2) dy Wigner-Ville distribution of U and V
Progress Towards Chirped-Pulse Fourier Transform Thz Spectroscopy
NASA Astrophysics Data System (ADS)
Douglass, Kevin O.; Plusquellic, David F.; Gerecht, Eyal
2010-06-01
New opportunities are provided by the development of higher power THz frequency multiplier sources, the development of a broadband Chirped-Pulse FTMW spectroscopy technique at microwave and mm Wave frequencies, and recently demonstrated heterodyne hot electron bolometer detection technology in the THz frequency region with near quantum noise-limited performance and high spectral resolution. Combining these three technologies and extending the chirped-pulse technique to 0.85 THz enables a host of new applications. NIST is currently pursing applications as a point sensor for greenhouse gases, volatile organic compounds, and potentially human breath. The generation and detection of phase stable chirped pulses at 850 GHz will be demonstrated. A description of the experimental setup and preliminary data will be presented for nitrous oxide. G.G. Brown, B.C. Dian, K.O. Douglass, S.M. Geyer, S. Shipman and B.H. Pate, Rev.Sci.Instrum. 79 (2008) 053103. E. Gerecht, D. Gu, L. You, K.S. Yngvesson, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. 56, (2008) 1083.
NASA Astrophysics Data System (ADS)
Borghesani, P.; Pennacchi, P.; Chatterton, S.; Ricci, R.
2014-02-01
Diagnostics of rotating machinery has developed significantly in the last decades, and industrial applications are spreading in different sectors. Most applications are characterized by varying velocities of the shaft and in many cases transients are the most critical to monitor. In these variable speed conditions, fault symptoms are clearer in the angular/order domains than in the common time/frequency ones. In the past, this issue was often solved by synchronously sampling data by means of phase locked circuits governing the acquisition; however, thanks to the spread of cheap and powerful microprocessors, this procedure is nowadays rarer; sampling is usually performed at constant time intervals, and the conversion to the order domain is made by means of digital signal processing techniques. In the last decades different algorithms have been proposed for the extraction of an order spectrum from a signal sampled asynchronously with respect to the shaft rotational velocity; many of them (the so called computed order tracking family) use interpolation techniques to resample the signal at constant angular increments, followed by a common discrete Fourier transform to shift from the angular domain to the order domain. A less exploited family of techniques shifts directly from the time domain to the order spectrum, by means of modified Fourier transforms. This paper proposes a new transform, named velocity synchronous discrete Fourier transform, which takes advantage of the instantaneous velocity to improve the quality of its result, reaching performances that can challenge the computed order tracking.
Sene, CFB.; McCann, M. C.; Wilson, R. H.; Grinter, R.
1994-01-01
Infrared and Raman spectra of sequentially extracted primary cell walls and their pectic polymers were obtained from five angiosperm plants. Fourier-transform Raman spectrometry was shown to be a powerful tool for the investigation of primary cell-wall architecture at a molecular level, providing complementary information to that obtained by Fourier-transform infrared microspectroscopy. The use of an extraction procedure using imidazole instead of cyclohexane trans-1,2-N,N,N[prime],N[prime]-diaminotetraacetate allows the extension of the infrared spectral window for data interpretation from 1300 to 800 cm-1, to 2000 to 800 cm-1, and allows us to obtain Raman spectra from extracted cell-wall material. Wall constituents such as pectins, proteins, aromatic phenolics, cellulose, and hemicellulose have characteristic spectral features that can be used to identify and/or fingerprint these polymers without, in most cases, the need for any physical separation. The Gramineae (rice [Oryza sativa], polypogon [Polypogon fugax steud], and sweet corn [Zea mays]) are spectroscopically very different from the nongraminaceous monocotyledon (onion [Allium cepa]) and the dicotyledon (carrot [Daucus carota]); this reflects differences in chemical composition and cross-linking of the walls. The possibility of a taxonomic classification of plant cell walls based on infrared and Raman spectroscopies and the use of spectral fingerprinting for authentication and detection of adulteration of products rich in cell-wall materials are discussed. PMID:12232436
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.
Ito, Satoshi; Yamada, Yoshifumi
2008-08-01
An image reconstruction technique that reduces aliasing artifacts by scalable image reconstruction in magnetic resonance imaging (MRI) is proposed. The signal obtained by the phase-scrambling Fourier transform (PSFT) imaging technique can be transformed to the signal described in the Fresnel transform equation of the objects. Therefore, image reconstruction can be performed not only by inverse FT but also by inverse Fresnel transform. When a phase-scrambling coefficient is given in a certain range, image reconstruction by inverse Fresnel transform allows shrinking of images over rather wide scales. Thus, reduced aliasing images can be reconstructed even from signals that produce serious aliasing artifacts by standard inverse FT reconstruction. Simulation and experimental studies reveal that the proposed method can be used to produce reduced aliasing images. PMID:18666133
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.
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.
Multiple-image encryption based on phase mask multiplexing in fractional Fourier transform domain.
Liansheng, Sui; Meiting, Xin; Ailing, Tian
2013-06-01
A multiple-image encryption scheme is proposed based on the phase retrieval process and phase mask multiplexing in the fractional Fourier transform domain. First, each original gray-scale image is encoded into a phase only function by using the proposed phase retrieval process. Second, all the obtained phase functions are modulated into an interim, which is encrypted into the final ciphertext by using the fractional Fourier transform. From a plaintext image, a group of phase masks is generated in the encryption process. The corresponding decrypted image can be recovered from the ciphertext only with the correct phase mask group in the decryption process. Simulation results show that the proposed phase retrieval process has high convergence speed, and the encryption algorithm can avoid cross-talk; in addition, its encrypted capacity is considerably enhanced. PMID:23722815
Representation of the Fourier transform as a weighted sum of the complex error functions
S. M. Abrarov; B. M. Quine
2015-07-05
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 availability of the rapid and highly accurate rational approximations for the complex error function, the numerical computation of the forward and inverse Fourier transforms is advantageous in practical applications. The weighted sum of the complex error functions sustains accuracy despite increasing oscillatory behavior that occurs due to presence of the exponential multiplier $e^{\\pm 2\\pi i \
Zhao, Jianlin; Jiang, Hongzhen; Di, Jianglei
2008-02-18
The numerical recording and reconstruction of a color holographic image are achieved by using digital lensless Fourier transform holography. Firstly, for a color object, three monochromatic digital holograms with different wavelengths (red, green, blue) are recorded by a black-white CCD, respectively. Then the reconstructed monochromatic holographic images (red, green, blue) are adjusted to be same in size through padding digital holograms with zeros, and the corresponding digital color holographic image is acquired by accurately syncretizing the resized reconstructed monochromatic images. One of the advantages using lensless Fourier transform holography is that it can well assure the precise superposition of the reconstructed images. By applying median filtering technique and superposing the speckle fields with different distributions, the speckle noises are well suppressed and the quality of the digital color holographic image is greatly improved. This digital color holography with high quality of reconstruction effect would have potential applications on digital holographic display of color objects. PMID:18542331
Tabletop single-shot extreme ultraviolet Fourier transform holography of an extended object.
Malm, Erik B; Monserud, Nils C; Brown, Christopher G; Wachulak, Przemyslaw W; Xu, Huiwen; Balakrishnan, Ganesh; Chao, Weilun; Anderson, Erik; Marconi, Mario C
2013-04-22
We demonstrate single and multi-shot Fourier transform holography with the use of a tabletop extreme ultraviolet laser. The reference wave was produced by a Fresnel zone plate with a central opening that allowed the incident beam to illuminate the sample directly. The high reference wave intensity allows for larger objects to be imaged compared to mask-based lensless Fourier transform holography techniques. We obtain a spatial resolution of 169 nm from a single laser pulse and a resolution of 128 nm from an accumulation of 20 laser pulses for an object ~11x11?m(2) in size. This experiment utilized a tabletop extreme ultraviolet laser that produces a highly coherent ~1.2 ns laser pulse at 46.9 nm wavelength. PMID:23609701
NASA Astrophysics Data System (ADS)
Cui, Huakun; Wang, Dayong; Wang, Yunxin; Liu, Changgeng; Zhao, Jie; Li, Yan
2010-10-01
As the lensless Fourier transform digital holography is applied into the microscopic phase-contrast imaging on the live cells, the motion of the cells will lead to the non-coplanarity phenomena between the object and the reference source. This could result in the imaging aberration. An effective and robust autofocus procedure based on the phase distribution is presented in the paper. With the initial measurement of the distance between the reference source and the hologram, the optimum parameters corresponding to the phase-contrast image can be achieved by a single hologram, combined with the linearity fitting. The lensless Fourier transform digital holographic system is built and the experiments on the phase-contrast imaging of the live cervical carcinoma cells are performed. Finally, the good experiment results are demonstrated. Both the theoretical analysis and the experimental investigation verify the feasibility and validity of the automatic procedure for the non-coplanar aberration compensation.
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 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
Shi, Xiaoyan; Zhao, Daomu
2011-02-10
Based on joint transform correlator (JTC) architecture and holographic techniques, a new method for image hiding is presented. A hidden image encrypted by JTC architecture is embedded in the Fourier hologram of the host image. Inverse Fourier transform can be used to obtain the watermarked image, and JTC architecture is used to decode the hidden image from the watermarked hologram. Unlike other watermarking techniques, by prechoosing information, the noise added to the recovered hidden image by the host can be reduced. Unlike other watermarking systems based on double random-phase encoding, no conjugate key is used to recover the hidden image. Theoretical analyses have shown the system's feasibility. Computer simulations are presented to verify the system's validity and efficiency. Numerical simulations also show that the proposed system is robust enough to resist attacks, such as occlusion, noise, and filtering. PMID:21343999
Image encryption based on extended fractional Fourier transform and digital holography technique
NASA Astrophysics Data System (ADS)
Wang, Xiaogang; Zhao, Daomu; Chen, Linfei
2006-04-01
We present a new optical image encryption algorithm that is based on extended fractional Fourier transform (FRT) and digital holography technique. We can perform the encryption and decryption with more parameters compared with earlier similar methods in FRT domain. In the extended FRT encryption system, the input data to be encrypted is extended fractional Fourier transformed two times and random phase mask is placed at the output plane of the first extended FRT. By use of an interference with a wave from another random phase mask, the encrypted data is stored as a digital hologram. The data retrieval is operated by all-digital means. Computer simulations are presented to verify its validity and efficiency.
Suzuki, M. [Japan Synchrotron Radiation Research Institute/Spring-8, Sayo, Hyogo 671-5198 (Japan); Kondo, Y. [Akita Research and Development Center, Akita 010-1623 (Japan); Isogami, S.; Tsunoda, M. [Department of Electronic Engineering, Tohoku University, Sendai 980-8579 (Japan); Takahashi, S.; Ishio, S. [Faculty of Engineering and Resource Science, Akita University, Akita 010-8502 (Japan)
2011-09-09
We present a fabrication method for a reference source that is efficient when used for lensless Fourier transform holography. This method produces a reference source that yields high spatial resolution and enhanced signal-to-noise ratio in a Fourier-transformed real-space image, and is particularly useful for Fourier transform holography experiments in the hard x-ray region.
NASA Astrophysics Data System (ADS)
Suzuki, M.; Kondo, Y.; Isogami, S.; Tsunoda, M.; Takahashi, S.; Ishio, S.
2011-09-01
We present a fabrication method for a reference source that is efficient when used for lensless Fourier transform holography. This method produces a reference source that yields high spatial resolution and enhanced signal-to-noise ratio in a Fourier-transformed real-space image, and is particularly useful for Fourier transform holography experiments in the hard x-ray region.
M. Suzuki; Y. Kondo; S. Isogami; M. Tsunoda; S. Takahashi; S. Ishio
2011-01-01
We present a fabrication method for a reference source that is efficient when used for lensless Fourier transform holography. This method produces a reference source that yields high spatial resolution and enhanced signal-to-noise ratio in a Fourier-transformed real-space image, and is particularly useful for Fourier transform holography experiments in the hard x-ray region.
Main fatty acid classes in vegetable oils by SB-ATR-Fourier transform infrared (FTIR) spectroscopy
S. T. H. Sherazi; M. Younis Talpur; S. A. Mahesar; Aftab A. Kandhro; Sarfraz Arain
2009-01-01
The prospect of using single bounce attenuated total reflectance (SB-ATR)-Fourier transform infrared (FTIR) spectroscopy as a rapid quantitative tool to determine the main fatty acid groups present in different edible oils was investigated. Partial least squares (PLS) calibrations were developed using SB-ATR-FTIR spectra which were associated with fatty acid groups (saturated, trans, mono- and polyunsaturated) using quantitative data obtained by
Fourier and Wavelet Transformations for the Fault Detection of Induction Motor with Stator Current
Sang-hyuk Lee; Seong-pyo Cheon; Youn Tae Kim; Sungshin Kim
2006-01-01
\\u000a In this literature, fault detection of an induction motor is carried out using the information of stator current. After preprocessing\\u000a actual data, Fourier and Wavelet transforms are applied to detect characteristics under the healthy and various faulted conditions.\\u000a The most reliable phase current among 3-phase currents is selected by the fuzzy entropy. Data are trained with a neural network\\u000a system,
Sang-hyuk Lee; Yi-qi Wang; Jung-il Song
2010-01-01
Fault detection of an induction motor was carried out using the information of the stator current. After synchronizing the\\u000a actual data, Fourier and wavelet transformations were adopted in order to obtain the sideband or detail value characteristics\\u000a under healthy and various faulty operating conditions. The most reliable phase current among the three phase currents was\\u000a selected using an approach that
Fourier and Wavelet Transformations for the Fault Detection of Induction Motor with Stator Current
Sang-Hyuk Lee; Seong-Pyo Cheon; Yountae Kim; Sungshin Kim
\\u000a In this literature, fault detection of an induction motor is carried out using the information of stator current. After preprocessing\\u000a actual data, Fourier and Wavelet transforms are applied to detect characteristics under the healthy and various faulted conditions.\\u000a The most reliable phase current among 3-phase currents is selected by the fuzzy entropy. Data are trained with a neural network\\u000a system,
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
Nina Pan; Xiaoqiang Cai; Kai Tang; Guolin Zou
2005-01-01
Chemical unfolding of bovine testicular hyaluronidase (HAase) has been studied by fluorescence spectroscopy and Fourier transformed\\u000a infrared spectroscopy (FTIR). Thermodynamic parameters were determined for unfolding HAase from changes in the intrinsic fluorescence\\u000a emission intensity and the formations of several possible unfolding intermediates have been identified. This was further confirmed\\u000a by representation of fluorescence data in terms of ‘phase diagram’. The
Si Wu; Kai Zhang; Nathan K. Kaiser; James E. Bruce; David C. Prior; Gordon A. Anderson
2006-01-01
Flared inlet capillary tubes have been coupled with a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer\\u000a to help the ion transmission from the atmospheric pressure to the first vacuum region. We investigated different types of\\u000a atmospheric pressure ionization methods using flared inlet tubes. For most of the ionization methods, such as ESI and DESI,\\u000a increased ion current transmitted from
Metrology for an imaging Fourier transform spectrometer working in the far-UV (IFTSUV)
NASA Astrophysics Data System (ADS)
Ruiz de Galarreta Fanjul, C.; Philippon, A.; Vial, J.-C.; Maillard, J.-P.; Appourchaux, T.
2011-10-01
Imaging Fourier Transform Spectrometer working in the far UV (IFTSUV) may be the technical solution to answer many unsolved problems concerning the physics of the solar outer atmosphere. The VUV domain highly constrains the instruments design and performances as it demands a high optics surface quality and an accurate metrology to preserve IFTSUV spectral precision and Signal to Noise Ratio (SNR). We present the advancements on the specification of a metrology system, meeting the predicted performance requirements of an IFTSUV.
KC Schuster; R Goodacre; JR Gapes; M Young
2001-01-01
Strain degeneration in solventogenic clostridia is a known problem in the technical acetone–butanol fermentation bioprocess,\\u000a especially in the continuous process mode. Clostridial strain degeneration was studied by Fourier transform infrared (FT-IR)\\u000a spectroscopy of the bacterial cells. Degenerative variant formation in two strains, Clostridium beijerinckii NCIMB 8052 and Clostridium species AA332, was detected spectroscopically. Colonies on solid media were sampled, or
Arwah J. Jaber; Charles L. Wilkins
2005-01-01
The traditional solvent-based matrix-assisted laser desorption ionization (MALDI) preparation method has been used to analyze\\u000a nonpolar polymers of various molecular weights. High resolution silver cationized oligomers with masses of up to 12 KDa were\\u000a measured using 9.4 tesla Fourier transform mass spectrometry (FTMS) with an external ionization source. It was observed that\\u000a when time-of-flight mass spectrometry was used, the spectra
NASA Technical Reports Server (NTRS)
Powers, E. J.; Kim, Y. C.; Hong, J. Y.; Roth, J. R.; Krawczonek, W. M.
1978-01-01
A diagnostic, based on fast Fourier-transform spectral analysis techniques, that provides experimental insight into the relationship between the experimentally observable spectral characteristics of the fluctuations and the fluctuation-induced plasma transport is described. The model upon which the diagnostic technique is based and its experimental implementation is discussed. Some characteristic results obtained during the course of an experimental study of fluctuation-induced transport in the electric field dominated NASA Lewis bumpy torus plasma are presented.
G. CLIFFORD CARTER; CHARLES H. KNAPP; ALBERT H. NUTTALL
1973-01-01
A method for estimating the magnitude-squared coherence function for two zero-mean wide-sense-stationary random processes is presented. The estimation technique utilizes the weighted overlapped segmentation fast Fourier transform approach. Analytical and empirical results for statistics of the estimator are presented. The analytical expressions are limited to the nonoverlapped case; empirical results show a decrease in bias and variance of the estimator
A. Rohman; Y. B. Che Man
2010-01-01
Fourier transform infrared (FTIR) spectroscopy has been developed for analysis of extra virgin olive oil (EVOO) adulterated with palm oil (PO). Measurements were made on pure EVOO and that adulterated with varying concentrations of PO (1.0–50.0% wt.\\/wt. in EVOO). Two multivariate calibrations, namely partial least square (PLS) and principle component regression (PCR) were optimized for constructing the calibration models, either
Y. B Che Man; G Setiowaty
1999-01-01
The Fourier transform infrared (FT–IR) spectra of palm oil samples, in the range between 3025 and 2992 cm?1, were used to compare different multivariate calibration techniques for quantitative iodine value (IV) determination. Forty-two spectra of palm oil with IV ranging between 53 and 65 were used to create calibration models based on partial least squares (PLS) and principle component regression
Representation and Identification of Nonlinear Systems in the Short-Time Fourier Transform Domain
Yekutiel Avargel; Israel Cohen
In this chapter, we introduce a novel approach for improved nonlinear system identification in the short-time Fourier transform\\u000a (STFT) domain. We first derive explicit representations of discrete-time Volterra filters in the STFT domain. Based on these\\u000a representations, approximate nonlinear STFT models, which consist of parallel combinations of linear and nonlinear components,\\u000a are developed. The linear components are represented by crossband
Linear System Identification in the Short-Time Fourier Transform Domain
Yekutiel Avargel; Israel Cohen
Identification of linear systems in the short-time Fourier transform (STFT) domain has been studied extensively, and many\\u000a efficient algorithms have been proposed for that purpose. In this chapter, we introduce three models for linear system identification\\u000a in the STFT domain, and investigate the influence of model order on the estimation accuracy. The first model, which forms\\u000a a perfect STFT representation
Performance of the Fourier transform spectrometer (FTS) for FIS onboard ASTRO-F
Noriko Murakami; Mitsunobu Kawada; Hidenori Takahashi; Keita Ozawa; Tetsuo Imamura; Hiroshi Shibai; Takao Nakagawa
2004-01-01
We have developed the imaging Fourier Transform Spectrometer (FTS) for the FIS (Far-Infrared Surveyor) onboard the ASTRO-F satellite. A Martin-Puplett interferometer is adopted to achieve high optical efficiency in a wide wavelength range. The total optical efficiency of this spectrometer is achieved 40-80% of the ideal value which is 25% of the incident flux. The wavelength range of 50-200mum is
Michael Voit
1991-01-01
We show that the support of the Fourier transform of a positive, positive definite measure on a commutative hypergroupK contains a positive character. This generalizes the known fact that the support of the Plancherel measure ? contains a positive\\u000a character (which in general is not the identity character1). It follows that\\u000a $$supp(\\\\delta _\\\\alpha * \\\\delta _{\\\\bar \\\\alpha } )$$\\u000a contains
Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform
Lisa A. Poyneer; Donald T. Gavel; James M. Brase
2002-01-01
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 propa- gation comparable with that of, traditional vector-matrix-multiply reconstructors. The boundary problem that
Development of Scanning-Type X-ray Fourier Transform Holography
K. Nomura; N. Awaji; S. Doi; S. Isogami; K. Kodama; T. Nakamura; M. Suzuki; M. Tsunoda
2011-01-01
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
NASA Astrophysics Data System (ADS)
Sheoran, Gyanendra; Anand, Arun; Shakher, Chandra
2009-05-01
Lensless Fourier transform digital holographic technique is applied for measurement of diffusion in miscible transparent liquid solutions. The phase information at two time instances and a synthetic plane wavefront is used to determine the diffusion coefficient. The experiment was conducted to measure the diffusion coefficient of aqueous solution of NaCl in water. The measured values of diffusion coefficient deviates approximately 1.06% from the values given in literature.
Color holographic image by using digital lensless Fourier transform holography with optical fiber
NASA Astrophysics Data System (ADS)
Chen, Li; Ma, Xiao; Wang, Qu
2012-04-01
A new method of lensless Fourier transform holography for color reconstruction image is presented. With this method, the recording distance can be kept invariant in recording process. The resolutions of reconstruction images can be adjusted in the same recording distance. Three lasers with different wavelengths are used in an experimental setup to synthesize a color image in a reconstruction process. An optical fiber is used effectively, and the quality of the reconstruction image is improved after filter operation.
Gyanendra Sheoran; Shobhna Sharma; Chandra Shakher
2011-01-01
We have proposed and demonstrated a new application of lensless Fourier transform digital holographic interferometry to study\\/monitor the drying process and detection of cracking\\/disbonding of the painted surface by observing the dynamics of interference phase maps. The technique can monitor the rate of drying of paint and visualize the state of dryness and crack\\/disbond. The technique is simple and easy
NASA Astrophysics Data System (ADS)
Sheoran, Gyanendra; Sharma, Shobhna; Shakher, Chandra
2011-01-01
We have proposed and demonstrated a new application of lensless Fourier transform digital holographic interferometry to study/monitor the drying process and detection of cracking/disbonding of the painted surface by observing the dynamics of interference phase maps. The technique can monitor the rate of drying of paint and visualize the state of dryness and crack/disbond. The technique is simple and easy to implement.
Sheoran, Gyanendra; Anand, Arun; Shakher, Chandra
2009-05-01
Lensless Fourier transform digital holographic technique is applied for measurement of diffusion in miscible transparent liquid solutions. The phase information at two time instances and a synthetic plane wavefront is used to determine the diffusion coefficient. The experiment was conducted to measure the diffusion coefficient of aqueous solution of NaCl in water. The measured values of diffusion coefficient deviates approximately 1.06% from the values given in literature. PMID:19485491
Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms
D. F. McAlister; M. Beck; L. Clarke; A. Mayer; M. G. Raymer
1995-01-01
Phase-space tomography is experimentally demonstrated for the determination of the spatially varying amplitude and phase of a quasi-monochromatic optical f ield by measurements of intensity only. Both fully and partially coherent sources are characterized. The method, which makes use of the fractional-order Fourier transform, also yields the Wigner distribution of the f ield and works in one or two dimensions.
Short-time fourier transform based analysis to characterization of series arc fault
Cheng Hong; Chen Xiaojuan; Xiao Wei; Wang Cong
2009-01-01
Considering the non-periodic and non-stationary signatures of series arc fault current signals, a time-frequency analyzing method for series arc faults detection is presented based on short-time Fourier transform. The algorithm of STFT using the Hanning window function is described in detail, in which the length of the window function and the sliding step parameters are discussed to obtain 20 ms
Toney, M.L.
1999-07-01
The purpose of this testing program is to obtain uncontrolled and controlled hydrogen chloride (HCl) and speciated hydrocarbon Hazardous Air Pollutants (HAPs) emissions data from lime production plants to support a national emission standard for hazardous air pollutants (NESHAP). This report presents data from the Fourier Transform Infrared Spectroscopy (FTIR) measurements. FTIR source testing was conducted for the following purposes: Quantify HCl emission levels; and Gather screening (i.e., qualitative) data on other HAP emissions.
Feit, M D; Fleck, J A
1989-07-01
We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage. PMID:19752928
Feit, M. D.; Fleck, J. A., Jr.
1989-07-01
We describe a spectral method for solving the paraxial wave equation incylindrical geometry that is based on expansion of the exponential evolutionoperator in a Taylor series and use of fast Fourier transforms to evaluatederivatives. A fourth-order expansion gives excellent agreement with atwo-transverse-dimensional split-operator calculation at a fraction of the costin computation time per /ital z/ step and at a considerable savings in storage.
Local Fourier transform and epsilon factors joint work with Ahmed Abbes
Bannai, Kenichi
and the product formula: L(F, t) = (F)t-(CÂ¯k,F) L(F , (qt)-1 ). 1 #12;(F) = xC x(Fx). The local epsilon factors xLocal Fourier transform and epsilon factors joint work with Ahmed Abbes July 3, 2008, 17:00-18:00, at the Univ. of Tokyo Abstract The local epsilon factors appear in the constant term of the functional equa
Jacob L. Harley; Kevin C. Gross
2011-01-01
A Telops Hyper-Cam midwave infrared (1.5 - 5.5mum) imaging Fourier-transform spectrometer (IFTS) was used to estimate industrial smokestack total effluent mass flow rates by combining spectrally-determined species concentrations with flow rates estimated via analysis of sequential images in the raw interferogram cube. Measurements of the coalburning smokestack were made with the IFTS at a stand-off distance of 350m. 185 hyperspectral
Direct Reconstruction of Non-Cartesian k-Space Data Using a Nonuniform Fast Fourier Transform
Gordon E. Sart; Raoqiong Bennett; Robert W. Co
2001-01-01
An algorithm of Dutt and Rokhlin (SIAM J Sci Comput 1993;14: 1368 -1383) for the computation of a fast Fourier transform (FFT) of nonuniformly-spaced data samples has been extended to two dimensions for application to MRI image reconstruction. The 2D nonuniform or generalized FFT (GFFT) was applied to the reconstruction of simulated MRI data collected on radially oriented sinusoidal excursions
Analysis of Cod-Liver Oil Adulteration Using Fourier Transform Infrared (FTIR) Spectroscopy
Abdul Rohman; Yaakob B. Che Man
2009-01-01
Analysis of the adulteration of cod-liver oil with much cheaper oil-like animal fats has become attractive in recent years.\\u000a This study highlights an application of Fourier transform infrared (FTIR) spectroscopy as a nondestructive and fast technique\\u000a for the determination of adulterants in cod-liver oil. Attenuated total reflectance measurements were made on pure cod-liver\\u000a oil and cod-liver oil adulterated with different
The Laser Induced Fluorescence Spectrum of Te2 Studied by Fourier Transform Spectrometry
J. Vergès; C. Effantin; O. Babaky; J. d'Incan; S. J. Prosser; R. F. Barrow
1982-01-01
Laser induced fluorescence spectra of separated isotope tellurium dimers, 130Te2 and 128Te2, have been recorded with high precision Fourier transform spectrometry. Fixed frequency argon ion and krypton ion exciting lines ranging from 5145 Å to 4067 Å have been used and 64 series in 130Te2 and 32 in 128Te2 have been assigned and analyzed. Transitions involving four upper states, A0u+,
An FPGA-based Focal Plane Array interface for the Panchromatic Fourier Transform Spectrometer
Dmitriy L. Bekker; Jean-Francois L. Blavier; Richard W. Key; David M. Rider; Stanley P. Sander
2011-01-01
Panchromatic Fourier Transform Spectrometer (PanFTS) is an Instrument Incubator Program (IIP) funded development to build and demonstrate a single instrument ca- pable of meeting or exceeding the requirements of the Geo- stationary Coastal and Air Pollution Events (GEO-CAPE) mission. The PanFTS design provides atmospheric measure- ment capabilities in the IR and UV-Vis by using imaging FTS to provide full spatial
Implemention of 128Point Fast Fourier Transform Processor for UWB Systems
Sang-In Cho; Kyu-Min Kang; Sang-Sung Choi
2008-01-01
In this paper, we present a 4-parallel fast Fourier transform (FFT) processor for a multi-band orthogonal frequency division multiplexing (MB-OFDM) ultra wideband (UWB) system. The proposed FFT processor utilizes radix-24 structure so as to significantly enhance the hardware complexity by reducing the numbers of multipliers and adders. The hardware efficient 4-parellel 128-point FFT processor employing the decimation-in-frequency (DIF) and the
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
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
On q-EXTENSIONS of Mehta's Eigenvectors of the Finite Fourier Transform
NASA Astrophysics Data System (ADS)
Atakishiyev, Natig M.
Mehta has shown that eigenvectors Fj(k) of the finite Fourier transform with the matrix Aj,k(N): = (1)/(? {N)}exp ((2? i)/(N)jk; ), 0 ? j, k ? N-1, can be defined in terms of the classical Hermite functions { H}k(x) := Hk(x)exp (-x2/2) as Fj(k):= ? n=-? ? { H}k(x_n(j)), where xn(j) := ? {(2? )/(N)}(nN+j). We argue that the finite Fourier transform Aj,k(N) does actually govern also some q-extensions of Mehta's eigenvectors Fj(k), associated with certain well-known orthogonal q-polynomial families. For the pairs of the continuous q-Hermite and q-1-Hermite polynomials, the Rogers-Szeg? and Stieltjes-Wigert polynomials, and the discrete q-Hermite polynomials of types I and II such links are explicitly derived. In the limit when the base q ? 1 these q-extensions coincide with Mehta's eigenvectors Fj(k), whereas in the continuous limit (i.e. when the parameter N ? ?) they correspond to the classical Fourier integral transforms between the above-mentioned pairs of q-polynomial families.
High-SNR static Fourier-transform imaging spectrometer based on differential structure
NASA Astrophysics Data System (ADS)
Jin, Peng; Zhu, Shuaishuai; Zhang, Yu; Lin, Jie
2015-03-01
Fourier-transform imaging spectrometers are rapidly developed due to their extensive use in industrial monitoring, target detection, and chemical identification. Static Fourier-transform imaging spectrometer (SFIS) containing a birefringent interferometer is one of the most popular directions due to its inherent robustness. However, the SFIS suffers from its low achievable signal-to-noise ratio (SNR) because of the restriction of incident angle. Meanwhile, in applications, the SNR is perhaps the most important factor to determine the usefulness of an instrument. In this paper, we report here a Static Fourier-transform imaging spectrometer based on differential structure (SFIS-DS) in the 400-800nm wavelength range with a high SNR. As in electronic system, the differential structure can double optical efficiency and strongly restrain common mode error in the SFIS-DS. And the differential structure described here is also available for any instruments containing a birefringent interferometer. However, the drawback of the SFIS-DS is that the two images obtained by the two differential channels need precise registration which can be overcome by a sub-pixel spatial registration algorithm. The experimental results indicate the SFIS-DS can increase the SNR by no less than 40%.
Single-channel color image encryption based on iterative fractional Fourier transform and chaos
NASA Astrophysics Data System (ADS)
Sui, Liansheng; Gao, Bo
2013-06-01
A single-channel color image encryption is proposed based on iterative fractional Fourier transform and two-coupled logistic map. Firstly, a gray scale image is constituted with three channels of the color image, and permuted by a sequence of chaotic pairs which is generated by two-coupled logistic map. Firstly, the permutation image is decomposed into three components again. Secondly, the first two components are encrypted into a single one based on iterative fractional Fourier transform. Similarly, the interim image and third component are encrypted into the final gray scale ciphertext with stationary white noise distribution, which has camouflage property to some extent. In the process of encryption and description, chaotic permutation makes the resulting image nonlinear and disorder both in spatial domain and frequency domain, and the proposed iterative fractional Fourier transform algorithm has faster convergent speed. Additionally, the encryption scheme enlarges the key space of the cryptosystem. Simulation results and security analysis verify the feasibility and effectiveness of this method.
Camino, Fernando E.; Nam, Chang-Yong; Pang, Yutong T.; Hoy, Jessica; Eisaman, Matthew D.; Black, Charles T.; Sfeir, Matthew Y.
2014-01-01
We present a methodology for probing light-matter interactions in prototype photovoltaic devices consisting of an organic semiconductor active layer with a semitransparent metal electrical contact exhibiting surface plasmon-based enhanced optical transmission. We achieve high-spectral irradiance in a spot size of less than 100??m using a high-brightness laser-driven light source and appropriate coupling optics. Spatially resolved Fourier transform photocurrent spectroscopy in the visible and near-infrared spectral regions allows us to measure external quantum efficiency with high sensitivity in small-area devices (<1?mm2). This allows for rapid fabrication of variable-pitch sub-wavelength hole arrays in metal films for use as transparent electrical contacts, and evaluation of the evanescent and propagating mode coupling to resonances in the active layer. PMID:25705085
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 ...
Jas, Gouri S.; Wan, Chaozhi; Johnson, Carey K.
1995-05-01
Picosecond Time-Resolved Fourier Transform Raman Spectroscopy of 9,10-Diphenylanthracene i the Excited Singlet State GOURI S. JAS, CHAOZHI WAN, and CAREY K. JOHNSON* Department ofChemistry, University of Kansas, Lawrence, Kansas 66045 Time...
Technology Transfer Automated Retrieval System (TEKTRAN)
Analysis of DNA samples of Salmonella serotypes (Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky) were performed using Fourier transform infrared spectroscopy (FT-IR) spectrometer by placing directly in contact with a diamond attenua...
Franchetti, Franz
1 Discrete Fourier Transform on Multicores Franz Franchetti, Markus P¨uschel, Yevgen Voronenko is on Intel compatible multicores but we also discuss the IBM Cell, and briefly, graphics processing units
Transformations between symmetric sets of quantum states
Vedran Dunjko; Erika Andersson
2012-06-22
We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state discrimination, and as interfaces between systems whose information encodings are not related by a unitary transform, such as continuous-variable systems and finite-dimensional systems. In a probabilistic transform, information may be lost or leaked, and we explain the concepts of leak and redundancy. Following this, we show how the analysis of probabilistic transforms significantly simplifies for symmetric source and target sets of states. In particular, we give a simple linear program which solves the task of finding optimal transforms, and a method of characterizing the introduced leak and redundancy in information-theoretic terms. Using the developed techniques, we analyse a class of transforms which convert coherent states with information encoded in their relative phase to symmetric qubit states. Each of these sets of states on their own appears in many well studied quantum information protocols. Finally, we suggest an asymptotic realization based on quantum scissors.
NASA Astrophysics Data System (ADS)
Kendall, Anthony D.; Hyndman, David W.
Important characteristics of watershed processes can be extracted from hydrologic data using spectral methods. We extract quantitative information from precipitation, stream discharge, and groundwater head data from watersheds in northern-lower Michigan using Fourier Transform (FT) methods. By comparing the spectra of these data using similar units, we graphically illustrate the hydrologic processes that link precipitation to stream discharge and groundwater levels including evapotranspiration. We also demonstrate how unit hydrographs can be efficiently and non-parametrically derived using the FT in a manner that allows for a quantitative seasonal comparison of precipitation and the resulting stream discharge response. This analysis clearly illustrates the reduction in summer discharge levels due to canopy interception and evapotranspiration. We also develop a systematic application of the FT we call the Scaled-Windowed Fourier Transform (SWFT), which extracts time-varying spectral content using a similar approach to the wavelet transform. While computationally less efficient than the wavelet transform, the SWFT allows for embedded detrending and tapering. Application of this method clearly illustrates the non-stationarities of spectral content within the three chosen data types, leading to a greater understanding of discharge-generating processes.
D. Fu; K. Sung; K. A. Walker; C. D. Boone; P. F. Bernath
2006-01-01
Carbon Cycle Science by Fourier Transform Spectroscopy (CC-FTS) is an advanced study for a future satellite mission. The goal of this mission is to obtain a better understanding of the carbon cycle in the Earth's atmosphere by monitoring total columns of greenhouse gases CO2, CH4 and N2O plus CO and O2. A Fourier transform spectrometer (maximum spectral resolution of 0.2
Digital watermarking algorithm research of color images based on quaternion Fourier transform
NASA Astrophysics Data System (ADS)
An, Mali; Wang, Weijiang; Zhao, Zhen
2013-10-01
A watermarking algorithm of color images based on the quaternion Fourier Transform (QFFT) and improved quantization index algorithm (QIM) is proposed in this paper. The original image is transformed by QFFT, the watermark image is processed by compression and quantization coding, and then the processed watermark image is embedded into the components of the transformed original image. It achieves embedding and blind extraction of the watermark image. The experimental results show that the watermarking algorithm based on the improved QIM algorithm with distortion compensation achieves a good tradeoff between invisibility and robustness, and better robustness for the attacks of Gaussian noises, salt and pepper noises, JPEG compression, cropping, filtering and image enhancement than the traditional QIM algorithm.
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
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.
A new iterative Fourier transform algorithm for optimal design in holographic optical tweezers
NASA Astrophysics Data System (ADS)
Memmolo, P.; Miccio, L.; Merola, F.; Ferraro, P.; Netti, P. A.
2012-06-01
We propose a new Iterative Fourier Transform Algorithm (IFTA) capable to suppress ghost traps and noise in Holographic Optical Tweezers (HOT), maintaining a high diffraction efficiency in a computational time comparable with the others iterative algorithms. The process consists in the planning of the suitable ideal target of optical tweezers as input of classical IFTA and we show we are able to design up to 4 real traps, in the field of view imaged by the microscope objective, using an IFTA built on fictitious phasors, located in strategic positions in the Fourier plane. The effectiveness of the proposed algorithm is evaluated both for numerical and optical reconstructions and compared with the other techniques known in literature.
Rice, S.B.; Freund, H.; Huang, W.L.; Clouse, J.A. [Exxon Production Research Co., Houston, TX (United States); Isaacs, C.M. [Geological Survey, Menlo Park, CA (United States)
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.
Algorithms of the q2r× q2r-point 2D discrete Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, the concept of partitions revealing the two-dimensional discrete Fourier transform (2-D DFT) of order q2r × q2r, where r > 1 and q is a positive odd number, is described. Two methods of calculation of the 2-D DFT are analyzed. The q2r × q2r-point 2-D DFT can be calculated by the traditional column-row method with 2(q2r) 1-D DFTs, and we propose the fast algorithm which splits each 1-D DFT by the short transforms by means of the fast paired transforms. Another effective algorithm of calculation of the q2r × q2r-point 2-D DFT is based on the tensor or paired representations of the image when the image is represented as a set of 1-D signals which define the 2-D transform in the different subsets of frequency-points and they all together cover the complete set of frequencies. In this case, the splittings of the q2r × q2r-point 2-D DFT are performed by the 2-D discrete tensor or paired transforms, respectively, which lead to the calculation with a minimum number of 1-D DFTs. Examples of the transforms and computational complexity of the proposed algorithms are given.
NASA Astrophysics Data System (ADS)
Hight Walker, Angela Renee
1995-01-01
With the use of a Fourier transform microwave (FTM) spectrometer, structural determinations of two types of species; multiconformational molecules and van der Waals complexes, have been performed. Presented in this thesis are three sections summarizing this research effort. The first section contains a detailed explanation of the FTM instrument. In Section II, the study of three multiconformational molecules is presented as two chapters. Finally, three chapters in Section III outline the work still in progress on many van der Waals complexes. Section I was written to be a "manual" for the FTM spectrometer and to aid new additions to the group in their understanding of the instrument. An instruction guide is necessary for home-built instruments such as this one due to their unique design and application. Vital techniques and theories are discussed and machine operation is outlined. A brief explanation of general microwave spectroscopy as performed on an FTM spectrometer is also given. Section II is composed of two chapters pertaining to multiconformational molecules. In Chapter 2, a complete structural analysis of dipropyl ether is reported. The only conformer assigned had C_{rm s} symmetry. Many transitions are yet unassigned. Chapter 3 summarizes an investigation of two nitrosamines; methyl ethyl and methyl propyl nitrosamine. Only one conformer was observed for methyl ethyl nitrosamine, but two were assigned to methyl propyl nitrosamine. Nuclear hyperfine structure and internal methyl rotation complicated the spectra. The final section, Section III, contains the ongoing progress on weakly bound van der Waals complexes. The analysis of the OCS--HBr complex identified the structure as quasi-linear with large amplitude bending motions. Five separate isotopomers were assigned. Transitions originating from the HBr--DBr complex were measured and presented in Chapter 5. Although early in the analysis, the structure was determined to be bent and deuterium bonded. The final chapter of this section is meant to be a permanent record of transition frequencies whose molecular carrier is still in question. Two different groups of transitions from two different samples are listed. Further work is needed to unambiguously assign the frequencies with a carrier and quantum numbers, however the complexes (H_2 O)--(HCl)_2 and NO--H _2O are considered possible suspects.
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.
Gautam, Rekha; Chandrasekar, Bhagawat; Deobagkar-Lele, Mukta; Rakshit, Srabanti; Kumar B N, Vinay; Umapathy, Siva; Nandi, Dipankar
2012-01-01
Acetaminophen is a widely prescribed drug used to relieve pain and fever; however, it is a leading cause of drug-induced liver injury and a burden on public healthcare. In this study, hepatotoxicity in mice post oral dosing of acetaminophen was investigated using liver and sera samples with Fourier Transform Infrared microspectroscopy. The infrared spectra of acetaminophen treated livers in BALB/c mice show decrease in glycogen, increase in amounts of cholesteryl esters and DNA respectively. Rescue experiments using L-methionine demonstrate that depletion in glycogen and increase in DNA are abrogated with pre-treatment, but not post-treatment, with L-methionine. This indicates that changes in glycogen and DNA are more sensitive to the rapid depletion of glutathione. Importantly, analysis of sera identified lowering of glycogen and increase in DNA and chlolesteryl esters earlier than increase in alanine aminotransferase, which is routinely used to diagnose liver damage. In addition, these changes are also observed in C57BL/6 and Nos2(-/-) mice. There is no difference in the kinetics of expression of these three molecules in both strains of mice, the extent of damage is similar and corroborated with ALT and histological analysis. Quantification of cytokines in sera showed increase upon APAP treatment. Although the levels of Tnf? and Ifn? in sera are not significantly affected, Nos2(-/-) mice display lower Il6 but higher Il10 levels during this acute model of hepatotoxicity. Overall, this study reinforces the growing potential of Fourier Transform Infrared microspectroscopy as a fast, highly sensitive and label-free technique for non-invasive diagnosis of liver damage. The combination of Fourier Transform Infrared microspectroscopy and cytokine analysis is a powerful tool to identify multiple biomarkers, understand differential host responses and evaluate therapeutic regimens during liver damage and, possibly, other diseases. PMID:23029070
NASA Astrophysics Data System (ADS)
Orders, P. J.; Fadley, C. S.
1983-01-01
The results of single-scattering cluster (SSC) calculations of normal photoelectron diffraction (NPD) from the S 1s level in c(2×2)S on Ni(001) are compared with multiple-scattering (MS) calculations by Tong and co-workers over the energy range 100 to 600 eV. It is found that the kinematical ?(E) curves are in good agreement with the multiple-scattering curves over the energy range ~ 160 to ~ 400 eV but in poor agreement elsewhere. The range of agreement between the SSC and MS curves can be directly associated with a relatively strong peak in the backscattering amplitude over essentially the same 160- to 400- eV range. The SSC curve for an adsorbate vertical height of z=1.35 Å is also in good agreement with experimental data of Hussain and co-workers over the range of ~ 170-430 eV. Thus, it appears that this simple SSC model can be fruitfully used in analyzing NPD data, even if it may not be quantitative enough for refined structural determinations. The effects of cluster size are examined within the single-scattering model, and it is suggested that approximately eight Ni layers are needed to describe NPD at electron energies >~ 300 eV. Inclusion of instrumental angular broadening is also found to be significant, and in particular increases the agreement between SSC and MS curves. Fourier-transform analysis of both the single- and multiple-scattering curves shows that peaks in the magnitude of the Fourier transform are most directly related to path-length differences between the direct wave and various scattered waves and not to perpendicular interlayer distances as previously suggested. These results thus indicate that the Fourier transformation of normal photoelectron diffraction data is not a particularly reliable method of obtaining surface structural information unless a very limited number of path-length differences are strongly predominant in the scattering.
NASA Astrophysics Data System (ADS)
Carroll, Brandon; Finneran, Ian; Blake, Geoffrey
2014-06-01
We present the design and construction of a simple and low-cost waveguide chirped pulse Fourier transform microwave (CP-FTMW) spectrometer suitable for gas-phase rotational spectroscopy experiments in undergraduate physical chemistry labs as well as graduate level research. The spectrometer operates with modest bandwidth, using phased locked loop (PLL) microwave sources and a direct digital synthesis (DDS) chirp source, making it an affordable for undergraduate labs. The performance of the instrument is benchmarked by acquiring the pure rotational spectrum of the J = 1 - 0 transition OCS and its isotopologues from 11-12.5 GHz.
Waveguide Chirped-Pulse Fourier Transform Microwave Spectroscopy of 1-PROPANETHIOL
NASA Astrophysics Data System (ADS)
Gordon, Brittany P.; Shipman, Steven T.
2013-06-01
The rotational spectrum of 1-propanethiol was measured from 8.7 to 26.5 GHz at 250 K with a waveguide chirped-pulse Fourier transform microwave spectrometer. This thiol has a dense spectrum containing contributions from multiple conformers, excited vibrational states, and singly-substituted isotopomers (^{34}S and ^{13}C) in natural abundance. Further, the spectrum shows complications due to the presence of internal rotation. Despite this complexity, some progress has been made, and preliminary work on this molecule will be presented.
NASA Astrophysics Data System (ADS)
Zhao, Jianlin; Lu, Hongqiang; Song, Xiaoshan; Li, Jifeng; Ma, Yanghua
2005-05-01
A novel encryption for optical image based on multistage fractional Fourier transforms (FRTs) and pixel scrambling technique is presented in this paper. The principle of pixel scrambling is described and an optical approach to realize the pixel scrambling and decoding is also proposed. Numerical simulation results are given to verify the algorithm, and relative error (RE) between the decoded images and the original image versus the deviation of fractional orders is discussed. Comparing with single FRT encryption, the security using this method for optical image encryption is greatly improved due to the introduction of the pixel scrambling technique.
NASA Astrophysics Data System (ADS)
Wang, Yong-Ying; Wang, Yu-Rong; Wang, Yong; Li, Hui-Juan; Sun, Wen-Jia
2007-07-01
A new method of optical image encryption with binary Fourier transform computer-generated hologram (CGH) and pixel-scrambling technology is presented. In this method, the orders of the pixel scrambling, as well as the encrypted image, are used as the keys to decrypt the original image. Therefore, higher security is achieved. Furthermore, the encrypted image is binary, so it is easy to be fabricated and robust against noise and distortion. Computer simulation results are given to verify the feasibility of this method and its robustness against occlusion and additional noise.
High-resolution Fourier-transform infrared chemical imaging with multiple synchrotron beams
Nasse, Michael J; Walsh, Michael J; Mattson, Eric C; Reininger, Ruben; Kajdacsy-Balla, André; Macias, Virgilia; Bhargava, Rohit; Hirschmugl, Carol J
2013-01-01
Conventional Fourier-transform infrared (FTIR) microspectroscopic systems are limited by an inevitable trade-off between spatial resolution, acquisition time, signal-to-noise ratio (SNR) and sample coverage. We present an FTIR imaging approach that substantially extends current capabilities by combining multiple synchrotron beams with wide-field detection. This advance allows truly diffraction-limited high-resolution imaging over the entire mid-infrared spectrum with high chemical sensitivity and fast acquisition speed while maintaining high-quality SNR. PMID:21423192
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).
In vivo measurement of lower back deformations with Fourier-transform profilometry
Hanafi, Abdelmalek; Gharbi, Tijani; Cornu, Jean-Yves
2005-04-20
Through the variation of their cross sections, the in vivo response of lower back muscles to low loading in an upright seated posture is explored by the Fourier-transform profilometry technique. The maximization of its sensitivity allows us to reach an adequate resolution for the evaluation of low-back displacements. Refinements of the fringe pattern analysis permit the minimization of errors. The experiments show an asymmetric distribution of the displacement during head rotation movements. Significant contribution of the lower back to grasping exertions is also observed. These results are thought to be useful for early defect detection in the lower back.
Nanoprobe fourier-transform photoabsorption spectroscopy using a supercontinuum light source.
Ishibe, Kiyoshiro; Nakada, Satoru; Mera, Yutaka; Maeda, Koji
2012-06-01
A scheme of photoabsorption spectroscopy based on scanning tunneling microscopy (STM) has been developed by using a supercontinuum light as the wideband light source of a Fourier transform interferometer for spectroscopic measurements. The performance was demonstrated for a sample of GaAs. The proof-of-concept test showed that the use of the supercontinuum light instead of halogen lamps greatly enhances the signal-to-noise ratio due to the high brilliance of the supercontinuum light emitted from a small core of the photonic crystal fiber that enables tight focusing of the spectroscopy light onto the sample beneath the STM tip. PMID:22640967
NASA Astrophysics Data System (ADS)
Zhang, Yizhuo; Situ, Guohai; Pedrini, Giancarlo; Wang, Dayong; Javidi, Bahram; Osten, Wolfgang
2013-01-01
We propose a short-coherence lensless Fourier-transform digital holography for imaging through scattering media. The technique utilizes a low-power cw diode laser with short temporal coherence and enables the selection of the early-arriving photons through a diffusive medium by interfering with a spherical reference beam from the same source. An averaging technique is introduced to extract the weak signal from strong background noise. The proposed technique is verified using both theoretical analysis and experimental demonstration by imaging an object through a 3-mm-thick chicken breast tissue.
Application of numerical Fourier transformation on measurements made on board rotating spacecraft
NASA Astrophysics Data System (ADS)
Grabowski, R.; Boesch, B.; Wolf, H.
Use of a Fast Fourier Transform algorithm to perform digital evaluation of signals from spacecraft featuring spin modulation and nutational effects is described. The case of a rotating spacecraft without nutation is modeled, with account taken of demodulation performed simultaneously with respect to amplitude and phase. Applying the demodulation technique twice removes the nutational effects. Assumptions are made that the spectral functions do not vary as fast as the spin modulation, and the signal variance independent of spacecraft rotation occurs at a rate significantly less than the spin rate. A demodulation example is given for a signal received from a probe on the Porcupine 2 rocket.
NASA Astrophysics Data System (ADS)
Simonis, G. J.; Sattler, J. P.; Worchesky, T. L.; Leavitt, R. P.
1984-01-01
Nondispersive Fourier-transform-spectroscopic techniques are used to measure the complex indices of refraction of materials between frequencies of 120 and 550 GHz. Results are presented for crystal quartz, cross-linked polystyrene (Rexolite 1422), glass-loaded polytetrafluoroethylene (Duroid 5880) and a nickel ferrite (Trans-Tech 2-111). These results are compared with other data on these materials in this frequency range. The accuracy of these measurements yields a considerable improvement in the near-millimeter-wave characterization of several of these materials. For materials other than crystal quartz, the results are the first measurements of their properties over the entire frequency range studied.
Baraga, J J; Feld, M S; Rava, R P
1992-01-01
In this paper we demonstrate that near infrared Fourier transform Raman spectroscopy provides unprecedented biochemical information about the extent of atherosclerosis in human aorta. In particular, elastin, collagen, cholesterol, cholesterol esters, lipids, carotenoids, and calcium apatite deposits all can be discerned by using this technique, permitting study of each stage in the disease process. Additionally, these moieties can be detected over 1.5 mm below the irradiated surface of the tissue, possibly allowing extraction of three-dimensional information about the histology of atherosclerotic plaques. We propose that this technique may be utilized for in situ optical histochemical analysis of atherosclerosis in particular and human disease in general. PMID:1565640
Villé, H; Maes, G; De Schrijver, R; Spincemaille, G; Rombouts, G; Geers, R
1995-01-01
A method has been developed to determine the phospholipid content in fat extract with FTIR (Fourier Transform Infrared). l-?-Phosphatidylcholine from egg yolk in hexane solution was used as a reference for band identification at different concentrations. Phosphate bands were determined at different wavenumbers as described in the literature. A dilution series was made from meat extract and from 1-?-phosphatidylcholine. A linear calibration curve was obtained between the FTIR-results and the Iatroscan results, which were used as a reference. The band between 1282 cm(-1) and 1020 cm(-1) can be used for determination of phospholipid content. PMID:22060199
Improving imaging resolution of shaking targets by Fourier-transform ghost diffraction
Cong Zhang; Wenlin Gong; Shensheng Han
2012-07-26
For conventional imaging, shaking of the imaging system or the target leads to the degradation of imaging resolution. In this work, the influence of the target's shaking to fourier-transform ghost diffraction (FGD) is investigated. The analytical results, which are backed up by numerical simulation and experiments, demonstrate that the quiver of target has no effect on the resolution of FGD, thus the target's imaging with high spatial resolution can be always achieved by phase-retrieval method from the FGD patterns. This approach can be applied in high-precision imaging systems, to overcome the influence of the system's shaking to imaging resolution.
Stability determination of soy lecithin-based emulsions by Fourier transform infrared spectroscopy
J. M. Whittinghill; J. Norton; A. Proctor
2000-01-01
The stability of soy lecithin-stabilized emulsions was determined by Fourier transform infrared spectroscopy. Oilin-water\\u000a (o\\/w) emulsions were prepared with 6% (vol\\/vol) medium-chain triglycerides (MCT), 94% (vol\\/vol) water, and 4% (wt\\/vol) Lecigran\\u000a and Lecimulthin soy lecithin. There were little or no differences between the 4% Lecigran and 4% Lecimulthin emulsions for\\u000a all vibrational regions studied (OH at 3348 cm?1, C=O at
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
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.
Image encryption based on double folding operation in fractional Fourier transform domain
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Wang, Xiuying; Liu, Shutian
2009-11-01
Based on fractional Fourier transform, the double folding operation is studied and introduced into image encryption. This method can implement a kind of the encoding with real number. This characteristic is convenient to the storage and transmission of the encrypted image. The corresponding experimental setup is similar to the scheme of double random phase encoding. With computer, some numerical simulations have been achieved. The analysis on the algorithm from the aspects of validity, security and robustness is made. The calculated results have been demonstrated that the algorithm is effective and has good security.
Highly folded 5?m Fourier transform spectrometer for spaceborne wind lidar.
Luu, Jane; Willard, Bert
2015-07-10
We have designed and built a prototype Fourier transform spectrometer intended for a wind lidar system. The significant characteristics of this design include (1) an optical layout that folds a maximum optical path difference of 5.8 m to fit into a 1.2 m cavity, (2) two confocal parabolas to compensate for beam diffraction over the entire path length, and (3) a photon-counting detector for high sensitivity. The optical path difference is measured with a reference beam produced by the heterodyne technique. The reference beam is collinear with the data beam, and accounts for all mechanical vibrations along the optical path. PMID:26193393
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.
Real-time generation of atmospheric turbulence phase screen with non-uniform fast Fourier transform
NASA Astrophysics Data System (ADS)
Jia, Peng; Cai, Dongmei; Wang, Dong; Basden, Alastair
2015-06-01
High-fidelity Monte Carlo simulation of atmospheric turbulence phase screens is important for performance testing of astronomical adaptive optics systems. With a sparse spectrum model and an optimal sampling method, it is possible to generate an atmospheric turbulence phase screen with high fidelity. However, the phase screen generation speed is limited by the algorithm structure of this technique. A non-uniform fast Fourier transform technique is proposed in this paper to accelerate phase screen generation speed. This method is able to generate huge atmospheric turbulence phase screens with high fidelity and an acceptable time-cost enabling practical adaptive optics simulations of forthcoming Extremely Large Telescopes.
NASA Astrophysics Data System (ADS)
Jin, Weimin; Yan, Caijie
2007-01-01
The optical image encryption based on multichannel fractional Fourier transform (FRT) and double random phase encoding technique is proposed. Optical principles of encoding and decoding are analyzed in detail. With this method, one can encrypt different parts of input image, respectively. The system security can be improved to some extent, not only because fractional orders and random phase masks in every channel can be set with freedom, but also because the system parameters among all channels are independent. Numerical simulation results of optical image encryption based on four channel FRT and double random phase encoding are given to verify the feasibility of the method.
Tensor representation of color images and fast 2D quaternion discrete Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, a general, efficient, split algorithm to compute the two-dimensional quaternion discrete Fourier transform (2-D QDFT), by using the special partitioning in the frequency domain, is introduced. The partition determines an effective transformation, or color image representation in the form of 1-D quaternion signals which allow for splitting the N × M-point 2-D QDFT into a set of 1-D QDFTs. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. In particular, a proposed method of calculating the 2r × 2r -point 2-D QDFT uses 18N2 less multiplications than the well-known column-row method and method of calculation based on the symplectic decomposition. The proposed algorithm is simple to apply and design, which makes it very practical in color image processing in the frequency domain.
The price tag for a fast Fourier transform on any sample size
NASA Astrophysics Data System (ADS)
Cheek, James B.
1991-09-01
A computer program that makes a time-to-frequency domain transformation on a signal sampled with any number of equally spaced points has been available for over 10 years. That program, Glassman's discrete Fourier transform (DFT), is not generally used. Perhaps this low use is due to the wide and unpredictable variations in the processing time caused by small changes in the sample size. This paper examines that program and shows how the sample size controls the processing time. The procedure described in this paper establishes the relative computation cost of any sample size and shows that small adjustments to the sample size will provide the DFT capability at an affordable cost. So, this paper is largely about the workings of a computer-based signal processing tool and how to use it effectively.
The design of ROM-type holographic memory with iterative Fourier transform algorithm
NASA Astrophysics Data System (ADS)
Akamatsu, Hideki; Yamada, Kai; Unno, Noriyuki; Yoshida, Shuhei; Taniguchi, Jun; Yamamoto, Manabu
2013-03-01
The research and development of the holographic data storage (HDS) is advanced, as one of the high-speed, mass storage systems of the next generation. Recently, along the development of the write-once system that uses photopolymer media, large capacity ROM type HDS which can replace conventional optical discs becomes important. In this study, we develop the ROM type HDS using a diffractive optical element (DOE), and verify the effectiveness of our approach. In order to design DOE, iterative Fourier transform algorithm was adopted, and DOE is fabricated with electron beam (EB) cutting and nanoimprint lithography. We optimize the phase distribution of the hologram by iterative Fourier transform algorithm known as Gerchberg-Saxton (GS) algorithm with the angular spectrum method. In the fabrication process, the phase distribution of the hologram is implicated as the concavity and convexity structure by the EB cutting and transcribed with nanoimprint lithography. At this time, the mold is formed as multiple-stage concavity and convexity. The purpose of multiple-stage concavity and convexity is to obtain high diffraction efficiency and signal-to-noise ratio (SNR). Fabricated trial model DOE is evaluated by the experiment.
Fourier Transform Infrared Emission Spectroscopy and AB Initio Study of Hbo and BO
NASA Astrophysics Data System (ADS)
Li, G.; Hargreaves, R. J.; Bernath, P. F.
2010-06-01
The Fourier-transform infrared emission spectra of HBO and BO were recorded using a Bruker IFS-125HR Fourier transform spectrometer. HBO molecules were synthesized using a high temperature tube furnace at 1450 °C. Our spectra of the HBO molecule in the 1200-4000 cm-1 region contain the v1 and v3 fundamental vibrational modes plus numerous hot bands. An accurate potential energy surface using the MRCI method with correlation consistent core-valence basis sets aug-cc-PCVnZ (n=3, 4, 5) is being calculated and a vibrational configuration interaction (VCI) calculation based on this surface will be performed to assist in the assignment of the HBO hot bands. BO molecules were produced by applying a DC discharge to the furnace containing HBO. Our spectrum of BO in the 1200-2100 cm-1 region contains the fundamental bands of both isotopic species, 11BO, 10BO, and one hot band of the main isotopologue 11BO. The fundamental band of 11BO contains 95 lines roughly equally distributed between the P and R branches. A combined least-squares fit with ground state microwave data was performed to determine the spectroscopic constants. Further results on this ongoing project will be presented.
Flow-through Fourier transform infrared sensor for total hydrocarbons determination in water.
Pérez-Palacios, David; Armenta, Sergio; Lendl, Bernhard
2009-09-01
A new flow-through Fourier transform infrared (FT-IR) sensor for oil in water analysis based on solid-phase spectroscopy on octadecyl (C18) silica particles has been developed. The C18 non-polar sorbent is placed inside the sensor and is able to retain hydrocarbons from water samples. The system does not require the use of chlorinated solvents, reducing the environmental impact, and the minimal sample handling stages serve to ensure sample integrity whilst reducing exposure of the analyst to any toxic hydrocarbons present within the samples. Fourier transform infrared (FT-IR) spectra were recorded by co-adding 32 scans at a resolution of 4 cm(-1) and the band located at 1462 cm(-1) due to the CH(2) bending was integrated from 1475 to 1450 cm(-1) using a baseline correction established between 1485 and 1440 cm(-1) using the areas as analytical signal. The technique, which provides a limit of detection (LOD) of 22 mg L(-1) and a precision expressed as relative standard deviation (RSD) lower than 5%, is considerably rapid and allows for a high level of automation. PMID:19796483
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.)
Yin, Jian-Hua; Huang, Feng-Ling; Qian, Zhi-Yu; Xie, Jie-Ru
2014-02-01
Fourier transform infrared spectroscopy (FTIRS) and microimaging technique have been integrated together to evolve into Fourier transform infrared spectroscopic imaging (FTIRI) system. This system can provide not only the morphological information of the sample by visible image and FTIR image, but also the abundant information on the spectral, component and structure of specimen by FTIRS, especially of the heterogeneous solid mixture. The richer and more visualized information obtained by FTIRI greatly raised the research efficiency and usability of the spectral technique in biomedicine, pharmacology, forensic medicine, material science and chemistry, etc. The present paper depicts FTIRI development process, system structure, imaging principle and mode selection; and then introduces that FTIRI opened a new area of investigation for biomedicine, namely, research on bone disease by FTIRI. Then the paper illustrates the related research findings and progress in FTIRI use for osteopetrosis, osteogenesis imperfecta, osteoporosis and osteomalacia, as well as a couple of limitations. The prospective study for FTIRI in biomedical research field is also addressed. PMID:24822397
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.
Applications of 1.06-micron IR laser desorption on a Fourier transform mass spectrometer.
Ho, Y P; Fenselau, C
1998-12-01
Various sugars, peptides, and lipids were analyzed on a Fourier transform mass spectrometer using laser desorption and ionization with and without the assistance of matrixes. A compact Nd:YAG laser with an output at 1.06 microns corresponding to fundamental frequency was employed. Gram-negative and Gram-positive bacteria were also subjected to laser desorption mass spectrometry. Characteristics ions of conjugated lipid, formed by attachment of alkali metal cations, endogenous to the cells, were observed. Particle/liquid matrixes (e.g., cobalt in glycerol) proved to be useful with the 1.06-micron laser. The particles absorb efficiently laser radiation in a broad wavelength range. The liquid provides the same advantages as in fast atom bombardment: increased signal-to-noise ratios and enhanced sample lifetimes. The effect of laser power on total ion current was shown to differ for samples with and without the particle/liquid matrix. The Fourier transform analyzer provides MS/MS capability for both positive and negative ions from complex mixtures. Ions desorbed externally are introduced into the cell via a quadrupole ion guide with a lower mass cutoff. Such a setup allows matrix ions to be excluded and thus provides excellent signal-to-noise ratios for lower mass range fragment ions formed inside the cell. PMID:9852777
NASA Astrophysics Data System (ADS)
Zhao, Jie; Wang, Dayong; Wang, Yunxin; Liu, Changgeng; Li, Yan; Cui, Huakun; Wan, Yuhong
2010-08-01
The lensless Fourier transform digital holography has been widely employed in microscopic imaging. It enables quantitative phase analysis for both reflection and transmission objects. The phase image is obtained in the numerical reconstruction procedure. The in-focus reconstruction distance could be determined according to the extremum of the autofocusing criterion function, which is commonly applied in finding the in-focus amplitude image of the object. Then the reconstruction distance for the phase image is considered to be equal to the one for the amplitude image. When the object is a pure phase sample, such as the living cell, the minimum value of the autofocusing criterion function should be found to determine the in-focus reconstruction distance. However, in the experiment, the in-focus amplitude image is often not an ideal uniform bright field, so this method will result in some deviation. In this contribution, two derivatives-based criterion functions are applied to the phase image directly to accomplish the in-focus phase contrast imaging, which is more intuitive and precise. In our experiments, the set-up of the lensless Fourier transform digital holography is established firstly. Then the living cervical carcinoma cells are detected. The phase aberration is corrected by two-step algorithm. The final autofocusing results verify the algorithm proposed in this paper.
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
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.
A fractional Fourier transform analysis of the scattering of ultrasonic waves
Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony
2015-01-01
Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967
NASA Astrophysics Data System (ADS)
Zhang, B.; Sang, Jun; Alam, Mohammad S.
2013-03-01
An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.
NASA Astrophysics Data System (ADS)
Wu, Xuebin; Yan, Zhiyuan; Lin, Jun
2012-07-01
Long Reed-Solomon (RS) codes are desirable for digital communication and storage systems due to their improved error performance, but the high computational complexity of their decoders is a key obstacle to their adoption in practice. As discrete Fourier transforms (DFTs) can evaluate a polynomial at multiple points, efficient DFT algorithms are promising in reducing the computational complexities of syndrome based decoders for long RS codes. In this paper, we first propose partial composite cyclotomic Fourier transforms (CCFTs) and then devise syndrome based decoders for long RS codes over large finite fields based on partial CCFTs. The new decoders based on partial CCFTs achieve a significant saving of computational complexities for long RS codes. Since partial CCFTs have modular and regular structures, the new decoders are suitable for hardware implementations. To further verify and demonstrate the advantages of partial CCFTs, we implement in hardware the syndrome computation block for a $(2720, 2550)$ shortened RS code over GF$(2^{12})$. In comparison to previous results based on Horner's rule, our hardware implementation not only has a smaller gate count, but also achieves much higher throughputs.
NASA Astrophysics Data System (ADS)
Terki-Hassa?¨ne, M.; Claveau, Ch.; Valentin, A.; Pierre, G.
1999-10-01
The infrared spectrum of 28SiH4 between 2930 and 3300 cm-1 was recorded using the Laboratoire de Physique Moléculaire et Applications (LPMA.) Fourier transform spectrometer. The instrumental response function width chosen makes it possible to obtain a Doppler-limited spectrum. The observed spectrum belongs to the tetrad built with one quantum of stretching mode (?1 or ?3) and one quantum of bending mode (?2 or ?4). The excited states are formed from eight vibrational sublevels: ?1 + ?2(E), ?1 + ?4(F2), ?2 + ?3(F1 + F2), and ?3 + ?4(A1 + E + F1 + F2). The intricacy of the upper states was resolved using the variations of the line strength between the 297 K and 209 K spectra and the precise knowledge of the ground state. For analysis with the vibrational extrapolation method, we used the previous results for the fundamental bending dyad (?2/?4) and the stretching dyad (?1/?3). The Hamiltonian is expanded through the sixth order of approximation for the ground and the bending states, the fifth order for the stretching states, and the fourth order for the tetrad states in the Amat-Nielsen classification. About 1033 pieces of data are used in the analysis and the weighted standard deviation obtained is 4.6 × 10-3 cm-1.
Quantum optics of spatial transformation media
Leonhardt, U
2006-01-01
We show how transformation media [J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006); U. Leonhardt and T. G. Philbin, cond-mat/0607418] map quantum electromagnetism in physical space to QED in empty flat space. As a consequence, the Casimir force of left-handed dielectric media may become repulsive and may possibly levitate ultra-thin metal foils.
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)
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.
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 Astrophysics Data System (ADS)
Graf, Robert N.; Chen, Xiaoxin; Brown, William; Wax, Adam
2008-02-01
Fourier Domain Low Coherence Interferometry (fLCI) is a promising technique which combines the depth resolution of low coherence interferometry with the sensitivity of light scattering spectroscopy for probing the health of epithelial tissue layers. Our new fLCI system configuration utilizes a white light Xe arc lamp source and a 4-f interferometer which re-images light scattered from the sample onto the detection plane. The system employs an imaging spectrometer at the detection plane to acquire depth resolved profiles from 252 adjacent spatial points without the need for any scanning. The limited spatial coherence of the light source requires the resolution of adjacent spatial points for the generation of depth information. Depth-resolved spectral information is recovered by performing a short-time Fourier transform on the detected spectra, similar to spectroscopic optical coherence tomography. Wavelength dependent variations in scattering intensity are analyzed as a function of depth to obtain information about the neoplastic transformation of the probed cells. Previous studies have demonstrated fLCI as an excellent technique for probing the scatterer morphology of simple phantoms and of in vitro cancer cell monolayers. We now seek to assess the ability of the new fLCI system to measure the health of subsurface tissue layers using the hamster cheek pouch model. Seven hamsters will have one cheek pouch treated with the known carcinogen DMBA. At the conclusion of the 24 week treatment period the animals will be anesthetized and the cheek pouches will be extracted. We will use the fLCI optical system to measure the neoplastic transformation of the in situ subsurface tissue layers in both the normal and DMBA-treated cheek pouches. Traditional histological analysis will be used to verify the fLCI measurements. We expect our results to establish the feasibility of fLCI to distinguish between healthy and dysplastic epithelial tissues in the hamster cheek pouch.
Cavity QED implementation of the discrete quantum Fourier transform
Scully, Marlan O.; Zubairy, M. Suhail
2002-01-01
and we assume ua& to be the excited state and ub& to be the ground state. The correspond- ing time-evolution unitary operator is given by UI~ t !5expS2 i\\Vt D 5cos~Vt/2!~ ua&^au1ub&^bu! 2i sin~Vt/2!~e2ifua&^bu1eifub&^au!. ~8! This corresponds... scheme relies on the passage of a series of suitably chosen atoms through a sequence of classical fields and high- Q cavities. The QFT maps each state ua& into a superposition given by NQFTua&5 1A2q (c50 2q21 e2piac/2 quc&, ~1! where q...
Ancilla-approximable quantum state transformations
NASA Astrophysics Data System (ADS)
Blass, Andreas; Gurevich, Yuri
2015-04-01
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ?, but also address the question of arbitrarily close approximation.
Universal Quantum Circuit of Near-Trivial Transformations
Min Liang; Li Yang
2011-05-09
Any unitary transformation can be decomposed into a product of a group of near-trivial transformations. We investigate in details the construction of universal quantum circuit of near trivial transformations. We first construct two universal quantum circuits which can implement any single-qubit rotation $R_y(\\theta)$ and $R_z(\\theta)$ within any given precision, and then we construct universal quantum circuit implementing any single-qubit transformation within any given precision. Finally, a universal quantum circuit implementing any $n$-qubit near-trivial transformation is constructed using the universal quantum circuits of $R_y(\\theta)$ and $R_z(\\theta)$. In the universal quantum circuit presented, each quantum transformation is encoded to a bit string which is used as ancillary inputs. The output of the circuit consists of the related bit string and the result of near-trivial transformation. Our result may be useful for the design of universal quantum computer in the future.
Universal Quantum Circuit of Near-Trivial Transformations
Liang, Min
2011-01-01
Any unitary transformation can be decomposed into a product of a group of near-trivial transformations. We investigate in details the construction of universal quantum circuit of near trivial transformations. We first construct two universal quantum circuits which can implement any single-qubit rotation $R_y(\\theta)$ and $R_z(\\theta)$ within any given precision, and then we construct universal quantum circuit implementing any single-qubit transformation within any given precision. Finally, a universal quantum circuit implementing any $n$-qubit near-trivial transformation is constructed using the universal quantum circuits of $R_y(\\theta)$ and $R_z(\\theta)$. In the universal quantum circuit presented, each quantum transformation is encoded to a bit string which is used as ancillary inputs. The output of the circuit consists of the related bit string and the result of near-trivial transformation. Our result may be useful for the design of universal quantum computer in the future.
Compiling Quantum Circuits using the Palindrome Transform
Alfred V. Aho; Krysta M. Svore
2003-11-03
The design and optimization of quantum circuits is central to quantum computation. This paper presents new algorithms for compiling arbitrary 2^n x 2^n unitary matrices into efficient circuits of (n-1)-controlled single-qubit and (n-1)-controlled-NOT gates. We first present a general algebraic optimization technique, which we call the Palindrome Transform, that can be used to minimize the number of self-inverting gates in quantum circuits consisting of concatenations of palindromic subcircuits. For a fixed column ordering of two-level decomposition, we then give an numerative algorithm for minimal (n-1)-controlled-NOT circuit construction, which we call the Palindromic Optimization Algorithm. Our work dramatically reduces the number of gates generated by the conventional two-level decomposition method for constructing quantum circuits of (n-1)-controlled single-qubit and (n-1)-controlled-NOT gates.
Gridding-based direct Fourier inversion of the three-dimensional ray transform.
Penczek, Pawel A; Renka, Robert; Schomberg, Hermann
2004-04-01
We describe a fast and accurate direct Fourier method for reconstructing a function f of three variables from a number of its parallel beam projections. The main application of our method is in single particle analysis, where the goal is to reconstruct the mass density of a biological macromolecule. Typically, the number of projections is extremely large, and each projection is extremely noisy. The projection directions are random and initially unknown. However, it is possible to determine both the directions and f by an iterative procedure; during each stage of the iteration, one has to solve a reconstruction problem of the type considered here. Our reconstruction algorithm is distinguished from other direct Fourier methods by the use of gridding techniques that provide an efficient means to compute a uniformly sampled version of a function g from a nonuniformly sampled version of Fg, the Fourier transform of g, or vice versa. We apply the two-dimensional reverse gridding method to each available projection of f, the function to be reconstructed, in order to obtain Ff on a special spherical grid. Then we use the three-dimensional gridding method to reconstruct f from this sampled version of Ff. This stage requires a proper weighting of the samples of Ff to compensate for their nonuniform distribution. We use a fast method for computing appropriate weights that exploits the special properties of the spherical sampling grid for Ff and involves the computation of a Voronoi diagram on the unit sphere. We demonstrate the excellent speed and accuracy of our method by using simulated data. PMID:15078020
NASA Astrophysics Data System (ADS)
Schmidt, C. H.; Laitinen, T. A.; Eibert, T. F.
2011-10-01
Near-field measurement and transformation techniques are widely applied to characterize radiation patterns of antennas. Spherical and cylindrical near-field measurements have been researched extensively and various techniques with different probe compensation capabilities and complexities exist. Among those techniques applicable for (almost) arbitrary probes, the crucial computational efficiency has been achieved through the use of Fast Fourier Transform based preprocessing of the measurement data. It is shown in this paper that the Fast Fourier Transform based preprocessing can also be utilized in conjunction with the plane wave based fully probe-corrected near-field far-field transformation with low numerical complexity. The collection of probe signals is split into smaller subsets for individual orthogonal azimuthal Fourier modes by an Inverse Fast Fourier Transform. These smaller subsets can be transformed to the far field very efficiently with full probe correction. The technique presented in this paper is applicable for arbitrary "body of revolution" antenna measurement grids, including the important cases of cylindrical and spherical measurement grids. The "body of revolution" grids are rotationally symmetric around the z-axis and the probe signals must be available equidistantly in ?.
NASA Astrophysics Data System (ADS)
Terschlüsen, J. A.; Agåker, M.; Svanqvist, M.; Plogmaker, S.; Nordgren, J.; Rubensson, J.-E.; Siegbahn, H.; Söderström, J.
2014-12-01
In this experiment we used an 800 nm laser to generate high-order harmonics in a gas cell filled with Argon. Of those photons, a harmonic with 42 eV was selected by using a time-preserving grating monochromator. Employing a modified Mach-Zehnder type Fourier transform spectrometer for the VUV/XUV it was possible to measure the temporal coherence of the selected photons to about 6 fs. We demonstrated that not only could this kind of measurement be performed with a Fourier transform spectrometer, but also with some spatial resolution without modifying the XUV source or the spectrometer.