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.
Implementation of quantum and classical discrete fractional Fourier transforms
NASA Astrophysics Data System (ADS)
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-03-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-01-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089
Fourier transform spectra of quantum dots
NASA Astrophysics Data System (ADS)
Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.
2009-09-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
Fourier transform spectra of quantum dots
NASA Astrophysics Data System (ADS)
Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.
2010-05-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
Structural stability of the quantum Fourier transform
NASA Astrophysics Data System (ADS)
Nam, Y. S.; Blümel, R.
2015-04-01
While it is important to investigate the negative effects of decoherence on the performance of quantum information processors, Landauer was one of the first to point out that an equally basic problem, i.e., the effects of unavoidable hardware flaws in the real-world implementations of quantum gates, needs to be investigated as well. Following Landauer's suggestion, we investigated the structural stability of the quantum Fourier transform (QFT) via significantly changing the analytical form of its controlled rotation gates, thus modeling structural flaws in the Hamiltonian of the QFT. Three types of modified rotation gates were investigated, numerically and analytically, changing the exact QFT rotation angles to (1) , (2) , and (3) , where , , and are constants and is the integer distance between QFT qubits. Surprisingly good performance is observed in all the three cases for a wide range of , , and . This demonstrates the structural stability of the QFT Hamiltonian. Our results also demonstrate that the precise implementation of QFT rotation angles is not critical as long as the angles (roughly) observe a monotonic decrease in (hierarchy). This result is important since it indicates that stringent tolerances do not need to be imposed in the actual manufacturing process of quantum information hardware components.
Resource requirements for a fault-tolerant quantum Fourier transform
NASA Astrophysics Data System (ADS)
Goto, Hayato
2014-11-01
We investigate resource requirements for a fault-tolerant quantum Fourier transform. The quantum Fourier transform is a basic subroutine for quantum algorithms which provide an exponential speedup over known classical ones, such as Shor's algorithm for factoring. To implement single-qubit rotations required for a quantum Fourier transform in a fault-tolerant manner, we consider two types of approaches: gate synthesis and state distillation. While the gate synthesis approximates single-qubit rotations with basic quantum operations, the state distillation allows one to perform single-qubit rotations for a quantum Fourier transform exactly. It is unknown, however, which approach is better for a quantum Fourier transform. Here we develop a state-distillation method optimized for a quantum Fourier transform and compare this performance with those of state-of-the-art techniques for gate synthesis without and with ancillary states (ancillas). The performance is evaluated with the resource requirement for a quantum Fourier transform. The resource is measured by the total number of π /8 gates denoted by T , which is called the T count. Contrary to the expectation, the T count for the state distillation is considerably larger than those for the ancilla-free and ancilla-assisted gate synthesis. Thus, we conclude that the ancilla-assisted gate synthesis is a better approach to a fault-tolerant quantum Fourier transform.
Revisiting the quantum harmonic oscillator via unilateral Fourier transforms
NASA Astrophysics Data System (ADS)
Nogueira, Pedro H. F.; de Castro, Antonio S.
2016-01-01
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions.
Implementing quantum Fourier transform with integrated photonic devices
NASA Astrophysics Data System (ADS)
Tabia, Gelo Noel
2014-03-01
Many quantum algorithms that exhibit exponential speedup over their classical counterparts employ the quantum Fourier transform, which is used to solve interesting problems such as prime factorization. Meanwhile, nonclassical interference of single photons achieved on integrated platforms holds the promise of achieving large-scale quantum computation with multiport devices. An optical multiport device can be built to realize any quantum circuit as a sequence of unitary operations performed by beam splitters and phase shifters on path-encoded qudits. In this talk, I will present a recursive scheme for implementing quantum Fourier transform with a multimode interference photonic integrated circuit. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Quantum control in two-dimensional Fourier-transform spectroscopy
Lim, Jongseok; Lee, Han-gyeol; Lee, Sangkyung; Ahn, Jaewook
2011-07-15
We present a method that harnesses coherent control capability to two-dimensional Fourier-transform optical spectroscopy. For this, three ultrashort laser pulses are individually shaped to prepare and control the quantum interference involved in two-photon interexcited-state transitions of a V-type quantum system. In experiments performed with atomic rubidium, quantum control for the enhancement and reduction of the 5P{sub 1/2}{yields} 5P{sub 3/2} transition was successfully tested in which the engineered transitions were distinguishably extracted in the presence of dominant one-photon transitions.
Entanglement of periodic states, the quantum Fourier transform, and Shor's factoring algorithm
Most, Yonatan; Biham, Ofer; Shimoni, Yishai
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.
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.
NASA Astrophysics Data System (ADS)
Wang, Tong-Tong; Fan, Hong-Yi
2012-03-01
Using the Weyl quantization scheme and based on the Fourier slice transformation (FST) of the Wigner operator, we construct a new expansion formula of the density operator ρ, with the expansion coefficient being the FST of ρ's classical Weyl correspondence, and the latter the Fourier transformation of ρ's quantum tomogram. The coordinate-momentum intermediate representation is used as the Radon transformation of the Wigner operator.
Large quantum Fourier transforms are never exactly realized by braiding conformal blocks
Freedman, Michael H.; Wang, Zhenghan
2007-03-15
Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {l_brace}U(2), controlled-NOT{r_brace}, the discrete Fourier transforms F{sub N}=({omega}{sup ij}){sub NxN}, i,j=0,1,...,N-1, {omega}=e{sup 2{pi}}{sup i} at {sup {approx}}{sup sol{approx}} at {sup N}, can be realized exactly by quantum circuits of size O(n{sup 2}), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F{sub N} and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks.
Analysis of electronic structures of quantum dots using meshless Fourier transform kp method
NASA Astrophysics Data System (ADS)
Zhao, Qiuji; Mei, Ting
2011-03-01
We develop a complete Fourier transform k.p method and present its application for a theoretical investigation on electronic structures of quantum dots with consideration of the built-in strain effects. The Fourier transform technique is applied to the periodic position-dependent Hamiltonian, and a simple and neat expression of the Hamiltonian matrix in the Fourier domain is formulated due to the orthogonality of exponential functions. Spurious solutions can be avoided due to the truncation of high Fourier frequencies. A kinetic Hamiltonian matrix in momentum domain is formulated by entering the analytical Fourier transform of the quantum-dot shape function into the neat Hamiltonian matrix easily, which allows meshless numerical implementation. The formulation of strain Hamiltonian matrix is done by convolution of Fourier series of strain components and Fourier series of the quantum-dot shape functions. Therefore, an original Fourier transform-based k.p approach is developed by combining the kinetic Hamiltonian matrix and the strain Hamiltonian. This approach is adopted to study the dimension effect and strain effect on the ground states of electrons and holes of pyramidal quantum dots that are truncated to different heights. The ground-state energy variation shows that the electron state is the most sensitive to these effects and the strain effect on E1, LH1, and HH1 is more prominent for sharperquantum dots. This investigation shows that band mixing between the conduction band and valence band, and band mixing between heavy-hole and light-hole bands are reduced due to the strain effect, whereas this effect is more prominent for nontruncated pyramidal quantum dots due to the stress concentration. Among the three ground states, light-hole states are more weakly confined in the nonpyramidal quantum dot and shift to the tip of the pyramid due to the strain.
Suppression law of quantum states in a 3D photonic fast Fourier transform chip.
Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio
2016-01-01
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135
Suppression law of quantum states in a 3D photonic fast Fourier transform chip
NASA Astrophysics Data System (ADS)
Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio
2016-02-01
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms.
Suppression law of quantum states in a 3D photonic fast Fourier transform chip
Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio
2016-01-01
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135
NASA Astrophysics Data System (ADS)
Wang, Hong-Fu; Shao, Xiao-Qiang; Zhao, Yong-Fang; Zhang, Shou; Yeon, Kyu-Hwang
2010-03-01
We present a simple protocol and quantum circuit for efficient implementation of the N-bit discrete quantum Fourier transform by using two-qubit controlled-NOT gate and SWCZ gate that is a combination of -SWAP and controlled-Z gates in cavity quantum electrodynamics. In this protocol long-lived electronic states in circular Rydberg atoms are used as quantum bits and the one-bit and two-bit quantum gate operations required for implementing the discrete quantum Fourier transform in the quantum circuit can be easily achieved with atom-microwave resonant interaction and atom-cavity interaction occurring only between two nearest-neighbour atoms. We present the detailed experimental procedure and analyse the experimental feasibility.
Song, Xinbing; Sun, Yifan; Li, Pengyun; Qin, Hongwei; Zhang, Xiangdong
2015-01-01
We perform Bell's measurement for the non-separable correlation between polarization and orbital angular momentum from the same classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally. PMID:26369424
NASA Astrophysics Data System (ADS)
Shi, Jinjing; Shi, Ronghua; Guo, Ying; Peng, Xiaoqi; Lee, Moon Ho; Park, Dongsun
2012-04-01
A novel ( t, n)-threshold scheme for the multi-party quantum group signature is proposed based on the irregular quantum Fourier transform, in which every t-qubit quantum message needs n participants to generate the quantum group signature. All the quantum operation gates in the quantum circuit can be distributed and arranged randomly in the irregular QFT algorithm, which can increase the von Neumann entropy of the signed quantum message and the randomicity of the quantum signature generation significantly. The generation and verification of the quantum group signature can be both performed in quantum circuits with the parallel algorithm. Security analysis shows that an available and legal quantum ( t, n)-threshold group signature can be achieved.
NASA Astrophysics Data System (ADS)
Moody, Galan; Bristow, Alan; Siemens, Mark; Dai, Xingcan; Karaiskaj, Denis; Cundiff, Steven
2009-10-01
Optical 2D Fourier transform spectroscopy [1] is used to study the coherent nonlinear response from interfacial (or ``natural'') GaAs quantum dots [2], found within the monolayer fluctuations of a quantum well. The low temperature (˜6K) spectra show excitonic resonances from both the quantum dots and the quantum well, the former having a larger inhomogeneous distribution and narrower homogeneous linewidth. Variation of the population time delay (of the excitation sequence) and lattice temperature reveals a coupling associated with the phonon mediated, incoherent relaxation from the quantum well states to the lower energy quantum dots. [1] S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, X. Dai, Acc. Chem. Res. 42, 1423 (2009). [2] D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, and D. Park, PRL 76, 3005 (1996).
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
Enobio, Eli Christopher I.; Ohtani, Keita; Ohno, Yuzo; Ohno, Hideo
2013-12-02
We demonstrate the use of a Fourier Transform Infrared microscope system to detect and measure electroreflectance (ER) from mid-infrared quantum cascade laser (QCL) device. To characterize intersubband transition (ISBT) energies in a functioning QCL device, a microscope is used to focus the probe on the QCL cleaved mirror. The measured ER spectra exhibit resonance features associated to ISBTs under applied electric field in agreement with the numerical calculations and comparable to observed photocurrent, and emission peaks. The method demonstrates the potential as a characterization tool for QCL devices.
Photocurrent Measurements on a Quantum Cascade Laser Device by Fourier Transform Infrared Microscope
NASA Astrophysics Data System (ADS)
Enobio, Eli Christopher I.; Sato, Hiroki; Ohtani, Keita; Ohno, Yuzo; Ohno, Hideo
2012-06-01
Intersubband photocurrent in the InAs/AlSb mid-infrared quantum cascade laser (QCL) device is measured. To characterize subband energies in a fabricated and functioning QCL laser device, Fourier-transform infrared (FTIR) microscope is used to focus the probe light on the cleaved mirror of QCL. Photocurrent associated with intersubband transitions in the active layer are observed up to room temperature and the origin of peaks is identified by numerical simulation, which demonstrates the potential as a characterization tool for QCL devices.
Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics
NASA Astrophysics Data System (ADS)
Wu, Yinghua; Herman, Michael F.; Batista, Victor S.
2005-03-01
A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuit/split-operator Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MP/SOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.
Fourier Transform Mass Spectrometry
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-01-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook. PMID:21742802
NASA Astrophysics Data System (ADS)
Siemens, Mark; Moody, Galan; Bristow, Alan; Dai, Xingcan; Karaiskaj, Denis; Cundiff, Steven; Bracker, Allan; Gammon, Daniel
2010-03-01
Electronic structure and dynamics can be captured by optical 2D-Fourier-transform spectroscopy (2DFTS), which tracks the phase of the nonlinear signal during two time delays of a multi-pulse excitation sequence. We use optical 2DFTS [1] to study the coherent response of an ensemble of interfacial ``natural'' GaAs quantum dots (QD) [2], found within the monolayer fluctuations of a quantum well (QW). Low temperature (˜6K) spectra show excitonic resonances from both the QD and the QW. We simultaneously extract homogenous and inhomogeneous linewidths of both QW and QD states, indicating slow dephasing and size distribution in the QDs. Additionally, variation of the population time delay and lattice temperature reveals a coupling from the QW states to the lower energy QD mediated by incoherent phonon interactions. [1] S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, X. Dai, Acc. Chem. Res. 42, 1423 (2009). [2] D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, and D. Park, PRL 76, 3005 (1996).
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[-φmax2(n,b)/100] for n
Fourier Transform Mass Spectrometry.
ERIC Educational Resources Information Center
Gross, Michael L.; Rempel, Don L.
1984-01-01
Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)
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).
Fast Fourier transform telescope
Tegmark, Max; Zaldarriaga, Matias
2009-04-15
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog{sub 2}N rather than N{sup 2}) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Fast Fourier transform telescope
NASA Astrophysics Data System (ADS)
Tegmark, Max; Zaldarriaga, Matias
2009-04-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore’s law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog2N rather than N2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
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.
Fourier Transform Spectrometer System
NASA Technical Reports Server (NTRS)
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
NASA Astrophysics Data System (ADS)
Ermilov, A. S.; Zobov, V. E.
2007-12-01
To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3-10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.
NASA Astrophysics Data System (ADS)
Snehalatha, M.; Sekar, N.; Jayakumar, V. S.; Joe, I. Hubert
2008-01-01
Fourier transform infrared (FTIR) spectrum of a well-known food dye sunset yellow FCF (E110) has been recorded and analysed. Assignments of the vibrational spectrum has been facilitated by density functional theory (DFT) calculations. The results of the optimized molecular structure obtained on the basis of B3LYP with 6-31G(d) along with the 'LANL2DZ' basis sets give clear evidence for the intramolecular charge transfer (ICT) and strong hydrogen bonding enhancing the optical nonlinearity of the molecule. The first hyperpolarizability of the acidic monoazo dye 'E110' is computed. Azo stretching frequencies have been lowered due to conjugation and π-electron delocalization. Hydroxyl vibrations with intramolecular H-bonding are analyzed, supported by the computed results. The natural bond orbitals (NBO) analysis confirms this strong hydrogen bond between the hydrogen of the hydroxyl group and nitrogen of the azo group of the molecule. Assignments of benzene and naphthalene ring vibrations are found to agree well with the theoretical wave numbers.
NASA Astrophysics Data System (ADS)
Santhanam, Thalanayar S.; Santhanam, Balu
2009-05-01
Quantum mechanics of a linear harmonic oscillator in a finite-dimensional Hilbert space satisfying the correct equations of motion is studied. The connections to Weyl's formulation of the algebra of bounded unitary operators in finite space as well as to a truncated quantized linear harmonic oscillator are discussed. It is pointed out that the discrete Fourier transformation (DFT) plays a central role in determining the actual form of the position, the momentum, the number and the Hamiltonian operators. The explicit form of these operators in different bases is exhibited for some low values of the dimension of the Hilbert space. In this formulation, it is shown that the Hamiltonian is indeed the logarithm of the DFT and that by modifying Weyl's framework to include position and momentum operators with non-uniformly spaced spectra the equations of motion are satisfied.
NASA Astrophysics Data System (ADS)
Chen, Xin; Batista, Victor S.
2006-09-01
A simple approach for numerically exact simulations of nonadiabatic quantum dynamics in multidimensional systems is introduced and applied to the description of the photoabsorption spectroscopy of pyrazine. The propagation scheme generalizes the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] to simulations of nonadiabatic quantum dynamics. The time-evolution operator is applied, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state expansions. These representations are obtained by combining the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting computational approach are demonstrated in calculations of time-dependent survival amplitudes and photoabsorption cross sections, using a model Hamiltonian that allows for direct comparisons with benchmark calculations. Simulations in full-dimensional potential energy surfaces involve the propagation of a 24-dimensional wave packet to describe the S1/S2 interconversion of pyrazine after S0?S2 photoexcitation. The reported results show that the generalized MP/SOFT method is a practical and accurate approach to model nonadiabatic reaction dynamics in polyatomic systems.
Static Fourier transform infrared spectrometer.
Schardt, Michael; Murr, Patrik J; Rauscher, Markus S; Tremmel, Anton J; Wiesent, Benjamin R; Koch, Alexander W
2016-04-01
Fourier transform spectroscopy has established itself as the standard method for spectral analysis of infrared light. Here we present a robust and compact novel static Fourier transform spectrometer design without any moving parts. The design is well suited for measurements in the infrared as it works with extended light sources independent of their size. The design is experimentally evaluated in the mid-infrared wavelength region between 7.2 μm and 16 μm. Due to its large etendue, its low internal light loss, and its static design it enables high speed spectral analysis in the mid-infrared. PMID:27137061
NASA Astrophysics Data System (ADS)
Batista, Victor; Chen, Xin
2007-03-01
A simple approach for numerically exact simulations of nonadiabatic quantum dynamics in multidimensional systems is introduced and applied to the description of the photoabsorption spectroscopy of pyrazine. The propagation scheme generalizes the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)]. The time-evolution operator is applied, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state expansions. These representations are obtained by combining the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting computational approach are demonstrated in calculations of time-dependent survival amplitudes and photoabsorption cross sections, using a model Hamiltonian that allows for direct comparisons with benchmark calculations. Simulations in full-dimensional potential energy surfaces involve the propagation of a 24-dimensional wave packet to describe the S1 /S2 interconversion of pyrazine after after S0-S2 photoexcitation. The reported results show that the generalized MP/SOFT method is a practical and accurate approach to model nonadiabatic reaction dynamics in polyatomic systems.
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…
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
Fourier-transform optical microsystems
NASA Technical Reports Server (NTRS)
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
Fourier transform Raman optical activity
NASA Astrophysics Data System (ADS)
Polavarapu, P. L.
1988-07-01
Raman optical activity (ROA) is conventionally measured by modulating the incident laser polarization between right and left circular polarization states and detecting the difference in the scattered Raman intensities using a dispersive spectrograph attached to a multichannel detector. In this article, a Fourier transform technique using a Martin-Puplett interferometer is shown to be suitable for measuring both the ROA and ordinary Raman intensities in a single measurement. Novel features in this technique include: (a) incident laser radiation is plane polarized; (b) the scattered Raman light is collected without an analyzer.
Safouhi, Hassan . E-mail: hassan.safouhi@ualberta.ca; Berlu, Lilian
2006-07-20
Molecular overlap-like quantum similarity measurements imply the evaluation of overlap integrals of two molecular electronic densities related by Dirac delta function. When the electronic densities are expanded over atomic orbitals using the usual LCAO-MO approach (linear combination of atomic orbitals), overlap-like quantum similarity integrals could be expressed in terms of four-center overlap integrals. It is shown that by introducing the Fourier transform of delta Dirac function in the integrals and using the Fourier transform approach combined with the so-called B functions, one can obtain analytic expressions of the integrals under consideration. These analytic expressions involve highly oscillatory semi-infinite spherical Bessel functions, which are the principal source of severe numerical and computational difficulties. In this work, we present a highly efficient algorithm for a fast and accurate numerical evaluation of these multicenter overlap-like quantum similarity integrals over Slater type functions. This algorithm is based on the SD-bar approach due to Safouhi. Recurrence formulae are used for a better control of the degree of accuracy and for a better stability of the algorithm. The numerical result section shows the efficiency of our algorithm, compared with the alternatives using the one-center two-range expansion method, which led to very complicated analytic expressions, the epsilon algorithm and the nonlinear D-bar transformation.
FFTLog: Fast Fourier or Hankel transform
NASA Astrophysics Data System (ADS)
Hamilton, Andrew J. S.
2015-12-01
FFTLog is a set of Fortran subroutines that compute the fast Fourier or Hankel (= Fourier-Bessel) transform of a periodic sequence of logarithmically spaced points. FFTLog can be regarded as a natural analogue to the standard Fast Fourier Transform (FFT), in the sense that, just as the normal FFT gives the exact (to machine precision) Fourier transform of a linearly spaced periodic sequence, so also FFTLog gives the exact Fourier or Hankel transform, of arbitrary order m, of a logarithmically spaced periodic sequence.
Laser Field Imaging Through Fourier Transform Heterodyne
Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Galbraith, A.E.; Strauss, C.E.; Grubler, A.C.
1999-04-05
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LADAR systems, Fourier Transform Heterodyne incorporates transverse spatial encoding of the reference local oscillator for image capture. Appropriate selection of spatial encoding functions allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging may be accomplished with a single element detector/sensor requiring no additional scanning or moving components, (2) as detection is governed by heterodyne principles, near quantum limited performance is achievable, (3) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection, and (4) the concept is general with the applicable electromagnetic spectrum encompassing the RF through optical.
NASA Astrophysics Data System (ADS)
Sharma, Tarun Kumar; Fox, Natasha Elizabeth; Cockburn Hosea, Thomas Jeff; Nash, Geoffrey Richard; Coomber, Stuart David; Buckle, Louise; Emeny, Martin Trevor; Ashley, Tim
2008-06-01
At room temperature, we demonstrate an unambiguous detection of the ground- and excited-state transitions of mid-infrared GaInSb/AlGaInSb type I quantum well (QW) lasers grown on GaAs using a new technique based on Fourier transform infrared surface photovoltage spectroscopy. It is found that none of the currently established spectroscopic techniques is able to detect even the ground state transition of these mid-infrared QW lasers at room temperature. The spectroscopic results are in reasonable agreement with the laser emission spectra at low temperatures.
Picqu, Nathalie; Guelachvili, Guy; Kachanov, Alexander A
2003-03-01
Spectra composed of hundreds of time components for absorption path lengths of up to 130 km have been recorded near 1050 nm by combination of two recent techniques, intracavity laser spectroscopy with vertical external cavity surface-emitting multiple-quantum-well lasers and time-resolved Fourier transform spectroscopy. A sensitivity of 1 x 10(-10) cm(-1) Hz(-1/2) is achieved for 10(4) simultaneously acquired spectral elements, 3 orders of magnitude better than the sensitivity obtained in previous similar experiments. Specific advantages of the method, especially for frequency and intensity metrology of weak absorption transitions, are discussed. PMID:12659429
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
ERIC Educational Resources Information Center
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
NASA Astrophysics Data System (ADS)
Neeman, Elias M.; Dréan, Pascal; Huet, Thérèse R.
2016-04-01
Camphene (C10H16) is a bicyclic monoterpene of atmospheric interest. The structure of the unique stable conformer was optimized using density functional theory and ab initio calculations. The rotational spectrum of camphene was recorded in a supersonic jet expansion with a Fourier transform microwave spectrometer over the range 2-20 GHz. Signals from the parent species and from the ten 13C isotopomers were observed in natural abundance. The rotational and centrifugal distortion parameters were fitted to a Watson's Hamiltonian in the A-reduction. Complex line-shapes resulting from a magnetic interaction associated with the pairs of hydrogen nuclei in the methylene groups was observed and modeled. The rotational constants were used together with equilibrium structure to determine the r0 and the rm(1) gas-phase geometries of the carbon skeleton. The present work provides the first spectroscopic characterization of camphene in the gas phase.
NASA Astrophysics Data System (ADS)
Motyka, M.; Janiak, F.; Ryczko, K.; Sęk, G.; Misiewicz, J.; Bauer, A.; Weih, R.; Höfling, S.; Kamp, M.; Forchel, A.
2011-06-01
Modulation spectroscopy in its Fourier-transformed mode has been employed to investigate the optical properties of broken gap `W'-shaped GaSb/AlSb/InAs/InGaSb/InAs/AlSb/GaSb quantum well structures designed to emit in the mid infrared range of 3-4 μm for applications in laser-based gas sensing. Besides the optical transitions originating from the confined states in the type II quantum wells, a number of spectral features at the energy above the GaSb band gap have been detected. They have been analyzed in a function of InAs and GaSb layer widths and ultimately connected with resonant states in the range of AlSb tunneling barriers.
The Geostationary Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Key, Richard; Sander, Stanley; Eldering, Annmarie; Miller, Charles; Frankenberg, Christian; Natra, Vijay; Rider, David; Blavier, Jean-Francois; Bekker, Dmitriy; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for an earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. The GeoFTS instrument is a half meter cube size instrument designed to operate in geostationary orbit as a secondary "hosted" payload on a commercial geostationary satellite mission. The advantage of GEO is the ability to continuously stare at a region of the earth, enabling frequent sampling to capture the diurnal variability of biogenic fluxes and anthropogenic emissions from city to continental scales. The science goal is to obtain a process-based understanding of the carbon cycle from simultaneous high spatial resolution measurements of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) many times per day in the near infrared spectral region to capture their spatial and temporal variations on diurnal, synoptic, seasonal and interannual time scales. The GeoFTS instrument is based on a Michelson interferometer design with a number of advanced features incorporated. Two of the most important advanced features are the focal plane arrays and the optical path difference mechanism. A breadboard GeoFTS instrument has demonstrated functionality for simultaneous measurements in the visible and IR in the laboratory and subsequently in the field at the California Laboratory for Atmospheric Remote Sensing (CLARS) observatory on Mt. Wilson overlooking the Los Angeles basin. A GeoFTS engineering model instrument is being developed which will make simultaneous visible and IR measurements under space flight like environmental conditions (thermal-vacuum at 180 K). This will demonstrate critical instrument capabilities such as optical alignment stability, interferometer modulation efficiency, and high throughput FPA signal processing. This will reduce flight instrument development risk and show that the GeoFTS design is mature and flight ready.
Lagrange-mesh calculations and Fourier transform
Lacroix, Gwendolyn; Semay, Claude
2011-09-15
The Lagrange-mesh method is a very accurate procedure for computing eigenvalues and eigenfunctions of a two-body quantum equation written in the configuration space. Using a Gauss quadrature rule, the method only requires the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions, which vanish at all mesh points except one. Using the peculiarities of the method, it is shown that the Fourier transform of the eigenfunctions, computed in the configuration space, can easily be obtained with good accuracy in the physical domain of the momentum space. Also, observables in this space can easily be computed with good accuracy only using matrix elements and eigenfunctions computed in the configuration space.
Transforming quantum operations: Quantum supermaps
NASA Astrophysics Data System (ADS)
Chiribella, G.; D'Ariano, G. M.; Perinotti, P.
2008-08-01
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.
Polarizing Fourier transform spectroscopy: a forgotten frontier?
NASA Astrophysics Data System (ADS)
Naylor, David A.; Clark, T. A.; Davis, Gary R.
1994-01-01
It is almost 25 years since Martin and Puplett developed the technique of polarizing Fourier transform spectroscopy. While fabrication methods of early polarizers restricted the useful range of polarizing Fourier spectroscopy to far-infrared wavelengths (> 100 micrometers ), advances in the production of precision, low period, large format polarizers have extended this range to mid-infrared wavelengths.
Plasma Spectrochemistry with a Fourier Transform Spectrometer.
NASA Astrophysics Data System (ADS)
Manning, Thomas Joseph John
1990-01-01
This dissertation can be interpreted as being two-dimensional. The first dimension uses the Los Alamos Fourier Transform Spectrometer to uncover various physical aspects of a Inductively Coupled Plasma. The limits of wavenumber accuracy and resolution are pushed to measure line shifts and line profiles in an Inductively Coupled Argon Plasma. This is new physical information that the plasma spectroscopy community has been seeking for several years. Other plasma spectroscopy carried out includes line profile studies, plasma diagnostics, and exact identification of diatomic molecular spectra. The second aspect of the dissertation involves studies of light sources for Fourier Transform Spectroscopy. Sources developed use an inductively coupled plasma (ICP) power supply. New sources (neon ICP, closed cell ICP, and helium ICP) were developed and new methods to enhance the performance and understand a Fourier Transform Spectrometer were studied including a novel optical filter, a spectrum analyzer to study noises, and a standard to calibrate and evaluate a Fourier Transform Spectrometer.
ERIC Educational Resources Information Center
Glasser, L.
1987-01-01
This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…
A Primer of Fourier Transform NMR.
ERIC Educational Resources Information Center
Macomber, Roger S.
1985-01-01
Fourier transform nuclear magnetic resonance (NMR) is a new spectroscopic technique that is often omitted from undergraduate curricula because of lack of instructional materials. Therefore, information is provided to introduce students to the technique of data collection and transformation into the frequency domain. (JN)
Fast Fourier Transforms of Piecewise Constant Functions
NASA Astrophysics Data System (ADS)
Sorets, Eugene
1995-02-01
We present an algorithm for the evaluation of the Fourier transform of piecewise constant functions of two variables. The algorithm overcomes the accuracy problems associated with computing the Fourier transform of discontinuous functions; in fact, its time complexity is O (N2 logN + NP log2 (1/ε) + V log3 (1/ε)), where ε is the accuracy, N is the size of the problem, P is the perimeter of the set of discontinuities, and V is its number of vertices. The algorithm is based on the Lagrange interpolation formula and the Green's theorem, which are used to preprocess the data before applying the fast Fourier transform. It readily generalizes to higher dimensions and to piecewise smooth functions.
Fast Fourier Transform algorithm design and tradeoffs
NASA Technical Reports Server (NTRS)
Kamin, Ray A., III; Adams, George B., III
1988-01-01
The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.
Fourier Transform and Reflective Imaging Pyrometry
Stevens, G. D.
2011-07-01
A stationary Fourier transform pyrometer was used to record mid-wavelength IR spectra in dynamic shock experiments. The gated-IR camera used with this system was also used to record images of light produced and light reflected from shocked metals in order to constrain the dynamic emissivity and provide temperature estimates. This technique will be referred to as reflective imaging pyrometry.
Fourier type transforms on Lie symmetry groups
NASA Astrophysics Data System (ADS)
Craddock, Mark
2015-09-01
In this paper, we construct operators on a Lie symmetry group which may be regarded as Fourier transforms. Essentially, we integrate solutions generated by Lie symmetries against suitable test functions. We show that this idea leads to a powerful method for solving Cauchy problems for parabolic and hyperbolic equations in two and higher dimensions. We also discuss applications to the elliptic case.
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.
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.
Discrete Fourier transforms of nonuniformly spaced data
NASA Technical Reports Server (NTRS)
Swan, P. R.
1982-01-01
Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.
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.
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.
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.
Electro-optic Imaging Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin
2005-01-01
JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-O IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 micron (1000-4000/cm) to allow high-resolution, high-speed hyperspectral imaging applications. One application will be the remote sensing of the measurement of a large number of different atmospheric gases simultaneously in the same airmass. Due to the use of a combination of birefringent phase retarders and multiple achromatic phase switches to achieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventional Fourier transform spectrometer but without any moving parts. In this paper, the principle of operations, system architecture and recent experimental progress will be presented.
Electro-optic Imaging Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin
2005-01-01
JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-0IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 pm (1000 -4000 cm-') to allow high-resolution, high-speed hyperspectral imaging applications [l-51. One application will be theremote sensing of the measurement of a large number of different atmospheric gases simultaneously in the sameairmass. Due to the use of a combination of birefiingent phase retarders and multiple achromatic phase switches toachieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventionalFourier transform spectrometer but without any moving parts. In this paper, the principle of operations, systemarchitecture and recent experimental progress will be presen.
Fourier Transform Fabry-Perot Interferometer
NASA Astrophysics Data System (ADS)
Snell, Hilary E.; Hays, Paul B.
1992-06-01
We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.
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.
Electrocardiogram analysis through time discrete Fourier transform
NASA Astrophysics Data System (ADS)
Lancaster, Cameron; Zhang, Guoping
2011-03-01
The motivation for this research is to find an alternative method to diagnose heart conditions. This can be accomplished by analyzing wave patterns in EKG data, and using the Fourier Transform to compare steady wave patterns against fibrillating wave patterns. The two main contributors are the following: heart electricity and Fourier Transform. Also, it is recognized that ion movement has potential to change the frequency in any heart beat signal. This effect is caused due to a strong electrostatic attraction that causes the membrane capacitance to build charge. For a single ion focus, the Nernst Potential influences the equilibrium potential for the membrane of an ion. If two or more ions are contributing to an electric field charge, the Goldman-Hodgkin-Katz will find the membrane equilibrium potential. If a membrane has an efflux, or influx, of ions, then it is possible to get the passive flow of the electric current to zero. In continued research, we will gain knowledge of solving equations; such as ionic flux, quantitative diffusion, electric current density, and more. The finishing portion of this research will be to compare the Fourier Transformed wave graphs to determine heart conditions. Supported by U.S. Department of Energy under Contract No. DE-FG02-06ER46304 and Indiana State University.
Diffraction theory for an achromatic Fourier transformation.
Morris, G M
1981-06-01
A three-lens achromatic Fourier transform system is analyzed in the context of paraxial Fresnel diffraction theory. From the analysis a general solution for the required wavelength dependence of the various lenses is found. A particular arrangement of the general system is then considered. Using first-order lens design principles, it is shown that each dispersive lens can be fabricated using a holographic zone lens and glass element cascade. The paraxial chromatic aberrations of the resulting system are calculated. It is found that this system design yields an achromatic transformation that is well corrected (paraxially) over the entire visible spectrum. PMID:20332876
Diffraction theory for an achromatic Fourier transformation
Morris, G.M.
1981-06-01
A three-lens achromatic Fourier transform system is analyzed in the contex of parazial Fresnel diffraction theory. From the analysis a general solution for the required wavelength dependence of the various lenses is found. A particular arrangement of the general system is then considered. Using first-order lens design principles, it is shown that each dispersive lens cand be fabricated using a holographic zone lens and glas element cascade. The parazial chromatic aberrations of the resulting system are calculated. It is found that this system design yields an achromatic transformation that is well corrected (parazially) over the entire visible spectrum.
On Superoscillations Longevity: A Windowed Fourier Transform Approach
NASA Astrophysics Data System (ADS)
Aharonov, Y.; Colombo, F.; Sabadini, I.; Struppa, D. C.; Tollaksen, J.
In this paper we prove that the evolution of a superoscillating sequence of functions Y N (x), which we take as the initial value of the Schrdinger equation, remains superoscillating for all values of the time t
Optical image encryption based on multifractional Fourier transforms.
Zhu, B; Liu, S; Ran, Q
2000-08-15
We propose a new image encryption algorithm based on a generalized fractional Fourier transform, to which we refer as a multifractional Fourier transform. We encrypt the input image simply by performing the multifractional Fourier transform with two keys. Numerical simulation results are given to verify the algorithm, and an optical implementation setup is also suggested. PMID:18066153
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.
Alternating multivariate trigonometric functions and corresponding Fourier transforms
NASA Astrophysics Data System (ADS)
Klimyk, A. U.; Patera, J.
2008-04-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group An, which is a subgroup of the permutation (symmetric) group Sn. These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel.
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.
Two-dimensional Fourier transform electronic spectroscopy
NASA Astrophysics Data System (ADS)
Jonas, David
2012-02-01
Sensitive interference detection of the electric field of femtosecond four-wave mixing signals (stimulated photon echoes) at their point of origin in the sample can be used to record two-dimensional (2D) Fourier transform electronic spectra. In direct analogy to 2D nuclear magnetic resonance, 2D Fourier transform spectra have nearly homogeneous linewidths in each frequency dimension and sort the signal spectrum according to the initial excitation frequency. The initial excitation frequency information is stored in a robust population grating, so 2D spectra can be used to study both coherent and incoherent processes, and have revealed coherent aspects of energy transfer processes. Femtosecond 2D spectra also have the advantage of ``freezing out'' vibrational motions as inhomogeneities, raising interesting questions about what kinds of broadening can be rephased in 2D spectra recorded with stimulated photon echo pulse sequences. This talk will focus on coherent aspects of non-adiabatic electronic curve crossing and their manifestation in 2D electronic spectra.
Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.
ERIC Educational Resources Information Center
Glasser, L.
1987-01-01
Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
ERIC Educational Resources Information Center
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
ERIC Educational Resources Information Center
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",
Fourier Transform Raman spectroscopy with polarization modulation
NASA Astrophysics Data System (ADS)
Polavarapu, P. L.
Fourier Transform Raman spectroscopy can be performed with either a Martin—Puplett interferometer (MPI) or a Michelson interferometer (MI). With linearly polarized exciting light, the MPI provides information on the Stokes parameters S1, and S3 of the scattered Raman light, from a single measurement. The parameter S1 represents the difference in the scattered intensities with parallel and perpendicular polarizations while S3 represents the difference in the scattered intensities with right and left circular polarizations. A procedure to extract these parameters with a Michelson interferometer is developed in this paper. A comparison of both approaches indicates that the use of the MPI is favored if the objective is to extract the Stokes parameters. Both approaches are equally favored if the objective is to measure the depolarization ratios. For measuring total Raman scattering, the use of a Michelson interferometer appears preferable.
Optical correction using fourier transform heterodyne
NASA Astrophysics Data System (ADS)
Laubscher, Bryan E.; Nemzek, Robert J.; Cooke, Bradly J.; Olivas, Nicholas L.; Jorgensen, Anders M.; Smith, J. A.; Weisse-Bernstein, Nina R.
2005-08-01
In this paper we briefly present the theory of Fourier Transform Heterodyne (FTH), describe past verification experiments carried out, and discuss the experiment designed to use this new imaging technology to perform optical correction. FTH uses the scalar projection of a reference laser beam and a test laser beam onto a single element detector. The complex current in the detector yields the coefficient of the scalar projection. By projecting a complete orthonormal basis set of reference beams onto the test beam, the amplitude and phase of the test beam can be measured, allowing the reconstruction of the phasefront of the image. Experiments to determine this technique's applicability to optical correction and optical self-correction are continuing. Applications of this technique beyond optical correction include adaptive optics; interferometry; and active, high background, low signal imaging.
Surface Inspection using fourier transform infrared spectroscopy
Powell, G.L.; Smyrl, N.R.; Williams, D.M.; Meyers, H.M. III; Barber, T.E.; Marrero-Rivera, M.
1994-08-08
The use of reflectance Fourier transform infrared (FTIR) spectroscopy as a tool for surface inspection is described. Laboratory instruments and portable instruments can support remote sensing probes that can map chemical contaminants on surfaces. Detection limits under the best of conditions are in the subnanometer range (i.e., near absolute cleanliness), excellent performance is obtained in the submicrometer range, and useful performance may exist for films tens of microns thick. Identifying and quantifying contamination such as mineral oils and greases, vegetable oils, and silicone oils on aluminum foil, galvanized sheet steel, smooth aluminum tubing, and gritblasted 7075 aluminum alloy and D6AC steel are described. The ability to map in time and space the distribution of oil stains on metals is demonstrated. Techniques for quantitatively applying oils to metals, subsequently verifying the application, and nonlinear relationships between reflectance and the quantity of oil are discussed.
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.
Compact snapshot birefringent imaging Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Kudenov, Michael W.; Dereniak, Eustace L.
2010-08-01
The design and implementation of a compact multiple-image Fourier transform spectrometer (FTS) is presented. Based on the multiple-image FTS originally developed by A. Hirai, the presented device offers significant advantages over his original implementation. Namely, its birefringent nature results in a common-path interferometer which makes the spectrometer insensitive to vibration. Furthermore, it enables the potential of making the instrument ultra-compact, thereby improving the portability of the sensor. The theory of the birefringent FTS is provided, followed by details of its specific embodiment. A laboratory proof of concept of the sensor, designed and developed at the Optical Detection Lab, is also presented. Spectral measurements of laboratory sources are provided, including measurements of light-emitting diodes and gas-discharge lamps. These spectra are verified against a calibrated Ocean Optics USB2000 spectrometer. Other data were collected outdoors, demonstrating the sensor's ability to resolve spectral signatures in standard outdoor lighting and environmental conditions.
Quantum indeterminism: a direct consequence of Fourier ontology
NASA Astrophysics Data System (ADS)
Croca, J. R.
2013-10-01
Fourier ontology and consequent quantum indeterminism and the way to overcome it shall be discussed. Furthermore it shall be proven that recent experimental technology goes far beyond the limits imposed by Heisenberg indetermination relations. These experiments are perfectly integrated in the new causal nonlinear quantum physics. Keywords: Orthodox quantum mechanics, Fourier ontology, Heisenberg indetermination relations, nonlinear quantum physics, general uncertainty relations, beyond Heisenberg limits.
Geometric interpretations of the Discrete Fourier Transform (DFT)
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
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.
Imaging Fourier transform spectrometry of chemical plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.; Gross, Kevin C.; Perram, Glen P.
2009-05-01
A midwave infrared (MWIR) imaging Fourier transform spectrometer (FTS), the Telops FIRST-MWE (Field-portable Imaging Radiometric Spectrometer Technology - Midwave Extended) has been utilized for the standoff detection and characterization of chemical plumes. Successful collection and analysis of MWIR hyperspectral imagery of jet engine exhaust has allowed us to produce spatial profiles of both temperature and chemical constituent concentrations of exhaust plumes. Successful characterization of this high temperature combustion event has led to the collection and analysis of hyperspectral imagery of lower temperature emissions from industrial smokestacks. This paper presents MWIR data from remote collection of hyperspectral imagery of methyl salicilate (MeS), a chemical warfare agent simulant, during the Chemical Biological Distributed Early Warning System (CBDEWS) test at Dugway Proving Grounds, UT in 2008. The data did not contain spectral lines associated with emission of MeS. However, a few broad spectral features were present in the background-subtracted plume spectra. Further analysis will be required to assign these features, and determine the utility of MWIR hyperspectral imagery for analysis of chemical warfare agent plumes.
Fourier transform spectroscopy for future planetary missions
NASA Astrophysics Data System (ADS)
Brasunas, John C.; Hewagama, Tilak; Kolasinski, John R.; Kostiuk, Theodor
2015-11-01
Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system.Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, NASA Goddard was funded via the Planetary Instrument Definition and Development Progrem (PIDDP) to develop CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. Following the initial validation of CIRS-lite operation in the laboratory, we have been acquiring atmospheric data in the 8-12 micron window at the 1.2 m telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) in Greenbelt, MD. Targets so far have included Earth's atmosphere (in emission, and in absorption against the moon), and Venus.We will present the roadmap for making CIRS-lite a viable candidate for future planetary missions.
2D Fourier-transform Spectroscopy of Potassium Vapor
NASA Astrophysics Data System (ADS)
Dai, Xingcan; Bristow, Alan D.; Karaiskaj, Denis; Cundiff, Steven T.
2010-03-01
2D Fourier-transform (2DFT) spectroscopy is a time-domain technique that measures the coherent optical response in two spectral dimensions. This method has elucidated the structure and electronic dynamics in molecules and semiconductors [1], where many-body interactions are expected. Here we demonstrate how 2DFT spectroscopy isolates specific quantum excitation pathways in a simple quantum system, namely potassium vapor in a thin transmission cell [2]. A femtosecond pulse sequence excites both the D1 and D2 lines simultaneously to reveal coupling between the transitions as a result of quantum interference and Raman-like coherences. Observations agree well with numerical simulations based on the optical Bloch equations. The non-radiative Raman pathways have population-time dependence and are isolated by altering the 2DFT projection. Density-dependent measurements show distortion of the 2DFT spectral features due to pulse propagation effects. Unexpected two-quantum coherences are observed and attributed to interatomic interactions.[4pt] [1] Cundiff et al, Acc. Chem. Res. 42, 1423 (2009).[0pt] [2] Dai et al, arXiv:1001.1955v1
Determination of Fourier Transforms on an Instructional Analog Computer
ERIC Educational Resources Information Center
Anderson, Owen T.; Greenwood, Stephen R.
1974-01-01
An analog computer program to find and display the Fourier transform of some real, even functions is described. Oscilloscope traces are shown for Fourier transforms of a rectangular pulse, a Gaussian, a cosine wave, and a delayed narrow pulse. Instructional uses of the program are discussed briefly. (DT)
Three-dimensional Fourier-transform spectroscopy of potassium vapor
NASA Astrophysics Data System (ADS)
Li, Hebin; Bristow, Alan; Siemens, Mark; Moody, Galan; Cundiff, Steven
2011-03-01
We have implemented three-dimensional (3D) Fourier-transform spectroscopy to study potassium vapor contained in a ~ 20 μ m transmission cell with argon buffer gas. The four-wave mixing signal is measured in three time dimensions corresponding to the delays between three ~ 100 fs, phase-stabilized excitation pulses that are arranged in the box geometry. The emission is detected using a phase-stabilized reference pulse by spectral interferometry, and other time axes are Fourier transformed to construct the 3D spectra. The 3D spectra contain the full information of third-order coherent response of the vapor, yet the contribution from each of the single-quantum excitation pathways is unambiguously isolated. Projecting a 3D spectrum onto a specific two-dimensional (2D) plane retrieves rephasing, non-rephasing, and T-scan 2D spectra, as well as the spectra that are not accessible by conventional 2D scans. The spectral features which overlap in congested 2D spectra can be isolated for studying unique processes represented by a single pathway.
Signal Processing Issues in Fourier Transform Spectrometers
NASA Astrophysics Data System (ADS)
Hayes, Monson H.
2002-12-01
There are a number of interesting and challenging signal processing problems related to the design of a Fourier Transform Spectrometer (FTS). In this project, we look at a few of these problems in two different types of spectrometers-the Geostationary Imaging Fourier Transform Spectrometer (GIFTS), and a Far Infrared (FIR) FTS. One of the si nal processing challenges in GIFTS is the reduction of the massive data rate (2.4 x 109 bps) to an affordable telemetry rate of less than 60 Mbps. Since the GIFTS interferograms are heavily over-sampled, the first step is to decimate (down-sample) the interferograms with minimal distortion while keeping the signal processing algorithms simple enough to be implemented in the GIFTS hardware. Therefore, the first problem we looked at was the design of the decimation filters. Specifically, we performed a detailed analysis of two competing approaches that were being considered. The first, proposed by the Space Dynamics Lab (SDL), was to use a double sideband (real) band-pass filter. The second, proposed by Lincoln Laboratories (LL), was to use a single sideband (complex) band-pass filter. What the study showed was that a complex filter (LL approach) results in a savings of about 25% in the filtering requirements for the long-wave band, while in the mid-wave band the savings are approximately 50%. As a result, the decision was made to use a complex filter. Once the decision to use a complex filter had been made, we looked at some of the consequences of this decision. The most significant of these was the discovery that, with a complex filter, it is possible to extend the long-wave IR band beyond the folding frequency of 1174/cm and recover the SO2 line at 1176.5/cm. What this requires is the design of a band-pass decimation filter with a wider passband, and consequently of higher order. Specifically, it was shown that with about 25% more filter operations, the elusive SO2 line, believed to be irretrievable, could in fact be recovered. While working on the decimation filtering requirements, an issue arose with respect to how the 16-bit long-wave interferogram data should be processed by a 15-bit USES chip. There were two approaches being considered, and each one had at least one serious drawback. Therefore, given the nature of the data that is to be processed by the USES chip, we developed an efficient loss-less encoder that is robust to errors, and is easily decoded. Since the encoder eliminates the drawbacks of the other two approaches, and greatly simplifies the signal processing requirements, the downlink board is currently being redesigned to include this encoder. The last problem that was looked at involved an investigation into the optimum sampling strategy in the design of a far infrared FTS. The problem was to minimize the amount of spectral noise that is induced by non-uniform mirror velocity.
Air pollution measurement by Fourier transform spectroscopy.
Hanst, P L
1978-05-01
The use of infrared methods in pollution measurement has been hampered by sensitivity limitations and by interferences from water vapor. Fourier transform spectrometer systems reduce these limitations by their high optical efficiency and their ability to manipulate spectra for removal of interfering bands. At the Environmental Protection Agency we have sought to further increase the sensitivity of the infrared technique by evolving optimal long path cell designs and sample concentration techniques. Reactive pollutants such as O(3), H(2)O(2), HNO(3), HNO(2), H(2)CO, HCOOH, PAN, HCl, NH(3), NO, and NO(2) are best measured in the open atmosphere. In this case one strives toward large absorption cells with the paths as long as practical. Our largest cell is being used to measure pollutants in the smog at Riverside, California. This cell uses an eight-mirror system for multiple-passing radiation along a 23-m base path, yielding total paths measured in kilometers. Reactive gases at levels of just a few ppb have been measured. For measuring nonreactive pollutants, such as hydrocarbons and halocarbons, maximum detection sensitivity is achieved with small folded-path cells rather than with large cells. In this case a pollutant concentrate is prepared and introduced into a miniaturized multiple-pass cell designed for maximum path-to-volume ratio. Cryogenic trapping to separate the pollutants from the major constituents of the air has yielded concentration factors as high as one million. The smallest multiple-pass cell we have built to date encloses a 115-cm light path within a volume of 3 cm(3). This cell when used with the FTS spectrometer and mercury-cadmium-telluride detector permits the detection of nanogram quantities of pollutant gases. Measurements have been made of trace gases in the air at mixing ratios as low as 2 x 10(-11). PMID:20197989
Fourier transform based scalable image quality measure.
Narwaria, Manish; Lin, Weisi; McLoughlin, Ian; Emmanuel, Sabu; Chia, Liang-Tien
2012-08-01
We present a new image quality assessment (IQA) algorithm based on the phase and magnitude of the 2D (twodimensional) Discrete Fourier Transform (DFT). The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the Human Visual Systems (HVSs) sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of nonuniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Lastly, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is therefore further scalable for RR scenarios. We report extensive experimental results using a total of 9 publicly available databases: 7 image (with a total of 3832 distorted images with diverse distortions) and 2 video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing fullreference (FR) algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar. PMID:22562758
Cryogenic Scan Mechanism for Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Brasunas, John C.; Francis, John L.
2011-01-01
A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses
Lim, Lucy; Yan, Fangzhi; Bach, Stephen; Pihakari, Katianna; Klein, David
2016-01-01
Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS) has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices. PMID:26784175
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses.
Lim, Lucy; Yan, Fangzhi; Bach, Stephen; Pihakari, Katianna; Klein, David
2016-01-01
Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS) has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices. PMID:26784175
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.
Implementation of weighted summation type fractional Fourier transform on FPGA
NASA Astrophysics Data System (ADS)
Zou, Qiming; Li, Longlong; Huang, Qian; Wang, Fei
2015-07-01
Recently Fractional Fourier transform (FrFT) has got a variety of applications in digital signal and image processing. This paper presents a novel hardware architecture for real-time computation of Discrete Fractional Fourier Transform (DFrFT), which can easily be extended to other fractional transforms. The proposed architecture has been verified on Xilinx FPGA(XC6VLX240T), which can run at a frequency up to 291MHz while with high accuracy.
Image reconstruction from pairs of Fourier-transform magnitude
Hunt, B.R.; Overman, T.L.; Gough, P.
1998-07-01
The retrieval of phase information from only the magnitude of the Fourier transform of a signal remains an important problem for many applications. We present an algorithm for phase retrieval when there exist two related sets of Fourier-transform magnitude data. The data are assumed to come from a single object observed in two different polarizations through a distorting medium, so the phase component of the Fourier transform of the object is corrupted. Phase retrieval is accomplished by minimization of a suitable criterion function, which can take three different forms. {copyright} {ital 1998} {ital Optical Society of America}
NASA Technical Reports Server (NTRS)
Marko, H.
1978-01-01
A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.
Xgremlin: Interferograms and spectra from Fourier transform spectrometers analysis
NASA Astrophysics Data System (ADS)
Nave, G.; Griesmann, U.; Brault, J. W.; Abrams, M. C.
2015-11-01
Xgremlin is a hardware and operating system independent version of the data analysis program Gremlin used for Fourier transform spectrometry. Xgremlin runs on PCs and workstations that use the X11 window system, including cygwin in Windows. It is used to Fourier transform interferograms, plot spectra, perform phase corrections, perform intensity and wavenumber calibration, and find and fit spectral lines. It can also be used to construct synthetic spectra, subtract continua, compare several different spectra, and eliminate ringing around lines.
Automatic Fourier transform and self-Fourier beams due to parabolic potential
NASA Astrophysics Data System (ADS)
Zhang, Yiqi; Liu, Xing; Belić, Milivoj R.; Zhong, Weiping; Petrović, Milan S.; Zhang, Yanpeng
2015-12-01
We investigate the propagation of light beams including Hermite-Gauss, Bessel-Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams-that is, the beams whose Fourier transforms are the beams themselves.
Quantum number theoretic transforms on multipartite finite systems.
Vourdas, A; Zhang, S
2009-06-01
A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied. A representation of the Heisenberg-Weyl group in this context is also discussed. PMID:19488175
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 (ω1, ω2) is defined in the exponential kernel of the transformation by a nonlinear form L(x, y; ω1, ω2). The traditional concept of the 2-D DFT uses the Diaphanous form xω1 +yω2 and this 2-D DFT is the particular case of the Fourier transform described by the form L(x, y; ω1, ω2). 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.
NASA Astrophysics Data System (ADS)
Spencer, Locke Dean
The Herschel Space Observatory (Herschel), a flagship mission of the European Space Agency (ESA), is comprised of three cryogenically cooled instruments commissioned to explore the far-infrared/submillimetre universe. Herschel's remote orbit at the second Lagrangian point (L2) of the Sun-Earth system, and its cryogenic payload, impose a need for thorough instrument characterization and rigorous testing as there will be no possibility for any servicing after launch. The Spectral and Photometric Imaging Receiver (SPIRE) is one of the instrument payloads aboard Herschel and consists of a three band imaging photometer and a two band imaging spectrometer. The imaging spectrometer on SPIRE consists of a Mach-Zehnder (MZ)-Fourier transform spectrometer (FTS) coupled with bolometric detector arrays to form an imaging FTS (IFTS). This thesis presents experiments conducted to verify the performance of an IFTS system from a space based platform, Le. the use of the SPIRE IFTS within the Herschel space observatory. Prior to launch, the SPIRE instrument has undergone a series of performance verification tests conducted at the Rutherford Appleton Laboratory (RAL) near Oxford, UK. Canada is involved in the SPIRE project through provision of instrument development hardware and software, mission flight software, and support personnel. Through this thesis project I have been stationed at RAL for a period spanning fifteen months to participate in the development, performance verification, and characterization of both the SPIRE FTS and photometer instruments. This thesis discusses Fourier transform spectroscopy and related FTS data processing (Chapter 2). Detailed discussions are included on the spectral phase related to the FTS beamsplitter (Chapter 3), the imaging aspects of the SPIRE IFTS instrument (Chapter 4), and the noise characteristics of the SPIRE bolometer detector arrays as measured using the SPIRE IFTS (Chapter 5). This thesis presents results from experiments performed both on site at the RAL Space Science and Technology Department (SSTD) Assembly Integration Verification (AIV) instrument test facility as well as from the Astronomical Instrumentation Group (AIG) research laboratories within the Department of Physics & Astronomy at the University of Lethbridge.
The Pegg-Barnett phase operator and the discrete Fourier transform
NASA Astrophysics Data System (ADS)
Perez-Leija, Armando; Andrade-Morales, Luis A.; Soto-Eguibar, Francisco; Szameit, Alexander; Moya-Cessa, Héctor M.
2016-04-01
In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg-Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London-Susskind-Glogower phase operator, whose natural logarithm gives rise to the Pegg-Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties.
Electro-Optical Imaging Fourier-Transform Spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin; Zhou, Hanying
2006-01-01
An electro-optical (E-O) imaging Fourier-transform spectrometer (IFTS), now under development, is a prototype of improved imaging spectrometers to be used for hyperspectral imaging, especially in the infrared spectral region. Unlike both imaging and non-imaging traditional Fourier-transform spectrometers, the E-O IFTS does not contain any moving parts. Elimination of the moving parts and the associated actuator mechanisms and supporting structures would increase reliability while enabling reductions in size and mass, relative to traditional Fourier-transform spectrometers that offer equivalent capabilities. Elimination of moving parts would also eliminate the vibrations caused by the motions of those parts. Figure 1 schematically depicts a traditional Fourier-transform spectrometer, wherein a critical time delay is varied by translating one the mirrors of a Michelson interferometer. The time-dependent optical output is a periodic representation of the input spectrum. Data characterizing the input spectrum are generated through fast-Fourier-transform (FFT) post-processing of the output in conjunction with the varying time delay.
Fourier-Transform Microwave Spectroscopy of HCCNSi and NCNSi
NASA Astrophysics Data System (ADS)
Thorwirth, S.; Kaiser, R. I.; McCarthy, M. C.; Crabtree, K. N.; Martinez, O., Jr.
2013-06-01
By means of Fourier transform microwave spectroscopy of a supersonic jet, the pure rotational spectra of the silicon-bearing chain molecules silaisocyanoacetylene, HCCNSi, and cyanosilaisocyanide, NCNSi, have been studied for the first time. The molecules were observed in low-current dc discharges through appropriate gas mixtures comprising CH_3CN/SiH_4 and cyanogen/SiH_4 heavily diluted in neon. Spectroscopic searches and identification were based on predictions from high-level quantum-chemical calculations at the CCSD(T) level of theory in combination with large basis sets. Excellent agreement between experimental and calculated molecular parameters is found. In addition to the parent isotopic species, rotational lines of rare isotopologs were also observed. Because of the close relationship of these two species to known astronomical molecules and due to their sizable dipole moments of μ=1.4 D (HCCNSi) and μ=5.4 D (NCNSi) both are plausible targets for future astronomical searches using large radio telescopes.
Blind digital watermarking method in the fractional Fourier transform domain
NASA Astrophysics Data System (ADS)
Lang, Jun; Zhang, Zheng-guang
2014-02-01
In this paper, we proposed a novel blind digital image watermarking algorithm based on the fractional Fourier transform (FRFT), which is a generalization of the ordinary Fourier transform and its output has the mixed time and frequency components of the signal. The original image is segmented into non-overlapping blocks for watermarking, and each block is transformed by the two dimensional fractional Fourier transform with two fractional orders. Then each pixel value of binary watermark is embedded by modifying the back-diagonal FRFT coefficients of each image block at the same location with a random array. After perform an inverse two dimensional fractional Fourier transform, we can obtain the watermarked image and the transform orders can be consider as the encryption keys in this method. A series of attacking experiments are performed on the proposed method. The experiments results show that the proposed algorithm not only is of good imperceptibility and security and is very robust to JPEG compression noise attacks and image manipulation operations, but also can provide protection even under compound attacks.
Parallel fast Fourier transforms for non power of two data
Semeraro, B.D.
1994-09-01
This report deals with parallel algorithms for computing discrete Fourier transforms of real sequences of length N not equal to a power of two. The method described is an extension of existing power of two transforms to sequences with N a product of small primes. In particular, this implementation requires N = 2{sup p}3{sup q}5{sup r}. The communication required is the same as for a transform of length N = 2{sup p}. The algorithm presented is intended for use in the solution of partial differential equations, or in any situation in which a large number of forward and backward transforms must be performed and in which the Fourier Coefficients need not be ordered. This implementation is a one dimensional FFT but the techniques are applicable to multidimensional transforms as well. The algorithm has been implemented on a 128 node Intel Ipsc/860.
Double image encryption based on iterative fractional Fourier transform
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Liu, Shutian
2007-07-01
We present an image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders. From the encrypted image we can get two original images independently by fractional Fourier transforms with two different fractional orders. This algorithm can be independent of additional random phases as the encryption/decryption keys. Numerical results are given to analyze the capability of this proposed method. A possible extension to multi-image encryption with a fractional order multiplexing scheme has also been given.
Fourier-transform and global contrast interferometer alignment methods
Goldberg, Kenneth A.
2001-01-01
Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.
Fractional Fourier transform in temporal ghost imaging with classical light
Setaelae, Tero; Shirai, Tomohiro; Friberg, Ari T.
2010-10-15
We investigate temporal, second-order classical ghost imaging with long, incoherent, scalar plane-wave pulses. We prove that in rather general conditions, the intensity correlation function at the output of the setup is given by the fractional Fourier transform of the temporal object. In special cases, the correlation function is shown to reduce to the ordinary Fourier transform and the temporal image of the object. Effects influencing the visibility and the resolution are considered. This work extends certain known results on spatial ghost imaging into the time domain and could find applications in temporal tomography of pulses.
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.
Gas Analysis by Fourier Transform Mm-Wave Spectroscopy
NASA Astrophysics Data System (ADS)
Harris, Brent J.; Steber, Amanda L.; Lehmann, Kevin K.; Pate, Brooks H.
2013-06-01
Molecular rotational spectroscopy of low pressure, room temperature gases offers high chemical selectivity and sensitivity with the potential for a wide range of applications in gas analysis. A strength of the technique is the potential to identify molecules that have not been previously studied by rotational spectroscopy by comparing experimental results to predictions of the spectroscopic parameters from quantum chemistry -6 so called library-free detection. The development of Fourier transform mm-wave spectrometers using high peak power (30 mW) active multiplier chain mm-wave sources brings new measurement capabilities to the analysis of complex gas mixtures. Strategies for gas analysis based on high-throughput mm-wave spectroscopy and arbitrary waveform generator driven mm-wave sources are described. Several new measurement capabilities come from the intrinsic time-domain measurement technique. High-sensitivity double-resonance measurements can be performed to speed the analysis of a complex gas sample containing several species. This technique uses a "pi-pulse" to selectively invert the population of two selected rotational energy levels and the effect of this excitation pulse on all other transitions in the spectrometer operating range is monitored using segmented chirped-pulse Fourier transform spectroscopy. This method can lead to automated determination of the molecular rotational constants. Rapid pulse duration scan experiments can be used to estimate the magnitude and direction of the dipole moment of the molecule from an unknown spectrum. Coherent pulse echo experiments, using the traditional Hahn sequence or two-color population recovery methods, can be used to determine the collisional relaxation rate of the unknown molecule. This rate determination improves the ability to estimate the mass of the unknown molecule from the determination of the Doppler dephasing rate. By performing a suite of automated, high-throughput measurements, there is the potential to determine the shape (via the rotational constant), electric properties (the dipole moments and its direction in the principal axis system), and the mass of the molecule to aid its identification.
Discrete Fourier Transform in a Complex Vector Space
NASA Technical Reports Server (NTRS)
Dean, Bruce H. (Inventor)
2015-01-01
An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.
Discrete Fourier Transform Analysis in a Complex Vector Space
NASA Technical Reports Server (NTRS)
Dean, Bruce H.
2009-01-01
Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.
Jacobi {theta}-functions and discrete Fourier transforms
Ruzzi, M.
2006-06-15
Properties of the Jacobi {theta}{sub 3}-function and its derivatives under discrete Fourier transforms are investigated, and several interesting results are obtained. The role of modulo N equivalence classes in the theory of {theta}-functions is stressed. An important conjecture is studied.
Theoretical study of Fourier-transform acousto-optic imaging.
Barjean, Kinia; Ramaz, François; Tualle, Jean-Michel
2016-05-01
We propose a full theoretical study of Fourier-transform acousto-optic imaging, which we recently introduced and experimentally assessed in [Opt. Lett.40, 705-708 (2015)OPLEDP0146-959210.1364/OL.40.000705] as an alternative to achieve axial resolution in acousto-optic imaging with a higher signal-to-noise ratio. PMID:27140883
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...
Fourier transform spectroscopy of cotton and cotton trash
Technology Transfer Automated Retrieval System (TEKTRAN)
Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
NASA Technical Reports Server (NTRS)
Dean, Bruce H. (Inventor)
2012-01-01
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
ERIC Educational Resources Information Center
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
Transfer Functions Via Laplace- And Fourier-Borel Transforms
NASA Technical Reports Server (NTRS)
Can, Sumer; Unal, Aynur
1991-01-01
Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.
A Student's Guide to Fourier Transforms - 2nd Edition
NASA Astrophysics Data System (ADS)
James, J. F.
2002-09-01
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science. Expanded to include more emphasis on applications An established successful textbook for undergraduate and graduate students Includes worked examples and copious diagrams throughout
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.
Microholography by Numerical Wavefront Reconstruction in the Fourier Transform Geometry.
NASA Astrophysics Data System (ADS)
Haddad, Waleed Sami
New techniques for pulsed holographic microimaging with x-rays and visible light based on the Fourier transform geometry are presented. A charge-coupled device (CCD) is used to record the holographic information. Images are reconstructed numerically by fast Fourier transform (FFT) and by a novel "stigmatic" aberration-free technique. It is shown by numerical simulation that reconstruction by FFT inherently suffers from coma. An innovative design for a Fourier transform x -ray holographic microscope incorporating a metallic microsphere as the reference wave producing element is presented. The design is optimized for use with an x-ray laser source operating in the range lambda~eq43 A; nickel is found to be the best material for the reference sphere in this range. A visible light analog of the x-ray microscope was built and tested yielding an image of Ascaris larva. Two unique visible light Fourier transform holographic microscopes are also presented. The first incorporates a glycerol microdrop reference lens. This microscope was operated at N.A. ~ 0.25 with an argon ion laser at lambda = 514.5 nm. The transverse point spread function of the system was measured to be 1.40 mum, near the theoretical diffraction limit of 1.29 mu m. The second is a design based on a Mach-Zehnder interferometer. This Fourier Mach Zehnder holographic microscope (FMZHM) offers great flexibility and many advantages. The FMZHM was operated at N.A. _sp{~ }{>} 0.25 with lambda = 514.5 nm and yielded many 2-D and 3-D images of biological samples. A study of potential biological applications of visible and x-ray holographic microscopy is also presented.
NASA Astrophysics Data System (ADS)
Chow, T. H.; Gulam Razul, S.; Ng, B. K.; Ho, Gideon; Yeo, C. B. A.
2008-02-01
In this paper, we address the problem of spectral data sampling in Fourier domain optical coherence tomography (FD-OCT). The interferometric information in a Fourier Domain OCT system is retrieved from spectral measurements made using a linear array spectrometer. In such spectrometers, spectral data are available as an array of points equally spaced in the wavelength domain. To obtain the spatial profile, the spectral data have to be converted to the frequency domain before applying the Fourier transform. The inverse relationship between these domains causes an unequal spacing of data points after the spectral data is converted to the frequency domain, resulting in the degradation of the FD-OCT images. The current practice typically utilizes zero-padding and spline interpolation to circumvent this problem. While these algorithms do improve the FD-OCT images, our investigations showed that more can be done to enhance the images. Toward this end, we propose a signal processing algorithm based on non-uniform discrete Fourier transform (NUDFT). The results of our algorithm are compared against the current algorithms on both simulated and experimental results.
Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie
2015-10-20
In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance. PMID:26560376
Nakamura, Shin; Ota, Kai; Shibuya, Yuichi; Noguchi, Takumi
2016-01-26
Photosynthetic water oxidation takes place at the Mn4CaO5 cluster in photosystem II. Around the Mn4CaO5 cluster, a hydrogen bond network is formed by several water molecules, including four water ligands. To clarify the role of this water network in the mechanism of water oxidation, we investigated the effects of the removal of Ca(2+) and substitution with metal ions on the vibrations of water molecules coupled to the Mn4CaO5 cluster by means of Fourier transform infrared (FTIR) difference spectroscopy and quantum mechanics/molecular mechanics (QM/MM) calculations. The OH stretching vibrations of nine water molecules forming a network between D1-D61 and YZ were calculated using the QM/MM method. On the the calculated normal modes, a broad positive feature at 3200-2500 cm(-1) in an S2-minus-S1 FTIR spectrum was attributed to the vibrations of strongly hydrogen-bonded OH bonds of water involving the vibrations of water ligands to a Mn ion and the in-phase coupled vibration of a water network connected to YZ, while bands in the 3700-3500 cm(-1) region were assigned to the coupled vibrations of weakly hydrogen-bonded OH bonds of water. All the water bands were lost upon Ca(2+) depletion and Ba(2+) substitution, which inhibit the S2 → S3 transition, indicating that a solid water network was broken by these treatments. By contrast, Sr(2+) substitution slightly altered the water bands around 3600 cm(-1), reflecting minor modification in water interactions, consistent with the retention of water oxidation activity with a decreased efficiency. These results suggest that the water network around the Mn4CaO5 cluster plays an essential role in the water oxidation mechanism particularly in a concerted process of proton transfer and water insertion during the S2 → S3 transition. PMID:26716470
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.
Development of a multi-Fourier-transform interferometer: fundamentals
NASA Astrophysics Data System (ADS)
Ohta, Izumi S.; Hattori, Makoto; Matsuo, Hiroshi
2006-04-01
We describe the development of an instrument that uses a Martin-Puplett-type Fourier-transform spectrometer to apply an aperture synthesis technique to millimeter and submillimeter waves. We call this instrument a multi-Fourier-transform interferometer (MuFT). The MuFT performs wideband imaging, spectroscopy, and polarimetry, at millimeter and submillimeter wavelengths. We describe the fundamentals of the MuFT and give an example of one potential implementation. A full description of the observables with a MuFT is provided. A physical explanation of the observability of complex visibility by the MuFT is given. Fundamental restrictions on observations with the MuFT, e.g., limits on spectral and spatial resolution and on fields of view, are discussed. The advantages of the MuFT are summarized.
Development of a multi-Fourier-transform interferometer: fundamentals.
Ohta, Izumi S; Hattori, Makoto; Matsuo, Hiroshi
2006-04-20
We describe the development of an instrument that uses a Martin-Puplett-type Fourier-transform spectrometer to apply an aperture synthesis technique to millimeter and submillimeter waves. We call this instrument a multi-Fourier-transform interferometer (MuFT). The MuFT performs wideband imaging, spectroscopy, and polarimetry, at millimeter and submillimeter wavelengths. We describe the fundamentals of the MuFT and give an example of one potential implementation. A full description of the observables with a MuFT is provided. A physical explanation of the observability of complex visibility by the MuFT is given. Fundamental restrictions on observations with the MuFT, e.g., limits on spectral and spatial resolution and on fields of view, are discussed. The advantages of the MuFT are summarized. PMID:16633405
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
Fourier spectroscopy with a one-million-point transformation
NASA Technical Reports Server (NTRS)
Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.
1972-01-01
A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.
Apparatus and methods for continuous beam fourier transform mass spectrometry
McLuckey, Scott A.; Goeringer, Douglas E.
2002-01-01
A continuous beam Fourier transform mass spectrometer in which a sample of ions to be analyzed is trapped in a trapping field, and the ions in the range of the mass-to-charge ratios to be analyzed are excited at their characteristic frequencies of motion by a continuous excitation signal. The excited ions in resonant motions generate real or image currents continuously which can be detected and processed to provide a mass spectrum.
Optimizing holographic data storage using a fractional Fourier transform.
Pégard, Nicolas C; Fleischer, Jason W
2011-07-01
We demonstrate a method to optimize the reconstruction of a hologram when the storage device has a limited dynamic range and a minimum grain size. The optimal solution at the recording plane occurs when the object wave has propagated an intermediate distance between the near and far fields. This distance corresponds to an optimal order and magnification of the fractional Fourier transform of the object. PMID:21725476
Fast Fourier transform analysis of rotor-bearing systems
NASA Technical Reports Server (NTRS)
Choy, K. C.; Gunter, E. J.; Allaire, P. E.
1978-01-01
Nonlinear transient analysis of rotor-bearing systems is becoming increasingly important in the analysis of modern-day rotating machinery to model such phenomena as oil film whirl. This paper develops an analysis technique incorporating modal analysis and fast Fourier transform techniques to analyze rotors with residual shaft bow and realistic nonlinear bearings. The technique is demonstrated on single-mass and three-mass rotor examples. Comparisons of the theoretical results with experimental data give excellent agreement.
Fourier transform methods for the regulation of solar spectral devices.
NASA Astrophysics Data System (ADS)
Kozhevatov, I. E.; Kulikova, E. Kh.; Cheragin, N. P.
1998-06-01
The techniques based on the principles of Fourier transform (FT) spectroscopy are suggested to increase stability of solar spectral devices: spectrographs, Fabry-Perot filters, FT tachometers, and magnetometers. Devices that carry out the developed techniques are described, and results that testify to the effectiveness of these techniques are presented. They can be used in measurements that require high-precision reference to the absolute value of wavelengths.
A neural net approach to discrete Hartley and Fourier transforms
Culhane, A.D. ); Peckerar, M.C. ); Marrian, C.R.K. )
1989-05-01
In this paper the authors present an electronic circuit, based on a neural (i.e. multiply connected) net to compute the discrete Fourier transform. They show both analytically and by simulation that the circuit is guaranteed to settle into the correct values within RC time constants (on the order of hundreds of nanoseconds), and compare its performance to other on-chip DFT implementations.
Wavelength-encoded tomography based on optical temporal Fourier transform
Zhang, Chi; Wong, Kenneth K. Y.
2014-09-01
We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150 -μm (ideally 36 μm) 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.
Wigner distribution moments in fractional Fourier transform systems.
Bastiaans, Martin J; Alieva, Tatiana
2002-09-01
It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. Since Wigner distribution moments are identical to derivatives of the ambiguity function at the origin, a similar relation holds for these derivatives. The general input-output relationship is then broken down into a number of rotation-type input-output relationships between certain combinations of moments. It is shown how the Wigner distribution moments (or ambiguity function derivatives) can be measured as intensity moments in the output planes of a set of appropriate fractional Fourier transform systems and thus be derived from the corresponding fractional power spectra. The minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments is derived. As an important by-product we get a number of moment combinations that are invariant under (anamorphic) fractional Fourier transformation. PMID:12216870
Mass Spectral Peak Distortion Due to Fourier Transform Signal Processing
NASA Astrophysics Data System (ADS)
Rockwood, Alan L.; Erve, John C. L.
2014-12-01
Distortions of peaks can occur when one uses the standard method of signal processing of data from the Orbitrap and other FT-based methods of mass spectrometry. These distortions arise because the standard method of signal processing is not a linear process. If one adds two or more functions, such as time-dependent signals from a Fourier transform mass spectrometer and performs a linear operation on the sum, the result is the same as if the operation was performed on separate functions and the results added. If this relationship is not valid, the operation is non-linear and can produce unexpected and/or distorted results. Although the Fourier transform itself is a linear operator, the standard algorithm for processing spectra in Fourier transform-based methods include non-linear mathematical operators such that spectra processed by the standard algorithm may become distorted. The most serious consequence is that apparent abundances of the peaks in the spectrum may be incorrect. In light of these considerations, we performed theoretical modeling studies to illustrate several distortion effects that can be observed, including abundance distortions. In addition, we discuss experimental systems where these effects may manifest, including suggested systems for study that should demonstrate these peak distortions. Finally, we point to several examples in the literature where peak distortions may be rationalized by the phenomena presented here.
Improved digital filters for evaluating Fourier and Hankel transform integrals
Anderson, Walter L.
1975-01-01
New algorithms are described for evaluating Fourier (cosine, sine) and Hankel (J0,J1) transform integrals by means of digital filters. The filters have been designed with extended lengths so that a variable convolution operation can be applied to a large class of integral transforms having the same system transfer function. A f' lagged-convolution method is also presented to significantly decrease the computation time when computing a series of like-transforms over a parameter set spaced the same as the filters. Accuracy of the new filters is comparable to Gaussian integration, provided moderate parameter ranges and well-behaved kernel functions are used. A collection of Fortran IV subprograms is included for both real and complex functions for each filter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms
Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
Santa Maria, Odilyn L.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Wavelets for approximate Fourier transform and data compression
NASA Astrophysics Data System (ADS)
Guo, Haitao
This dissertation has two parts. In the first part, we develop a wavelet-based fast approximate Fourier transform algorithm. The second part is devoted to the developments of several wavelet-based data compression techniques for image and seismic data. We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The classical Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. The main advantage of our algorithm is that the good time and frequency localization of wavelets can be exploited to approximate the Fourier transform for many classes of signals, resulting in much less computation. Thus the new algorithm provides an efficient complexity versus accuracy tradeoff. When approximations are allowed, under certain sparsity conditions, the algorithm can achieve linear complexity, i.e. O(N). The proposed algorithm also has built-in noise reduction capability. For waveform and image compression, we propose a novel scheme using the recently developed Burrows-Wheeler transform (BWT). We show that the discrete wavelet transform (DWT) should be used before the Burrows-Wheeler transform to improve the compression performance for many natural signals and images. We demonstrate that the simple concatenation of the DWT and BWT coding performs comparably as the embedded zerotree wavelet (EZW) compression for images. Various techniques that significantly improve the performance of our compression scheme are also discussed. The phase information is crucial for seismic data processing. However, traditional compression schemes do not pay special attention to preserving the phase of the seismic data, resulting in the loss of critical information. We propose a lossy compression method that preserves the phase as much as possible. The method is based on the self-adjusting wavelet transform that adapts to the locations of the significant signal components. The elegant method of embedded zerotree wavelet compression is modified and incorporated into our compression scheme. Our method can be applied to both one dimensional seismic signals and two dimensional seismic images.
Coherent electromagnetic field imaging through Fourier transform heterodyne
Cooke, B.J.; Laubscher, B.E.; Olivas, N.L.; Goeller, R.M.; Cafferty, M.; Briles, S.D.; Galbraith, A.E. |; Grubler, A.C. |
1998-12-31
The authors present a detection process capable of directly imaging the transverse amplitude, phase, and if desired, Doppler shift of coherent electromagnetic fields. Based on coherent detection principles governing conventional heterodyned RADAR/LIDAR systems, Fourier Transform Heterodyne (FTH) incorporates transverse spatial encoding of the local oscillator for image capture. Appropriate selection of spatial encoding functions, or basis set, allows image retrieval by way of classic Fourier manipulations. Of practical interest: (1) imaging is accomplished on a single element detector requiring no additional scanning or moving components, and (2) a wide variety of appropriate spatial encoding functions exist that may be adaptively configured in real-time for applications requiring optimal detection. In this paper, they introduce the underlying principles governing FTH imaging, followed by demonstration of concept via a simple experimental setup based on a HeNe laser and a 69 element spatial phase modulator.
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
ERIC Educational Resources Information Center
Miller, Tierney C.; Richardson, John N.; Kegerreis, Jeb S.
2016-01-01
This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to
ERIC Educational Resources Information Center
Miller, Tierney C.; Richardson, John N.; Kegerreis, Jeb S.
2016-01-01
This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…
Fiber-optic thermometer using Fourier transform spectroscopy
NASA Astrophysics Data System (ADS)
Beheim, Glenn; Sotomayor, Jorge L.; Flatico, Joseph M.; Azar, Massood T.
1991-12-01
An integrated-optic Mach-Zender interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This configuration provides a high degree of immunity to the effects of changes in the source spectrum, and it readily permits the interrogation of a number of different sensors using a single spectrometer. In addition, this system has a potentially low cost because it uses optical communications hardware that may in the future be manufactured in large quantities.
Hard X-Ray Fourier Transform Holography with Zone Plates
Watanabe, Norio; Yokosuka, Hiroki; Ohigashi, Takuji; Aoki, Sadao; Takano, Hidekazu; Takeuchi, Akihisa; Suzuki, Yoshio
2004-05-12
Using two zone plates, a hard x-ray lens-less Fourier transform holographic microscope with cone-beam illumination was investigated at SPring-8 BL20XU. One zone plate was placed on the optical axis, and another zone plate was placed 16 mm downstream and 9 {mu}m off the optical axis. The diverging x-rays from the focus of the upstream zone plate illuminated a specimen where the focus of the downstream zone plate was placed. A hologram of a copper mesh of 12.7 {mu}m pitch could be obtained. The intensity and the phase could be successfully reconstructed with sub-micron resolution.
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 μm 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.
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
NASA Astrophysics Data System (ADS)
Klimyk, A.; Patera, J.
2007-09-01
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms involving the symmetric and antisymmetric multivariate sine and cosine functions.
Optical Two Dimensional Fourier Transform Spectroscopy of Layered Metal Dichalcogenides
NASA Astrophysics Data System (ADS)
Dey, P.; Paul, J.; Stevens, C. E.; Kovalyuk, Z. D.; Kudrynskyi, Z. R.; Romero, A. H.; Cantarero, A.; Hilton, D. J.; Shan, J.; Karaiskaj, D.; Z. D. Kovalyuk; Z. R. Kudrynskyi Collaboration; A. H. Romero Collaboration; A. Cantarero Collaboration; D. J. Hilton Collaboration; J. Shan Collaboration
2015-03-01
Nonlinear two-dimensional Fourier transform (2DFT) measurements were used to study the mechanism of excitonic dephasing and probe the electronic structure of the excitonic ground state in layered metal dichalcogenides. Temperature-dependent 2DFT measurements were performed to probe exciton-phonon interactions. Excitation density dependent 2DFT measurements reveal exciton-exciton and exciton-carrier scattering, and the lower limit for the homogeneous linewidth of excitons on positively and negatively doped samples. U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0012635.
Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.
2013-01-01
A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.
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).
Ultrafast Fourier Transform with a Femtosecond-Laser-Driven Molecule
NASA Astrophysics Data System (ADS)
Hosaka, Kouichi; Shimada, Hiroyuki; Chiba, Hisashi; Katsuki, Hiroyuki; Teranishi, Yoshiaki; Ohtsuki, Yukiyoshi; Ohmori, Kenji
2010-05-01
Wave functions of electrically neutral systems can be used as information carriers to replace real charges in the present Si-based circuit, whose further integration will result in a possible disaster where current leakage is unavoidable with insulators thinned to atomic levels. We have experimentally demonstrated a new logic gate based on the temporal evolution of a wave function. An optically tailored vibrational wave packet in the iodine molecule implements four- and eight-element discrete Fourier transform with arbitrary real and imaginary inputs. The evolution time is 145 fs, which is shorter than the typical clock period of the current fastest Si-based computers by 3 orders of magnitudes.
Fiber-optic thermometer using Fourier transform spectroscopy
NASA Technical Reports Server (NTRS)
Beheim, Glenn; Sotomayor, Jorge L.; Flatico, Joseph M.; Azar, Massood T.
1991-01-01
An integrated-optic Mach-Zender interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This configuration provides a high degree of immunity to the effects of changes in the source spectrum, and it readily permits the interrogation of a number of different sensors using a single spectrometer. In addition, this system has a potentially low cost because it uses optical communications hardware that may in the future be manufactured in large quantities.
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 ν(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.
Beam profile for the Herschel-SPIRE Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Makiwa, Gibion; Naylor, David A.; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H. D.
2013-06-01
One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile.
Fourier transform vibrational circular dichroism of small pharmaceutical molecules
NASA Astrophysics Data System (ADS)
Long, Fujin; Freedman, Teresa B.; Nafie, Laurence A.
1998-06-01
Fourier transform vibrational circular dichroism (FT-VCD) spectra of the small pharmaceutical molecules propanolol, ibuprofen and naproxen have been measured in the hydrogen stretching and mid-infrared regions to obtain information on solution conformation and to identify markers for absolute configuration determination. Ab initio molecular orbital calculations of low energy conformations, vibrational frequencies and VCD intensities for fragments of the drugs were utilized in interpreting the spectra. Features characteristic of five conformers of propranolol were identified. The weak positive CH stretching VCD signal in ibuprofen and naproxen is characteristic of the S-configuration of the chiral center common to these two analgesics.
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.
Triple image encryption scheme in fractional Fourier transform domains
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Dai, Jingmin; Sun, Xiaogang; Liu, Shutian
2009-02-01
We proposed a triple image encryption scheme by use of fractional Fourier transform. In this algorithm, an original image is encoded in amplitude part and other two images are encoded into phase information. The key of encryption algorithm is obtained from the difference between the third image and the output phase of transform. In general case, random phase encoding technology is not required in the proposed algorithm. Moreover, all information of images is preserved in theory when image are decrypted with correct key. The optical implementation of the algorithm is presented with an electro-optical hybrid structure. Numerical simulations have demonstrated the efficiency and the security of this algorithm. Based on this scheme a multiple image algorithm is expanded and designed.
2D discrete Fourier transform on sliding windows.
Park, Chun-Su
2015-03-01
Discrete Fourier transform (DFT) is the most widely used method for determining the frequency spectra of digital signals. In this paper, a 2D sliding DFT (2D SDFT) algorithm is proposed for fast implementation of the DFT on 2D sliding windows. The proposed 2D SDFT algorithm directly computes the DFT bins of the current window using the precalculated bins of the previous window. Since the proposed algorithm is designed to accelerate the sliding transform process of a 2D input signal, it can be directly applied to computer vision and image processing applications. The theoretical analysis shows that the computational requirement of the proposed 2D SDFT algorithm is the lowest among existing 2D DFT algorithms. Moreover, the output of the 2D SDFT is mathematically equivalent to that of the traditional DFT at all pixel positions. PMID:25585421
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 10μsec. 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.
Imaging Fourier transform spectrometer (IFTS): parametric sensitivity analysis
NASA Astrophysics Data System (ADS)
Keller, Robert A.; Lomheim, Terrence S.
2005-06-01
Imaging Fourier transform spectrometers (IFTS) allow for very high spectral resolution hyperspectral imaging while using moderate size 2D focal plane arrays in a staring mode. This is not the case for slit scanning dispersive imaging spectrometers where spectral sampling is related to the focal plane pixel count along the spectral dimension of the 2D focal plane used in such an instrument. This can become a major issue in the longwave infrared (LWIR) where the operability and yield of highly sensitivity arrays (i.e.HgCdTe) of large dimension are generally poor. However using an IFTS introduces its own unique set of issues and tradeoffs. In this paper we develop simplified equations for describing the sensitivity of an IFTS, including the effects of data windowing. These equations provide useful insights into the optical, focal plane and operational design trade space that must be considered when examining IFTS concepts aimed at a specific sensitivity and spectral resolution application. The approach is illustrated by computing the LWIR noise-equivalent spectral radiance (NESR) corresponding to the NASA Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) concept assuming a proven and reasonable noise-equivalent irradiance (NEI) capability for the focal plane.
Soft x-ray microscope using Fourier transform holography
McNulty, I.; Kirz, J.; Jacobsen, C.; Anderson, E.; Howells, M.R.; Rarback, H. . Dept. of Physics; Lawrence Berkeley Lab., CA; Brookhaven National Lab., Upton, NY )
1989-01-01
A Fourier transform holographic microscope with an anticipated resolution of better than 100 nm has been built. Extensive testing of the apparatus has begun. Preliminary results include the recording of interference fringes using 3.6 nm x-rays. The microscope employs a charge-coupled device (CCD) detector array of 576 {times} 384 elements. The system is illuminated by soft x-rays from a high brightness undulator. The reference point source is formed by a Fresnel zone plate with a finest outer zone width of 50 nm. Sufficient temporal coherence for hologram formation is obtained by a spherical grating monochromator. The x-ray hologram intensities at the recording plane are to be collected, digitized and reconstructed by computer. Data acquisition is under CAMAC control, while image display and off-line processing takes place on a VAX graphics workstation. Computational models of Fourier transform hologram synthesis, and reconstruction in the presence of noise, have demonstrated the feasibility of numerical methods in two dimensions, and that three-dimensional information is potentially recoverable. 13 refs., 3 figs.
Relationship between fractional calculus and fractional Fourier transform
NASA Astrophysics Data System (ADS)
Zhang, Yanshan; Zhang, Feng; Lu, Mingfeng
2015-09-01
The fractional calculus (FC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. The fractional Fourier transform (FRFT), which has been found having many applications in optics and other areas, is a generalization of the usual Fourier transform. The FC and the FRFT are two of the most interesting and useful fractional areas. In recent years, it appears many papers on the FC and FRFT, however, few of them discuss the connection of the two fractional areas. We study their relationship. The relational expression between them is deduced. The expectation of interdisciplinary cross fertilization is our motivation. For example, we can use the properties of the FC (non-locality, etc.) to solve the problem which is difficult to be solved by the FRFT in optical engineering; we can also through the physical meaning of the FRFT optical implementation to explain the physical meaning of the FC. The FC and FRFT approaches can be transposed each other in the two fractional areas. It makes that the success of the fractional methodology is unquestionable with a lot of applications, namely in nonlinear and complex system dynamics and image processing.
Progress report of a static Fourier transform spectrometer breadboard
NASA Astrophysics Data System (ADS)
Rosak, A.; Tint, F.
2004-06-01
MOLI instrument - for MOtionLess Interferometer - takes advantage of the new concept of static Fourier transform spectrometer. It is a high-resolution spectrometer working over a narrow bandwidth, which is adapted to a wide range of atmospheric sounding missions and compatible with micro-satellite platform. The core of this instrument is an echelette cube. Mirrors on the classical design are replaced by stepped mirrors - integrated into that interference cube - thus suppressing any moving part. The steps' directions being set over a perpendicular axis, the overlap of both stepped mirrors creates a cluster of so-called "echelettes", each one corresponding to a different optical path difference (OPD). Hence the Fourier transform of the incoming radiance is directly imaged on a CCD array in a single acquisition. The frequency domain of the measurements is selected by an interferential filter disposed on the incoming optical path. A rotating wheel equipped with several filters allows the successive measurement of spectra around some bands of interest, i.e. O2, CO2 and CO absorption bands.
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
Coherent coupling of magneto-excitons probed by two-dimensional Fourier transform spectroscopy
NASA Astrophysics Data System (ADS)
Paul, Jagannath; Liu, Cunming; McGill, Stephen; Hilton, David; Karaiskaj, Denis
We present the coherent two dimensional Fourier Transform (2DFT) spectra of magneto-excitons in undoped GaAs quantum wells at high magnetic field up to 10 Tesla. The 2DFT data reveal strong coherent coupling between resonances and line shapes which are strikingly different from the zero field spectra. 2DFT spectra measured using co-linear and co-circular polarizations at low temperatures will be discussed. The work at USF and UAB was supported by the National Science Foundation under Grant Number DMR-1409473. The work at NHMFL, Florida State University was supported by the National Science Foundation under Grant Numbers DMR-1157490 and DMR-1229217.
On integral and finite Fourier transforms of continuous q-Hermite polynomials
Atakishiyeva, M. K.; Atakishiyev, N. M.
2009-05-15
We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials H{sub n}(x vertical bar q) of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.
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
Fourier-transform microwave spectroscopy of the CCCCl radical.
Yoshikawa, Takashi; Sumiyoshi, Yoshihiro; Endo, Yasuki
2009-03-01
Pure rotational spectra of the CCCCl radical in a supersonic jet have been observed for the first time by Fourier-transform microwave spectroscopy. The radical was produced by a pulsed electric discharge in a C(2)H(2) and CCl(4) mixture diluted to 0.3% and 0.2% with Ne, respectively. Transitions with spin and hyperfine splittings were observed for two isotopologs, CCC(35)Cl and CCC(37)Cl, in the region from 11.4 GHz for N=2-1 to 34.2 GHz for N=6-5. The molecular constants including the hyperfine coupling constants due to the Cl nucleus have been determined precisely. From the rotational analyses and high-level ab initio calculations, the molecular structure of the CCCCl radical is concluded to be bent in the ground electronic state. PMID:19275398
Fourier-transform absorption spectroscopy in reciprocating engines.
Rein, Keith D; Sanders, Scott T
2010-09-01
We have adapted our in-cylinder Fourier-transform spectroscopy technique to measure absorption spectra in a reciprocating engine. Previously, we had used the technique for emission spectroscopy; the upgrade to absorption spectroscopy mode is important because it allows for more quantitative analysis of gas properties than is possible with emission spectroscopy. Here, we discuss fuel, H(2)O, and CO(2) spectra measured in an engine using a spark-plug-based probe for optical access and use the water portion of the spectra to determine in-cylinder gas temperature. The temperature results show that heat transfer effects can significantly bias thermometry when fiber-coupled engine probes are used. PMID:20820214
Identification of Amanita mushrooms by fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Zhao, Dezhang; Liu, Gang; Song, Dingshan; Liu, Jian-hong; Zhou, Yilan; Ou, Jiaming; Sun, Shizhong
2006-09-01
Amanita is one of cosmopolitan genera of basidiomycetes. This genus contains some of the most poisonous toadstools, as well as several species of the most favorite edible mushrooms. In this paper, Fourier transform infrared spectroscopy was used for obtaining vibrational spectra of the fruiting bodies of wild growing Amanita mushrooms. The results show that the mushrooms exhibit characteristic spectra, whose strong absorption bands appear at about 1655, 1076, and 1040 cm -1. The vibrational spectra indicate that the main compositions of the Amanita mushrooms are proteins and polysaccharides. The observed spectral differences might be used to discriminate different species of Amanita. It is showed that FTIR spectroscopic method is a valuable tool for rapid and nondestructive identification of Amanita mushrooms.
A fast Fourier transform spectrometer design for submillimeter site testing
NASA Astrophysics Data System (ADS)
Velázquez, Miguel; Ferrusca, Daniel; Hughes, David H.
2006-06-01
We report the design of a sub-millimeter Fourier Transform Spectrometer of the Martin Puplett type (FTS-MP here after). The instrument will be installed on Sierra La Negra, and will operate from ~215 GHz to 1 THz approximately with a moderate resolution of 500 MHz. The main motivations of the work are the development of basic instrumentation for characterizing the LMT site (Large Millimeter Telescope) as well as optical components and to provide a portable broadband system for site testing. The collected data will be used for transmission model validation. The data also will influence the design of the new generation of sub-millimeter and millimeter cameras for the LMT. In the present work we emphasize cryogenic detector system design (bolometer detector and coupling optics) and the optical system layout for the FTS-MP. Test measurements in the laboratory are reported in this work.
Structural Characterization of Carbohydrates by Fourier Transform Tandem Mass Spectrometry.
Zhou, Wen; Hkansson, Kristina
2011-12-01
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
Color image encryption based on joint fractional Fourier transform correlator
NASA Astrophysics Data System (ADS)
Lu, Ding; Jin, Weimin
2011-06-01
In this paper, an optical color image encryption/decryption technology based on joint fractional Fourier transform correlator and double random phase encoding (DRPE) is developed. In this method, the joint fractional power spectrum of the image to be encrypted and the key codes is recorded as the encrypted data. Different from the case with classical DRPE, the same key code was used both in the encryption and decryption. The security of the system is enhanced because of the fractional order as a new added key. This method takes full advantage of the parallel processing features of the optical system, and could optically realize single-channel color image encryption. The experimental results indicate that the new method is feasible.
[Influence of collimation system on static Fourier transform spectrometer].
Jiang, Cheng-Zhi; Liang, Jing-Qiu; Liang, Zhong-Zhu; Sun, Qiang; Wang, Wei-Biao
2014-01-01
Collimation system provides collimated light for the static Fourier-transform spectroscopy (SFTS). Its quality is crucial to the signal to noise ratio (SNR) of SFTS. In the present paper, the physical model of SFTS was established based on the Fresnel diffraction theory by means of numerical software. The influence of collimation system on the SFTS was discussed in detail focusing on the aberrations of collimation lens and the quality of extended source. The results of simulation show that the influences of different kinds of aberrations on SNR take on obvious regularity, and in particular, the influences of off-axis aberrations on SNR are closely related to the location of off-axis point source. Finally the extended source's maximum radius allowed was obtained by simulation, which equals to 0.65 mm. The discussion results will be used for the design of collimation system. PMID:24783575
Instrument concept of the imaging Fourier transform spectrometer GLORIA
NASA Astrophysics Data System (ADS)
Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.
2014-03-01
The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the Upper Troposphere/Lower Stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated in a gimbal. The assembly can be mounted in the belly pod of the German high altitude and long range research aircraft HALO and in instrument bays of the Russian M55 Geophysica. Measurements are made predominantly in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
Instrument concept of the imaging Fourier transform spectrometer GLORIA
NASA Astrophysics Data System (ADS)
Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.
2014-10-01
The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the upper troposphere/lower stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated into a gimbal. The assembly can be mounted in the belly pod of the German High Altitude and Long Range research aircraft (HALO) and in instrument bays of the Russian M55 Geophysica. Measurements are made in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, and the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition, the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
On the abstracted dataflow complexity of Fast Fourier Transforms
Boehm, A.P.W.; Hiromoto, R.E.; Kelly, K.A.; Ashley, J.M.
1992-05-01
In this paper we develop and analyze the simulated performance of codes for the Fast Fourier Transform written in If and targeted for execution on Motorola`s dataflow machine Monsoon. The FFT application is of interest because of its computational parallelism, its requirement for global communications, and its array element data dependences. We use the parallel profiling simulator Id World to study the dataflow performance of various implementations. Our approach is comparative. We study two approaches, a recursive and an iterative one, and in each version we examine the effect of a variety of implementations. We contend that only through such comparative evaluations can significant insight be gained in understanding the computational and structural details of functional algorithms.
A rheumatoid arthritis study by Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Carvalho, Carolina S.; Silva, Ana Carla A.; Santos, Tatiano J. P. S.; Martin, Airton A.; dos Santos Fernandes, Ana Célia; Andrade, Luís E.; Raniero, Leandro
2012-01-01
Rheumatoid arthritis is a systemic inflammatory disease of unknown causes and a new methods to identify it in early stages are needed. The main purpose of this work is the biochemical differentiation of sera between normal and RA patients, through the establishment of a statistical method that can be appropriately used for serological analysis. The human sera from 39 healthy donors and 39 rheumatics donors were collected and analyzed by Fourier Transform Infrared Spectroscopy. The results show significant spectral variations with p<0.05 in regions corresponding to protein, lipids and immunoglobulins. The technique of latex particles, coated with human IgG and monoclonal anti-CRP by indirect agglutination known as FR and CRP, was performed to confirm possible false-negative results within the groups, facilitating the statistical interpretation and validation of the technique.
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.
Generation of Fourier-transform-limited heralded single photons
U'Ren, Alfred B.; Jeronimo-Moreno, Yasser; Garcia-Gracia, Hipolito
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.
A Fourier transform spectrometer for site testing at Dome A
NASA Astrophysics Data System (ADS)
Li, Xin-Xing; Paine, Scott; Yao, Qi-Jun; Shi, Sheng-Cai; Matsuo, Hiroshi; Yang, Ji; Zhang, Qi-Zhou
2009-07-01
Observations in tera-hertz astronomy can only be done at a site with good atmospheric transmission at millimeter and submillimeter wavelengths. With extremely dry weather and calm atmosphere resulted by high altitude and cold temperature, Dome A (or Dome Argus), Antarctica, is possibly the best site on this earth for THz astronomy. To evaluate the site condition there, we are constructing a Fourier Transform Spectrometer (FTS) based on Martin-Puplett interferometer to measure the atmospheric transmission in the frequency range of 0.75~15THz. The whole FTS system is designed for unattended and outdoor (temperatures even below -70 degrees Celsius) operation. Its total power consumption is estimated to be approximately 200W. This contribution will give a brief overview of this FTS development.
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.
Detection of moving mirror tilt in Fourier transform infrared spectrometer
NASA Astrophysics Data System (ADS)
Sun, Xiaojie; Hua, Jianwen; Dai, Zuoxiao; Xia, Xiang; Li, Tao; Wang, Zhirui
2012-10-01
Moving mirror tilt, which causes misalignment of two reflectors, is a key issue in Fourier Transform Infrared Spectrometer (FTIRS). Dynamic alignment system (DAS) is adopted to solve misalignment problem. High precision detection of dynamic misalignment angle is one of the most important steps in DAS, mainly upon which the adjustment performances of DAS depend. A new measuring algorithm is presented which is based on amplitude detecting [1][2] between laser interference signals generated by reference laser source in this paper. Mathematical analysis is described and experiment results are shown. These results show that the measuring precision of 0.6 micro-radians of dynamic tilting angle is achieved with this method. This is a guarantee for a FTIRS to acquire high interference efficiency.
University of Toronto's balloon-borne Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Wunch, Debra; Midwinter, Clive; Drummond, James R.; Thomas McElroy, C.; Bagès, Anne-Flore
2006-09-01
A commercial ABB-Bomem DA5 Fourier transform spectrometer (FTS) was refitted with new software and electronics to create a FTS that is appropriate for both ground-based and balloon-based measurements. Nearly all the electronics were replaced, and new control software was written that allows the instrument to run remotely, provides access to all housekeeping information, and permits considerable freedom in data processing approaches. A ``delta'' tracker was used for fine tracking of the sun over a small tracking range, using the main gondola pointing system for coarse azimuth tracking. This facilitated a simple, effective method of instrument integration onto the payload. The new design reduced the mass of the FTS from 90 to 55 kg and reduced the power consumption from 145 to 65 W.
Fast fourier transform processors using Gaussian residue arithmetic
Despain, A.M.; Peterson, A.M.; Rothaus, O.S.; Wold, E.H.
1985-08-01
Residue arithmetic using moduli which are Gaussian primes is suggested as a method for computing the fast Fourier transform (FFT). For complex operations, a substantial savings in hardware and time over residue arithmetic using real moduli can be obtained using complex moduli. Gaussian residue arithmetic is discussed and methods for conversion into and out of the complex residue representation are developed. This representation lends itself to table-driven computation, allowing very low latency designs to be developed. A 64-point Cooley-Tukey style processor and a 60-point Rader-Winograd style processor using this technique are described and compared. Hardware savings are realized by approximating the rotations necessary to perform the FFT by small complex integers and by scaling the results of the computation at an intermediate point. It is shown that further hardware reductions can be made by developing custom integrated circuits at the expense of latency.
A build-up cavity for Fourier transform emission experiments
NASA Astrophysics Data System (ADS)
Crozet, P.; Vallon, R.; Erba, B.; Néri, M.; Ross, A. J.
2005-07-01
We have recorded electronic spectra of some diatomic species (I 2, K 2, and NaK), to illustrate the potential power of the combination of two high resolution techniques: intra-cavity laser induced fluorescence (ICLIF) and Fourier transform (FT) spectroscopy. Active and passive optical cavities have been used, working with visible continuous wave (cw) laser sources. The active cavity is a modified commercial ring dye laser, allowing for a sample up to 25 cm in length. Dispersed fluorescence spectra recorded on a Bomem Fourier transform spectrometer showed a signal enhancement of about 10 when a molecular source was placed within the resonator. The system was tested with a heatpipe source, producing alkali metal vapour at about 300 °C. These experiments illustrate enhanced cascade excitation mechanisms in K 2; the highest vibrational levels of the electronic ground state of K 2 can be observed with surprising ease. The increase in available power within the cavity has also led to the observation of fluorescence in NaK excited by a two-photon transition ( Q (66) 6 1Σ + ← X1Σ + transition). Spatial limitations have driven us to build a more versatile ring cavity able to accommodate larger sources. This broad-band (590-650 nm) build-up cavity is locked by a Hänsch-Couillaud servo-loop to an input laser of (instantaneous) bandwidth ˜1 MHz. Power enhancement factors of around 30 have been obtained with a 2.6% input coupler. The performance of the build-up cavity has been tested by recording FT spectra of intra-cavity laser induced fluorescence of iodine. The technique clearly has useful applications for weakly absorbing species, or for those whose electronic states are inaccessible to single-photon absorption techniques. This paper describes the arrangement we have used, highlighting some of the advantages and describing some of the particular difficulties we have encountered.
High-resolution lensless Fourier transform holography for microstructure imaging
NASA Astrophysics Data System (ADS)
Zhao, Jie; Wang, Dayong; Wang, Huaying; Xie, Jianjun
2007-12-01
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. In the paper, based on the Fresnel diffraction theory and the off-axis lensless Fourier transform recording architecture, the experimental optimization and correspondingly the digital reconstruction was investigated. Also, the lateral resolution of the reconstructed image was analyzed and improved by the proposed techniques. When the USAF test target was imaged without any pre-magnification, the lateral resolution of 3.1μm was achieved, which matched the theoretical prediction very well. The key points to achieve high resolution image are to use the smaller object and to arrange the distance between the object and the CCD plane as short as possible. Meanwhile, properly overlapping the reconstructed image with the DC term was helpful to improve the resolution. The noise in the reconstructed image could be reduced greatly by choosing the optical elements precisely and adjusting the beam path finely. The experimental results demonstrated that it is possible for the digital holographic microscopy to produce the high resolution image without the objective pre-magnification. The results also showed that, with a high quality hologram, the special image processing during the reconstruction may be unnecessary to obtain a high quality image.
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.
Imaging sensor for the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS)
NASA Astrophysics Data System (ADS)
Stobie, James A.; Hairston, Allen W.; Tobin, Stephen P.; Huppi, Ronald J.; Huppi, Ray
2002-12-01
Accurate high resolution temperature sounding through our atmosphere is paramount to improving our weather forecasting, monitoring, and analysis capability. From the vantagepoint of earth Orbit, remote temperature sounding is becoming a reality and its accuracy is bolstered by recent advances in infrared hyper-spectral sensor capability. One promising approach takes advantage of a two-dimensional, imaging Fourier transform spectrometer to obtain a data cube with the field of view along one plane and multiple IR spectra (one for every FPA pixel) along the orthogonal axis. The spatial resolution is limited only by the pixel pitch in the imaging focal plane and the optics used to collect the data. The maximum optical path difference in the Michelson FTS defines the spectral resolution and dictates the number of path-length interferogram samples (FPA frames required per cube. This paper discusses the unique challenges placed on the focal plane by the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) approach and how advanced focal plane technology is applied to satisfy these challenges. Two focal planes are required to provide spectral coverage from 4.4 to 6.1um and 8.85-14.6um. Currently, the GIFT"s LWIR focal plane is the longest wavelength two-dimensional PV HgCdTe array of this size (128 square on 60 um centers) planned for space deployment. The paper presents performance data of Liquid Phase Epitaxy (LPE) fabricated HgCdTe detectors and design details of the advanced readout integrated circuit necessary to meet the demanding requirements of the imaging sensor for the GIFTS instrument.
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.
NASA Astrophysics Data System (ADS)
Vilardy, Juan M.; Torres, Yezid; Millán, María S.; Pérez-Cabré, Elisabet
2014-12-01
We propose a generalization of the encryption system based on double random phase encoding (DRPE) and a joint transform correlator (JTC), from the Fourier domain to the fractional Fourier domain (FrFD) by using the fractional Fourier operators, such as the fractional Fourier transform (FrFT), fractional traslation, fractional convolution and fractional correlation. Image encryption systems based on a JTC architecture in the FrFD usually produce low quality decrypted images. In this work, we present two approaches to improve the quality of the decrypted images, which are based on nonlinear processing applied to the encrypted function (that contains the joint fractional power spectrum, JFPS) and the nonzero-order JTC in the FrFD. When the two approaches are combined, the quality of the decrypted image is higher. In addition to the advantages introduced by the implementation of the DRPE using a JTC, we demonstrate that the proposed encryption system in the FrFD preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The feasibility of this encryption system is verified and analyzed by computer simulations.
Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups
Guedes, Carlos; Oriti, Daniele; Raasakka, Matti; LIPN, Institut Galilée, Université Paris-Nord, 99, av. Clement, 93430 Villetaneuse
2013-08-15
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-product carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.
Quantum Noise of Fourier-Coded Aperture Imaging System
NASA Astrophysics Data System (ADS)
Chou, Chien; King, Hong-Jueng
1994-04-01
The single-grating aperture (SGA) and Fourier aperture (FA) both behave as variable frequency gratings to record the object spectrum directly in a Fourier domain when quantum noise is originally generated in this region. This is in contrast to a stationary coded aperture in which the noise appears in the space domain in the shadow-casting images. The noise properties of SGA and FA imaging systems, using the summation filtered backprojection reconstruction algorithm, have been determined. They are proportional to the square root of the intensity distribution of the object. From the theoretical calculations, signal-to-noise ratios of SGA and FA show the same performance as the SNR of a pinhole camera for small objects. However, for larger objects, SGA and FA show better performance than the pinhole camera. The calculated SNRs of a point and a disc object agree with the experimental results.
Pulsed Fourier-transform NQR of sup 14 N with a dc SQUID
Huerlimann, M.D.; Pennington, C.H.; Fan, N.Q.; Clarke, J.; Pines, A.; Hahn, E.L. Department of Chemistry, University of California, Berkeley, Berkeley, California 94720 Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720 )
1992-07-27
The zero-field free induction decay of solid ammonium perchlorate at 1.5 K has been directly detected with a dc superconducting quantum interference device. The Fourier-transform spectrum consists of three sharp lines at 17.4, 38.8, and 56.2 kHz arising from pure {sup 14}N nuclear quadrupole resonance transitions. The absence of splittings and resonance transitions from dipolar-coupled proton spins is attributed to reorientation of the ammonium groups by quantum tunneling in combination with motional averaging in the three proton levels characterized by the irreducible representation {ital T}. The measured {sup 14}N spin-spin relaxation time is 22{plus minus}2 ms and the spin-lattice relaxation time is 63{plus minus}6 ms.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Paul, J.; Dey, P.; Tokumoto, T.; Reno, J. L.; Hilton, D. J.; Karaiskaj, D.
2014-10-07
The dephasing of excitons in a modulation doped single quantum well was carefully measured using time integrated four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. These are the first 2DFT measurements performed on a modulation doped single quantum well. The inhomogeneous and homogeneous excitonic line widths were obtained from the diagonal and cross-diagonal profiles of the 2DFT spectra. The laser excitation density and temperature were varied and 2DFT spectra were collected. A very rapid increase of the dephasing decay, and as a result, an increase in the cross-diagonal 2DFT linewidths with temperature was observed. Furthermore, the lineshapes of the 2DFT spectra suggest the presence of excitation induced dephasing and excitation induced shift.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Paul, J.; Dey, P.; Tokumoto, T.; Reno, J. L.; Hilton, D. J.; Karaiskaj, D.
2014-10-07
The dephasing of excitons in a modulation doped single quantum well was carefully measured using time integrated four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. These are the first 2DFT measurements performed on a modulation doped single quantum well. The inhomogeneous and homogeneous excitonic line widths were obtained from the diagonal and cross-diagonal profiles of the 2DFT spectra. The laser excitation density and temperature were varied and 2DFT spectra were collected. A very rapid increase of the dephasing decay, and as a result, an increase in the cross-diagonal 2DFT linewidths with temperature was observed. Furthermore, the lineshapes of themore » 2DFT spectra suggest the presence of excitation induced dephasing and excitation induced shift.« less
Identification of formation interfaces by using wavelet and Fourier transforms
NASA Astrophysics Data System (ADS)
Mukherjee, Bappa; Srivardhan, V.; Roy, P. N. S.
2016-05-01
The identification of formation interfaces is of prime importance from well log data. The interfaces are not clearly discernible due to the presence of high and low frequency noise in the log response. Accurate bed boundary information is very crucial in hydrocarbon exploration and the problem has received considerable attention and many techniques have been proposed. Frequency spectrum based filtering techniques aids us in interpretation, but usually leads to inaccurate amplification of unwanted components of the log response. Wavelet transform is very effective in denoising the log response and can be carried out to filter low and high frequency components of signal. The use of Fourier and Wavelet transform in denoising the log data for obtaining formation interfaces is demonstrated in this work. The feasibility of the proposed technique is tested so that it can be used in the industry to decipher formation interfaces. The work flow is demonstrated by testing on wells belonging to the Upper Assam Basin, which are self-potential, gamma ray, and resistivity log responses.
The use of Fourier reverse transforms in crystallographic phase refinement
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.
[Biological Process Oriented Online Fourier Transform Infrared Spectrometer].
Xie, Fei; Wu, Qiong-shui; Zeng, Li-bo
2015-08-01
An online Fourier Transform Infrared Spectrometer and an ATR (Attenuated Total Reflection) probe, specifically at the application of real time measurement of the reaction substrate concentration in biological processes, were designed. (1) The spectrometer combined the theories of double cube-corner reflectors and flat mirror, which created a kind of high performance interferometer system. The light path folding way was utilized to makes the interferometer compact structure. Adopting double cube-corner reflectors, greatly reduces the influence of factors in the process of moving mirror movement such as rotation, tilt, etc. The parallelogram oscillation flexible support device was utilized to support the moving mirror moves. It cancelled the friction and vibration during mirror moving, and ensures the smooth operation. The ZnSe splitter significantly improved the hardware reliability in high moisture environment. The method of 60° entrance to light splitter improves the luminous flux. (2) An ATR in situ measuring probe with simple structure, large-flux, economical and practical character was designed in this article. The transmission of incident light and the light output utilized the infrared pipe with large diameter and innerplanted-high plating membrane, which conducted for the infrared transmission media of ATR probe. It greatly reduced the energy loss of infrared light after multiple reflection on the inner wall of the light pipe. Therefore, the ATR probe obtained high flux, improved the signal strength, which make the signal detected easily. Finally, the high sensitivity of MCT (Mercury Cadmium Telluride) detector was utilized to realize infrared interference signal collection, and improved the data quality of detection. The test results showed that the system yields the advantages of perfect moisture-proof performance, luminous flux, online measurement, etc. The designed online Fourier infrared spectrometer can real-time measured common reactant substrates such as glycerin in the bioreactor under high quality. There is a large potential market, such as online analysis in biological, chemical testing and material analysis. PMID:26672325
[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
Vector power multiple-parameter fractional Fourier transform of image encryption algorithm
NASA Astrophysics Data System (ADS)
Ran, Qiwen; Zhao, Tieyu; Yuan, Lin; Wang, Jian; Xu, Lei
2014-11-01
In this paper, we propose a multiple-parameter fractional Fourier transform with its transform order being a real vector, based on which a high-security image encryption scheme is also given. This novel fractional Fourier transform has removed the restriction on the dimension of transform order and highly enhances the security of image encryption scheme proposed in this paper without increasing the computational complexity and hardware cost. The numerical results verify the efficacy and security of this image encryption method. The vector power multi-parameter fractional Fourier transform is a generalized form of the classical fractional Fourier transform with all the previous fractional Fourier transform as its special cases and has theoretical significance in information processing and information security.
Fourier transform infrared spectroscopy for Kona coffee authentication.
Wang, Jun; Jun, Soojin; Bittenbender, H C; Gautz, Loren; Li, Qing X
2009-06-01
Kona coffee, the variety of "Kona typica" grown in the north and south districts of Kona-Island, carries a unique stamp of the region of Big Island of Hawaii, U.S.A. The excellent quality of Kona coffee makes it among the best coffee products in the world. Fourier transform infrared (FTIR) spectroscopy integrated with an attenuated total reflectance (ATR) accessory and multivariate analysis was used for qualitative and quantitative analysis of ground and brewed Kona coffee and blends made with Kona coffee. The calibration set of Kona coffee consisted of 10 different blends of Kona-grown original coffee mixture from 14 different farms in Hawaii and a non-Kona-grown original coffee mixture from 3 different sampling sites in Hawaii. Derivative transformations (1st and 2nd), mathematical enhancements such as mean centering and variance scaling, multivariate regressions by partial least square (PLS), and principal components regression (PCR) were implemented to develop and enhance the calibration model. The calibration model was successfully validated using 9 synthetic blend sets of 100% Kona coffee mixture and its adulterant, 100% non-Kona coffee mixture. There were distinct peak variations of ground and brewed coffee blends in the spectral "fingerprint" region between 800 and 1900 cm(-1). The PLS-2nd derivative calibration model based on brewed Kona coffee with mean centering data processing showed the highest degree of accuracy with the lowest standard error of calibration value of 0.81 and the highest R(2) value of 0.999. The model was further validated by quantitative analysis of commercial Kona coffee blends. Results demonstrate that FTIR can be a rapid alternative to authenticate Kona coffee, which only needs very quick and simple sample preparations. PMID:19646032
Spectroscopic Stokes polarimetry based on Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Liu, Yeng-Cheng; Lo, Yu-Lung; Li, Chang-Ye; Liao, Chia-Chi
2015-02-01
Two methods are proposed for measuring the spectroscopic Stokes parameters using a Fourier transform spectrometer. In the first method, it is designed for single point measurement. The parameters are extracted using an optical setup comprising a white light source, a polarizer set to 0°, a quarter-wave plate and a scanning Michelson interferometer. In the proposed approach, the parameters are extracted from the intensity distributions of the interferograms produced with the quarter-wave plate rotated to 0°, 22.5°, 45° and -45°, respectively. For the second approach, the full-field and dynamic measurement can be designed based upon the first method with special angle design in a polarizer and a quarter-wave plate. Hence, the interferograms of two-dimensional detection also can be simultaneously extracted via a pixelated phase-retarder and polarizer array on a high-speed CCD camera and a parallel read-out circuit with a multi-channel analog to digital converter. Thus, a full-field and dynamic spectroscopic Stokes polarimetry without any rotating components could be developed. The validity of the proposed methods is demonstrated both numerically and experimentally. To the authors' knowledge, this could be the simplest optical arrangement in extracting the spectral Stokes parameters. Importantly, the latter one method avoids the need for rotating components within the optical system and therefore provides an experimentally straightforward means of extracting the dynamic spectral Stokes parameters.
Analysis of the modulation efficiency of imaging Fourier transform spectrometers
NASA Astrophysics Data System (ADS)
Fu, Yan-peng; Li, Xun-niu; Zheng, Wei-jian; Liao, Ning-fang; Su, Jun-hong
2013-08-01
The concept of high-throughput imaging Fourier transform spectrometer is introduced. Starting from the principle of the lateral shearing interferometer, it analyses the decline reason for the signal modulation efficiency and theoretically analyses the several aspects of the surface errors of the plane mirror, the beamsplitter properties change and the incident light angle influence the modulation efficiency. Based on analysis results, some expressions of modulation efficiency are provided. Furthermore, the relationship between modulation efficiency and performance parameters is pointed out. The reasons for the interferometer signal modulation efficiency decline can contain the following several aspects: (1) the influence of the surface errors of the plane mirror, (2) the polarization state change because of the influence of the reflection and the transmission in the light incident process makes the signal modulation efficiency decline, (3) the influence of the incident light angle. The results show that: this class of system is inherently optomechanics robust, no-moving part system, simple and compact structure, easy assembly and adjustment, strong vibration resistance as well as high resolution and high-throughput. Our results will provide a theoretical and practical guide for studying, developing and engineering Michelson lateral shearing interference imaging spectrometers. It can be widely used in the long-wave infrared (LWIR) imaging spectrometer system for thermal infrared remote sensing community.
Phase error in Fourier transform spectrometers employing polarization interferometers
NASA Astrophysics Data System (ADS)
Wang, Yifan; Kudenov, Michael W.; Craven-Jones, Julia
2014-05-01
Phase error is common in reflective interferometers, such as the Michelson. This yields highly asymmetric interferograms that complicate the post-processing of single-sided interference data. Common methods of compensating for phase errors include the Mertz, Forman, and Cannes phase correction techniques. However, birefringent interferometers often have highly symmetric interferograms; thus, compensating for phase errors may represent an unnecessary and/or detrimental step in post processing. In this paper, an analysis of the phase error generated by the Infrared Hyperspectral Imaging Polarimeter (IHIP) is conducted. First, a model of the IHIP is presented that quantifies the phase error in the system. The error associated with calculating spectra from single-sided interferograms, using Mertz phase correction and simple singlesided to double-sided mirroring, is then investigated and compared to "true" double-sided Cannes phase corrected spectra. These error calculations are set within the context of measurements taken from a Michelson interferometer-based Fourier transform spectrometer. Results demonstrate that the phase error of the IHIP is comparatively small and that Mertz phase correction may not be necessary to minimize error in the spectral calculation.
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.
Applications of the VUV Fourier Transform Spectrometer at Synchrotron Soleil
NASA Astrophysics Data System (ADS)
de Oliveira, Nelson; Joyeux, Denis; Ito, Kenji; Gans, Berenger; Nahon, Laurent
2015-06-01
Fourier transform spectrometers (FTS) are usually based upon amplitude division interferometers through beamsplitters (BS) as in the Michelson interferometer geometry. However, the manufacture of broadband BS is difficult and even impossible in the far VUV (below λ = 140 nm). We therefore conceived an instrument based upon an original design involving only reflective plane surfaces, giving access to the whole VUV range without the restrictions associated with BS. The VUV- FTS is a permanent endstation connected to one of the three experimental branches of the DESIRS beamline and devoted to high resolution photoabsorption in the UV-VUV spectral range, typically between λ = 300 and 40 nm Since 2008, a large international community of users interested in laboratory measurements with applications in astrophysics, molecular physics or planetary atmospheres has been attracted by the VUV - FTS capabilities including its efficiency in terms of signal to noise ratio, even when high spectral resolution was not an issue. A large number of dedicated gas phase sample environments have been developed including a windowless cell that can be cooled down, a heated windowless cell, a free molecular jet set-up and various windowed cells. Besides, a new discharge gas cell for production and study of transient species gave recently its first results. As an illustration, the VUV absorption spectrum of the CH_3 radical down to 140 nm will be shown in this presentation. Nahon et al., J. Synchrotron Radiat., 19, 508(2012) De Oliveira et al., Nat. Photonics, 5, 149(2011)
External Second Gate-Fourier Transform Ion Mobility Spectrometry.
Tarver, Edward E., III
2005-01-01
Ion mobility spectrometry (IMS) is recognized as one of the most sensitive and versatile techniques for the detection of trace levels of organic vapors. IMS is widely used for detecting contraband narcotics, explosives, toxic industrial compounds and chemical warfare agents. Increasing threat of terrorist attacks, the proliferation of narcotics, Chemical Weapons Convention treaty verification as well as humanitarian de-mining efforts has mandated that equal importance be placed on the analysis time as well as the quality of the analytical data. (1) IMS is unrivaled when both speed of response and sensitivity has to be considered. (2) With conventional (signal averaging) IMS systems the number of available ions contributing to the measured signal to less than 1%. Furthermore, the signal averaging process incorporates scan-to-scan variations decreasing resolution. With external second gate Fourier Transform ion mobility spectrometry (FT-IMS), the entrance gate frequency is variable and can be altered in conjunction with other data acquisition parameters to increase the spectral resolution. The FT-IMS entrance gate operates with a 50% duty cycle and so affords a 7 to 10-fold increase in sensitivity. Recent data on high explosives are presented to demonstrate the parametric optimization in sensitivity and resolution of our system.
Liquid chromatography/Fourier transform IR spectrometry interface flow cell
Johnson, Charles C.; Taylor, Larry T.
1986-01-01
A zero dead volume (ZDV) microbore high performance liquid chromatography (.mu.HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a .mu.HPLC column end fitting to minimize the transfer volume of the effluents exiting the .mu.HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF.sub.2), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.
Remote detection of organics using Fourier transform infrared spectroscopy
Demirgian, J.C.; Spurgash, S.M.
1990-01-01
Fourier transform infrared (FTIR) spectroscopy is an ideal technique for remote detection of organic emissions. There is an atmospheric window in the 1200 to 800 cm{sup {minus}1} region, which corresponds to the fingerprint'' region for organic molecules. Virtually all organic molecules have a unique absorption/emission pattern in the fingerprint region. A remote-passive FTIR relies on ambient emission of infrared energy from organics to obtain spectra. The instrumentation consists of inlet optics, and interferometer, a mercury cadmium telluride (MCT) detector, and an on-board computer. The transportable unit measures 40 cm by 50 cm and has been used to collect data while mounted on a helicopter or ground vehicle. Through the use of this FTIR combined with least squares software, it is possible to analyze qualitatively and quantitatively for organic vapors from either the air or ground. The data presented will include quantitative releases of common organics present in incinerator stacks, hazardous wastes, and illegal laboratories. Data will be presented for pure compounds, mixtures, and target analytes in the presence of interfering compounds. The sensitivity, reproducibility, and the potential of the technique will be discussed. 1 ref., 8 figs., 6 tabs.
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.
Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability
NASA Technical Reports Server (NTRS)
Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.
2007-01-01
The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.
A Fourier transform infrared trace gas analyser for atmospheric applications
NASA Astrophysics Data System (ADS)
Griffith, D. W. T.; Deutscher, N. M.; Caldow, C. G. R.; Kettlewell, G.; Riggenbach, M.; Hammer, S.
2012-05-01
Concern in recent decades about human impacts on Earth's climate has led to the need for improved and expanded measurement capabilities for greenhouse gases in the atmosphere. In this paper we describe in detail an in situ trace gas analyser based on Fourier Transform Infrared (FTIR) spectroscopy that is capable of simultaneous and continuous measurements of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), nitrous oxide (N2O) and 13C in CO2 in air with high precision and accuracy. Stable water isotopes can also be measured in undried airstreams. The analyser is automated and allows unattended operation with minimal operator intervention. Precision and accuracy meet and exceed the compatibility targets set by the World Meteorological Organisation - Global Atmosphere Watch Programme for baseline measurements in the unpolluted troposphere for all species except 13C in CO2. The analyser is mobile and well suited to fixed sites, tower measurements, mobile platforms and campaign-based measurements. The isotopic specificity of the optically-based technique and analysis allows application of the analyser in isotopic tracer experiments, for example 13C in CO2 and 15N in N2O. We review a number of applications illustrating use of the analyser in clean air monitoring, micrometeorological flux and tower measurements, mobile measurements on a train, and soil flux chamber measurements.
Fourier transform spectrometer for Greenhouse Gases Observing Satellite (GOSAT)
NASA Astrophysics Data System (ADS)
Hamazaki, Takashi; Kaneko, Yutaka; Kuze, Akihiko; Kondo, Kayoko
2005-01-01
Global warming has become a very serious issue for human beings. In 1997, the Kyoto Protocol was adopted at the Third Session of the Conference of the Parties to the United Nations Framework Convention on Climate Change (COP3), making it mandatory for developed nations to reduce carbon dioxide emissions by six (6) to eight (8) per cent of their total emissions in 1990, and to meet this goal sometime between 2008 and 2012. The Greenhouse gases Observing SATellite (GOSAT) is designed to monitor the global distribution of carbon dioxide (CO2) from the space. GOSAT is a joint project of Japan Aerospace Exploration Agency (JAXA), the Ministry of Environment (MOE), and the National Institute for Environmental Studies (NIES). JAXA is responsible for the satellite and instrument development, MOE is involved in the instrument development, and NIES is responsible for the satellite data retrieval. The satellite is scheduled to be launched in 2008. In order to detect the CO2 variation of boundary layers, both the technique to measure the column density and the retrieval algorithm to remove cloud and aerosol contamination are investigated. Main mission sensor of the GOSAT is a Fourier Transform Spectrometer with high optical throughput, spectral resolution and wide spectral coverage, and a cloud-aerosol detecting imager attached to the satellite. The paper presents the mission sensor system of the GOSAT together with the results of performance demonstration with proto-type instrument aboard an aircraft.
Single beam Fourier transform digital holographic quantitative phase microscopy
Anand, A. Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Faridian, A.; Pedrini, G.; Osten, W.; Dubey, S. K.; Javidi, B.
2014-03-10
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
Cryogenic Fourier transform infrared spectrometer from 4 to 20 micrometers
NASA Astrophysics Data System (ADS)
Kaplan, Simon G.; Woods, Solomon I.; Jung, Timothy M.; Carter, Adriaan C.
2010-07-01
We describe the design and performance of a cryogenic Fourier transform spectrometer (Cryo-FTS) operating at a temperature of approximately 15 K. The instrument is based on a porch-swing scanning mirror design with active alignment stabilization using a fiber-optic coupled diode laser and voice-coil actuator mechanism. It has a KBr beamsplitter and has been integrated into an infrared radiometer containing a calibrated Si:As blocked impurity band (BIB) detector. Due to its low operating temperature, the spectrometer exhibits very small thermal background signal and low drift. Data from tests of basic spectrometer function, such as modulation efficiency, scan jitter, spectral range, and spectral resolution are presented. We also present results from measurements of faint point-like sources in a low background environment, including background, signal offset and gain, and spectral noise equivalent power, and discuss the possible use of the instrument for spectral characterization of ground-based infrared astronomy calibration sources. The Cryo-FTS is presently limited to wavelengths below 25 micrometers but can be in principle extended to longer wavelengths with changes in beamsplitter and detector.
Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS)
NASA Technical Reports Server (NTRS)
Sromovsky, L. A.
2002-01-01
This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).
Single beam Fourier transform digital holographic quantitative phase microscopy
NASA Astrophysics Data System (ADS)
Anand, A.; Faridian, A.; Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Dubey, S. K.; Pedrini, G.; Osten, W.; Javidi, B.
2014-03-01
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
Toward a soft x-ray Fourier-transform spectrometer
Howells, M.R.; Frank, K.; Hussain, Z.; Moler, E.J.; Reich, T. |; Moeller, D.; Shirley, D.A.
1993-10-29
The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range {+-}1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330.
Fourier transform infrared 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
Transmission fourier transform Raman spectroscopy of pharmaceutical tablet cores.
Pelletier, Michael J; Larkin, Peter; Santangelo, Matthew
2012-04-01
Transmission Fourier transform (FT) Raman spectroscopy of pharmaceutical tablet cores is demonstrated using traditional, unmodified commercial instrumentation. The benefits of improved precision over backscattering Raman spectroscopy due to increased sample volume are demonstrated. Self-absorption effects on analyte band ratios and sample probe volume are apparent, however. A survey of near-infrared (NIR) absorption spectra in the FT-Raman spectral range (approximately 0 to 3500 wavenumber shift from 1064 nm, or 1064 to 1700 nm) of molecules with a wide range of NIR-active functional groups shows that although absorption at the laser wavelength (1064 nm) is relatively small, some regions of the Raman spectrum coincide with NIR absorbances of 0.5 per cm or greater. Fortunately, the pharmaceutically important regions of the Raman shift spectrum from 0 to 600 cm(-1) and from 1400 to 1900 cm(-1) exhibit low self-absorption for most organic materials. A statistical analysis of transmission FT-Raman noise in spectra collected from different regions of a pharmaceutical tablet provides insight into both spectral distortion and reduced sampling volume caused by self-absorption. PMID:22449328
Ribosomal DNA Nanoprobes studied by Fourier Transform Infrared spectroscopy
NASA Astrophysics Data System (ADS)
Fagundes, Jaciara; Castilho, Maiara L.; Téllez Soto, Claudio A.; Vieira, Laís de Souza; Canevari, Renata A.; Fávero, Priscila P.; Martin, Airton A.; Raniero, Leandro
2014-01-01
Paracoccidioides brasiliensis (P. brasiliensis) is a thermo-dimorphic fungus that causes paracoccidioidomycosis. Brazil epidemiological data shows that endemic areas are the subtropical regions, especially where agricultural activities predominate such as the Southeast, South, and Midwest. There are several tests to diagnose paracoccidioidomycosis, but they have many limitations such as low sensitivity, high cost, and a cross-reacting problem. In this work, gold nanoprobes were used to identify P. brasiliensis as an alternative diagnostic technique, which is easier to apply, costs less, and has great potential for application. The specific Ribosomal sequence of P. brasiliensis DNA was amplified and used to design the nanoprobes using a thiol-modified oligonucleotide. The results of positive and negative tests were done by UV-visible and Fourier Transform Infrared (FT-IR) measurements. The deconvolution of FT-IR sample spectra showed differences in the vibrational modes from the hydrogen bridge NHN and NHO bands that form the double helix DNA for samples matching the DNA sequence of nanoprobes that could be used to classify the samples.
Fourier transform optical profilometry using fiber optic Lloyd's mirrors.
Kart, Trkay; Kso?lu, Gl?en; Yksel, Heba; ?nci, Mehmet Naci
2014-12-10
A fiber optic Lloyd's mirror assembly is used to obtain various optical interference patterns for the detection of 3D rigid body shapes. Two types of fiber optic Lloyd's systems are used in this work. The first consists of a single-mode optical fiber and a highly reflecting flat mirror to produce bright and dark strips. The second is constructed by locating a single-mode optical fiber in a v-groove, which is formed by two orthogonal flat mirrors to allow the generation of square-type interference patterns for the desired applications. The structured light patterns formed by these two fiber Lloyd's techniques are projected onto 3D objects. Fringe patterns are deformed due to the object's surface topography, which are captured by a digital CCD camera and processed with a Fourier transform technique to accomplish 3D surface topography of the object. It is demonstrated that the fiber-optic Lloyd's technique proposed in this work is more compact, more stable, and easier to configure than other existing surface profilometry systems, since it does not include any high-cost optical tools such as aligners, couplers, or 3D stages. The fringe patterns are observed to be more robust against environmental disturbances such as ambient temperature and vibrations. PMID:25608057
SAR-based vibrometry using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Campbell, Justin B.; Wang, Qi; Ade-Bello, Jelili; Caudana, Humberto; Trujillo, Nicole B.; Bhatta, Ishwor; Dunkel, Ralf; Atwood, Thomas; Doerry, Armin; Gerstle, Walter H.; Santhanam, Balu; Hayat, Majeed M.
2015-05-01
A fundamental assumption when applying Synthetic Aperture Radar (SAR) to a ground scene is that all targets are motionless. If a target is not stationary, but instead vibrating in the scene, it will introduce a non-stationary phase modulation, termed the micro-Doppler effect, into the returned SAR signals. Previously, the authors proposed a pseudosubspace method, a modification to the Discrete Fractional Fourier Transform (DFRFT), which demonstrated success for estimating the instantaneous accelerations of vibrating objects. However, this method may not yield reliable results when clutter in the SAR image is strong. Simulations and experimental results have shown that the DFRFT method can yield reliable results when the signal-to-clutter ratio (SCR) > 8 dB. Here, we provide the capability to determine a target's frequency and amplitude in a low SCR environment by presenting two methods that can perform vibration estimations when SCR < 3 dB. The first method is a variation and continuation of the subspace approach proposed previously in conjunction with the DFRFT. In the second method, we employ the dual-beam SAR collection architecture combined with the extended Kalman filter (EKF) to extract information from the returned SAR signals about the vibrating target. We also show the potential for extending this SAR-based capability to remotely detect and classify objects housed inside buildings or other cover based on knowing the location of vibrations as well as the vibration histories of the vibrating structures that house the vibrating objects.
Quantitative analysis of vitamin A using Fourier transform Raman spectroscopy
NASA Astrophysics Data System (ADS)
Hancewicz, Thomas M.; Petty, Chris
1995-11-01
Near infrared Fourier transform Raman spectroscopy has been successfully used to quantitatively analyze vitamin A additives in a sorbitan mono-oleate base vehicle. Although measurements can be made on the raw materials, their high viscosity causes them to be difficult to handle in an industrial testing lab. Accurate quantitation is possible using a simple dilution of the sample. This reduces the overall measurement time by speeding up preparation and clean-up. Results are quantified over a range of 0.05 ml -1 up to 1 mg ml -1 using a partial least-squares analysis model. A discussion is made of factors affecting quantitative analysis using FT Raman instrumentation in an industrial environment. Application of the multiplicative scatter correction (MSC) as a pretreatment step for Raman data is discussed with reference to the partial least squares (PLS) calibration. A discussion is presented to the information imbedded in the latent PLS factors and how analysis of these factors can often add to an understanding of the chemical information being modeled.
Eliminating zero spectra in Fourier transform profilometry by application of Hilbert transform
NASA Astrophysics Data System (ADS)
Luo, Feng; Chen, Wenjing; Su, Xianyu
2016-04-01
Hilbert transform has the features of inducing a phase shifting of 90 degree and removing the DC component. We propose a novel method based on the piecewise Hilbert transform to suppress the background intensity of the deformed fringe pattern using only one fringe pattern in Fourier transform profilometry according to the approximation that the background of the fringe is a slowly varying function and its distribution in each half period of the fringe can be regarded as a constant. In the method, Hilbert transform deals with each segmented fringe section to remove the DC component and then forms a result fringe whose background intensity is suppressed well by putting the fringe pieces together. The proposed method can enlarge the measurement range and reduce the measurement error of FTP. The theoretical analysis is given. Computer simulations and experimental results demonstrate the effectiveness of the proposed method.
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.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Paul, J.; Dey, P.; Karaiskaj, D.; Tokumoto, T.; Hilton, D. J.; Reno, J. L.
2014-10-07
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{sup 11} cm{sup −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” (S{sub 1}) 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 S{sub 1} 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” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.
An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.
ERIC Educational Resources Information Center
Eastman, M. P.; And Others
1986-01-01
Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.
NASA Astrophysics Data System (ADS)
Xia, Xiang-Gen; Wang, Genyuan; Chen, Victor C.
2001-03-01
This paper first reviews some basic properties of the discrete chirp-Fourier transform and then present an adaptive chirp- Fourier transform, a generalization of the amplitude and phase estimation of sinusoids (APES) algorithm proposed by Li and Stoica for sinusoidal signals. We finally applied it to the ISAR imaging of maneuvering targets.
The Green's function for the three-dimensional linear Boltzmann equation via Fourier transform
NASA Astrophysics Data System (ADS)
Machida, Manabu
2016-04-01
The linear Boltzmann equation with constant coefficients in the three-dimensional infinite space is revisited. It is known that the Green's function can be calculated via the Fourier transform in the case of isotropic scattering. In this paper, we show that the three-dimensional Green's function can be computed with the Fourier transform even in the case of arbitrary anisotropic scattering.
Practical aspects of Fourier transform and correlation based processing of spectrochemical data
NASA Astrophysics Data System (ADS)
Ng, R. C. L.; Horlick, Gary
Fourier transform based signal processing methods are beginning to be widely used for the treatment of spectrochemical data. The most common approach to Fourier transformation is through the utilization of the so called Fast Fourier Transform algorithm or FFT as it is usually designated. However, several versions of the FFT abound in the literature and in program libraries and many subtleties exist with respect to data pre-treatment, data post-treatment, inverse Fourier transformation and manipulation of real and imaginary arrays that can cause considerable grief to the uninitiated. In this presentation numerous examples will be presented illustrating several practical aspects of implementing FFT's and cross-correlations (Fourier transform route) on spectrochemical data sets. Particular attention is paid to the manipulation to the input and output real and imaginary arrays.
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).
FTS: Fourier transform spectrometer onboard ASTRO-F/FIS
NASA Astrophysics Data System (ADS)
Takahashi, Hidenori; Kawada, Mitsunobu; Murakami, Noriko; Ozawa, Keita; Shibai, Hiroshi; Nakagawa, Takao
2003-03-01
Far-Infrared Surveyor (FIS) is one of the two focal plane instruments of ASTRO-F which is a Japanese infrared astronomical satellite and is planned to launch in 2004. The FIS has spectroscopic capability by a Fourier transform spectrometer (FTS) covering 50-200cm-1 with spectral resolution of 0.2-0.33 cm-1 in addition to the primary purpose of FIS (an all-sky photometric survey). The Martin-Puplett interferometer is adopted as the method for spectroscopy in order to achieve high optical efficiency in a wide wavelength range. The most important issue of the FTS is the development of driving mechanism in order to scan a moving mirror with high optical performances. By the present we succeed to develop the driving mechanism satisfying a lot of limitations and requirements as a instrument onboard satellite. Furthermore the wire-grid polarizers are evaluated in optical performance, these are usable for polarized interferomter. We also measure FIR spectrum using Spectroscopy mode of FIS, and many absorption lines of H2O are detected on continuum spectrum of atmosphere. And the interferogram and spectrum are derived at low temperature (2K) that is practically used in space. The spectrum resembles expected one which are considered with optical components for flight model. The detection limit are estimated combining performances of optical components and detectors, the FISP has sufficient performance to archive objective sciences. FTS will provide a lot of astronomical information; determination of the SED in high-z objects detected by the survey observation of ASTRO-F, the redshift of such objects, and the physical conditions that are hard to be derived by optical/NIR-MIR observations, from FIR lines.
The University of Toronto's balloon-borne Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Wunch, D.; Drummond, J. R.; Midwinter, C.; Taylor, J. R.; Fu, D.; Walker, K. A.; McElroy, C. T.; Strong, K.; Bernath, P.; Fast, H.
The University of Toronto s Fourier transform spectrometer U of T FTS derived from a Bomem DA5 Michelson-type interferometer was rebuilt and flown on the Middle Atmosphere Nitrogen TRend Assessment MANTRA high-altitude balloon platform in September 2004 The U of T FTS has a resolution of 0 02 cm -1 a spectral range covering 1200-5000 cm -1 and InSb and MCT detectors that measure simultaneously The spectrometer was originally built in the 1980s and purchased by the Meteorological Service of Canada To prepare the instrument for flight the original software was replaced with new LabVIEW control software creating a robust and easily-controlled instrument adaptable to either remote control or lab-based work As a result of replacing the software most of the electronics had to be replaced creating a lighter lower-power more robust instrument A description of the refurbishment will be presented Despite balloon launch and gondola pointing system failures during the MANTRA 2004 campaign two spectra were recorded on each detector during sunset from a float height of 35 km The data indicate that the instrument performed well throughout the flight and had the payload pointing been under control would have retrieved a full set of occultation data The data that were acquired will be shown The U of T FTS has since participated in a ground-based FTS inter-comparison campaign with two other FTS instruments the University of Toronto s Toronto Atmospheric Observatory TAO FTS a complementary NDACC station Network for the Detection of
Systematic characterization of the Herschel SPIRE Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Hopwood, R.; Polehampton, E. T.; Valtchanov, I.; Swinyard, B. M.; Fulton, T.; Lu, N.; Marchili, N.; van der Wiel, M. H. D.; Benielli, D.; Imhof, P.; Baluteau, J.-P.; Pearson, C.; Clements, D. L.; Griffin, M. J.; Lim, T. L.; Makiwa, G.; Naylor, D. A.; Noble, G.; Puga, E.; Spencer, L. D.
2015-05-01
A systematic programme of calibration observations was carried out to monitor the performance of the Spectral and Photometric Imaging REceiver (SPIRE) Fourier Transform Spectrometer (FTS) instrument on board the Herschel Space Observatory. Observations of planets (including the prime point-source calibrator, Uranus), asteroids, line sources, dark sky and cross-calibration sources were made in order to monitor repeatability and sensitivity, and to improve FTS calibration. We present a complete analysis of the full set of calibration observations and use them to assess the performance of the FTS. Particular care is taken to understand and separate out the effect of pointing uncertainties, including the position of the internal beam steering mirror for sparse observations in the early part of the mission. The repeatability of spectral-line centre positions is <5 km s-1, for lines with signal-to-noise ratios >40, corresponding to <0.5-2.0 per cent of a resolution element. For spectral-line flux, the repeatability is better than 6 per cent, which improves to 1-2 per cent for spectra corrected for pointing offsets. The continuum repeatability is 4.4 per cent for the SPIRE Long Wavelength spectrometer (SLW) band and 13.6 per cent for the SPIRE Short Wavelength spectrometer (SSW) band, which reduces to ˜1 per cent once the data have been corrected for pointing offsets. Observations of dark sky were used to assess the sensitivity and the systematic offset in the continuum, both of which were found to be consistent across the FTS-detector arrays. The average point-source calibrated sensitivity for the centre detectors is 0.20 and 0.21 Jy [1σ; 1 h], for SLW and SSW. The average continuum offset is 0.40 Jy for the SLW band and 0.28 Jy for the SSW band.
Phase retrieval using iterative Fourier transform and convex optimization algorithm
NASA Astrophysics Data System (ADS)
Zhang, Fen; Cheng, Hong; Zhang, Quanbing; Wei, Sui
2015-05-01
Phase is an inherent characteristic of any wave field. Statistics show that greater than 25% of the information is encoded in the amplitude term and 75% of the information is in the phase term. The technique of phase retrieval means acquire phase by computation using magnitude measurements and provides data information for holography display, 3D field reconstruction, X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Mathematically, solving phase retrieval problem is an inverse problem taking the physical and computation constraints. Some recent algorithms use the principle of compressive sensing, such as PhaseLift, PhaseCut and compressive phase retrieval etc. they formulate phase retrieval problems as one of finding the rank-one solution to a system of linear matrix equations and make the overall algorithm a convex program over n n matrices. However, by "lifting" a vector problem to a matrix one, these methods lead to a much higher computational cost as a result. Furthermore, they only use intensity measurements but few physical constraints. In the paper, a new algorithm is proposed that combines above convex optimization methods with a well known iterative Fourier transform algorithm (IFTA). The IFTA iterates between the object domain and spectral domain to reinforce the physical information and reaches convergence quickly which has been proved in many applications such as compute-generated-hologram (CGH). Herein the output phase of the IFTA is treated as the initial guess of convex optimization methods, and then the reconstructed phase is numerically computed by using modified TFOCS. Simulation results show that the combined algorithm increases the likelihood of successful recovery as well as improves the precision of solution.
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.
Fourier transform infrared spectroscopy for molecular analysis of microbial cells.
Ojeda, Jesús J; Dittrich, Maria
2012-01-01
A rapid and inexpensive method to characterise chemical cell properties and identify the functional groups present in the cell wall is Fourier transform infrared spectroscopy (FTIR). Infrared spectroscopy is a well-established technique to identify functional groups in organic molecules based on their vibration modes at different infrared wave numbers. The presence or absence of functional groups, their protonation states, or any changes due to new interactions can be monitored by analysing the position and intensity of the different infrared absorption bands. Additionally, infrared spectroscopy is non-destructive and can be used to monitor the chemistry of living cells. Despite the complexity of the spectra, the elucidation of functional groups on Gram-negative and Gram-positive bacteria has been already well documented in the literature. Recent advances in detector sensitivity have allowed the use of micro-FTIR spectroscopy as an important analytical tool to analyse biofilm samples without the need of previous treatment. Using FTIR spectroscopy, the infrared bands corresponding to proteins, lipids, polysaccharides, polyphosphate groups, and other carbohydrate functional groups on the bacterial cells can now be identified and compared along different conditions. Despite some differences in FTIR spectra among bacterial strains, experimental conditions, or changes in microbiological parameters, the IR absorption bands between approximately 4,000 and 400 cm(-1) are mainly due to fundamental vibrational modes and can often be assigned to the same particular functional groups. In this chapter, an overview covering the different sample preparation protocols for infrared analysis of bacterial cells is given, alongside the basic principles of the technique, the procedures for calculating vibrational frequencies based on simple harmonic motion, and the advantages and disadvantages of FTIR spectroscopy for the analysis of microorganisms. PMID:22639215
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.
Continuously tunable optical multidimensional Fourier-transform spectrometer.
Dey, P; Paul, J; Bylsma, J; Deminico, S; Karaiskaj, D
2013-02-01
A multidimensional optical nonlinear spectrometer (MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. The MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delays between them while maintaining phase stability. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy. The present work reports on overcoming some important limitations on the original design of the MONSTR apparatus. One important advantage of the MONSTR is the fact that it is a closed platform, which provides the high stability. Once the optical alignment is performed, it is desirable to maintain the alignment over long periods of time. The previous design of the MONSTR was limited to a narrow spectral range defined by the optical coating of the beam splitters. In order to achieve tunability over a broad spectral range the internal optics needed to be changed. By using broadband coated and wedged beam splitters and compensator plates, combined with modifications of the beam paths, continuous tunability can be achieved from 520 nm to 1100 nm without changing any optics or performing alignment of the internal components of the MONSTR. Furthermore, in order to achieve continuous tunability in the spectral region between 520 nm and 720 nm, crucially important for studies on numerous biological molecules, a single longitudinal mode laser at 488.5 nm was identified and used as a metrology laser. The shorter wavelength of the metrology laser as compared to the usual HeNe laser has also increased the phase stability of the system. Finally, in order to perform experiments in the reflection geometry, a simple method to achieve active phase stabilization between the signal and the reference beams has been developed. PMID:23464195
Geostationary Imaging Fourier Transform Spectrometer (GIFTS): science applications
NASA Astrophysics Data System (ADS)
Smith, W. L.; Revercomb, H. E.; Zhou, D. K.; Bingham, G. E.; Feltz, W. F.; Huang, H. L.; Knuteson, R. O.; Larar, A. M.; Liu, X.; Reisse, R.; Tobin, D. C.
2006-12-01
A revolutionary satellite weather forecasting instrument, called the "GIFTS" which stands for the "Geostationary Imaging Fourier Transform Spectrometer", was recently completed and successfully tested in a space chamber at the Utah State University's Space Dynamics Laboratory. The GIFTS was originally proposed by the NASA Langley Research Center, the University of Wisconsin, and the Utah State University and selected for flight demonstration as NASA's New Millennium Program (NMP) Earth Observing-3 (EO-3) mission, which was unfortunately cancelled in 2004. GIFTS is like a digital 3-d movie camera that, when mounted on a geostationary satellite, would provide from space a revolutionary four-dimensional view of the Earth's atmosphere. GIFTS will measure the distribution, change, and movement of atmospheric moisture, temperature, and certain pollutant gases, such as carbon monoxide and ozone. The observation of the convergence of invisible water vapor, and the change of atmospheric temperature, provides meteorologists with the observations needed to predict where, and when, severe thunderstorms, and possibly tornados, would occur, before they are visible on radar or in satellite cloud imagery. The ability of GIFTS to observe the motion of moisture and clouds at different altitudes enables atmospheric winds to be observed over vast, and otherwise data sparse, oceanic regions of the globe. These wind observations would provide the means to greatly improve the forecast of where tropical storms and hurricanes will move and where and when they will come ashore (i.e., their landfall position and time). GIFTS, if flown into geostationary orbit, would provide about 80,000 vertical profiles per minute, each one like a low vertical resolution (1-2km) weather balloon sounding, but with a spacing of 4 km. GIFTS is a revolutionary atmospheric sensing tool. A glimpse of the science measurement capabilities of GIFTS is provided through airborne measurements with the NPOESS Airborne Sounding Testbed - Interferometer (NAST-I).
Kyatkin, A.B.; Chirikjian, G.S.
1999-06-01
The authors apply the Fourier transform on the discrete-motion group to the problem of computing the configuration-space obstacles of mobile robots which move among static obstacles, the problem of finding the workspace density of binary manipulators with many actuators, and the problem of determining workspace boundaries of manipulators with continuous-motion actuators. They develop and implement Fourier transforms for the discrete-motion group of the plane. These transforms allow them to apply fast Fourier transform methods to the computation of convolution-like integrals that arise in robot kinematics and motion planning. The results of the implementation are discussed for particular examples.
Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Heisler, R.
1978-01-01
A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
NASA Technical Reports Server (NTRS)
Campbell, Joel
2008-01-01
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
Experimental determination of Hamiltonian via 3D Fourier-transform spectroscopy
NASA Astrophysics Data System (ADS)
Li, Hebin; Bristow, Alan; Siemens, Mark; Moody, Galan; Cundiff, Steven
2012-02-01
Prediction and control of quantum mechanical processes requires knowledge about the system Hamiltonian. For coherent control, information about interfering quantum pathways or the underlying Hamiltonian is essential for achieving deterministic control. Even in cases of closed-loop control, a priori knowledge about the system Hamiltonian provides guidance for designing an efficient learning algorithm and a good initial guess for faster convergence. The complete Hamiltonian of a complicated system, especially the effects of inter-particle interactions and coupling to the environments, can only be determined experimentally. Here we demonstrate an experimental determination of the Hamiltonian of an atomic vapor, achieved by using 3-dimensional Fourier transform (3DFT) spectroscopy. The 3DFT spectra provide complete information about the third-order coherent response of the vapor. The contributions from different quantum pathways are unambiguously isolated such that the components of the Hamiltonian, including energy levels, dipole moments and relaxation rates, can be determined. The 3DFT spectroscopy opens an avenue towards identifying the Hamiltonian of complex molecular systems, which can be useful for designing coherent control strategies and for studying the molecular dynamics.
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.
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 μm. 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 μm. 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.
Spectral resolution of space-borne Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Liu, Peng; Wang, Peigang; Hua, Jianwen; Wang, Huzhan
2007-12-01
One of infrared remote sensing instruments carried by FY-4 meteorology satellite is a space-borne Fourier Transform Spectrometer (SBFTS). It acquires temperature, pressure and humidity of atmosphere on geostationary orbit, and supplies the valuable weather data for future numerical weather prediction. It uses a 16x4 plane array rectangular detector, so it can measure the spectra and spatial image simultaneously. The maximum optical path difference of the SBFTS is 0.8cm. Objective: This paper's mainly analyses the three factors (maximum optical path difference, off axes detectors, the tilt angle of the moving mirror) that influence spectral resolution of SBFTS and convinces through experiment. Methods: First, the three primary factors that will influence the instrument line shape (ILS) are discussed here. The ILS is deduced when the three factors are taken into account separately. The final function of ILS is the convolution of the three parts. And the spectral resolution is the half width of the ILS. The gases NH3 and CO are used to detect the ILS of the instrument in the long wave band and middle wave band separately. Their absorption line shape is Lorentz distribution in atmospheric pressure and room temperature. Now the absorption line shape of the gases and the ILS are given. They can be combined to the instrument detecting line shape theoretically. Finally it is compared with the line shape that is really detected by the instrument using gas cell methodology. The lines almost have the same shape and width. Results: The spectral resolution of SBFTS is presented leave each other in theory and experiment. The results are according to each other. Conclusion: The spectral resolution of SBFTS mainly lies on the maximum optical path difference. The interferogram is referred to as being "auto-apodized" since the off-axis effect and tilt angle of the moving mirror theirself appear to impose an apodization function on the interferogram. The auto-apodization of the interferogram is likely to result in a ILS that is broadened in frequency and reduced in amplitude. In addition, the ILS appears to be shifted in frequency and the side-lobes of the ILS are asymmetric. In the long wave band the spectral resolution of SBFTS only rest with the maximum optical path difference. It is not infected by off axes effect because of using plane array detectors and the small tilt angle of the moving mirror. But in the middle wave band its spectral resolution is debased by the off axes effect.
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".
NASA Astrophysics Data System (ADS)
Patiño, A.; Durand, P.-E.; Fogret, É.; Pellat-Finet, P.
2011-01-01
According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.
Fourier transform of delayed fluorescence as an indicator of herbicide concentration.
Guo, Ya; Tan, Jinglu
2014-12-21
It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. PMID:25152216
The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.
ERIC Educational Resources Information Center
King, Roy W.; Williams, Kathryn R.
1989-01-01
Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)
NASA Technical Reports Server (NTRS)
Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.
2000-01-01
A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).
A commercial Fourier transform infrared (FTIR) spectrometer, modified for automated analysis of particulate-associated sulfate, was used to obtain transmission spectra samples of particulate matter collected from the ambient air onto Teflon filters. n evaluation of this instrumen...
NASA Technical Reports Server (NTRS)
Bowman, K.; Worden, H.; Beer, R.
1999-01-01
Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.
Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.
ERIC Educational Resources Information Center
Perkins, W. D.
1987-01-01
This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)
Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...
This project explored the feasibility of developing new techniques for evaluation of the effects of environmental toxic materials on complex biopolymer systems using high sensitivity Fourier transform nuclear magnetic resonance (nmr) spectroscopy. Commercial instrumentation avail...
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: • The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms. • The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform. • The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988
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
Wang, Ruhang; Huang, Jianguo; Ma, Tian; Zhang, Qunfei
2010-12-01
This letter presents an improved space time prewhitening method for linear frequency modulation (LFM) reverberation. The proposed method transforms the reverberation to fractional Fourier domain to whiten using fractional Fourier transform. The linear varying frequency in LFM reverberation is focused on a stationary frequency, and the adjacent block signal is used as the reference signal of prewhitening. Finally, experiment results with real reverberation data verify that the proposed method improves the detection performance of active sonar in shallow sea significantly. PMID:21218858
Quantum computation of multifractal exponents through the quantum wavelet transform
Garcia-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand
2009-05-15
We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum algorithms for multifractal exponents with a polynomial gain compared to classical simulations. Numerical results indicate that a rough estimate of fractality could be obtained exponentially fast. Our findings are relevant, e.g., for quantum simulations of multifractal quantum maps and of the Anderson model at the metal-insulator transition.
Dynamic measurements by color gratings projection method using a two-step Fourier transform method
NASA Astrophysics Data System (ADS)
Kamiya, Kazuhide; Nomura, Takashi; Tanbo, Ami; Kimihisa, Matsumoto; Hatsuzou, Tashiro; Suzuki, Shinya
2012-11-01
The Fourier transform method is an analytical method for interferograms with a spatial linear carrier. Interferograms with a spatial linear carrier are analyzed to obtain the phase, by eliminating the noise from the shape components of the interferograms in the Fourier domain. However, when the noise and shape components overlap in the Fourier domain, it is difficult to eliminate only the overlapped noise components using conventional filtering techniques, such as bandpass filtering. Accordingly, a method is proposed to solve this problem using two interferograms with slightly different carrier frequencies. In this method, the Fourier transforms of two interferograms with slightly different carrier frequencies are separately calculated. Both of the spectra resulting from the Fourier transforms of the interferograms contain the same noise components; however, the locations of these components differ slightly for the two spectra. By subtracting the two Fourier spectra, the noise components are removed, and the main components are generated, because the frequency difference between the two components is small. We have named the proposed method the "two-step Fourier transpose method". The validity of the proposed filtering method is confirmed by experiments in which two color fringes are projected simultaneously onto a scatter object. Images of the color fringes are acquired via a CCD camera under the slow deformation of the scatter object. The images are then analyzed via the proposed method.
Vonau, F; Aubel, D; Gewinner, G; Zabrocki, S; Peruchetti, J C; Bolmont, D; Simon, L
2005-10-21
The semimetallic ErSi2 layer grown on Si(111) substrates provides an ideally confined 2D electron and hole gas that reflects in complex standing wave pattern at 77 K. The quasiparticles exist in a wide energy range from -800 to 300 meV without mixing with silicon bulk excitations. By comparing high resolution Fourier transform of dI/dV maps, with joint density of states calculations, we are able to determine the 2D band structure. We also clearly demonstrate that hole-hole and hole-electron quantum interferences dominate over electron-electron ones. PMID:16383855
A Graphical Presentation to Teach the Concept of the Fourier Transform
ERIC Educational Resources Information Center
Besalu, E.
2006-01-01
A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.
Development of out-of-core fast Fourier transform software for the connection machine. Final report
Sweet, R.; Wilson, J.
1995-10-01
This report describes the algorithm and implementation of an out-of-core Fast Fourier Transform routine for the Thinking Machines Corp. CM-5 parallel computer. The software has the capability of transforming multi-dimensional arrays that are both real and complex.
NASA Astrophysics Data System (ADS)
Onishi, Hiroyuki; Suzuki, Hisashi
1997-03-01
Let a reference image and an input image that is magnified, rotated, and parallel-translated from the reference image be given. This paper discusses a method of computing the scale of magnification, the angle of rotation, and the quantity of parallel translation with a Hough transform of O'Gorman- Clowes version and a Fourier-Mellin transform. Differently from known methods using Fourier or Hough transforms, the discussed method can compute uniquely the angle of rotation. Moreover, the discussed method can process even low quality images since it does not require extracting feature points differently from known methods. Experiments were applied to actual images of bills.
Orthonormal mode sets for the two-dimensional fractional Fourier transformation.
Alieva, Tatiana; Bastiaans, Martin J
2007-05-15
A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied. PMID:17440542
A study of pyrolysis of polymethylsiloxanes by Fourier transform infrared.
Alexandrov, S E; Filatov, L A; Solovyeva, A S
2011-09-01
This paper is dedicated to a comparative study of pyrolysis of decamethylcyclopentasiloxane and hexamethyldisiloxane, widely used as precursors for CVD of silicon dioxide films. The pyrolysis process was carried out in a hot-wall horizontal tube reactor made from quartz within the temperature range 25-1000 degrees C. FTIR spectroscopy has been used for the analysis of gaseous reaction products in the exhaust line of the reactor. It has been found that transformation of DMPSO was initiated by the open ring in the precursor molecules with its further transformation to linear biradicals followed by the chain's growth due to radical reactions. HMDSO transformation is connected with separation of silanon, silyl and methyl radicals with following multi-type interactions of siloxane radicals and formation of non-rigorously organized three-dimensional molecules. PMID:22097543
Does the entorhinal cortex use the Fourier transform?
Orchard, Jeff; Yang, Hao; Ji, Xiang
2013-01-01
Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4–12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed “theta precession.” Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415
Optical image encryption based on two-dimensional N-parameter fractional Fourier transform
NASA Astrophysics Data System (ADS)
Zhang, Haiying; Ran, Qiwen; Xiao, Yu; Ma, Jing; Tan, Liying; Zhang, Jin; Wei, Deyun
2009-07-01
In this paper, the weighted fractional Fourier transform with dilation parameter (N-PFRFT) is proposed as the weighted combination of the first four integer-order ordinary Fourier transforms. This N-PFRFT is an extension of four-item weighted fractional Fourier transform (N-PFRFT) defined by Shih[1] and it owns four free parameters in the weight coefficients besides the order of the fractional Fourier transform. A novel image encryption algorithm is presented by the N-PFRFT.The method owns more secret keys than the encryption methods operated by other fractional Fourier transforms without any increase of the computational complexity. On the other hand, the image still can't be decrypted correctly even though the order of FRFT which is treated as a secret key is known. So do the four free parameters. Therefore, both the order parameter and the vector parameter can be chosen in the real domain to improve the security of the encryption method. Digital simulations are presented to verify the more validity and efficiency of the algorithm.
A faster method to reconstruct seismic data using anti-leakage Fourier transform
NASA Astrophysics Data System (ADS)
Jahanjooy, Saber; Nikrouz, Ramin; Mohammed, Nematullah
2016-02-01
Despite the simplicity of the anti-leakage Fourier transform (ALFT), and its ability to regularize pure non-uniform data sets and handle higher dimension seismic data, ALFT still remains less appealing because of its iterative algorithm and so its costly computation. During this study a set of parameters and techniques were studied to reduce needed computation and speed up ALFT. Having a good weighting function and cautiously selecting more Fourier coefficients at each iteration could improve the resolution of each iteration and subsequently enhance the converge speed of ALFT. Here a precomputed matrix by exponential term of Fourier transform is used to compute Fourier components at each iteration of the ALFT. This proposed matrix dramatically reduces the needed complex multiplication and speeds up the ALFT. By merging this process with a proper weighting function, the fast-ALFT will be quicker than the original ALFT, while it will have almost the same output.
Locke, Jonathan; White, Paul R
2011-10-01
The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species. PMID:21973352
Products of multiple Fourier series with application to the multiblade transformation
NASA Technical Reports Server (NTRS)
Kunz, D. L.
1981-01-01
A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.
Wigner distribution and fractional Fourier transform for two-dimensional symmetric optical beams.
Alieva, T; Bastiaans, M J
2000-12-01
A useful relationship between the fractional Fourier transform power spectra of a two-dimensional symmetric optical beam, on the one hand, and its Wigner distribution, on the other, is established. This relationship allows a significant simplification of the standard procedure for the reconstruction of the Wigner distribution from the field intensity distributions in the fractional Fourier domains. The Wigner distribution of a symmetric optical beam is analyzed, both in the coherent and in the partially coherent case. PMID:11140492
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
Image encryption based on nonseparable fractional Fourier transform and chaotic map
NASA Astrophysics Data System (ADS)
Ran, Qiwen; Yuan, Lin; Zhao, Tieyu
2015-08-01
In this paper an image cryptosystem is constructed by using double random phase masks and a chaotic map together with a novel transform which is similar to fractional Fourier transform and gyrator transform to some extent. The new transform is not periodic with respect to the transform order and cannot be expressed as a tensor product of two one-dimensional transforms neither in the space domain nor in the Wigner space-frequency domain. In the cryptosystem, the parameters of Arnold map, transform orders of the proposed transform and phase information serve as the main keys. The numerical simulations have demonstrated the validity and high security level of the image cryptosystem based on the proposed transform.
Fourier-transform spectroscopy and potential construction of the (2){sup 1}Π state in KCs
Birzniece, I.; Nikolayeva, O.; Tamanis, M.; Ferber, R.
2015-04-07
The paper presents an empirical pointwise potential energy curve (PEC) of the (2){sup 1}Π state of the KCs molecule constructed by applying the Inverted Perturbation Approach routine. The experimental term values in the energy range E(v′, J′) ∈ [15 407; 16 579] cm{sup −1} involved in the fit were based on Fourier-Transform spectroscopy data obtained with 0.01 cm{sup −1} accuracy from the laser-induced (2){sup 1}Π → X{sup 1}Σ{sup +} fluorescence spectra. Buffer gas Ar was used to facilitate the appearance of rotation relaxation lines in the spectra, thus enlarging the (2){sup 1}Π data set and allowing determination of the Λ-splitting constants. The data set included vibrational v′ ∈ [0, 28] and rotational J′ ∈ [7, 274] quantum numbers covering about 67% of the potential well. The present PEC reproduces the overall set of data included in the fit with a standard deviation of 0.5 cm{sup −1}. The obtained value of the Λ-doubling constant q = + 1.8 × 10{sup −6} cm{sup −1} for J′ > 50 and v′ ∈ [0, 6] is in an excellent agreement with q = + 1.84 × 10{sup −6} cm{sup −1} reported in Kim, Lee, and Stolyarov [J. Mol. Spectrosc. 256, 57-67 (2009)].
Fourier Transform Infrared spectrum of the OCD bending mode in methanol-D1
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Indra
2016-03-01
The infrared (IR) spectra corresponding to OCD bending vibration of asymmetrically deuterated methanol species CH2DOH have been recorded with a Fourier Transform Spectrometer. The spectrum shows a typical structure of a parallel a-type band. This is expected because the bending vibration mainly executed parallel to the symmetry axis The Q-branch lines are grouped closely around 896 cm-1 and the P- and R-Branches show complex structure. Nonetheless it was possible to assign a-type P- and R-branch lines up to K value of 8 and J value up to about 20 in most cases. The Q-branch lines for higher K values can be followed to about J = 15, the presence of which confirmed the assignments. The observations suggest that in the OCD bend some energy levels are highly interacted by highly excited torsional state from the ground torsional state. A full catalogue is presented along with the effective molecular parameters. An intensity anomaly was also observed in the transitions. So far it has been possible to assign only transitions between e0 ← e0 states. Plausible explanations of intensity anomaly are presented. Lastly, a number of optically pumped far infrared (FIR) laser lines have been assigned either to exact or tentative quantum states. These assignments should prove valuable for production of new FIR laser lines.
Fourier-transform spectroscopy and potential construction of the (2)1Π 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)1Π 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)1Π → X1Σ+ fluorescence spectra. Buffer gas Ar was used to facilitate the appearance of rotation relaxation lines in the spectra, thus enlarging the (2)1Π data set and allowing determination of the Λ-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 Λ-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)].
Fourier transform synchrotron spectroscopy of torsional and CO-stretching bands of CH 3 17 OH
NASA Astrophysics Data System (ADS)
Moruzzi, G.; Murphy, R. J.; Vos, J.; Lees, R. M.; Predoi-Cross, A.; Billinghurst, B. E.
2011-07-01
The Fourier transform spectrum of the CH 317OH isotopologue of methanol has been recorded in the 65-1200 cm -1 spectral region at a resolution of 0.00096 cm -1 using synchrotron source radiation at the Canadian Light Source. Here we present an extension to higher torsional states of our investigation of the torsion-rotation transitions within the small-amplitude vibrational ground state, now including assignments of more than 16 500 lines involving quantum numbers in the ranges v t ⩽ 3, J ⩽ 30 and | K| ⩽ 12, as well as a study of the strong CO-stretching band centered at 1020 cm -1. Energy term values have been determined for assigned ground and CO-stretching levels by use of the Ritz program, and have been fitted to series expansions in powers of J( J + 1) to determine substate origins and effective B values. Several Fermi anharmonic and Coriolis level-crossing resonances coupling the CO stretch with high torsional ground-state levels have been identified and characterized. The study is motivated by astrophysical applications, with a principal aim being the compilation of an extensive set of energy term values to permit prediction of astronomically observable sub-millimetre transitions to within an uncertainty of a few MHz.
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.
Fourier-transform spectroscopy: new methods and applications: introduction by the feature editors
NASA Astrophysics Data System (ADS)
Traub, Wesley A.; Winkel, Raymond J., Jr.; Goldman, Aaron
1996-06-01
We are pleased to introduce this special issue of papers on Fourier-transform spectroscopy, which grew out of a recent topical meeting sponsored by the Optical Society of America. The topical meeting welcomed all researchers who practice the art of Fourier-transform spectroscopy in the laboratory, in the atmosphere, and in space. The power and the wide applicability of Fourier-transform spectroscopy unite these fields with a common mathematical and instrumental bond. The meeting probed each of these areas in depth, bringing out new ideas for instrumentation, analysis, and applications. There was a strong sentiment at the meeting that the quality of papers and posters was exceptionally high and that it would be important for future progress in the field to have the results of this meeting captured in print. This special issue is the fruit of that effort.
Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion
NASA Astrophysics Data System (ADS)
Yükçü, Niyazi
2016-03-01
Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical properties of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.
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 6μm.
Integrated test plan for the demonstration of a commercial Fourier Transform Infrared instrument
Koegler, K.J.
1993-08-01
This integrated test plan describes the use of a commercial Fourier Transform Infrared instrument for measuring Carbon Tetrachloride concentrations. The Fourier Transform Infrared will measure CCL4 concentrations in a line of sight path average mode in mass per cubic meter as a function of time. The goal of this test is to demonstrate the usefulness of a long path Fourier Transform Infrared instrument in determining CCL4 fluxes from the soil in the 200 area adjacent to disposal cribs where high soil fluxes are believed to exist. The instrument will be set up such that it can have a clear line of site path to it`s reflector and this line of site will be as near to the Z-9 fence as possible and have a path length as long as possible.
NASA Astrophysics Data System (ADS)
van Agthoven, Maria A.; Barrow, Mark P.; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A.; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B.
2015-12-01
Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules.
Meng, Xin; Li, Jianxin; Song, Huaqing; Zhu, Rihong
2014-08-20
A Fourier-transform imaging spectropolarimeter is presented and demonstrated. It is composed of a time-division polarization modulator and a high radiation throughput Fourier-transform spectrometer. Four polarization states of the input light are generated by rotating the retarder. Then, the polarized light enters the Fourier-transform spectrometer to create four sets of interferometric images, where we can recover four polarization spectra and calculate the full-Stokes vector in various wavenumber frequency. The method has good performance to resist instrument noise and has the advantage of high spatial resolution. The laboratory setup is described and the noise source is analyzed. Two proven experiments have been carried out in visible light. PMID:25321096
NASA Astrophysics Data System (ADS)
Griesmann, Ulf; Kling, Rainier; Burnett, John H.; Bratasz, Lukasz
1999-09-01
In the minds of many, Fourier transform spectrometry is restricted to applications in the infrared. In the ultraviolet, the increasingly severe demands on optical, data acquisition, and motion control systems of the interferometer diminish the effectiveness of the technique. However, with recent advances in ultraviolet optics, data acquisition and sampling techniques for Fourier transform spectrometers, these stringent demands are easier to meet at vacuum ultraviolet wavelengths and significantly reduce the cost of Fourier transform spectrometers. The FT700 spectrometer at NIST can operate at wavelengths as low as 140 nm, limited by the short wavelength cut-off of the calcium fluoride optics. We illustrate the capabilities of the FT700 spectrometer in the ultraviolet with several recent results in atomic emission spectrometry, plasma diagnostics, and refractometry.
Yang, Jiao-lan; Luo, Tian
2002-08-01
This paper expatriated the applications for Fourier transform infrared spectrum analysis technique in preventive medicine field from four aspects of environmental pollution, life science, and the latest infrared analysis methods and near infrared analysis technique. In the environmental pollution field, it mainly described the advantages, the limitations and the solutions of the combined applications for gas chromatograph and Fourier transform infrared spectrum. In the life science field, it described the application for Fourier transform infrared spectrum analysis technique on protein secondary structure, membrane protein, phospholipid, nucleic acid, cell, tissue. In addition, it also introduced a few latest infrared analysis methods and the applications for near infrared spectrum analysis technique in food, cosmetic, drug. PMID:12938378
Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions
NASA Technical Reports Server (NTRS)
Holmes, J. J.; Balanis, C. A.
1974-01-01
Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.
Reduction and coding of synthetic aperture radar data with Fourier transforms
NASA Technical Reports Server (NTRS)
Tilley, David G.
1995-01-01
Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.
Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage
NASA Astrophysics Data System (ADS)
Ahmad, Salman; Hussain, Shafqat; Siddiqui, Abuzar Abid; Ali, Asad; Aqeel, Muhammad
2014-06-01
Magneto-Hydrodynamic (MHD) flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.
Three-dimensional radiative transfer using a Fourier-transform matrix-operator method
NASA Technical Reports Server (NTRS)
Martonchik, J. V.; Diner, D. J.
1985-01-01
The three-dimensional equation of transfer for a scattering medium with planar geometry is solved by using a spatial Fourier transform and extending matrix-operator techniques developed previously for the one-dimensional equation. Doubling and adding algorithms were derived by means of an interaction principle for computing the Fourier-transformed radiation field. The resulting expressions fully describe the radiative transfer process in a scattering medium, inhomogeneous in the x-, y- and z-directions, illuminated from above by an arbitrarily general intensity field and bounded from below by a surface with completely general reflection properties.
Linear and Nonlinear Crosstalk Evaluation in DWDM Networks Using Optical Fourier Transformers
NASA Astrophysics Data System (ADS)
Llorente, R.; Clavero, R.; Ramos, F.; Marti, J.
2005-12-01
A novel DWDM channel monitoring technique based on the conversion from wavelength domain to time domain by performing a real-time optical Fourier transform over the whole DWDM system bandwidth is proposed and experimentally demonstrated. The use of chromatic dispersion-based optical Fourier transformers has been validated in the case of a spectrum comprising light from different uncorrelated sources. Linear and nonlinear crosstalks between the DWDM channels appear as amplitude noise at specific time positions. The correspondence of this amplitude noise with the crosstalk spectral distribution is evaluated theoretically and experimentally.
Ordered fast Fourier transforms on a massively parallel hypercube multiprocessor
NASA Technical Reports Server (NTRS)
Tong, Charles; Swarztrauber, Paul N.
1991-01-01
The present evaluation of alternative, massively parallel hypercube processor-applicable designs for ordered radix-2 decimation-in-frequency FFT algorithms gives attention to the reduction of computation time-dominating communication. A combination of the order and computational phases of the FFT is accordingly employed, in conjunction with sequence-to-processor maps which reduce communication. Two orderings, 'standard' and 'cyclic', in which the order of the transform is the same as that of the input sequence, can be implemented with ease on the Connection Machine (where orderings are determined by geometries and priorities. A parallel method for trigonometric coefficient computation is presented which does not employ trigonometric functions or interprocessor communication.
NASA Astrophysics Data System (ADS)
Vdovenko, Sergey I.; Gerus, Igor I.; Zhuk, Yuri I.; Kukhar, Valery P.; Röschenthaler, Gerd-Volker
2014-10-01
IR Fourier spectra of two enaminoketones with general formula F3Csbnd COsbnd CRdbnd CHsbnd N(CH3)2, R = F (DMTFBN); R = CH3, (DMTMBN) were studied in various pure solvents. For comparison results of earlier investigated enaminoketone R = H (DMTBN) was also presented. On the basis of NMR and IR spectra it was shown that enaminoketones DMTBN, DMTFBN and DMTMBN presented in solutions as equilibrium of two conformers, (E-s-Z) ⇌ (E-s-E) (for DMTFBN these conformers are denoted as (Z-s-Z) and (Z-s-E), respectively). DFT calculations were carried out to evaluate relative energy and dipole moment of each spatial form. It was shown that ‘closed-ring' complex formation between (E-s-Z) and (E-s-E) conformers of DMTBN accounts for discrepancies between DFT calculations of conformer relative energies and experimentally evaluated enthalpies of (E-s-Z) ⇌ (E-s-E) equilibrium. In α-substituted DMTFBN and DMTMBN, where formation of ‘closed-ring' complex was impossible we did not observe such discrepancies. For both (E-s-Z) and (E-s-E) conformers of the DMTBN and DMTMBN the main influence on the ν˜(Cdbnd O) vibrations has the solvent's hydrogen bond donor (HBD) acidity, whereas for the DMTFBN an influence of the solvent's polarity/polarizability dominated.
NASA Astrophysics Data System (ADS)
Locklin, Scott Christopher
This dissertation is an account of an attempt to develop a novel type of vacuum ultraviolet spectrometer; with the most obvious application being the study of quantum chaos in the electronic spectrum of helium, as a classic example of the three body problem. The three-body problem in the form of the earth-moon-sun system has a history dating back to the ancient Greeks. It remains today an object of intense study in atomic physics. Classically, the problem is chaotic, yet, it remains a quantum mechanical problem. The history of the classical three-body problem is briefly examined. Some ideas in chaotic dynamics are explored, with a numeric investigation of the double-pendulum being used as an example. The quantum mechanics of the helium atom is reviewed, and the tension between classical and quantum physics; and the signs that one expects from the so-called "quantum chaos" are explored. Finally, a novel Fourier transform spectrometer designed to operate in the soft X-ray regime and based on a division-of-wavefront strategy is discussed. This is eventually to be used for the ultra-high resolution study of the helium atom. The instrument is described, and directions for future progress with this system are given.
S-duality as Fourier transform for arbitrary ɛ1, ɛ2
NASA Astrophysics Data System (ADS)
Nemkov, N.
2014-03-01
The Alday-Gaiotto-Tachikawa relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that, for the four-point conformal block, the modular transform up to the non-perturbative contributions can be written in the form of the ordinary Fourier transform when β ≡ -ɛ1/ɛ2 = 1. Here I extend this conjecture to general values of ɛ1, ɛ2. Namely, I argue that, for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters ɛ1, ɛ2. The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant g2 ≡ -ɛ1ɛ2 and hypermultiplet masses.
Nonequispaced grid sampling in photoacoustics with a nonuniform fast Fourier transform
NASA Astrophysics Data System (ADS)
Schmid, Julian; Glatz, Thomas; Zabihian, Behrooz; Liu, Mengyang; Drexler, Wolfgang; Scherzer, Otmar
2016-01-01
To obtain the initial pressure from the collected data on a planar sensor arrangement in photoacoustic tomography, there exists an exact analytic frequency-domain reconstruction formula. An efficient realization of this formula needs to cope with the evaluation of the data's Fourier transform on a nonequispaced mesh. We use the nonuniform fast Fourier transform to handle this issue and show its feasibility in three-dimensional experiments with real and synthetic data. This is done in comparison to the standard approach that uses linear, polynomial, or nearest neighbor interpolation. Moreover, we investigate the effect and the utility of flexible sensor location to make optimal use of a limited number of sensor points. The computational realization is accomplished by the use of a multidimensional nonuniform fast Fourier algorithm, where nonuniform data sampling is performed both in frequency and spatial domain. Examples with synthetic and real data show that both approaches improve image quality.
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.
NASA Astrophysics Data System (ADS)
Ryczkowski, Janusz
1994-01-01
The purpose of this work was to determine what kind of original/new information could be obtained by examining EDTA (ethylenediaminetetraacetic acid and its sodium salts) adsorption on (gamma) -alumina surface studied by Fourier-transform infrared (FTIR) and FTIR photoacoustic (FTIR PAS) spectroscopy.
Alpha-rooting method of color image enhancement by discrete quaternion Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2014-02-01
This paper presents a novel method for color image enhancement based on the discrete quaternion Fourier transform. We choose the quaternion Fourier transform, because it well-suited for color image processing applications, it processes all 3 color components (R,G,B) simultaneously, it capture the inherent correlation between the components, it does not generate color artifacts or blending , finally it does not need an additional color restoration process. Also we introduce a new CEME measure to evaluate the quality of the enhanced color images. Preliminary results show that the ?-rooting based on the quaternion Fourier transform enhancement method out-performs other enhancement methods such as the Fourier transform based ?-rooting algorithm and the Multi scale Retinex. On top, the new method not only provides true color fidelity for poor quality images but also averages the color components to gray value for balancing colors. It can be used to enhance edge information and sharp features in images, as well as for enhancing even low contrast images. The proposed algorithms are simple to apply and design, which makes them very practical in image enhancement.
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.
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...
Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform
ERIC Educational Resources Information Center
Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos
2010-01-01
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g
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 of O3 in the 3-micron region
NASA Technical Reports Server (NTRS)
Smith, M. A. H.; Rinsland, C. P.; Malathy Devi, V.; Flaud, J.-M.; Camy-Peyret, C.
1989-01-01
Fourier transform spectra of ozone have been recorded in the 2-5-micron region at a resolution of 0.01/cm. Absorption lines belonging to numerous vibration-rotation transitions have been observed in these spectra, and a detailed analysis of the band system centered at 3.6 microns has been completed.
Technology Transfer Automated Retrieval System (TEKTRAN)
The automated quantification of three greenhouse gases, ammonia, methane and nitrous oxide, in the vicinity of a large dairy farm by open-path Fourier transform infrared (OP/FT-IR) spectrometry at intervals of 5 minutes is demonstrated. Spectral pretreatment, including the detection and correction ...
Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform
ERIC Educational Resources Information Center
Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos
2010-01-01
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…
USE OF A FOURIER TRANSFORM SPECTROMETER AS A REMOTE SENSOR AT SUPERFUND SITES
A Fourier transform infrared remote sensor (FTIR-RS) was used to measure chemical emissions at the Shaver's Park Superfund site in northwestern Georgia. he system was bistatic with a source/receiver at one end of a 250 path and a retroreflector at the other end. he source/receive...
Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding
NASA Technical Reports Server (NTRS)
Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.
1977-01-01
An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.
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...
Fourier-Transform Infrared Spectroscopy Analysis of Modified Cotton Trash Extracts
Technology Transfer Automated Retrieval System (TEKTRAN)
In a previous study, Fourier transform infrared spectroscopy (FTIR) was utilized in identifying different types of botanical cotton trash as each was subjected to simulations of ginning and textile processing. Changes in the infrared spectra that occurred after heat treatment indicated that the nee...
Fourier-transform ghost imaging with pure far-field correlated thermal light
Liu Honglin; Shen Xia; Han Shensheng; Zhu Daming
2007-11-15
Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed.
Improved radar range resolution using frequency agility and the fast Fourier transform
NASA Astrophysics Data System (ADS)
Russell, R. F.; Gaines, D. P.; Sedenquist, F. W.
New techniques for improving radar range resolution have followed recent advances in radar and computer technology. A method which couples frequency agility and fast Fourier transforms to improve range resolution is presented. Experiments using the Polarimeteric Technology Seeker (PTS) have demonstrated that a 0.3 meter range resolution can be achieved utilizing an uncompressed 50 ns pulsed radar.
As part of the Online Surface Cleanliness Project, the Naval Facilities Engineering Service Center (NFESC) conducted a study of grazing-angle reflectance Fourier Transform Infrared (FTIR) Spectroscopy as a tool for online cleanliness verification at Department of Defense (DoD) cl...
Technology Transfer Automated Retrieval System (TEKTRAN)
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...
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 ...
Technology Transfer Automated Retrieval System (TEKTRAN)
Soil science research is increasingly applying Fourier transform infrared (FTIR) spectroscopy for analysis of soil organic matter (SOM). However, the compositional complexity of soils and the dominance of the mineral component can limit spectroscopic resolution of SOM and other minor components. The...
ATMOSPHERIC MEASUREMENTS OF TRACE POLLUTANTS; LONG PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY
Described are the results of a four-year study to measure trace pollutant concentrations in polluted atmospheres by kilometer pathlength Fourier transform infrared (FT-IR) absorption spectroscopy. The study covers selected smog episodes during the years 1976 to 1979. During 1976 ...
ERIC Educational Resources Information Center
Perkins, W. D.
1986-01-01
Discusses: (1) the design of the Fourier Transform-Infrared Spectroscopy (FT-IR) spectrometer; (2) the computation of the spectrum from the interferogram; and (3) the use of apodization. (Part II will discuss advantages of FT-IR over dispersive techniques and show applications of FT-IR to difficult spectroscopic measurements.) (JN)
Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM.
Sorokina, Mariia; Sygletos, Stylianos; Ellis, Andrew; Turitsyn, Sergei
2015-07-01
We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats). PMID:26125381
Technology Transfer Automated Retrieval System (TEKTRAN)
Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...
Technology Transfer Automated Retrieval System (TEKTRAN)
This study deals with transferring the near-infrared (NIR) calibration models for quality assessment of barley between two instruments with different resolutions and number of data points, a Fourier transform instrument (master) and a dispersive instrument (slave). A file of spectra from 206 ground ...
The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.
ERIC Educational Resources Information Center
Suslick, Kenneth S.; And Others
1987-01-01
Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)
NASA Astrophysics Data System (ADS)
Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin
2015-03-01
The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.
Introduction to Quantum Simulation
NASA Technical Reports Server (NTRS)
Williams, Colin P.
2005-01-01
This viewgraph presentation addresses the problem of efficiently simulating the evolution of a quantum system. The contents include: 1) Quantum Simulation; 2) Extracting Answers from Quantum Simulations; 3) Quantum Fourier Transform; 4) Eigenvalue Estimation; 5) Fermionic Simulations.
NASA Astrophysics Data System (ADS)
Tian, Jiangxue; Qi, Lin; Wang, Yaxing
2015-12-01
As one of classic methods of frequency domain based saliency detection, Spectral residual (SR) method has shown several advantages. However, it usually produces higher saliency values at object edges instead of generating maps that uniformly cover the whole object, which results from failing to exploit all the spatial frequency content of the original image. The Two-Dimensional Fractional Fourier transform (2D-FRFT) is a generalized form of the traditional Fourier Transform (FT) which can abstract more meaningful information of the image under certain conditions. Based on this property, we propose a new method which detects the salient region based on 2D-FRFT domain. Moreover, we also use Hough transform detection and a band-pass filter to refine the saliency map. We conduct experiments on a common used dataset: MSRA. The proposed method is compared with several other saliency detection methods and shown to achieve superior result.
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
NASA Astrophysics Data System (ADS)
Ohta, Izumi S.; Hattori, Makoto; Takahashi, Jyun'ichi; Chinone, Yuji; Luo, Yuan; Matsuo, Hiroshi
2006-06-01
We propose an instrument by applying the aperture synthesis technique to the Martin & Puplett type Fourier Transform Spectrometer in millimeter and sub-millimeter waves. We call this equipment Multi-Fourier Transform interferometer (MuFT). MuFT realizes a wide band imaging, spectroscopy and polarimetry in millimeter and sub-millimeter waves. The direct detectors, eg. bolometer, SIS video detector, can be used as the focal plane detectors. These type of detectors have a great advantage in FIR band since they are free from the quantum limit of the noise which limits the sensitivity of the heterodyne detectors used in the usual interferometers. Further, the direct detectors are able to make a large format array contrary to the usual interferometers in which usage of array detector is practically difficult. Above three characteristics make one be possible to develop high sensitive super broad band FIR interferometer with wide field of view. Fundamentals of the MuFT with results of laboratory experiments and current status of astronomical observations with MuFT are summarized. We did test observation with this system in the winter 2005. We also report concerning the observational result in 2006.
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.
A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis
NASA Technical Reports Server (NTRS)
Ioup, G. E.
1980-01-01
Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.
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.
NASA Astrophysics Data System (ADS)
Maccone, Claudio
2007-04-01
The present article describes that the range of any radiotelescope (and radar in general) may be increased by virtue of software, if one replaces the fast Fourier transform by the Karhunen Loève transform. The range increases with the inverse of the fourth root of the signal-to-noise ratio when this ratio decreases. Thus, the range on any radiotelescope (and radar) may be increased without changing the hardware at all, but by changing the software only. This improvement in the range of the radiotelescope is currently implemented at the 32-m antenna located at Medicina, near Bologna, in Italy, for both SETI and general radioastronomy.
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.
Ancilla-approximable quantum state transformations
Blass, Andreas; Gurevich, Yuri
2015-04-15
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 ε, but also address the question of arbitrarily close approximation.
Simulation of micromechanical behavior of polycrystals: finite elements vs. fast Fourier transforms
Lebensohn, Ricardo A; Prakash, Arun
2009-01-01
In this work, we compare finite element and fast Fourier transform approaches for the prediction of micromechanical behavior of polycrystals. Both approaches are full-field approaches and use the same visco-plastic single crystal constitutive law. We investigate the texture and the heterogeneity of the inter- and intragranular, stress and strain fields obtained from the two models. Additionally, we also look into their computational performance. Two cases - rolling of aluminium and wire drawing of tungsten - are used to evaluate the predictions of the two mode1s. Results from both the models are similar, when large grain distortions do not occur in the polycrystal. The finite element simulations were found to be highly computationally intensive, in comparison to the fast Fourier transform simulations.
The X1? +g ground state of Mg2 studied by Fourier-transform spectroscopy
NASA Astrophysics Data System (ADS)
Knckel, H.; Rhmann, 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.
NASA Astrophysics Data System (ADS)
Ohta, Izumi S.; Hattori, Makoto; Matsuo, Hiroshi
2007-05-01
We have developed a millimeter and submillimeter Michelson-type bolometric interferometer based on a Martin-Puplett-type Fourier-transform spectrometer named multi-Fourier-transform interferometer (MuFT). We have succeeded in proving that the MuFT is capable of performing broadband imaging observations as theoretically proposed by our previous paper (OHM) [Appl. Opt. 45, 2576 (2006)]. We succeeded in acquiring the mutual coherence signal for an extended source in broadband. By analyzing the obtained mutual coherence signal following the formula proposed in OHM, 2D source images for each wavenumber from 5 cm-1 (150 GHz) to 35 cm-1 (1.05 THz) with a wavenumber interval of 0.4 cm-1 (12 GHz) were successfully extracted. The large dynamic range advantage of the MuFT proposed in OHM was confirmed experimentally.
Ohta, Izumi S; Hattori, Makoto; Matsuo, Hiroshi
2007-05-20
We have developed a millimeter and submillimeter Michelson-type bolometric interferometer based on a Martin-Puplett-type Fourier-transform spectrometer named multi-Fourier-transform interferometer (MuFT). We have succeeded in proving that the MuFT is capable of performing broadband imaging observations as theoretically proposed by our previous paper (OHM) [Appl. Opt. 45, 2576 (2006)]. We succeeded in acquiring the mutual coherence signal for an extended source in broadband. By analyzing the obtained mutual coherence signal following the formula proposed in OHM, 2D source images for each wavenumber from 5 cm(-1) (150 GHz) to 35 cm(-1) (1.05 THz) with a wavenumber interval of 0.4 cm(-1) (12 GHz) were successfully extracted. The large dynamic range advantage of the MuFT proposed in OHM was confirmed experimentally. PMID:17514233
Laude, D.A. Jr.; Pentoney, S.L. Jr.; Griffiths, P.R.; Wilkins, C.L.
1987-09-15
A Fourier transform mass spectrometer used as a detector and identifier for supercritical fluid chromatography demonstrates low nanogram detection limits and a pressure-limited resolution in excess of 10,000 at m/z 128 for the molecular ion of naphthalene. Supercritical carbon dioxide is introduced directly into the source of a dual differential pumped trapped ion cell generating pressures in the low 10/sup -4/ Torr range with sample detection occurring in the analyzer cell at pressures a factor of 100 lower. Ionization is accomplished by charge exchange with carbon dioxide to yield spectra exhibiting 70-eV-like fragmentation patterns. Supercritical fluid chromatography/Fourier transform mass spectrometry data for three test samples, a six-component mixture of substituted aromatic compounds and polyaromatic hydrocarbons, a five-component barbiturate mixture, and a seven-component pesticide mixture, are presented.
Sperling, Edit; Bunner, Anne E.; Sykes, Michael T.; Williamson, James R.
2008-01-01
Quantitative proteomic mass spectrometry involves comparison of the amplitudes of peaks resulting from different isotope labeling patterns, including fractional atomic labeling and fractional residue labeling. We have developed a general and flexible analytical treatment of the complex isotope distributions that arise in these experiments, using Fourier transform convolution to calculate labeled isotope distributions and least-squares for quantitative comparison with experimental peaks. The degree of fractional atomic and fractional residue labeling can be determined from experimental peaks at the same time as the integrated intensity of all of the isotopomers in the isotope distribution. The approach is illustrated using data with fractional 15N-labeling and fractional 13C-isoleucine labeling. The least-squares Fourier transform convolution approach can be applied to many types of quantitive proteomic data, including data from stable isotope labeling by amino acids in cell culture and pulse labeling experiments. PMID:18522437
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
The keyed optical Hash function based on cascaded phase-truncated Fourier transforms
NASA Astrophysics Data System (ADS)
He, Wenqi; Peng, Xiang; Qin, Wan; Meng, Xiangfeng
2010-06-01
An approach for constructing keyed optical Hash function (KOHF) is proposed, which is based on cascaded phase-truncated Fourier transforms (CPTFTs). The KOHF is created from a two-step one-way encryption process with a secret key imbedded. The non-linearity and one-way functionality is introduced by cascaded optical Fourier transforms with the phase-truncation operations, which could be implemented either digitally or optically. Once two 64-bit keyed Hash values are obtained in the two-step one-way encryption processes, respectively, they are then combined to form a final 128-bit keyed Hash value, which can also be regarded as a message authentication code (MAC). Moreover, the avalanche effect is also evaluated to show the performance of constructed KOHF with a set of numerical experiments.
The ν3 band system of SCCCS: High-resolution Fourier transform and diode laser measurements
NASA Astrophysics Data System (ADS)
Holland, Frank; Winnewisser, Manfred; Jarman, Clive; Kroto, Harry W.; Yamada, Koichi M. T.
1988-08-01
The high-resolution infrared spectrum of the ν3 band system of carbon subsulfide, SCCCS, was measured around 2100 cm -1 using a Fourier transform interferometer and a tunable diode laser spectrometer. The linewidths (FWHH) in the Fourier transform spectrum were determined to be ca. 0.0060 cm -1 whereas the linewidths in the diode laser spectrum were 0.0036 cm -1. The rotational structure of the ν3 fundamental and the first two hot bands associated with the low-lying CCC bending mode ν7 were assigned. The adjusted effective constants for the l components of each band as well as constants taking the l-type doubling and resonance effects into account were determined. The band center of the ν3 fundamental and the B0 value were determined to be 2100.098908(58) and 0.03059602(31) cm -1, respectively. The analysis confirmed that SCCCS displays the dynamics of a linear molecule.
Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer
Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.
1993-10-01
We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.
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 μm 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
Schrottke, L. Lü, X.; Grahn, H. T.
2015-04-21
We present a self-consistent model for carrier transport in periodic semiconductor heterostructures completely formulated in the Fourier domain. In addition to the Hamiltonian for the layer system, all expressions for the scattering rates, the applied electric field, and the carrier distribution are treated in reciprocal space. In particular, for slowly converging cases of the self-consistent solution of the Schrödinger and Poisson equations, numerous transformations between real and reciprocal space during the iterations can be avoided by using the presented method, which results in a significant reduction of computation time. Therefore, it is a promising tool for the simulation and efficient design of complex heterostructures such as terahertz quantum-cascade lasers.
High-resolution Fourier transform spectrum of H 2S in the region of 8500-8900 cm -1
NASA Astrophysics Data System (ADS)
Ulenikov, O. N.; Liu, A.-W.; Bekhtereva, E. S.; Grebneva, S. V.; Deng, W.-P.; Gromova, O. V.; Hu, S.-M.
2004-11-01
High-resolution Fourier transform infrared spectrum of H 2S was recorded and analyzed in the region of the v=v1+{1}/{2}v2+v3=3.5 polyad. More than 450 transitions were assigned to the 3 ν1 + ν2 and 2 ν1 + ν2 + ν3 bands with the maximum values of quantum numbers J and Ka equal to 14, 7, and 14, 9 for these two bands, respectively. The theoretical analysis was fulfilled with the Hamiltonian which takes into account strong resonance interactions among the studied vibrational states (3 1 0), (2 1 1), and also "dark" states (0 3 2) and (2 3 0). The rms deviation is 0.0019 cm -1. The intensity borrowing effect in the doublets in the P-branch transitions of the 3 ν1 + ν2 and 2 ν1 + ν2 + ν3 bands is observed and discussed.
Niida, Chisato; Nakajima, Masakazu; Endo, Yasuki; Sumiyoshi, Yoshihiro; Ohshima, Yasuhiro; Kohguchi, Hiroshi
2014-03-14
Pure rotational transitions of the Ar–CS van der Waals complex have been observed by Fourier Transform Microwave (FTMW) and FTMW-millimeter wave double resonance spectroscopy. Rotational transitions of v{sub s} = 0, 1, and 2 were able to be observed for normal CS, together with those of C{sup 34}S in v{sub s} = 0, where v{sub s} stands for the quantum number of the CS stretching vibration. The observed transition frequencies were analyzed by a free rotor model Hamiltonian, where rovibrational energies were calculated as dynamical motions of the three nuclei on a three-dimensional potential energy surface, expressed by analytical functions with 57 parameters. Initial values for the potential parameters were obtained by high-level ab initio calculations. Fifteen parameters were adjusted among the 57 parameters to reproduce all the observed transition frequencies with the standard deviation of the fit to be 0.028 MHz.
Metabolic fingerprinting of lichen Usnea baileyi by Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Bakar, Siti Zaharah Abu; Latip, Jalifah; bin Din, Laily; Samsuddin, Mohd Wahid
2014-09-01
The lichen Usnea baileyi collected from different environments was characterised using Fourier transform infrared spectroscopy. This preliminary study was done to determine the effects of different environment populations on U. baileyi chemical composition. Results showed that the absorbance peaks of Golf Course 2 (GCU2) are more intense compared to Taman Awana (TA), Jalan Awana (JA) and Jalan Gohtong (JG). U. baileyi contains of dibenzofurans, depsides, depsidones, xanthones and terpenoids.
Using single buffers and data reorganization to implement a multi-megasample fast Fourier transform
NASA Technical Reports Server (NTRS)
Brown, R. D.
1992-01-01
Data ordering in large fast Fourier transforms (FFT's) is both conceptually and implementationally difficult. Discribed here is a method of visualizing data orderings as vectors of address bits, which enables the engineer to use more efficient data orderings and reduce double-buffer memory designs. Also detailed are the difficulties and algorithmic solutions involved in FFT lengths up to 4 megasamples (Msamples) and sample rates up to 80 MHz.
3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography.
Martin, Michael C; Dabat-Blondeau, Charlotte; Unger, Miriam; Sedlmair, Julia; Parkinson, Dilworth Y; Bechtel, Hans A; Illman, Barbara; Castro, Jonathan M; Keiluweit, Marco; Buschke, David; Ogle, Brenda; Nasse, Michael J; Hirschmugl, Carol J
2013-09-01
We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical and morphological localization by determining a complete infrared spectrum for every voxel (millions of spectra determined per sample). PMID:23913258
Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform.
Alieva, T; Bastiaans, M J
2000-12-01
The ambiguity function and Cohen's class of bilinear phase-space distributions are represented in a quasipolar coordinate system instead of in a Cartesian system. Relationships between these distributions and the fractional Fourier transform are derived; in particular, derivatives of the ambiguity function are related to moments of the fractional power spectra. A simplification is achieved for the description of underspread signals, for optical beam characterization, and for the generation of signal-adaptive phase-space distributions. PMID:11140493
Hanna, Magdy Tawfik; Shaarawi, Amr Mohamed; Seif, Nabila Philip Attalla; Ahmed, Waleed Abd El Maguid
2011-08-01
A technique is proposed for computing the field radiated from a rectangular aperture. This technique, based on the discrete fractional Fourier transform, avoids the complexities of computing the diffraction pattern by the direct evaluation of the Fresnel integral. The advocated approach provides a fast and accurate computational tool, especially in the case of evaluating pulsed fields radiated through two-dimensional screens of complex amplitude. A detailed numerical study that demonstrates the efficacy of this approach is carried out. PMID:21811323
Study of supermolecular structure by optical fourier transforms of scattered-light patterns
Gudkov, V.A.
1992-02-01
A method for decoding of the supermolecular structure of condensed media (polymers, liquid crystals, solids, etc.) is described that consists of optical Fourier transforms of scattered-light patterns by Fraunhofer diffraction. It is shown by the example of polyethylene films that the method makes it possible to determine macrostructure elements and the nature of their mutual arrangement, which allows it to be used in a production technology for materials with specified properties. 7 refs., 4 figs.
NASA Astrophysics Data System (ADS)
Kamnev, A. A.; Ristić, M.; Antonyuk, L. P.; Chernyshev, A. V.; Ignatov, V. V.
1997-06-01
The data of Fourier transform infrared (FTIR) spectroscopic measurements performed on intact cells of the soil nitrogen-fixing bacterium Azospirillum brasilense grown in a standard medium and under the conditions of an increased metal uptake are compared and discussed. The structural FTIR information obtained is considered together with atomic absorption spectrometry (AAS) data on the content of metal cations in the bacterial cells. Some methodological aspects concerning preparation of bacterial cell samples for FTIR measurements are also discussed.
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
Affine cryptosystem of double-random-phase encryption based on the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Xin, Zhou; Sheng, Yuan; Sheng-Wei, Wang; Jian, Xie
2006-11-01
An affine mapping mathematical expression of the double-random-phase encryption technique has been deduced utilizing the matrix form of discrete fractional Fourier transforms. This expression clearly describes the encryption laws of the double-random-phase encoding techniques based on both the fractional Fourier transform and the ordinary Fourier transform. The encryption process may be regarded as a substantial optical realization of the affine cryptosystem. It has been illustrated that the encryption process converts the original image into a white Gaussian noise with a zero-mean value. Also, the decryption process converts the data deviations of the encrypted image into white Gaussian noises, regardless of the type of data deviations. These noises superimpose on the decrypted image and degrade the signal-to-noise ratio. Numerical simulations have been implemented for the different types of noises introduced into the encrypted image, such as the white noise with uniform distribution probability, the white noise with Gaussian distribution probability, colored noise, and the partial occlusion of the encrypted image.
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.
Holland, Alexander; Aboy, Mateo
2009-07-01
We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb-Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations. PMID:19247700
Signal-detection tradeoff-analysis of optical vs digital Fourier transform computers.
Granrath, D J; Hunt, B R
1979-01-01
Signal detection theory is used to develop analytic models which yield comparisons between optical and digital Fourier transform computers in terms of their ability to detect transformed signals within small spectral regions of their Fourier domains. Stochastic noise models are first given describing the quantization noise introduced by the finite register length involved in a digital transformation. The signal detection models are then developed which describe the detectability of a transformed signal among this kind of noise, with models given for fixed-point and floating-point machines and for the signal-known-exactly and the signalunknown detection cases. These models provide the optimum detection statistic to be used in each case, a means for choosing the cutoff points used in the detection process, the over-all performance curve of the detector, and detection indices which summarize this performance. The optical and digital computers are compared by equating their detectabilities as obtained from these models, thus allowing a digital processor with given specifications to be paired with an optical processor with a specific SNR in its output plane. Analytical results are presented demonstrating these comparisons in which computer number-representation, register length, transform-array size, detection-array size, and type of detection are the independent variables under consideration. PMID:20208658
The parallel implementation of the one-dimensional Fourier transformed Vlasov Poisson system
NASA Astrophysics Data System (ADS)
Eliasson, Bengt
2005-08-01
A parallel implementation of an algorithm for solving the one-dimensional, Fourier transformed Vlasov-Poisson system of equations is documented, together with the code structure, file formats and settings to run the code. The properties of the Fourier transformed Vlasov-Poisson system is discussed in connection with the numerical solution of the system. The Fourier method in velocity space is used to treat numerical problems arising due the filamentation of the solution in velocity space. Outflow boundary conditions in the Fourier transformed velocity space removes the highest oscillations in velocity space. A fourth-order compact Padé scheme is used to calculate derivatives in the Fourier transformed velocity space, and spatial derivatives are calculated with a pseudo-spectral method. The parallel algorithms used are described in more detail, in particular the parallel solver of the tri-diagonal systems occurring in the Padé scheme. Program summaryTitle of program:vlasov Catalogue identifier:ADVQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating system under which the program has been tested: Sun Solaris; HP-UX; Read Hat Linux Programming language used: FORTRAN 90 with Message Passing Interface (MPI) Computers: Sun Ultra Sparc; HP 9000/785; HP IPF (Itanium Processor Family) ia64 Cluster; PCs cluster Number of lines in distributed program, including test data, etc.:3737 Number of bytes in distributed program, including test data, etc.:18 772 Distribution format: tar.gz Nature of physical problem: Kinetic simulations of collisionless electron-ion plasmas. Method of solution: A Fourier method in velocity space, a pseudo-spectral method in space and a fourth-order Runge-Kutta scheme in time. Memory required to execute with typical data: Uses typically of the order 10 5-10 6 double precision numbers. Restriction on the complexity of the problem: The program uses periodic boundary conditions in space. Typical running time: Depends strongly on the problem size, typically few hours if only electron dynamics is considered and longer if both ion and electron dynamics is important. Unusual features of the program: No
Transformation quantum optics: designing spontaneous emission using coordinate transformations
NASA Astrophysics Data System (ADS)
Zhang, Jingjing; Wubs, Martijn; Ginzburg, Pavel; Wurtz, Gregory; Zayats, Anatoly V.
2016-04-01
Spontaneous decay is a fundamental quantum property of emitters that can be controlled in a material environment via modification of the local density of optical states (LDOS). Here we use transformation optics methods in order to design required density of states and thus spontaneous emission (SE) rate. Specifically, we show that the SE rate can be either enhanced or suppressed using invisibility cloaks or gradient index lenses. Furthermore, the anisotropic material profile of the cloak enables the directional control of SE. We also discuss how the practical issues, such as dispersion and losses, affect the LDOS in complex materials. Tailoring SE properties using transformation optics approach provides an innovative way for designing emission properties in a complex material environment needed for the development of active nanophotonic devices.
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.
Potential-Field Forward Modeling and Inversion Using 3D Fast Fourier Transforms
NASA Astrophysics Data System (ADS)
Phillips, J. D.; Caratori Tontini, F.; Cocchi, L.
2008-12-01
Although 1D and 2D fast Fourier transforms (FFTs) have long been used for the filtering, interpretation, and modeling of potential-field data, 3D FFTs have not enjoyed similar popularity. This may change with the recent discovery (Caratori Tontini et al., in press, JGR) that simple 3D FFT filters can be used to transform distributions of density (or magnetization) within a box-shaped 3D volume into gravity (or magnetic) fields within the same volume. For example, the continuous 3D Fourier transform of the vertical gravity anomaly Δgz(x,y,z) in a volume is related to the 3D Fourier transform of the density ρ(x,y,z) in the volume by ℑ[Δgz] = i4πG(kz/ | k | 2)ℑ[ρ]; | k | ≠0, (1) where G is the gravitational constant, kx, ky, kz are wavenumbers, and | k | 2 = kx2+ ky2+ kz2. (2) Translating (1) into a digital FFT filtering operation requires careful consideration of the periodicity of the density distribution and the gravity field. Nevertheless, (1) provides a highly efficient way to calculate the vertical gravity anomaly of a 3D density distribution within a few minutes. The calculated gravity anomaly can be sampled at random points or on an arbitrary surface using tri-linear interpolation. An equivalent space- domain calculation of the gravity field on an arbitrary surface can take many hours. The inverse relation to (1) does not appear to offer a practical approach for calculating a reliable density distribution from observed gravity data. This is because the data would have to cover a substantial portion of the model volume, and because the transformation is undefined on the plane kz = 0, where both the denominator of the filter kernel and the Fourier transform of the gravity field are identically zero. Numerical experiments show that the density distribution resulting from the power on the plane kz = 0 represents a classic Parker annihilator. This annihilator can be calculated from the density distribution but not from the gravity field, as would be required for direct inversion. In forward modeling mode, equations such as (1) permit rapid testing of geological models against observed potential-field data. The calculation speed of the 3D FFT suggests that a practical iterative inversion algorithm could be developed from (1) using Markov perturbation of an initial density model. Such an algorithm would have immediate application to problems of hydrogeology, resource assessment, and tunnel detection.
A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws
Levenhagen, R. S.
2014-12-10
Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).
Non-destructive evaluation (NDE) using multi-aperture DSPI system and fast Fourier transform method
NASA Astrophysics Data System (ADS)
Bhaduri, Basanta; Krishna Mohan, N.; Kothiyal, M. P.
2007-09-01
Digital speckle pattern interferometry (DSPI) and digital shearography (DS) are two independent whole-field non-contacting optical methods for nondestructive flaw detection and precision measurements. A multi-aperture arrangement in front the imaging lens provides the grid structure within the speckles to yield desired diffraction halos at the Fourier transform plane. A three aperture arrangement in front of the imaging system is proposed here to combine coherently three waves at the CCD plane and also to introduce spatial carrier fringes within the speckle. One of the apertures is used for imaging the object onto the CCD plane, the second aperture for introducing smooth reference wave, while the third aperture carries a small angle wedge plate to provide the shear. This method allows simultaneous phase evaluation of the out-of-plane displacement and its first order derivative (slope) by filtering the appropriate diffraction halos of the Fourier spectrum. In this paper, we describe a (1, N) phase shifting technique with fast Fourier transform (FFT) for non destructive evaluation (NDE) of quasi-dynamic behavior of objects subject to slowly varying loads. The prominent advantage of the technique is that, it requires only a single frame prior to the object deformation and N number of frames during the object deformation for NDE. Experimental results are presented on a honeycomb structure subjected to thermal load.
A Fourier transform telescope for sub-arcsecond imaging of X-rays and gamma rays
NASA Technical Reports Server (NTRS)
Crannell, C. J.; Orwig, L. E.; Hurford, G. J.; Prince, T. A.
1986-01-01
This paper describes a Fourier transform telescope designed to image solar flare X-rays and gamma rays at energies up to 1 MeV with arcsec resolution. The imaging technique makes use of a bigrid collimator divided into a number of smaller areas called subcollimators. The grids in each subcollimator consist of a set of linear apertures so configured that each subcollimator provides a measurement of a single Fourier component of the angular distribution of the source. The imaging concept is therefore a mathematical analog to aperture synthesis in radio astronomy. For X-ray and gamma-ray astronomy, this approach has significant advantages in terms of relaxed requirements for astronomy, this approach has significant advantages in terms of relaxed requirements for position sensitivity in the detector and for control of grid alignment in the large scale telescope structure. The concept of the Fourier transform telescope will be illustrated with numerical parameters of a version now under study for the Pinhole/Occulter Facility.
Quantum control of a molecular ionization process by using Fourier-synthesized laser fields
NASA Astrophysics Data System (ADS)
Ohmura, Hideki; Saito, Naoaki
2015-11-01
In photoexcitation processes, if the motion of excited electrons can be precisely steered by the instantaneous electric field of an arbitrary waveform of a Fourier-synthesized laser field, the resultant matter response can be achieved within one optical cycle, usually within the attosecond (1 as =10-18s) regime. Fourier synthesis of laser fields has been achieved in various ways. However, the general use of Fourier-synthesized laser fields for the control of matter is extremely limited. Here, we report the quantum control of a nonlinear response of a molecular ionization process by using Fourier-synthesized laser fields. The directionally asymmetric molecular tunneling ionization induced by intense (5.0 ×1012W /c m2) Fourier-synthesized laser fields consisting of fundamental, second-, third-, and fourth-harmonic light achieves the orientation-selective ionization; we utilized the orientation-selective ionization for measurement of the relative phase differences between the fundamental and each harmonic light. Our findings impact not only light-wave engineering but also the control of matter, possibly triggering the creation and establishment of a new methodology that uses Fourier-synthesized laser fields.
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.
NASA Astrophysics Data System (ADS)
Lang, Jun; Tao, Ran; Wang, Yue
2010-05-01
In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. In this paper, we propose a new approach for image encryption based on the multiple-parameter discrete fractional Fourier transform and chaotic logistic maps in order to meet the requirements of the secure image transmission. In the proposed image encryption scheme, the image is encrypted by juxtaposition of sections of the image in the multiple-parameter discrete fractional Fourier domains and the alignment of sections is determined by chaotic logistic maps. This method does not require the use of phase keys. The new method has been compared with several existing methods and shows comparable or superior robustness to blind decryption.
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.
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.
Multipartite Entanglement: Transformations, Quantum Secret Sharing, Quantum Error Correction
NASA Astrophysics Data System (ADS)
Helwig, Wolfram
Most applications in quantum information processing make either explicit or implicit use of entanglement. It is thus important to have a good understanding of entanglement and the role it plays in these protocols. However, especially when it comes to multipartite entanglement, there still remain a lot of mysteries. This thesis is devoted to getting a better understanding of multipartite entanglement, and its role in various quantum information protocols. First, we investigate transformations between multipartite entangled states that only use local operations and classical communication (LOCC). We mostly focus on three qubit states in the GHZ class, and derive upper and lower bounds for the successful transformation probability between two states. We then focus on absolutely maximally entangled (AME) states, which are highly entangled multipartite states that have the property that they are maximally entangled for any bipartition. With them as a resource, we develop new parallel teleportation protocols, which can then be used to implement quantum secret sharing (QSS) schemes. We further prove the existence of AME states for any number of parties, if the dimension of the involved quantum systems is chosen appropriately. An equivalence between threshold QSS schemes and AME states shared between an even number of parties is established, and further protocols are designed, such as constructing ramp QSS schemes and open-destination teleportation protocols with AME states as a resource. As a framework to work with AME states, graph states are explored. They allow for efficient bipartite entanglement verification, which makes them a promising candidate for the description of AME states. We show that for all currently known AME states, absolutely maximally entangled graph states can be found, and we were even able to use graph states to find a new AME state for seven three-dimensional systems (qutrits). In addition, the implementation of QSS schemes from AME states can be conveniently described within the graph state formalism. Finally, we use the insight gained from entanglement in QSS schemes to derive necessary and sufficient conditions for quantum erasure channel and quantum error correction codes that satisfy the quantum Singleton bound, as these codes are closely related to ramp QSS schemes. This provides us with a very intuitive approach to codes for the quantum erasure channel, purely based on the entanglement required to protect information against losses by use of the parallel teleportation protocol.
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 ...
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...
[The meteorological satellite spectral image registration based on Fourier-Mellin transform].
Wang, Liang; Liu, Rong; Zhang, Li; Duan, Fu-Qing; Lü, Ke
2013-03-01
The meteorological satellite spectral image is an effective tool for researches on meteorological science and environmental remote sensing science. Image registration is the basis for the application of the meteorological satellite spectral image data. In order to realize the registration of the satellite image and the template image, a new registration method based on the Fourier-Mellin transform is presented in this paper. Firstly, we use the global coastline vector map data to build a landmark template, which is a reference for the meteorological satellite spectral image registration. Secondly, we choose infrared sub-image of no cloud according to the cloud channel data, and extract the edges of the infrared image by Sobel operator. Finally, the affine transform model parameters between the landmark template and the satellite image are determined by the Fourier-Mellin transform, and thus the registration is realized. The proposed method is based on the curve matching in essence. It needs no feature point extraction, and can greatly simplify the process of registration. The experimental results using the infrared spectral data of the FY-2D meteorological satellite show that the method is robust and can reach a high speed and high accuracy. PMID:23705469
NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS
BAJAJ, CHANDRAJIT; BAUER, BENEDIKT; BETTADAPURA, RADHAKRISHNA; VOLLRATH, ANTJE
2013-01-01
The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ∈ SO(3), t ∈ ℝ3 that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup either with respect to the sought translation or rotation. We present PFcorr, a new exhaustive solution, based on the non-equispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PFcorr can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogs of the above problems in which the flexibility of the protein is relevant. PMID:24379643
Fractional Fourier plane image encryption technique using radial hilbert-, and Jigsaw transform
NASA Astrophysics Data System (ADS)
Joshi, Madhusudan; Shakher, Chandra; Singh, Kehar
2010-07-01
A new method for image encryption using integral order radial Hilbert transform (RHT) filter in the fractional Fourier transform (FRT) domain has been proposed. The technique is implemented using the popular double random phase encoding method in the fractional Fourier domain. The random phase masks (RPMs), integral orders of the RHT, fractional orders of FRT, and indices of the Jigsaw transform (JT) have been used as keys for encryption and decryption. Simulation results have been presented and the schematic representation for optical implementation has been proposed. The mean-square-error and signal-to-noise ratio between the decrypted image and the input image have been calculated for the correct as well as incorrect orders of the RHT. Effect of occlusion and noise on the performance of the proposed scheme has also been studied. The robustness of the technique has been verified against attack using partial windows of the correct random phase masks. Similar investigations have also been carried out for the chosen-, and the known-plain-text attacks.
New Potentials for Old: The Darboux Transformation in Quantum Mechanics
ERIC Educational Resources Information Center
Williams, Brian Wesley; Celius, Tevye C.
2008-01-01
The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics
New Potentials for Old: The Darboux Transformation in Quantum Mechanics
ERIC Educational Resources Information Center
Williams, Brian Wesley; Celius, Tevye C.
2008-01-01
The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…
NASA Astrophysics Data System (ADS)
Galizzi, Gustavo E.; Cuadrado-Laborde, Christian
2015-10-01
In this work we study the joint transform correlator setup, finding two analytical expressions for the extensions of the joint power spectrum and its inverse Fourier transform. We found that an optimum efficiency is reached, when the bandwidth of the key code is equal to the sum of the bandwidths of the image plus the random phase mask (RPM). The quality of the decryption is also affected by the ratio between the bandwidths of the RPM and the input image, being better as this ratio increases. In addition, the effect on the decrypted image when the detection area is lower than the encrypted signal extension was analyzed. We illustrate these results through several numerical examples.
NASA Astrophysics Data System (ADS)
Boucherit, S.; Bouamama, L.; Zegadi, R.; Simöens, S.
2008-09-01
The follow-up of particles of the tracer type in the fluids constitutes a field of study rather significant and at the same time rather complex owing to the fact that the number of parameters studied and at the same time significant and concerning the random one. The use of holography as a technique of imagery for the follow-up of these particles was applied by various laboratories for a long time. With the appearance of digital holography, the application of this technique became more than of topicality owing to the fact that it became possible to record in real time a succession of holograms using a camera CCD rapid, that it will be possible to put in perspective there after in a numerical way and to try to extract information related to the movements described by these particles which will be automatically those of the studied fluids. The numerical reconstruction of digital holograms being based on the laws of light propagation such as, the Fresnel integral and the traditional Fourier transform. The fractional Fourier Transform (FrFT) is defined as being a generalization of the traditional Fourier transform. It was proposed by Namias and was reintroduced in the optical systems by Lohmann, Mendlovic and Ozaktas. Pellat-Finet studied the relationship between (FrFT) and the Fresnel diffraction, therefore this operator also allows rebuilding the holograms. In this study we use the (FrFT) to reconstruct in line holograms of small particles plunged in a fluid. Three-dimensional information on the particles can be extracted by sweeping the fractional order.
Terki-Hassaïne; Claveau; Valentin; Pierre
1999-10-01
The infrared spectrum of (28)SiH(4) 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 (nu(1) or nu(3)) and one quantum of bending mode (nu(2) or nu(4)). The excited states are formed from eight vibrational sublevels: nu(1) + nu(2)(E), nu(1) + nu(4)(F(2)), nu(2) + nu(3)(F(1) + F(2)), and nu(3) + nu(4)(A(1) + E + F(1) + F(2)). 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 (nu(2)/nu(4)) and the stretching dyad (nu(1)/nu(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 x 10(-3) cm(-1). Copyright 1999 Academic Press. PMID:10479596
NASA Astrophysics Data System (ADS)
Terki-Hassaı¨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 (ν1 or ν3) and one quantum of bending mode (ν2 or ν4). The excited states are formed from eight vibrational sublevels: ν1 + ν2(E), ν1 + ν4(F2), ν2 + ν3(F1 + F2), and ν3 + ν4(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 (ν2/ν4) and the stretching dyad (ν1/ν3). 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.
Application of the partial-Fourier-transform approach for tunnel ionization of molecules
NASA Astrophysics Data System (ADS)
Liu, Mingming; Liu, Yunquan
2016-04-01
Combining the partial-Fourier-transform approach with Wenzel-Kramers-Brillouin approximation, we theoretically study the strong-field tunneling ionization of diatomic and polyatomic molecules. First we obtain the analytical expression of momentum distribution at the tunnel exit of diatomic molecules, and then we calculate the alignment-dependent ionization rate at different laser intensities and internuclear distances. We show that the internuclear distance has a significant effect on the alignment dependence of the ionization rate. Using this approach, we can also separate the contributions of each atomic center and show the interference effect between them. Finally, we extend this method to a polyatomic molecule, benzene, as an example.
Taylor, Samuel E.; Cao, Tuoxin; Talauliker, Pooja M.; Lifshitz, Jonathan
2016-01-01
Quantification of immunohistochemistry (IHC) and immunofluorescence (IF) using image intensity depends on a number of variables. These variables add a subjective complexity in keeping a standard within and between laboratories. Fast Fourier Transformation (FFT) algorithms, however, allow for a rapid and objective quantification (via statistical analysis) using cell morphologies when the microscopic structures are oriented or aligned. Quantification of alignment is given in terms of a ratio of FFT intensity to the intensity of an orthogonal angle, giving a numerical value of the alignment of the microscopic structures. This allows for a more objective analysis than alternative approaches, which rely upon relative intensities.
Applications of asynoptic space - Time Fourier transform methods to scanning satellite measurements
NASA Technical Reports Server (NTRS)
Lait, Leslie R.; Stanford, John L.
1988-01-01
A method proposed by Salby (1982) for computing the zonal space-time Fourier transform of asynoptically acquired satellite data is discussed. The method and its relationship to other techniques are briefly described, and possible problems in applying it to real data are outlined. Examples of results obtained using this technique are given which demonstrate its sensitivity to small-amplitude signals. A number of waves are found which have previously been observed as well as two not heretofore reported. A possible extension of the method which could increase temporal and longitudinal resolution is described.
A highly linear superconducting bolometer for quantitative THz Fourier transform spectroscopy.
Kehrt, Mathias; Monte, Christian; Beyer, Jörn; Hollandt, Jörg
2015-05-01
A superconducting transition edge sensor (TES) bolometer operating in the spectral range from 0.1 THz to 3 THz was designed. It is especially intended for Fourier transform spectroscopy and features a higher dynamic range and a highly linear response at a similar response compared to commercially available silicon composite bolometers. The design is based on a thin film metal mesh absorber, a superconducting thermistor and Si3N4 membrane technology. A prototype was set up, characterized and successfully used in first applications. PMID:25969213
Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Lu, Ming-Feng; Zhang, Feng; Tao, Ran; Ni, Guo-Qiang; Bai, Ting-Zhu; Yang, Wen-Ming
2015-11-01
Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton's rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.
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.
Vehicle Classification Using the Discrete Fourier Transform with Traffic Inductive Sensors
Lamas-Seco, José J.; Castro, Paula M.; Dapena, Adriana; Vazquez-Araujo, Francisco J.
2015-01-01
Inductive Loop Detectors (ILDs) are the most commonly used sensors in traffic management systems. This paper shows that some spectral features extracted from the Fourier Transform (FT) of inductive signatures do not depend on the vehicle speed. Such a property is used to propose a novel method for vehicle classification based on only one signature acquired from a sensor single-loop, in contrast to standard methods using two sensor loops. Our proposal will be evaluated by means of real inductive signatures captured with our hardware prototype. PMID:26516855
NASA Technical Reports Server (NTRS)
Beecken, Brian P.; Kleinman, Randall R.
2004-01-01
New developments in infrared sensor technology have potentially made possible a new space-based system which can measure far-infrared radiation at lower costs (mass, power and expense). The Stationary Imaging Fourier Transform Spectrometer (SIFTS) proposed by NASA Langley Research Center, makes use of new detector array technology. A mathematical model which simulates resolution and spectral range relationships has been developed for analyzing the utility of such a radically new approach to spectroscopy. Calculations with this forward model emulate the effects of a detector array on the ability to retrieve accurate spectral features. Initial computations indicate significant attenuation at high wavenumbers.
NASA Astrophysics Data System (ADS)
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.
Multicomponent FM demodulation of speech based on the short-time Fourier transform (STFT) phase
NASA Astrophysics Data System (ADS)
Nelson, Douglas J.
2001-03-01
Speech is a signal which is produced as a combination of frication and a quasi periodic train of glottal pulses excites the vocal tract and causes it to resonate. Information is encoded on the signal as the vocal tract changes configuration, resulting in a rapid change of the resonant frequencies. We develop methods, based on differentiation of the short time Fourier transform (STFT) phase, which effectively demodulates the speech signal and produces accurate, high resolution time-frequency estimates of both the resonances and the signal excitation. The method effectively condenses the STFT surface along curves representing the instantaneous frequencies of the vocal tract resonances and the channel group delay function.
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.
Universal and special keys based on phase-truncated Fourier transform
NASA Astrophysics Data System (ADS)
Qin, Wan; Peng, Xiang; Meng, Xiangfeng; Gao, Bruce
2011-08-01
We propose a novel optical asymmetric cryptosystem based on a phase-truncated Fourier transform. Two decryption keys independent of each other are generated. They are referred to as universal key and special key, respectively. Each of them can be used for decryption independently in absence of the other. The universal key is applicable to decrypt any ciphertext encoded by the same encryption key, but with poor legibility. On the contrary, the special key is adequate for legible decryption, but only valid for one ciphertext corresponding to the specified plaintext. A set of simulation results show the interesting performance of two types of decryption keys.
Okino, Tomoya; Yamanouchi, Kaoru; Shimizu, Toshihiko; Ma, Ri; Nabekawa, Yasuo; Midorikawa, Katsumi
2008-10-28
The interferometric autocorrelation functions of attosecond pulse trains in the time domain were measured by detecting CO{sub 2}{sup 2+} as well as the atomic and molecular fragment ions generated via two-photon absorption of intense vacuum ultraviolet-extreme ultraviolet light by CO{sub 2}. It was demonstrated that the Fourier transformation of the interferometric autocorrelation functions of the respective fragment ions appearing in a time-of-flight mass spectrum exhibit spectroscopic information in the frequency domain corresponding to the two-photon photofragment excitation spectra of CO{sub 2} and the double ionization excitation spectrum to form CO{sub 2}{sup 2+}.
High Throughput Proteomics Using Fourier Transform Ion Cyclotron Resonance Mass Spectrometry
Qian, Weijun; Camp, David G.; Smith, Richard D.
2004-06-01
The advent of high throughput proteomics technology for global detection and quantitation of proteins creates new opportunities and challenges for those seeking to gain greater understanding of cellular machinery. Here, we review recent advances in high-resolution capillary liquid chromatography coupled to Fourier transform ion cyclotron resonance (FTICR) mass spectrometry along with its potential application to high throughput proteomics. These technological advances combined with quantitative stable isotope labeling methodologies provide powerful tools for expanding our understanding of biology at the system-level.
NASA Astrophysics Data System (ADS)
Tavares, Paulo J.; Vaz, Mário A. P.
2013-03-01
Gradient range and spatial resolution in Fourier Transform Profilometry depend on the size of the filter window in reciprocal space. The proposed methods to date for the elimination of the fundamental frequency and enlargement of the filter window are either too computationally complex or depend on the possibility of using two frames, thus disabling the method's ability to cope with dynamic situations and subjecting the results to possible intensity changes between the two frame acquisitions. This article describes a simple method for using a single crossed fringe pattern to accomplish that objective, greatly improving the previously reported technique, whilst retaining its main advantages.
Mao, Zhuoxiong; McIntosh, M.J.; Demirgian, J.C.
1992-06-01
Incineration of chlorobenzene in a small laboratory incinerator was monitored by using Fourier transform infrared spectroscopy (FTIR) coupled with a heated long-path cell (LPC) to analyze and quantify flue gas emissions in near real time. The effects of operating conditions under stable and decreasing incineration temperatures on the destruction of chlorobenzene were studied. The results from the decreasing temperature experiments were found to be consistent with those from experiments at stable temperatures. This finding demonstrates that the FTIR/LPC, as a continuous emissions monitor, can effectively detect dynamic changes in the incinerator emissions and can contribute significantly to the safety of incinerators.
Mao, Zhuoxiong; McIntosh, M.J.; Demirgian, J.C.
1992-01-01
Incineration of chlorobenzene in a small laboratory incinerator was monitored by using Fourier transform infrared spectroscopy (FTIR) coupled with a heated long-path cell (LPC) to analyze and quantify flue gas emissions in near real time. The effects of operating conditions under stable and decreasing incineration temperatures on the destruction of chlorobenzene were studied. The results from the decreasing temperature experiments were found to be consistent with those from experiments at stable temperatures. This finding demonstrates that the FTIR/LPC, as a continuous emissions monitor, can effectively detect dynamic changes in the incinerator emissions and can contribute significantly to the safety of incinerators.
NASA Technical Reports Server (NTRS)
Parsons, C. L.; Gerlach, J. C.; Whitehurst, M.
1982-01-01
The development of a prototype, ground-based, Sun-pointed Michelson interferometric spectrometer is described. Its intended use is to measure the atmospheric amount of various gases which absorb in the near-infrared, visible, and near-ultraviolet portions of the electromagnetic spectrum. Preliminary spectra which contain the alpha, 0.8 micrometer, and rho sigma tau water vapor absorption bands in the near-infrared are presented to indicate the present capability of the system. Ultimately, the spectrometer can be used to explore the feasible applications of Fourier transform spectroscopy in the ultraviolet where grating spectrometers were used exclusively.
Linear crosstalk spectral analysis in DWDM networks by a real-time optical Fourier transformer
NASA Astrophysics Data System (ADS)
Llorente, Roberto; Perez, Joaquin; Clavero, Raquel; Marti, Javier
2005-06-01
In this paper a spectral crosstalk monitoring technique is proposed and demonstrated. The technique is based on optically perform a real-time continuous Fourier Transform (OFT) comprising the whole set of transmitted wavelengths. This approach does not require to stop the channel operation. Once the spectral information has been brought to time domain, the basic parameters as amplitude (channel power) or central wavelength can be evaluated. This technique is theoretically developed and demonstrated in a three channel DWDM system at 10 GBit/s channel bitrate in a proof-of-concept experiment.
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.
Chelliah, Pandian; Sahoo, Trilochan; Singh, Sheela; Sujatha, Annie
2015-10-20
A Fourier transform spectrometer (FTS) used for interrogating a fiber Bragg grating (FBG) consists of a scanning-type interferometer. The FTS has a broad wavelength range of operation and good multiplexing capability. However, it has poor wavelength resolution and interrogation speed. We propose a modification to the FTS using path delay multiplexing to improve the same. Using this method, spatial resolution and interrogation time can be improved by n times by using n path delays. In this paper, simulation results for n=2, 5 are shown. PMID:26560372
NASA Astrophysics Data System (ADS)
Li, YaSheng; Chen, Yan; Liao, Ningfang; Lyu, Hang; He, Shufang; Wan, Lifang
2015-08-01
A new calibration method for infrared hyperspectral imaging Fourier transform spectrometer is presented. Two kinds of common materials as Polypropylene (PP) and Polyethylene Terephthalate (PET) films which have special absorption peaks in the infrared band were used in the calibration experiment. As the wavelengths at the sharp absorption peaks of the films are known, an infrared imaging spectrometer can be calibrated on spectra with two or three peaks. With high precision and stability, this method simplifies the calibration work. It is especially appropriate for the measuring condition with a lack of calibration equipment or with inconvenience to calibrate the multiple light sources outdoors.
Set-up for broadband Fourier-transform multidimensional electronic spectroscopy.
Al Haddad, A; Chauvet, A; Ojeda, J; Arrell, C; van Mourik, F; Auböck, G; Chergui, M
2015-02-01
We present a compact passively phase-stabilized ultra-broadband 2D Fourier transform setup. A gas (argon)-filled hollow core fiber pumped by an amplified Ti:Al2O3 laser is used as a light source providing spectral range spanning from 420 to 900 nm. Sub-10-fs pulses were obtained using a deformable mirror-based pulse shaper. We probe the nonlinear response of Rhodamine 101 using 90 nm bandwidth and resolve vibrational coherences of 150 fs period in the ground state. PMID:25680035
Fourier-transform microwave spectroscopy of 24Mg 35Cl generated by laser ablation
NASA Astrophysics Data System (ADS)
Ohshima, Yasuhiro; Endo, Yasuki
1993-10-01
The rotational spectrum of 24Mg 35Cl in its X 2Σ + (ν=0 and 1 ) state has been observed in the 14 GHz region by using a Fourier- transform microwave spectrometer combined with a laser-ablation source. The radical was produced by the reaction of atomic Mg vaporized by 532 nm laser light with Cl 2 diluted in Ar. The present observation of the lowest N transition by a high-resolving power instrument has provided accurate hyperfine coupling constants associated with the 35Cl nucleus of this molecule.
Niece, Krista L.
2015-01-01
Colistin use has increased in response to the advent of infections caused by multidrug-resistant organisms. It is administered parenterally as an inactive prodrug, colistin methanesulfonate (CMS). Various formulations of CMS and labeling conventions can lead to confusion about colistin dosing, and questions remain about the pharmacokinetics of CMS. Since CMS does not have strong UV absorbance, current methods employ a laborious process of chemical conversion to colistin followed by precolumn derivatization to detect formed colistin by high-performance liquid chromatography. Here, we report a method for direct quantification of colistin methanesulfonate by attenuated total reflectance Fourier transform infrared spectroscopy (ATR FTIR). PMID:26124160
Assessment of fibre orientation in reinforced concrete using Fourier image transform.
Redon; Chermant; Chermant; Coster
1998-09-01
In this study, ribbon-shaped amorphous cast-iron fibres were used to reinforce a concrete matrix. X-ray photographs have been taken to detect fibres in situ. Their orientation has been investigated by automatic image analysis methods. However, this measurement should not be influenced by the digitization on the square frame of the analyser. For that purpose, the Fourier transform was used rather than the rose of direction method. This analysis revealed the transverse isotropic nature of the spatial arrangement of these fibres, whose axis of revolution corresponds to the concrete casting axis. Such a morphological characterization of the fibre-reinforced concrete reveals its mechanical behaviour. PMID:9767490
NASA Astrophysics Data System (ADS)
Serfas, Ottmar; Naumann, Dieter; Standfuss, Gabriele; Brueggemann, Lutz; Flemming, Ingeborg
1992-03-01
The Fourier-transform infrared spectra of intact procaryotic cells (bacteria) have already been used in the past to characterize (differentiate, classify and identify) a variety of bacterial strains and taxa. In this paper the essential features of a methodology are described which extend the FT-IR pattern recognition approach to intact eucaryotic cells (yeasts/fungi). Basically, the characteristic information pertaining to microbial FT-IR patterns is explored by applying multivariate statistics and cluster analysis to both the time and frequency domain of the mid-ir spectral data.
Côté, Alex; Levasseur, Simon; Boudreau, Sylvain; Genest, Jérôme
2014-07-01
This paper presents a concept using field cameras in combination with Fourier transform spectrometers. The device can produce five-dimensional (position-angle-spectra) data cubes. This can lead to accurate measurements in both spectrum and distance and allows a thorough characterization of the interferometer, as well as adds passive ranging information to hyperspectral images. Shear and tilt fringes are simultaneously observed in a fixed optical path difference interferometer, and a passive spectral ranging demonstration is done in both absorption and emission for the 500-900 nm spectral bands. PMID:25089997
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.
Fourier transform C-13 NMR analysis of some free and potassium-ion complexed antibiotics.
NASA Technical Reports Server (NTRS)
Ohnishi, M.; Fedarko, M.-C.; Baldeschwieler, J. D.; Johnson, L. F.
1972-01-01
Fourier transforms of the noise-decoupled, natural abundance C-13 NMR free induction decays of the cyclic antibiotic valinomycin and its potassium-ion complex have been obtained at 25.2 MHz. Comparisons are made with C-13 NMR spectra taken at 22.6 MHz of the cyclic antibiotic nonactin and the synthetic polyether dicyclohexyl-18-crown-6 and their potassium complexes. The results obtained suggest that conformational rearrangements of the molecule as a whole can compete with direct interactions between carbons and the potassium ion in determining C-13 chemical shift differences between the free and complexed species.
Vehicle Classification Using the Discrete Fourier Transform with Traffic Inductive Sensors.
Lamas-Seco, José J; Castro, Paula M; Dapena, Adriana; Vazquez-Araujo, Francisco J
2015-01-01
Inductive Loop Detectors (ILDs) are the most commonly used sensors in traffic management systems. This paper shows that some spectral features extracted from the Fourier Transform (FT) of inductive signatures do not depend on the vehicle speed. Such a property is used to propose a novel method for vehicle classification based on only one signature acquired from a sensor single-loop, in contrast to standard methods using two sensor loops. Our proposal will be evaluated by means of real inductive signatures captured with our hardware prototype. PMID:26516855
Trousson, P.; Lion, Y.
1985-05-09
A study of long-range proton coupling in nitroxide radicals has been performed with a numerical analysis program using the Fourier transform technique. The present method provides a means for further identification of radicals which is particularly useful for species that are otherwise indistinguishable. The superhyperfine structure of piperidine and pyrrolidine-1-oxyl derivatives, showing ..gamma..-nuclei coupling constants as small as 0.2 G, has been brought out. The results are in good agreement with those obtained by other resolution-enhancement methods. 17 references, 7 figures, 3 tables.
High-resolution Fourier Transform Spectroscopy of Nb I in the Near-Infrared
NASA Astrophysics Data System (ADS)
Er, A.; Güzelçimen, F.; Başar, Gö.; Öztürk, I. K.; Tamanis, M.; Ferber, R.; Kröger, S.
2015-11-01
In this study, a Fourier Transform spectrum of Niobium (Nb) is investigated in the near-infrared spectral range from 6000 to 12,000 cm-1 (830-1660 nm). The Nb spectrum is produced using a hollow cathode discharge lamp in an argon atmosphere. Both Nb and Ar spectral lines are visible in the spectrum. A total of 110 spectral lines are assigned to the element Nb. Of these lines, 90 could be classified as transitions between known levels of atomic Nb. From these classified Nb i transitions, 27 have not been listed in literature previously. Additionally, 8 lines are classified for the first time.
Quantitative analysis of oils and fats by Fourier transform Raman spectroscopy
NASA Astrophysics Data System (ADS)
Sadeghi-Jorabchi, H.; Wilson, R. H.; Belton, P. S.; Edwards-Webb, J. D.; Coxon, D. T.
The rapid analysis of fats and oils is of great importance in the food industry. It is shown that Fourier transform Raman spectroscopy may be used for this purpose. Good quality spectra, free of fluorescence, may be obtained and the spectra may be interpreted in terms of changes in total unsaturation, cis/trans isomer ratios and the number of double bonds in the hydrocarbon chains. Quantitative analysis of total unsaturation and cis/trans is possible and offers considerable improvements in speed when compared with conventional methods.
Planetary infrared astronomy using a cryogenic postdisperser on Fourier transform spectrometers
NASA Technical Reports Server (NTRS)
Jennings, D. E.; Kunde, V. G.; Hanel, R. A.; Maguire, W. C.; Lamb, G. M.
1986-01-01
High resolution infrared spectra of planets from ground-based observatories were analyzed and instrumentation to improve sensitivity was developed. A cryogenic postdisperser (a narrow bandpass spectral filter) for use with Fourier transform spectrometers (FTS's) at facility observatories was constructed. This instrument has improved the sensitivity of FTS observations at 8 to 20 microns by about an order of magnitude. Spectra of Jupiter, Saturn and Comet Halley were obtained using the postdisperser with FTS facilities at the Kitt Peak 4-meter and McMath telescopes. Spectral resolution as high as 0.01/cm was achieved.
Room temperature chirped-pulse Fourier transform microwave spectroscopy of anisole
NASA Astrophysics Data System (ADS)
Reinhold, B.; Finneran, I. A.; Shipman, S. T.
2011-12-01
The room-temperature rotational spectrum of anisole from 8.7 to 18.3 GHz was collected with a waveguide-based chirped-pulse Fourier transform microwave spectrometer whose operating principles are described. Three spectra were assigned, corresponding to the vibrational ground state and the first and second excited states of the lowest frequency torsional mode. Results for the ground state and first excited state are in agreement with prior millimeter wave studies of this molecule. Microwave-microwave double resonance measurements also confirm these assignments.
Zhang, Kang; Kang, Jin U.
2010-01-01
We implemented fast Gaussian gridding (FGG)-based non-uniform fast Fourier transform (NUFFT) on the graphics processing unit (GPU) architecture for ultrahigh-speed, real-time Fourier-domain optical coherence tomography (FD-OCT). The Vandermonde matrix-based non-uniform discrete Fourier transform (NUDFT) as well as the linear/cubic interpolation with fast Fourier transform (InFFT) methods are also implemented on GPU to compare their performance in terms of image quality and processing speed. The GPU accelerated InFFT/NUDFT/NUFFT methods are applied to process both the standard half-range FD-OCT and complex full-range FD-OCT (C-FD-OCT). GPU-NUFFT provides an accurate approximation to GPU-NUDFT in terms of image quality, but offers >10 times higher processing speed. Compared with the GPU-InFFT methods, GPU-NUFFT has improved sensitivity roll-off, higher local signal-to-noise ratio and immunity to side-lobe artifacts caused by the interpolation error. Using a high speed CMOS line-scan camera, we demonstrated the real-time processing and display of GPU-NUFFT-based C-FD-OCT at a camera-limited rate of 122 k line/s (1024 pixel/A-scan). PMID:21164690
Optical Fresnel transformation and quantum tomography
NASA Astrophysics Data System (ADS)
Fan, Hong-Yi; Hu, Li-yun
2009-09-01
Corresponding to optical Fresnel transformation characteristic of a ray transfer matrix (A,B,C,D),AD-BC=1, there exists Fresnel operator F(A,B,C,D) in quantum optics, we show that under the Fresnel transformation the pure-state position density ∣x> sp=∫∫-∞∞dp'dx'δp-Ax'-Cp')Δx',p', where ∣p>
Kazachenko, V N; Kochetkov, K V; Aslanidi, O V; Grinevich, A A
2001-01-01
Sets of the channel open times (tau o), closed times (tau c) and the full set of the channel open and closed times (tau o, tau c) in the activity of single Ca(2+)-activated K+ channels in cultured kidney cells Vero were analyzed using the fast Fourier transform. It was found that in the low-frequency range (about 0.01-10 Hz), power density can be described by the equation S(f) approximately f-alpha (as a rule, 0 < alpha < 1), and this part of the Fourier spectrum usually consists of narrow peaks at almost multiple frequencies. It was shown that the upper frequency boundary of this spectrum is determined by the kinetic parameters tau o [symbol: see text] tau c. The data obtained show that ion channel gating is a fractal process (correlated in time) and can be regarded as a random signal modulated by some periodical functions (sinuses). The data obtained by the Fourier method are in agreement with the earlier results obtained using the rescaled-range analysis. PMID:11771279
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.
Long-distance super-resolution imaging assisted by enhanced spatial Fourier transform.
Tang, Heng-He; Liu, Pu-Kun
2015-09-01
A new gradient-index (GRIN) lens that can realize enhanced spatial Fourier transform (FT) over optically long distances is demonstrated. By using an anisotropic GRIN metamaterial with hyperbolic dispersion, evanescent wave in free space can be transformed into propagating wave in the metamaterial and then focused outside due to negative-refraction. Both the results based on the ray tracing and the finite element simulation show that the spatial frequency bandwidth of the spatial FT can be extended to 2.7k(0) (k(0) is the wave vector in free space). Furthermore, assisted by the enhanced spatial FT, a new long-distance (in the optical far-field region) super-resolution imaging scheme is also proposed and the super resolved capability of λ/5 (λ is the wavelength in free space) is verified. The work may provide technical support for designing new-type high-speed microscopes with long working distances. PMID:26368459
High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides.
Velasco, Aitor V; Cheben, Pavel; Bock, Przemek J; Delâge, André; Schmid, Jens H; Lapointe, Jean; Janz, Siegfried; Calvo, María L; Xu, Dan-Xia; Florjańczyk, Mirosław; Vachon, Martin
2013-03-01
We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm2. Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm. PMID:23455272
Optimal quantum learning of a unitary transformation
Bisio, Alessandro; Chiribella, Giulio; D'Ariano, Giacomo Mauro; Facchini, Stefano; Perinotti, Paolo
2010-03-15
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary with maximum fidelity. Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine) and subsequently retrieving it. We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a 'measure-and-rotate' retrieving. Differing from the case of quantum cloning, where the incoherent 'measure-and-prepare' strategies are typically suboptimal, in the case of learning the 'measure-and-rotate' strategy is optimal even when the learning machine is asked to reproduce a single copy of the unknown unitary. We finally address the problem of the optimal inversion of an unknown unitary evolution, showing also in this case the optimality of the 'measure-and-rotate' strategies and applying our result to the optimal approximate realignment of reference frames for quantum communication.
Universal linear Bogoliubov transformations through one-way quantum computation
Ukai, Ryuji; Yoshikawa, Jun-ichi; Iwata, Noriaki; Furusawa, Akira; Loock, Peter van
2010-03-15
We show explicitly how to realize an arbitrary linear unitary Bogoliubov (LUBO) transformation on a multimode quantum state through homodyne-based one-way quantum computation. Any LUBO transformation can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBO transformations. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO transformation. Arbitrary-input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.
An Intelligent Dynamic Alignment System for Interferometer of Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Yang, Kun; Zeng, Libo
An intelligent dynamic alignment system for a Michelson interferometer which is applied to a Mid-infrared band Fourier transform spectrometer (FTS) is presented. Three photodiodes are used to detect the tilt of moving mirror opposite to fixed mirror with the assistance of the interfered signal of a reference He-Ne laser. This technique is based on detecting the phase difference of laser signal between every two diodes in two perpendicular directions. And four magnetic actuators behind the mounting brace of fixed mirror are used to change the pose of fixed mirror. The system is controlled by a digital signal processor (DSP) in real-time. A feedback algorithm is used to tilt fixed mirror following the action of moving mirror so as to keep both mirror planes in perpendicular. Experiment result shows that the relative tilt between two reflecting mirrors can be restricted in a range no more than ±1.5×10-6rad. This system is effective and reliable to be applied to scanning interferometer of Fourier transform spectrometer.
The data processing pipeline for the Herschel SPIRE Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Fulton, T.; Naylor, D. A.; Polehampton, E. T.; Valtchanov, I.; Hopwood, R.; Lu, N.; Baluteau, J.-P.; Mainetti, G.; Pearson, C.; Papageorgiou, A.; Guest, S.; Zhang, L.; Imhof, P.; Swinyard, B. M.; Griffin, M. J.; Lim, T. L.
2016-05-01
We present the data processing pipeline to generate calibrated data products from the Spectral and Photometric Imaging Receiver (SPIRE) imaging Fourier Transform Spectrometer on the Herschel Space Observatory. The pipeline processes telemetry from SPIRE observations and produces calibrated spectra for all resolution modes. The spectrometer pipeline shares some elements with the SPIRE photometer pipeline, including the conversion of telemetry packets into data timelines and calculation of bolometer voltages. We present the following fundamental processing steps unique to the spectrometer: temporal and spatial interpolation of the scan mechanism and detector data to create interferograms; Fourier transformation; apodization; and creation of a data cube. We also describe the corrections for various instrumental effects including first- and second-level glitch identification and removal, correction of the effects due to emission from the Herschel telescope and from within the spectrometer instrument, interferogram baseline correction, temporal and spatial phase correction, non-linear response of the bolometers, and variation of instrument performance across the focal plane arrays. Astronomical calibration is based on combinations of observations of standard astronomical sources and regions of space known to contain minimal emission.
Identification of Earthquake Induced Damage Areas Using Fourier Transform and SPOT HRVIR Pan Images.
Sertel, Elif
2009-01-01
A devastating earthquake with a magnitude of Mw 7.4 occurred on the North Anatolian Fault Zone (NAFZ) of Turkey on August 17, 1999 at 00:01:39 UTC (3:01 a.m. local time). The aim of this study is to propose a new approach to automatically identify earthquake induced damage areas which can provide valuable information to support emergency response and recovery assessment procedures. This research was conducted in the Adapazari inner city, covering a 3 × 3 km area, where 11,373 buildings collapsed as a result of the earthquake. SPOT high resolution visible infrared (HRVIR) Pan images obtained before (25 June 1999) and after (4 October 1999) the earthquake were used in the study. Five steps were employed to conduct the research and these are: (i) geometric and radiometric correction of satellite images, (ii) Fast Fourier Transform (FFT) of pre- and post-earthquake images and filtering the images in frequency domain, (iii) generating difference image using Inverse Fast Fourier Transform (IFFT) pre- and post- earthquake images, (iv) application of level slicing to difference image to identify the earthquake-induced damages, (v) accuracy assessment of the method using ground truth obtained from a 1/5,000 scale damage map. The total accuracy obtained in the research is 80.19 %, illustrating that the proposed method can be successfully used to automatically identify earthquake-induced damage areas. PMID:22573966
NASA Astrophysics Data System (ADS)
Sato, Yusuke; Sakamoto, Yuji
2012-03-01
A computer-generated hologram (CGH) is generated by simulating light waves propagated from virtual objects, and we are able to observe natural 3-D images without feeling tired. However, the resolution of current output devices, liquid crystal displays, is not high enough to display CGH data, so the size of reconstructed images are restricted. To increase image size, a method by using the Fourier transform optical system has been proposed. The Fourier transform optical system converges reconstructed light by arranging a lens between an observer and hologram and reconstructs floating images near the observer. In the system, a reconstruction position is confined around a focal point of the lens because a CGH calculation method had not yet been developed . To solve this problem, this describes a CGH calculation method using a unified formula to reconstruct images at arbitrary depth. This formula is derived by considering image formation of a lens and hologram. Moreover, process for eliminating unnecessary light elimination processing is described in this paper. By changing the elimination process according to the reconstruction position, images are reconstructed without overlapping unnecessary light at arbitrary depth. To confirm the effectiveness of the proposed method, we conducted optical reconstruction experiments. The results show that correctly sized images are reconstructed at correct depth, and unnecessary light is eliminated. It is possible to observe large and free-depth 3-D images with the proposed method.
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.
Application of Fast Fourier Transform in thermo-magnetic convection analysis
NASA Astrophysics Data System (ADS)
Pyrda, L.
2014-08-01
Application of Fast Fourier Transform in thermo-magnetic convection is reported. Cubical enclosure filled with paramagnetic fluid heated from below and placed in the strong magnetic field gradients was investigated. The main aim of study was connected with identification of flow types, especially transition to turbulence. For this purpose the Fast Fourier Transform (FFT) analysis was applied. It was followed by the heat transfer characteristic for various values of magnetic induction gradient. The analysis was done at two Rayleigh numbers 7.89·105 and 1.86·106 with thermo-magnetic Rayleigh numbers up to 1.8·108 and 4.5·108 respectively. The presented results clearly indicate flow types and also demonstrate augmented heat transfer in dependence on magnetic induction gradient. Detailed analysis of flow transition to turbulent state was compared with transition line for natural convection reported in literature. The transition to turbulence in the case of thermo-magnetic convection of paramagnetic fluid was in very good agreement with transition in the case of natural convection.
NASA Astrophysics Data System (ADS)
Sui, Liansheng; Duan, Kuaikuai; Liang, Junli; Zhang, Zhiqiang; Meng, Haining
2014-11-01
A multiple-image encryption scheme is proposed based on the asymmetric technique, in which the encryption keys are not identical to the decryption ones. First, each plain image is scrambled based on a sequence of chaotic pairs generated with a system of two symmetrically coupled identical logistic maps. Then, the phase-only function of each scrambled image is retrieved with an iterative phase retrieval process in the fractional Fourier transform domain. Second, all phase-only functions are modulated into an interim, which is encrypted into the ciphertext with stationary white noise distribution by using the fractional Fourier transform and chaotic diffusion. In the encryption process, three random phase functions are used as encryption keys to retrieve the phase-only functions of plain images. Simultaneously, three decryption keys are generated in the encryption process, which make the proposed encryption scheme has high security against various attacks, such as chosen plaintext attack. The peak signal-to-noise is used to evaluate the quality of the decrypted image, which shows that the encryption capacity of the proposed scheme is enhanced considerably. Numerical simulations demonstrate the validity and efficiency of the proposed method.
NASA Astrophysics Data System (ADS)
Naylor, David A.; Gom, Bradley G.; Schofield, Ian; Tompkins, Gregory; Davis, Gary R.
2003-02-01
Astronomical spectroscopy at submillimeter wavelengths holds much promise for fields as diverse as the study of planetary atmospheres, molecular clouds and extragalactic sources. Fourier transform spectrometers (FTS) represent an important class of spectrometers well suited to observations that require broad spectral coverage at intermediate spectral resolution. In this paper we present the design and performance of a novel FTS, which has been developed for use at the James Clerk Maxwell Telescope (JCMT). The design uses two broadband intensity beamsplitters in a Mach-Zehnder configuration, which provide access to all four interferometer ports while maintaining a high and uniform efficiency over a broad spectral range. Since the interferometer processes both polarizations it is twice as efficient as the Martin-Puplett interferometer (MPI). As with the MPI, the spatial separation of the two input ports allows a reference blackbody to be viewed at all times in one port, while continually viewing the astronomical source in the other. Furthermore, by minimizing the size of the optical beam at the beamsplitter, the design is well suited to imaging Fourier transform spectroscopy (IFTS) as evidenced by its selection for the SPIRE instrument on Herschel.
[The study of photo-elastic modulator-based Fourier transform spectroscopy].
Chen, You-hua; Wang, Zhao-ba; Wang, Zhi-bin; Wang, Yan-chao; Li, Yong-shuai; Zhang, Yu-han
2014-06-01
In order to enhance the spectrum resolution of current photo-elastic modulator-based Fourier transform spectrometer, a multi-reflected photo-elastic modulator-based interferometer structure was proposed in the present paper. Through coating reflecting film alternatingly on the photo-elastic crystal and light oblique incidence, and allowing the incident ray to have the multi-reflection in the crystal and exit from the other side of the crystal, the authors increased the light propagation distance in the crystal and enhanced the optical path difference at last. Based on this, the function of interference-spectrum retrieval was established, the optical system matched to the multi-reflected PEM-based interferometer was designed, and finally, the experimental system of multi-reflected PEM-based Fourier transform spectroscopy for telemetry was established. The principle of verification tests by using 671 nm laser and xenon lamp shows that the interferogram was clear and stable, and the feasibility of the principle of the system was verified. The expected result shows that the spectrum resolution of the designed PEM-FTs with multi-reflection achieved 13 cm(-1), and its luminous flux just didn't reduce too much, which ensured the SNR. Through spectral inversion of the interference fringes, the technical feasibility of the spectrum system developed was verified. This work established the basic condition of prototype fabrication, radiation precise calibration, spectral calibration and instrument signal-to-noise ratio test and so on. PMID:25358154
NASA Astrophysics Data System (ADS)
Dai, Xianglu; Xie, Huimin; Wang, Qinghua
2014-06-01
The geometric phase analysis (GPA), an important image-based deformation measurement method, has been used at both micro- and nano-scale. However, when a deformed image has apparent distortion, non-ignorable error in the obtained deformation field could occur by using this method. In this paper, the geometric phase analysis based on the windowed Fourier transform (WFT) is proposed to solve the above-mentioned issue, defined as the WFT-GPA method. In WFT-GPA, instead of the Fourier transform (FT), the WFT is utilized to extract the phase field block by block, and therefore more accurate local phase information can be acquired. The simulation tests, which include detailed discussion of influence factors for measurement accuracy such as window size and image noise, are conducted with digital deformed grids. The results verify that the WFT-GPA method not only keeps all advantages of traditional GPA method, but also owns a better accuracy for deformation measurement. Finally, the WFT-GPA method is applied to measure the machining distortion incurred in soft ultraviolet nanoimprint lithography (UV-NIL) process. The successful measurement shows the feasibility of this method and offers a full-field way for characterizing the replication quality of UV-NIL process.
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.
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)
Lanyi, G.; Kahn, R.
1997-01-01
An algorithm is presented for detection of very weak spacecraft tones generated by an onboard auxiliary oscillator with stability specifications similar to those of the small deep space transponder. Signal power is evaluated via discrete Fourier transforms, and detection is determined by comparing the measured power with a predetermined threshold. Limited oscillator stability precludes coherent integration of the signal over time scales longer than a few seconds; thus, the Fourier transform is performed independently on successive segments of data. Resulting power spectra are then averaged; potential frequency drift is accounted for by shifting the spectra when forming the average. The detection scheme is well suited to the proposed automated spacecraft monitoring system, in which a spacecraft sends a carrier signal modulated with one of four subcarrier frequencies to indicate the spacecraft's current state. Analysis based on theory and measurements indicates that reliable detection in a 1000-s interval can be achieved at a power signal to-noise-density level, P=N_0, as low as - 1 dB-Hz.
A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.
Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei
2015-09-01
A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress. PMID:26414526
Fresnel diffraction effects in Fourier-transform arrayed waveguide grating spectrometer.
Rodrigo, J A; Cheben, P; Alieva, T; Calvo, M L; Florjanczyk, M; Janz, S; Scott, A; Solheim, B; Xu, D X; Deláge, A
2007-12-10
We present an analysis of Fourier-transform arrayed waveguide gratings in the Fresnel diffraction regime. We report a distinct spatial modulation of the interference pattern referred to as the Moiré-Talbot effect. The effect and its influence in a FT AWG device is explained by deriving an original analytical expression for the modulated field, and is also confirmed by numerical simulations using the angular spectrum method to solve the Fresnel diffraction integral. We illustrate the retrieval of spectral information in a waveguide Fourier-transform spectrometer in the presence of the Moiré-Talbot effect. The simulated device comprises two interleaved waveguide arrays each with 180 waveguides and the interference order of 40. It is designed with a Rayleigh spectral resolution of 0.1 nm and 8 nm bandwidth at wavelength lambda approximately 1.5 mum. We also demonstrate by numerical simulations that the spectrometer crosstalk is reduced from -20 dB to -40 dB by Gaussian apodization. PMID:19550933
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.
The data processing pipeline for the Herschel SPIRE Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Fulton, T.; Naylor, D. A.; Polehampton, E. T.; Valtchanov, I.; Hopwood, R.; Lu, N.; Baluteau, J.-P.; Mainetti, G.; Pearson, C.; Papageorgiou, A.; Guest, S.; Zhang, L.; Imhof, P.; Swinyard, B. M.; Griffin, M. J.; Lim, T. L.
2016-02-01
We present the data processing pipeline to generate calibrated data products from the Spectral and Photometric Imaging Receiver (SPIRE) imaging Fourier Transform Spectrometer on the Herschel Space Observatory. The pipeline processes telemetry from SPIRE observations and produces calibrated spectra for all resolution modes. The spectrometer pipeline shares some elements with the SPIRE photometer pipeline, including the conversion of telemetry packets into data timelines and calculation of bolometer voltages. We present the following fundamental processing steps unique to the spectrometer: temporal and spatial interpolation of the scan mechanism and detector data to create interferograms; Fourier transformation; apodization; and creation of a data cube. We also describe the corrections for various instrumental effects including first- and second-level glitch identification and removal, correction of the effects due to emission from the Herschel telescope and from within the spectrometer instrument, interferogram baseline correction, temporal and spatial phase correction, non-linear response of the bolometers, and variation of instrument performance across the focal plane arrays. Astronomical calibration is based on combinations of observations of standard astronomical sources and regions of space known to contain minimal emission.
SITELLE: a wide-field imaging Fourier transform spectrometer for the Canada-France-Hawaii Telescope
NASA Astrophysics Data System (ADS)
Drissen, L.; Bernier, A.-P.; Rousseau-Nepton, L.; Alarie, A.; Robert, C.; Joncas, G.; Thibault, S.; Grandmont, F.
2010-07-01
We describe the concept of a new instrument for the Canada-France-Hawaii telescope (CFHT), SITELLE (Spectromètre Imageur à Transformée de Fourier pour l'Etude en Long et en Large de raies d'Emission), as well as a science case and a technical study of its preliminary design. SITELLE will be an imaging Fourier transform spectrometer capable of obtaining the visible (350 nm - 950 nm) spectrum of every source of light in a field of view of 15 arcminutes, with 100% spatial coverage and a spectral resolution ranging from R = 1 (deep panchromatic image) to R = 104 (for gas dynamics). SITELLE will cover a field of view 100 to 1000 times larger than traditional integral field spectrographs, such as GMOS-IFU on Gemini or the future MUSE on the VLT. It is a legacy from BEAR, the first imaging FTS installed on the CFHT and the direct successor of SpIOMM, a similar instrument attached to the 1.6-m telescope of the Observatoire du Mont-Mégantic in Québec. SITELLE will be used to study the structure and kinematics of HII regions and ejecta around evolved stars in the Milky Way, emission-line stars in clusters, abundances in nearby gas-rich galaxies, and the star formation rate in distant galaxies.
NASA Technical Reports Server (NTRS)
Hewagama, TIlak; Aslam, Shahid; Talabac, Stephen; Allen, John E., Jr.; Annen, John N.; Jennings, Donald E.
2011-01-01
Fourier transform spectrometers have a venerable heritage as flight instruments. However, obtaining an accurate spectrum exacts a penalty in instrument mass and power requirements. Recent advances in a broad class of non-scanning Fourier transform spectrometer (FTS) devices, generally called spatial heterodyne spectrometers, offer distinct advantages as flight optimized systems. We are developing a miniaturized system that employs photonics lightwave circuit principles and functions as an FTS operating in the 7-14 micrometer spectral region. The inteferogram is constructed from an ensemble of Mach-Zehnder interferometers with path length differences calibrated to mimic scan mirror sample positions of a classic Michelson type FTS. One potential long-term application of this technology in low cost planetary missions is the concept of a self-contained sensor system. We are developing a systems architecture concept for wide area in situ and remote monitoring of characteristic properties that are of scientific interest. The system will be based on wavelength- and resolution-independent spectroscopic sensors for studying atmospheric and surface chemistry, physics, and mineralogy. The self-contained sensor network is based on our concept of an Addressable Photonics Cube (APC) which has real-time flexibility and broad science applications. It is envisaged that a spatially distributed autonomous sensor web concept that integrates multiple APCs will be reactive and dynamically driven. The network is designed to respond in an event- or model-driven manner or reconfigured as needed.
Instrumental phase-based method for Fourier transform spectrometer measurements processing
Saggin, Bortolino; Scaccabarozzi, Diego; Tarabini, Marco
2011-04-20
Phase correction is a critical procedure for most space-borne Fourier transform spectrometers (FTSs) whose accuracy (owing to often poor signal-to-noise ratio, SNR) can be jeopardized from many uncontrollable environmental conditions. This work considers the phase correction in an FTS working under significant temperature change during the measurement and affected by mechanical disturbances. The implemented method is based on the identification of an instrumental phase that is dependent on the interferometer temperature and on the extraction of a linear phase component through a least-squares approach. The use of an instrumental phase parameterized with the interferometer temperature eases the determination of the linear phase that can be extracted using only a narrow spectral region selected to be immune from disturbances. The procedure, in this way, is made robust against phase errors arising from instrumental effects, a key feature to reduce the disturbances through spectra averaging. The method was specifically developed for the Mars IR Mapper spectrometer, that was designed for operation onboard a rover on the Mars surface; the validation was performed using ground and in-flight measurements of the Fourier transform IR spectrometer planetary Fourier spectrometer, onboard the MarsExpress mission. The symmetrization has been exploited also for the spectra calibration, highlighting the issues deriving from the cases of relevant beamsplitter emission. The applicability of this procedure to other instruments is conditional to the presence in the spectra of at least one spectral region with a large SNR along with a negligible (or known) beamsplitter emission. For the PFS instrument, the processing of data with relevant beamsplitter emission has been performed exploiting the absorption carbon dioxide bands present in Martian spectra.
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.
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.; Tipping, R. H.
2014-03-14
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS{sub 1} − S{sub 2} introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the S-circumflex operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters’ two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
Bangalore, Arjun S.; Demirgian, Jack C.; Boparai, Amrit S.; Small, Gary W.
1999-11-01
The Fourier transform infrared (FT-IR) spectral data of two nerve agent simulants, diisopropyl methyl phosphonate (DIMP) and dimethyl methyl phosphonate (DMMP), are used as test cases to determine the spectral resolution that gives optimal pattern recognition performance. DIMP is used as the target analyte for detection, while DMMP is used to test the ability of the automated pattern recognition methodology to detect the analyte selectively. Interferogram data are collected by using a Midac passive FT-IR instrument. The methodology is based on the application of pattern recognition techniques to short segments of single-beam spectra obtained by Fourier processing the collected interferogram data. The work described in this article evaluates the effect of varying spectral resolution on the pattern recognition results. The objective is to determine the optimal spectral resolution to be used for data collection. The results of this study indicate that the data with a nominal spectral resolution of 16 cm{sup -1} provide sufficient selectivity to give pattern recognition results comparable to that obtained by using higher resolution data. We found that, while higher resolution does not increase selectivity sufficiently to provide better pattern recognition results, lower resolution decreases selectivity and degrades the pattern recognition results. These results can be used as guidelines to maximize detection sensitivity, to minimize the time needed for data collection, and to reduce data storage requirements. (c) 2000 Society for Applied Spectroscopy.
Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.
Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José
2015-12-14
We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme. PMID:26699041
Liu, Derek Sloboda, Ron S.
2014-05-15
Purpose: Boyer and Mok proposed a fast calculation method employing the Fourier transform (FT), for which calculation time is independent of the number of seeds but seed placement is restricted to calculation grid points. Here an interpolation method is described enabling unrestricted seed placement while preserving the computational efficiency of the original method. Methods: The Iodine-125 seed dose kernel was sampled and selected values were modified to optimize interpolation accuracy for clinically relevant doses. For each seed, the kernel was shifted to the nearest grid point via convolution with a unit impulse, implemented in the Fourier domain. The remaining fractional shift was performed using a piecewise third-order Lagrange filter. Results: Implementation of the interpolation method greatly improved FT-based dose calculation accuracy. The dose distribution was accurate to within 2% beyond 3 mm from each seed. Isodose contours were indistinguishable from explicit TG-43 calculation. Dose-volume metric errors were negligible. Computation time for the FT interpolation method was essentially the same as Boyer's method. Conclusions: A FT interpolation method for permanent prostate brachytherapy TG-43 dose calculation was developed which expands upon Boyer's original method and enables unrestricted seed placement. The proposed method substantially improves the clinically relevant dose accuracy with negligible additional computation cost, preserving the efficiency of the original method.
Fast Fourier transform-based Retinex and alpha-rooting color image enhancement
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.; Gonzales, Analysa M.
2015-05-01
Efficiency in terms of both accuracy and speed is highly important in any system, especially when it comes to image processing. The purpose of this paper is to improve an existing implementation of multi-scale retinex (MSR) by utilizing the fast Fourier transforms (FFT) within the illumination estimation step of the algorithm to improve the speed at which Gaussian blurring filters were applied to the original input image. In addition, alpha-rooting can be used as a separate technique to achieve a sharper image in order to fuse its results with those of the retinex algorithm for the sake of achieving the best image possible as shown by the values of the considered color image enhancement measure (EMEC).
Laser Mode Behavior of the Cassini CIRS Fourier Transform Spectrometer at Saturn
NASA Technical Reports Server (NTRS)
Brasunas, John C.
2012-01-01
The CIRS Fourier transform spectrometer aboard the NASA/ESA/ASI Cassini orbiter has been acquiring spectra of the Saturnian system since 2004. The CIRS reference interferometer employs a laser diode to trigger the interferogram sampling. Although the control of laser diode drive current and operating temperature are stringent enough to restrict laser wavelength variation to a small fraction of CIRS finest resolution element, the CIRS instrument does need to be restarted every year or two, at which time it may start in a new laser mode. By monitoring the Mylar absorption features in uncalibrated spectra due to the beam splitter Mylar substrate, it can be shown that these jumps are to adjacent modes and that most of the eight-year operation so far is restricted to three adjacent modes. For a given mode, the wavelength stability appears consistent with the stability of the laser diode drive curren.t and operating temperature.
Color image encryption using iterative phase retrieve process in quaternion Fourier transform domain
NASA Astrophysics Data System (ADS)
Sui, Liansheng; Duan, Kuaikuai
2015-02-01
A single-channel color image encryption method is proposed based on iterative phase iterative process in quaternion Fourier transform domain. First, three components of the plain color image is confused respectively by using cat map. Second, the confused components are combined into a pure quaternion image, which is encode to the phase only function by using an iterative phase retrieval process. Finally, the phase only function is encrypted into the gray scale ciphertext with stationary white noise distribution based on the chaotic diffusion, which has camouflage property to some extent. The corresponding plain color image can be recovered from the ciphertext only with correct keys in the decryption process. Simulation results verify the feasibility and effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Tieng, S. M.; Lai, W. Z.
Because of the importance of the temperature scalar measurements in combination diagonostics, application of phase shift holographic interferometry to temperature measurement of an axisymmetrically premixed flame was experimentally investigated. The test apparatus is an axisymmetric Bunsen burner. Propane of 99 percent purity is used as the gaseous fuel. A fast Fourier transform, a more efficient and accurate approach for Abel inversion, is used for reconstructed the axisymmetric temperature field from the interferometric data. The temperature distribution is compared with the thermocouple-measured values. The comparison shows that the proposed technique is satisfactory. The result errors are analyzed in detail. It is shown that this technique overcomes most of the earlier problems and limitations detrimental to the conventional holographic interferometry.
Williams, E R; McLafferty, F W
1990-11-01
For ions formed by plasma desorption (PD) in a Fourier-transform mass spectrometer, high resolution measurements are demonstrated, such as 65,000 (FWHH) for the protonated molecularion of gramicidin S (MW 1140.7). Resolution is substantially improved by delaying measurements until a significant ion concentration has built up in the cell, and by collisionally deactivating the orbital kinetic energy of the ions. This also makes the ions available for subsequent dissociation steps, so that tandem mass spectrometry can be demonstrated for PD ions. With this for larger ions, collisionally activated dissociation (CAD) is effected with > 85% efficiency. The CAD spectra of (M + Na)(+) and of fragment ions from the PD of gramicidin S provide structurally useful information. PMID:24248976
Zhang, Yong; Cao, Chun-yu; Feng, Wen-ying; Xu, Ming; Su, Zhen-hua; Liu, Xiao-meng; Lü, Wei-jun
2011-03-01
As one of the most powerful tools to investigate the compositions of raw materials and the property of pulp and paper, infrared spectroscopy has played an important role in pulp and paper industry. However, the traditional transmission infrared spectroscopy has not met the requirements of the producing processes because of its disadvantages of time consuming and sample destruction. New technique would be needed to be found. Fourier transform attenuated total reflection infrared spectroscopy (ATR-FTIR) is an advanced spectroscopic tool for nondestructive evaluation and could rapidly, accurately estimate the production properties of each process in pulp and paper industry. The present review describes the application of ATR-FTIR in analysis of pulp and paper industry. The analysis processes will include: pulping, papermaking, environmental protecting, special processing and paper identifying. PMID:21595211
Relative-Coordinate Determination for Visual Double Stars by Applying Fourier Transforms
NASA Astrophysics Data System (ADS)
Radovic, V.; Pavlovic, R.; Cvetkovic, Z.
2013-06-01
We discuss the software developed for the purpose of determining the relative coordinates (position angle θ and separation ρ) for visual double or multiple stars. It is based on application of Fourier transforms in treating CCD frames of these systems. The objective was to determine the relative coordinates automatically to an extent as large as possible. In this way the time needed for the reduction of many CCD frames becomes shorter. The capabilities and limitations of the software are examined. Besides, the possibility of improving is also considered. The software has been tested and checked on a sample consisting of CCD frames of 165 double or multiple stars obtained with the 2m telescope at NAO Rozhen in Bulgaria in October 2011. The results have been compared with the corresponding results obtained by applying different software and the agreement is found to be very good.
Thompson, Sandra E.; Foster, Nancy S.; Johnson, Timothy J.; Valentine, Nancy B.; Amonette, James E.
2003-08-28
Fourier Transform Infrared Photoacoustic Spectroscopy (FTIR-PAS) has been applied for the first time to the identification and speciation of bacterial spores. With minimal preparation the spores were deposited into the photoacoustic sample cup and their spectra recorded. A total of 40 different samples of 5 different strains of Bacillus spores were analyzed: Bacillus subtilis ATCC 49760, Bacillus atrophaeus ATCC 49337, Bacillus subtilis 6051, Bacillus thuringiensis ssp. kurstaki, and Bacillus globigii Dugway. The statistical methods used included principal-component analysis (PCA), classification and regression trees (CART), and Mahalanobis-distance calculations. Internal cross-validation studies successfully classify the spores according to their bacterial strain in 38 of 40 cases (95%) and 36 of 40 (90%) in cross-validation. Analysis of fifteen blind samples, which included library and other spores, and nonbacterial materials, resulted in correct strain classification the blind samples that were members of the library and correct rejection of the nonbacterial samples.
NASA Astrophysics Data System (ADS)
Nagler, Peter C.; Fixsen, Dale J.; Kogut, Alan; Tucker, Gregory S.
2015-11-01
The detection of the primordial B-mode polarization signal of the cosmic microwave background (CMB) would provide evidence for inflation. Yet as has become increasingly clear, the detection of a such a faint signal requires an instrument with both wide frequency coverage to reject foregrounds and excellent control over instrumental systematic effects. Using a polarizing Fourier transform spectrometer (FTS) for CMB observations meets both of these requirements. In this work, we present an analysis of instrumental systematic effects in polarizing FTSs, using the Primordial Inflation Explorer (PIXIE) as a worked example. We analytically solve for the most important systematic effects inherent to the FTS—emissive optical components, misaligned optical components, sampling and phase errors, and spin synchronous effects—and demonstrate that residual systematic error terms after corrections will all be at the sub-nK level, well below the predicted 100 nK B-mode signal.
A comparison of WFTA and FFT programs. [Winograd Fourier Transform Algorithm
NASA Technical Reports Server (NTRS)
Nawab, H.; Mcclellan, J. H.
1979-01-01
Bounds on the minimum number of data transfers (i.e., loads and stores) required by WFTA (Winograd Fourier Transform Algorithm) and FFT programs are presented. The analysis is applicable to those general-purpose computers with a small number of general processor registers (e.g., the IBM370, PDP-11, etc.). It is shown that the 1008-point WFTA requires about 21% more data transfers than the 1024-point radix-4 FFT; on the other hand, the 120-point WFTA has about 22% fewer data transfers than the 128-point radix-2 FFT. Finally, comparisons of the 'total' program execution times (multiplications, additions, and data transfers, but not indexing or permutations) are presented.
Dynamic interferometer alignment and its utility in UV Fourier transform spectrometer systems
NASA Technical Reports Server (NTRS)
Dorval, Rick K.; Engel, James R.; Wyntjes, Geert J.
1993-01-01
Dynamic alignment has been demonstrated as a practical approach to alignment maintenance for systems in the infrared region of the spectrum. On the basis of work done by OPTRA, this technique was introduced in commercial Fourier transform spectrometer systems in 1982 and in various forms is now available from a number of manufacturers. This paper reports on work by OPTRA to extend the basic technique to systems operating in the ultraviolet. In addition, this paper reports the preliminary results of the development of an alignment system using a laser diode in place of a gas laser normally found in dynamic alignment systems. A unique optical system and spatial heterodyne technique allows for achievement of a metrology system with characteristics that fully satisfy the requirements of an ultraviolet spectrometer system.
NASA Astrophysics Data System (ADS)
Nand, Anbhawa; Kitcher, Daniel J.; Wade, Scott A.; Collins, Stephen F.; Baxter, Gregory W.
2005-05-01
The use of reflected power spectra arising from a chirped fiber Bragg grating (CFBG) to extract a nonuniform temperature distribution along the grating has been investigated. The technique uses a discrete Fourier transform (FFT) in which the measured spectrum of the CFBG due to a localised temperature change was simulated using the FFT grating design model. The model operated on the reference spectrum and hypothesis temperature distributions, T(z), to generate a spectrum representative of a localised temperature disturbance. The simulated spectrum was fitted to the measured spectrum using a three-parameter disturbance function operating on position, width and amplitude of temperature change. The rms deviation of the applied value for position of a localised temperature change was 0.14 mm.
Submillimeter fourier-transform spectrometer measurements of atmospheric opacity above mauna kea.
Serabyn, E; Weisstein, E W; Lis, D C; Pardo, J R
1998-04-20
We present accurately calibrated submillimeter atmospheric transmission spectra obtained with a Fourier-transform spectrometer at the Caltech Submillimeter Observatory on Mauna Kea, Hawaii. These measurements cover the 0.9-0.3-mm wavelength range and are the first in a series aimed at defining the terrestrial long-wave atmospheric transmission curve. The 4.1-km altitude of the Mauna Kea site provides access to extremely low zenith water-vapor columns, permitting atmospheric observations at frequencies well above those possible from sea level. We describe the calibration procedures, present our first well-calibrated transmission spectra, and compare our results with those of a single-layer atmospheric transmission model, AT. With an empirical best-fit continuum opacity term included, this simple single-layer model provides a remarkably good fit to the opacity data for H(2)O line profiles described by either van Vleck-Weisskopf or kinetic shapes. PMID:18273141
Fourier transform infrared spectroscopy techniques for the analysis of drugs of abuse
NASA Astrophysics Data System (ADS)
Kalasinsky, Kathryn S.; Levine, Barry K.; Smith, Michael L.; Magluilo, Joseph J.; Schaefer, Teresa
1994-01-01
Cryogenic deposition techniques for Gas Chromatography/Fourier Transform Infrared (GC/FT-IR) can be successfully employed in urinalysis for drugs of abuse with detection limits comparable to those of the established Gas Chromatography/Mass Spectrometry (GC/MS) technique. The additional confidence of the data that infrared analysis can offer has been helpful in identifying ambiguous results, particularly, in the case of amphetamines where drugs of abuse can be confused with over-the-counter medications or naturally occurring amines. Hair analysis has been important in drug testing when adulteration of urine samples has been a question. Functional group mapping can further assist the analysis and track drug use versus time.
Terahertz time-domain and Fourier-transform infrared spectroscopy of traditional Korean pigments
NASA Astrophysics Data System (ADS)
Hong, Taeyoon; Choi, Kyujin; Ha, Taewoo; Park, Byung Cheol; Sim, Kyung Ik; Kim, Jong Hyeon; Kim, Jae Hoon; Kwon, Jy Eun; Lee, Sanghyun; Kang, Dai Ill; Lee, Han Hyoung
2014-03-01
Representative traditional Korean pigments (oyster shell white [hobun], massicot [miltaseung], indigo [jjok], azurite [seokcheong], malachite [seokrok], and red lead [yeondan]) have been studied with terahertz time-domain spectroscopy (THz-TDS) and Fourier-transform infrared spectroscopy (FTIRS) over the spectral region of 0.1-7.5 THz. Both the refractive index n and the extinction coefficient k were simultaneously and independently determined in the terahertz region without a Kramers-Kronig analysis while the absoprtion coefficient spectra were acquired in the infrared region. All pigments studied in the present work exhibited a set of characteristic absorption peaks unique to the pigment species in addition to a background that increased with increasing frequency. Our study demonstrates that terahertz and infrared techniques can be useful identification and diagnostic tools for the traditional Korean pigments used in heritage buildings and artworks.
Du, Jian-Hua; Zhang, Ren-Cheng
2008-03-01
CO was chosen as an early fire detection factor through analyzing all kinds of characters in the process of fires, and an experiment system was established based on Fourier transform infrared spectrometer. Through this system, lots of early fire experiments were carried out, and the authors got the CO concentrations of all kinds of materials. Using the concentration of CO, an autoregressive integrated model was established by time series analysis, then the process characters phi1 and phi2 were extracted from them. Through analyzing the phase graph of the process characters, it was found that the real fires and the nuisance fires were distributed in different regions. Plenty of experiments indicate that this detection method can discriminate between real fire sources and nuisance sources quickly when fires occur. PMID:18536412
NASA Technical Reports Server (NTRS)
Tarbell, T. D.; Title, A. M.
1976-01-01
Fourier techniques have been exhaustively calibrated using Unno's (1956) results for the absorption profile of a simple Zeeman triplet. If a simple transformation is applied to the normalized line depths, then magnetic-field strengths and inclination angles can be measured very accurately from noisy saturated line profiles. Systematic errors caused by saturation effects can be estimated and reduced by varying one parameter. When a significant fraction of the line profile is unsplit and unpolarized, large errors may be made in measurements of low fields, unless the line is sufficiently weak. For a weak line, a vertical field of 1600 gauss can be measured to 10% accuracy even when 70% of the line profile is stray light. These stray-light errors are troublesome in measuring fields of gaps and pores but not sunspots. Numerical results of the error analysis are presented graphically.
Kelly, J F Daniel; Downey, Gerard
2005-05-01
Fourier transform infrared spectroscopy and attenuated total reflection sampling have been used to detect adulteration of single strength apple juice samples. The sample set comprised 224 authentic apple juices and 480 adulterated samples. Adulterants used included partially inverted cane syrup (PICS), beet sucrose (BS), high fructose corn syrup (HFCS), and a synthetic solution of fructose, glucose, and sucrose (FGS). Adulteration was carried out on individual apple juice samples at levels of 10, 20, 30, and 40% w/w. Spectral data were compressed by principal component analysis and analyzed using k-nearest neighbors and partial least squares regression techniques. Prediction results for the best classification models achieved an overall (authentic plus adulterated) correct classification rate of 96.5, 93.9, 92.2, and 82.4% for PICS, BS, HFCS, and FGS adulterants, respectively. This method shows promise as a rapid screening technique for the detection of a broad range of potential adulterants in apple juice. PMID:15853360
NASA Technical Reports Server (NTRS)
Verber, C. M.; Vahey, D. W.; Wood, V. E.; Kenan, R. P.; Hartman, N. F.
1977-01-01
The possibility of producing an integrated optics data processing device based upon Fourier transformations or other parallel processing techniques, and the ways in which such techniques may be used to upgrade the performance of present and projected NASA systems were investigated. Activities toward this goal include; (1) production of near-diffraction-limited geodesic lenses in glass waveguides; (2) development of grinding and polishing techniques for the production of geodesic lenses in LiNbO3 waveguides; (3) development of a characterization technique for waveguide lenses; and (4) development of a theory for corrected aspheric geodesic lenses. A holographic subtraction system was devised which should be capable of rapid on-board preprocessing of a large number of parallel data channels. The principle involved is validated in three demonstrations.
NASA Technical Reports Server (NTRS)
Truong, T. K.; Chang, J. J.; Hsu, I. S.; Pei, D. Y.; Reed, I. S.
1986-01-01
The complex integer multiplier and adder over the direct sum of two copies of finite field developed by Cozzens and Finkelstein (1985) is specialized to the direct sum of the rings of integers modulo Fermat numbers. Such multiplication over the rings of integers modulo Fermat numbers can be performed by means of two integer multiplications, whereas the complex integer multiplication requires three integer multiplications. Such multiplications and additions can be used in the implementation of a discrete Fourier transform (DFT) of a sequence of complex numbers. The advantage of the present approach is that the number of multiplications needed to compute a systolic array of the DFT can be reduced substantially. The architectural designs using this approach are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.
Li, Chao; Yang, Sheng-Chao; Guo, Qiao-Sheng; Zheng, Kai-Yan; Wang, Ping-Li; Meng, Zhen-Gui
2016-01-01
A combination of Fourier transform infrared spectroscopy with chemometrics tools provided an approach for studying Marsdenia tenacissima according to its geographical origin. A total of 128 M. tenacissima samples from four provinces in China were analyzed with FTIR spectroscopy. Six pattern recognition methods were used to construct the discrimination models: support vector machine-genetic algorithms, support vector machine-particle swarm optimization, K-nearest neighbors, radial basis function neural network, random forest and support vector machine-grid search. Experimental results showed that K-nearest neighbors was superior to other mathematical algorithms after data were preprocessed with wavelet de-noising, with a discrimination rate of 100% in both the training and prediction sets. This study demonstrated that FTIR spectroscopy coupled with K-nearest neighbors could be successfully applied to determine the geographical origins of M. tenacissima samples, thereby providing reliable authentication in a rapid, cheap and noninvasive way. PMID:26233789
The use of the fractional Fourier transform with coded excitation in ultrasound imaging.
Bennett, Michael J; McLaughlin, Steve; Anderson, Tom; McDicken, Norman
2006-04-01
Medical ultrasound systems are limited by a tradeoff between axial resolution and the maximum imaging depth which may be achieved. The technique of coded excitation has been used extensively in the field of RADAR and SONAR for some time, but has only relatively recently been exploited in the area of medical ultrasound. This technique is attractive because allows the relationship between the pulse length and the maximum achievable spatial resolution to be changed. The work presented here explores the possibility of using the fractional Fourier transform as an effective means for the processing of signals received after the transmission of linear frequency modulated chirps. Results are presented which demonstrate that this technique is able to offer spatial resolutions similar to those obtained with a single cycle duration signal. PMID:16602583