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
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
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.
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.
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.
Realization of a scalable coherent quantum Fourier transform
NASA Astrophysics Data System (ADS)
Debnath, Shantanu; Linke, Norbert; Figgatt, Caroline; Landsman, Kevin; Wright, Ken; Monroe, Chris
2016-05-01
The exponential speed-up in some quantum algorithms is a direct result of parallel function-evaluation paths that interfere through a quantum Fourier transform (QFT). We report the implementation of a fully coherent QFT on five trapped Yb+ atomic qubits using sequences of fundamental quantum logic gates. These modular gates can be used to program arbitrary sequences nearly independent of system size and distance between qubits. We use this capability to first perform a Deutsch-Jozsa algorithm where several instances of three-qubit balanced and constant functions are implemented and then examined using single qubit QFTs. Secondly, we apply a fully coherent five-qubit QFT as a part of a quantum phase estimation protocol. Here, the QFT operates on a five-qubit superposition state with a particular phase modulation of its coefficients and directly produces the corresponding phase to five-bit precision. Finally, we examine the performance of the QFT in the period finding problem in the context of Shor's factorization algorithm. This work is supported by the ARO with funding from the IARPA MQCO program and the AFOSR MURI on Quantum Measurement and Verification.
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.
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.
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
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
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.
Gurka, D F; Titus, R; Robins, K; Wong, A; Wurrey, C J; Durig, J R; Shen, Z; Burkhard, L P
1996-12-01
Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrared spectra was performed with the Gaussian quantum chemistry software. The Hartree-Fock/6-31G* level of theory was employed, with IR frequencies scaled by a standard factor of 0.89. This approach shows great promise as a means of characterizing or confirming environmental analyte identifications when standard spectra, or pure standards required to measure standard spectra, are unavailable. PMID:21619333
The quantum state vector in phase space and Gabor's windowed Fourier transform
NASA Astrophysics Data System (ADS)
Bracken, A. J.; Watson, P.
2010-10-01
Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schrödinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.
Imaging Fourier transform spectrometer
Bennett, C.L.
1993-09-13
This invention is comprised of an imaging Fourier transform spectrometer having a Fourier transform infrared spectrometer providing a series of images to a focal plane array camera. The focal plane array camera is clocked to a multiple of zero crossing occurrences as caused by a moving mirror of the Fourier transform infrared spectrometer and as detected by a laser detector such that the frame capture rate of the focal plane array camera corresponds to a multiple of the zero crossing rate of the Fourier transform infrared spectrometer. The images are transmitted to a computer for processing such that representations of the images as viewed in the light of an arbitrary spectral ``fingerprint`` pattern can be displayed on a monitor or otherwise stored and manipulated by the computer.
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
Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...
Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
1998-01-01
Understanding the global atmospheric changes is difficult with today's current technology. However, with high resolution and nearly continuous observations from a satellite, it's possible to transform our understanding of the atmosphere. To enable the next generation of atmospheric science, a new class of orbiting atmospheric sensors is being developed. The foundation of this advanced concept is the Fourier Transform Spectrometer, or FTS.
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).
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)
Obada, A.-S. F.; Hessian, H. A.; Mohamed, A.-B. A.; Homid, Ali H.
2013-11-01
Based on the one- and two-qubit gates defined and generated via superconducting transmon qubits homogeneously coupled to a superconducting stripline resonator, we present a new physical protocol for implementing an N-bit discrete quantum Fourier transform. We propose and illustrate a detailed experimental feasibility for realizing the algorithm. The average fidelity is computed to prove the success of this algorithm. Estimated time for implementing the protocol using the proposed scheme is compared with previous schemes. Estimates show that the protocol can be successfully implemented within the present experimental limits.
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.
Fourier transform interferometer alignment method.
Goldberg, Kenneth A; Naulleau, Patrick; Bokor, Jeffrey
2002-08-01
A rapid and convenient method has been developed to facilitate the alignment of the image-plane components of point-diffraction interferometers, including the phase-shifting point-diffraction interferometer. In real time, the Fourier transform of the detected image is used to calculate a pseudoimage of the electric field in the image plane of the test optic where thecritical alignment o f variousoptical components is performed. Reconstruction of the pseudoimage is similar to off-axis, Fourier transform holography. Intermediate steps in the alignment procedure are described. Fine alignment is aided by the introduction and optimization of a global-contrast parameter that is easily calculated from the Fourier transform. Additional applications include the alignment of image-plane apertures in general optical systems, the rapid identification of patterned image-plane alignment marks, and the probing of important image-plane field properties. PMID:12153074
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
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.
JPL Fourier transform ultraviolet spectrometer
NASA Technical Reports Server (NTRS)
Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.
1994-01-01
The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.
Fourier-Transform Infrared Spectrometer
NASA Technical Reports Server (NTRS)
Schindler, R. A.
1986-01-01
Fourier-transform spectrometer provides approximately hundredfold increase in luminosity at detector plane over that achievable with older instruments of this type. Used to analyze such weak sources as pollutants and other low-concentration substances in atmosphere. Interferometer creates fringe patterns on two distinct arrays of light detectors, which observe different wavelength bands. Objective lens focuses scene on image plane, which contains optical chopper. To make instrument less susceptible to variations in scene under observation, field and detector lenses focus entrance aperture, rather that image, onto detector array.
Improved Fourier-transform profilometry
Mao Xianfu; Chen Wenjing; Su Xianyu
2007-02-10
An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object.
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.
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.
Fourier transform infrared (FTIR) spectroscopy.
Berthomieu, Catherine; Hienerwadel, Rainer
2009-01-01
Fourier transform infrared (FTIR) spectroscopy probes the vibrational properties of amino acids and cofactors, which are sensitive to minute structural changes. The lack of specificity of this technique, on the one hand, permits us to probe directly the vibrational properties of almost all the cofactors, amino acid side chains, and of water molecules. On the other hand, we can use reaction-induced FTIR difference spectroscopy to select vibrations corresponding to single chemical groups involved in a specific reaction. Various strategies are used to identify the IR signatures of each residue of interest in the resulting reaction-induced FTIR difference spectra. (Specific) Isotope labeling, site-directed mutagenesis, hydrogen/deuterium exchange are often used to identify the chemical groups. Studies on model compounds and the increasing use of theoretical chemistry for normal modes calculations allow us to interpret the IR frequencies in terms of specific structural characteristics of the chemical group or molecule of interest. This review presents basics of FTIR spectroscopy technique and provides specific important structural and functional information obtained from the analysis of the data from the photosystems, using this method. PMID:19513810
The fractional Fourier transform and applications
NASA Technical Reports Server (NTRS)
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
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 Geo
The Geostationary Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Uncertainty relation for the discrete Fourier transform.
Massar, Serge; Spindel, Philippe
2008-05-16
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation. PMID:18518426
FOURIER TRANSFORM INFRARED SPECTROMETRY OF AMBIENT AEROSOLS
Fourier transform infrared (FTIR) spectrometry has been evaluated as a method for determining the concentration of selected species present in ambient aerosols collected on Teflon filters. The filters are analyzed by transmission measurements after collection of the fine fraction...
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.
Electronically-Scanned Fourier-Transform Spectrometer
NASA Technical Reports Server (NTRS)
Breckinridge, J. B.; Ocallaghan, F. G.
1984-01-01
Instrument efficient, lightweight, and stable. Fourier-transform spectrometer configuration uses electronic, instead of mechanical, scanning. Configuration insensitive to vibration-induced sampling errors introduced into mechanically scanned systems.
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
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.
High order generalized permutational fractional Fourier transforms
NASA Astrophysics Data System (ADS)
Ran, Qi-Wen; Yuan, Lin; Tan, Li-Ying; Ma, Jing; Wang, Qi
2004-02-01
We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +infty, M = 4k (k is a natural number) and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
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.
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space. PMID:16138556
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.
REMOTE FOURIER TRANSFORM INFRARED AIR POLLUTION STUDIES
A commercial Fourier transform infrared interferometer system has been installed in a van and used to make longpath absorption and single-ended emission measurements of gaseous pollutant concentrations at a variety of pollutant sources. The interferometer system is described and ...
Livermore Imaging Fourier Transform Infrared Spectrometer (LIFTIRS)
Carter, M.R.; Bennett, C.L.; Fields, D.J.; Lee, F.D.
1995-05-10
Lawrence Livermore National Laboratory is currently operating a hyperspectral imager, the Livermore Imaging Fourier Transform Infrared Spectrometer (LIFTIRS). This instrument is capable of operating throughout the infrared spectrum from 3 to 12.5 {mu}m with controllable spectral resolution. In this presentation we report on it`s operating characteristics, current capabilities, data throughput and calibration issues.
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.
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.
Miniaturization of holographic Fourier-transform spectrometers.
Agladze, Nikolay I; Sievers, Albert J
2004-12-20
Wave propagation equations in the stationary-phase approximation have been used to identify the theoretical bounds of a miniature holographic Fourier-transform spectrometer (HFTS). It is demonstrated that the HFTS throughput can be larger than for a scanning Fourier-transform spectrometer. Given room- or a higher-temperature constraint, a small HFTS has the potential to outperform a small multichannel dispersive spectrograph with the same resolving power because of the size dependence of the signal-to-noise ratio. These predictions are used to analyze the performance of a miniature HFTS made from simple optical components covering a broad spectral range from the UV to the near IR. The importance of specific primary aberrations in limiting the HFTS performance has been both identified and verified. PMID:15646777
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.
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
NASA Technical Reports Server (NTRS)
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
NASA Astrophysics Data System (ADS)
Debnath, Lokenath
2012-07-01
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.
Phase amplitude conformal symmetry in Fourier transforms
NASA Astrophysics Data System (ADS)
Kuwata, S.
2015-04-01
For the Fourier transform ℑ : L2(R) → L2(R) of a complex-valued even or odd function ψ, it is found that the amplitude invariance |ℑψ| = |ψ| leads to a phase invariance or inversion as arg(ℑψ) = ±argψ + θ (θ = constant). The converse holds unless arg ψ = constant. The condition |ψ| = |ℑψ| is required in dealing with, for example, the minimum uncertainty relation between position and momentum. Without the evenness or oddness of ψ, |ℑψ| = |ψ| does not necessarily imply arg(ℑψ) = ±argψ + θ, nor is the converse.
Noise figure of amplified dispersive Fourier transformation
Goda, Keisuke; Jalali, Bahram
2010-09-15
Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.
Advanced Techniques for Fourier Transform Wavefront Reconstruction
Poyneer, L A
2002-08-05
The performance of Fourier transform (FT) reconstructors in large adaptive optics systems with Shack-Hartmann sensors and a deformable mirror is analyzed. FT methods, which are derived for point-based geometries, are adapted for use on the continuous systems. Analysis and simulation show how to compensate for effects such as misalignment of the deformable mirror and wavefront sensor gain. Further filtering methods to reduce noise and improve performance are presented. All these modifications can be implemented at the filtering stage, preserving the speed of FT reconstruction. Simulation of a large system shows how compensated FT methods can have equivalent or better performance to slower vector-matrix-multiply reconstructions.
Fourier transform infrared spectroscopy of deuterated proteins
NASA Astrophysics Data System (ADS)
Marcano O., A.; Markushin, Y.; Melikechi, N.; Connolly, D.
2008-08-01
We report on Fourier transform spectra of deuterated proteins: Bovine Serum Albumin, Leptin, Insulin-like Growth Factor II, monoclonal antibody to ovarian cancer antigen CA125 and Osteopontin. The spectra exhibit changes in the relative amplitude and spectral width of certain peaks. New peaks not present in the non-deuterated sample are also observed. Ways for improving the deuteration of proteins by varying the temperature and dilution time are discussed. We propose the use of deuterated proteins to increase the sensitivity of immunoassays aimed for early diagnostic of diseases most notably cancer.
Coherent Fourier transform electrical pulse shaping.
Xiao, Shijun; Weiner, Andrew M
2006-04-01
Fourier synthesis pulse shaping methods allowing generation of programmable, user defined femtosecond optical waveforms have been widely applied in ultrafast optical science and technology. In the electrical domain, arbitrary waveform generation is well established at frequencies below approximately 1 GHz, but is difficult at higher frequencies due to limitations in digital-to-analog converter technology. In this paper we demonstrate a method for electrical waveform synthesis at substantially higher frequencies (approximately 20 GHz electrical bandwidth) by combining Fourier optical pulse shaping (extended to hyperfine frequency resolution) and heterodyne optical to electrical conversion. Our scheme relies on coherent manipulation of fields and phases at all stages, both for processing in the optical domain and for conversion from the optical to the electrical domain. We illustrate this technique through a number of examples, including programmable retardation or advancement of short electrical pulses in time over a range exceeding ten pulse durations. Such optically implemented, coherent Fourier transform electrical pulse shaping should open new prospects in ultrawideband electromagnetics. PMID:19516448
Optical interpretation of a complex-order Fourier transform.
Shih, C C
1995-05-15
It is demonstrated that the definition of a fractional-order Fourier transform can be extended into the complexorder regime. A complex-order Fourier transform deals with the imaginary part as well as the real part of the exponential function in the integral. As a result, while the optical implementation of fractional-order Fourier transform involves gradient-index media or spherical lenses, the optical interpretation of complex-order Fourier transform is practically based on the convolution operation and Gaussian apertures. The beam width of a Gaussian beam subjected to the complex-order Fourier transform is obtained analytically with the ABCD matrix approach. PMID:19859464
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.
FFTW: Fastest Fourier Transform in the West
NASA Astrophysics Data System (ADS)
Frigo, Matteo; Johnson, Steven G.
2012-01-01
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST). Benchmarks performed on a variety of platforms show that FFTW's performance is typically superior to that of other publicly available FFT software, and is even competitive with vendor-tuned codes. In contrast to vendor-tuned codes, however, FFTW's performance is portable: the same program will perform well on most architectures without modification. The FFTW library is required by other codes such as StarCrash and Hammurabi.
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.
Compact Fourier transform spectrometer without moving parts
NASA Astrophysics Data System (ADS)
Huang, Chu-Yu; Estroff, B.; Wang, Wei-Chih
2012-04-01
Fourier transform spectroscopy (FTS) is a potent analytical tool for chemical and biological analysis, but is limited by system size, expense, and robustness. To make FTS technology more accessible, we present a compact, inexpensive FTS system based on a novel liquid crystal (LC) interferometer. This design is unique because the optical path difference (OPD) is controlled by voltage applied to the LC cell. The OPD is further improved by reflecting the polarized incident light through the LC several times before reaching the second polarizer and measurement. This paper presents the theoretical model and numerical simulations for the liquid crystal Fourier transform spectrometer (LCFTS), and experimental results from the prototype. Based on the experimental results, the LCFTS performs in accordance with the theoretical predictions, achieving a maximum OPD of 210μm and a resolution of 1nm at a wavelength of 630nm. The instrumental response refresh rate is just under 1 second. Absorbance measurements were conducted for single and mixed solutions of deionized water and isopropyl alcohol, demonstrating agreement with a commercial system and literature values. We also present the LCFTS transmission spectra for varying concentrations of potassium permanganate to show system sensitivity.
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 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.
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.
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.
Fourier transform infrared spectroscopy for Mars science
NASA Astrophysics Data System (ADS)
Anderson, Mark S.; Andringa, Jason M.; Carlson, Robert W.; Conrad, Pamela; Hartford, Wayne; Shafer, Michael; Soto, Alejandro; Tsapin, Alexandre I.; Dybwad, Jens Peter; Wadsworth, Winthrop; Hand, Kevin
2005-03-01
Presented here is a Fourier transform infrared spectrometer (FTIR) for field studies that serves as a prototype for future Mars science applications. Infrared spectroscopy provides chemical information that is relevant to a number of Mars science questions. This includes mineralogical analysis, nitrogen compound recognition, truth testing of remote sensing measurements, and the ability to detect organic compounds. The challenges and scientific opportunities are given for the in situ FTIR analysis of Mars soil and rock samples. Various FTIR sampling techniques are assessed and compared to other analytical instrumentation. The prototype instrument presented is capable of providing field analysis in a Mars analog Antarctic environment. FTIR analysis of endolithic microbial communities in Antarctic rocks and a Mars meteor are given as analytical examples.
Fourier transform infrared spectroscopic study of truffles
NASA Astrophysics Data System (ADS)
Zhao, Dezhang; Liu, Gang; Song, Dingshan; Liu, Jian-hong; Zhou, Yilan; Ou, Jiaming; Sun, Shizhong
2006-01-01
Truffles are rare wild growing edible mushrooms belonging to Ascomycetes. In this paper, Fourier transform infrared (FTIR) spectroscopy was used to obtain vibrational spectra of truffles. The results show that the mushrooms exhibit characteristic spectra. The two strongest absorption bands appear at about 1077cm -1 and 1040 cm -1, which were described as C-O stretching in carbohydrate. The vibrational spectra indicate that the main compositions of the truffles are polysaccharide and protein. According to the characteristics bands and absorption ratios of spectra, different species of truffles can be discriminated. It is also found the great changes between moldy and healthy truffles, which the major differences are observed in the bands of protein. In addition, FTIR spectral differences are observed between the same species of truffles from different producing areas. It is showed that the FTIR spectroscopic method is valuable tool for rapid and nondestructive analysis of truffles prior to any extraction method used.
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.
NASA Astrophysics Data System (ADS)
Laude, David A., Jr.; Johlman, Carolyn; Wilkins, Charles L.
1985-12-01
During the past few years it has been demonstrated that linkage of multiple spectrometry systems with gas chromatography (GC) offers significant advantages for structural analysis of mixture components as they are sepa-rated. In the work to be described, a Fourier transform mass spectrometer (FTMS) has been linked in parallel with a Fourier transform infrared (FTIR) spectrometer for concurrent analysis of GC eluants from a fused silica capillary column. This system provides FTIR, electron impact, and chemical ionization mass spectral analysis of each mixture component as it emerges from the GC. Furthermore, mass measurement accuracy in the low ppm range in the absence of calibrant is made possible by the FTMS. Effective use of the com-plementary information obtained is shown to produce more reliable analytical performance than for any individual measurement.
Fourier transform imaging spectropolarimeter using simultaneous polarization modulation.
Meng, Xin; Li, Jianxin; Liu, Defang; Zhu, Rihong
2013-03-01
We introduce a Fourier transform imaging spectropolarimeter composed of a simultaneous polarization modulator and a Fourier transform spectrometer without slit. The spectropolarimeter enables the generation of four sets of fringe patterns with different polarization states of light from an object point. Fourier transform of the fringe patterns provides four equations of Stokes parameters in various wavenumbers. And we can obtain the full-stokes vector from the equations. The most significant advantage of the method is that the four polarized fringe patterns are obtained simultaneously and separated without aliasing. Additionally, the advantages of the Fourier transform spectrometer are maintained, such as high radiative throughput. PMID:23455296
Geostationary Fourier Transform Spectrometer (GeoFTS)
NASA Astrophysics Data System (ADS)
Sander, S. P.; Bekker, D. L.; Blavier, J. L.; Duren, R. M.; Eldering, A.; Frankenberg, C.; Key, R.; Manatt, K.; Miller, C. E.; Natraj, V.; Rider, D. M.; Wu, Y.
2012-12-01
In order to confidently project the future evolution of climate and support efforts to mitigate the climate change, quantifying the emissions of CO2 and CH4 is a national and international priority. To accomplish this goal, new observational approaches are required that operate over spatial scales ranging from regional to global, and temporal scales from diurnal to decadal. Geostationary satellite observations of CO2, CH4 and correlative quantities such as CO and chlorophyll fluorescence provide a new measurement approach to deliver the quantity and quality of data needed for improved flux estimates and an improved understanding of the partitioning between biogenic and anthropogenic sources. GeoFTS is an exciting new concept that combines the game changing technology of imaging Fourier Transform Spectroscopy with the observational advantages of a geostationary orbit. The GeoFTS observations enable well-posed surface-atmospheric carbon exchange assessments as well as quantify the atmospheric signatures of anthropogenic CO2 and CH4 emissions. GeoFTS uses a single instrument to make measurements in the near-infrared spectral region at high spectral resolution. The imaging FTS measures atmospheric CO2, CH4, and CO to deliver high-resolution maps multiple times per day. A half-meter-sized cube, the instrument is designed to be a secondary "hosted" payload on a commercial GEO satellite. The instrument leverages recent NASA technology investments, uses a flight-proven interferometer and sensor chip assemblies, and requires no new technology development. NASA and other government agencies have adopted the hosted payload implementation approach because it substantially reduces the overall mission cost. Dense continuous mapping (4 km x 4 km pixels at 40 deg. latitude) is a transformational advance beyond, and complementary to, the capabilities of the NASA missions of record in low earth orbit, providing two to three orders of magnitude improvement in the number of
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.
VLSI Implementation Of The Fast Fourier Transform
NASA Astrophysics Data System (ADS)
Chau, Paul M.; Ku, Walter H.
1986-03-01
A VLSI implementation of a Fast Fourier Transform (FFT) processor consisting of a mesh interconnection of complex floating-point butterfly units is presented. The Cooley-Tukey radix-2 Decimation-In-Frequency (DIF) formulation of the FFT was chosen since it offered the best overall compromise between the need for fast and efficient algorithmic computation and the need for a structure amenable to VLSI layout. Thus the VLSI implementation is modular, regular, expandable to various problem sizes and has a simple systolic flow of data and control. To evaluate the FFT architecture, VLSI area-time complexity concepts are used, but are now adapted to a complex floating-point number system rather than the usual integer ring representation. We show by our construction that the Thompson area-time optimum bound for the VLSI computation of an N-point FFT, area-time2oc = ORNlogN)1+a] can be attained by an alternative number representation, and hence the theoretical bound is a tight bound regardless of number system representation.
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.
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)
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
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
Color image registration based on quaternion Fourier transformation
NASA Astrophysics Data System (ADS)
Wang, Qiang; Wang, Zhengzhi
2012-05-01
The traditional Fourier Mellin transform is applied to quaternion algebra in order to investigate quaternion Fourier transformation properties useful for color image registration in frequency domain. Combining with the quaternion phase correlation, we propose a method for color image registration based on the quaternion Fourier transform. The registration method, which processes color image in a holistic manner, is convenient to realign color images differing in translation, rotation, and scaling. Experimental results on different types of color images indicate that the proposed method not only obtains high accuracy in similarity transform in the image plane but also is computationally efficient.
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.
Technique for the metrology calibration of a Fourier transform spectrometer
Spencer, Locke D.; Naylor, David A
2008-11-10
A method is presented for using a Fourier transform spectrometer (FTS) to calibrate the metrology of a second FTS. This technique is particularly useful when the second FTS is inside a cryostat or otherwise inaccessible.
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.
The quest for conformal geometric algebra Fourier transformations
NASA Astrophysics Data System (ADS)
Hitzer, Eckhard
2013-10-01
Conformal geometric algebra is preferred in many applications. Clifford Fourier transforms (CFT) allow holistic signal processing of (multi) vector fields, different from marginal (channel wise) processing: Flow fields, color fields, electro-magnetic fields, ... The Clifford algebra sets (manifolds) of √-1 lead to continuous manifolds of CFTs. A frequently asked question is: What does a Clifford Fourier transform of conformal geometric algebra look like? We try to give a first answer.
Simple optical setup implementation for digital Fourier transform holography
NASA Astrophysics Data System (ADS)
de Oliveira, G. N.; Rodrigues, D. M. C.; dos Santos, P. A. M.
2011-01-01
In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.
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.
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
Herz spaces and restricted summability of Fourier transforms and Fourier series
NASA Astrophysics Data System (ADS)
Weisz, Ferenc
2008-08-01
A general summability method, the so-called [theta]-summability is considered for multi-dimensional Fourier transforms and Fourier series. A new inequality for the Hardy-Littlewood maximal function is verified. It is proved that if the Fourier transform of [theta] is in a Herz space, then the restricted maximal operator of the [theta]-means of a distribution is of weak type (1,1), provided that the supremum in the maximal operator is taken over a cone-like set. From this it follows that over a cone-like set a.e. for all . Moreover, converges to f(x) over a cone-like set at each Lebesgue point of if and only if the Fourier transform of [theta] is in a suitable Herz space. These theorems are extended to Wiener amalgam spaces as well. The Riesz and Weierstrass summations are investigated as special cases of the [theta]-summation.
Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles
Warshaw, S I
2001-07-15
In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resulted from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.
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
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.
Computing the Fast Fourier Transform on a vector computer
NASA Technical Reports Server (NTRS)
Korn, D. G.; Lambiotte, J. J., Jr.
1979-01-01
Two algorithms are presented for performing a Fast Fourier Transform on a vector computer and are compared on the Control Data Corporation STAR-100. The relative merits of the two algorithms are shown to depend upon whether only a few or many independent transforms are desired. A theorem is proved which shows that a set of independent transforms can be computed by performing a partial transformation on a single vector. The results of this theorem also apply to nonvector machines and have reduced the average time per transform by a factor of two on the CDC 6600 computer.
[Spatially modulated Fourier transform imaging spectrometer data compression research].
Huang, Min; Xiangli, Bin; Yuan, Yan; Shen, Zhong; Lu, Qun-bo; Wang, Zhong-hou; Liu, Xue-bin
2010-01-01
Fourier transform imaging spectrometer is a new technic, and has been developed very fast in recent ten years. When it is used in satellite, because of the limit by the data transmission, the authors need to compress the original data obtained by the Fourier transform imaging spectrometer, then, the data can be transmitted, and can be incepted on the earth and decompressed. Then the authors can do data process to get spectrum data which can be used by user. Data compression technic used in Fourier transform imaging spectrometer is a new technic, and few papers introduce it at home and abroad. In this paper the authors will give a data compression method, which has been used in EDIS, and achieved a good result. PMID:20302132
Fixed-point error analysis of Winograd Fourier transform algorithms
NASA Technical Reports Server (NTRS)
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Parallel fast Fourier transforms for non power of two data
Semeraro, B.D.
1994-09-01
This report deals with parallel algorithms for computing discrete Fourier transforms of real sequences of length N not equal to a power of two. The method described is an extension of existing power of two transforms to sequences with N a product of small primes. In particular, this implementation requires N = 2{sup p}3{sup q}5{sup r}. The communication required is the same as for a transform of length N = 2{sup p}. The algorithm presented is intended for use in the solution of partial differential equations, or in any situation in which a large number of forward and backward transforms must be performed and in which the Fourier Coefficients need not be ordered. This implementation is a one dimensional FFT but the techniques are applicable to multidimensional transforms as well. The algorithm has been implemented on a 128 node Intel Ipsc/860.
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.
Application of Fourier transform spectroscopy to air pollution problems
NASA Astrophysics Data System (ADS)
Shaw, J. H.; Calvert, J. G.
1980-11-01
The nature of information that can be retrieved from spectra obtained with Fourier transform spectroscopy is discussed. Nonlinear, least squares analysis of spectra is capable of retrieving information that is beyond the reach of conventional methods and has improved precision and accuracy. Fourier transform infrared spectroscopy was used to study quantitatively the kinetics and mechanisms of several chemical reactions that are of interest to atmospheric chemists and are important in the development of air pollution control strategies. The systems studied include the metastable, reactive, gaseous species, peroxynitric acid, hypochlorous acid, and dimethylnitrosamine.
Fourier transform profilometry for 360-deg shape using TDI camera
NASA Astrophysics Data System (ADS)
Su, Xianyu; Sajan, M. R.; Asundi, Anand K.
1997-03-01
This paper demonstrates a Fourier transform profilometry for 360 degree shape using TDI camera. Single stripe structured light can be recorded sequentially on one image when the camera is in TDI mode. An extended and deformed grating could be recorded in high speed and high resolution. The deformed fringe pattern is regarded as a fringe pattern in the Telecentric Fourier Transform Profilometry (TFTP), of which a wrapped phase is obtained directly. The unwrapped phase of TFTP gives the extended 360 degree profile without high frequency noise. Theoretical and experimental results are presented.
Extending Fourier transformations to Hamilton's quaternions and Clifford's geometric algebras
NASA Astrophysics Data System (ADS)
Hitzer, Eckhard
2013-10-01
We show how Fourier transformations can be extended to Hamilton's algebra of quaternions. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Hamilton's algebra of quaternions is only one example of the larger class of Clifford's geometric algebras, complete algebras encoding a vector space and all its subspace elements. We introduce how Fourier transformations are extended to Clifford algebras and applied in electromagnetism, and in the processing of images, color images, vector field and climate data.
Fourier-transform and global contrast interferometer alignment methods
Goldberg, Kenneth A.
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.
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.
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
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.
Fourier and Hadamard transform spectrometers - A limited comparison
NASA Technical Reports Server (NTRS)
Tai, M. H.; Harwit, M.
1976-01-01
An encoding figure of merit is established for a detector-noise limited Fourier transform spectrometer (FTS) and compared to the comparable figure for a Hadamard transform spectrometer (HTS). The limitation of the Fourier system is partly that it does not truly Fourier analyze the radiation. Instead a cosine squared modulation is imposed on the different spectral frequencies. An additional difficulty is that neither the cosine nor the cosine squared functions form an orthonormal set. This makes the Fellgett's advantage (root-mean-squared figure of merit) for a single detector Michelson interferometer a factor of the square root of (N/8) greater than for a conventional grating instrument - rather than the square root of (N/2). The theoretical limit would be the square root of N.
Path Integrals, Fourier Transforms, and Feynman's Operational Calculus
Ahn, Byung Moo; Johnson, G. W.
1998-03-15
The disentangling process is the key to Feynman's operational calculus for noncommuting operators. The main result of his heuristic calculations deals with disentangling an exponential factor. We use the Wiener and Feynman integrals to make this disentangling (or time-ordering) mathematically rigorous in the case where the analytic functions from earlier work are replaced by Fourier transforms of complex-valued measures.
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...
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...
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
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.
A prescription of Winograd's discrete Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Zohar, S.
1979-01-01
A detailed and complete description of Winograd's discrete Fourier transform algorithm (DFT) is presented omitting all proofs and derivations. The algorithm begins with the transfer of data from the input vector array to the working array where the actual transformation takes place, otherwise known as input scrambling and output unscrambling. The third array holds constraints required in the transformation stage that are evaluated in the precomputation stage. The algorithm is made up of several FORTRAN subroutines which are not to be confused with practical software algorithmic implementation since they are designed for clarity and not for speed.
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.
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…
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.
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
Novel fringe scanning/Fourier transform method of synthetic imaging
Crawford, T.M.; Albano, R.K.
1993-08-01
We have developed a one-dimensional theory and a computer model for synthetically imaging scenes using a novel fringe scanning/Fourier transform technique. Our method probes a scene using two interfering beams of slightly different frequency. These beams form a moving fringe pattern which scans the scene and resonates with any spatial frequency components having the same spatial frequency as the scanning fringe pattern. A simple, non-imaging detector above the scene observes any scattered radiation from the scene falling onto it. If a resonance occurs between the scanning fringe pattern and the scene, then the scattered radiation will be modulated at the difference frequency between the two probing beams. By changing the spatial period of the fringe pattern and then measuring the amplitude and phase of the modulated radiation that is scattered from the scene, the Fourier amplitudes and phases of the different spatial frequency components making up the scene can be measured. A synthetic image of the scene being probed can be generated from this Fourier amplitude and phase data by taking the inverse Fourier transform of this information. This technique could be used to image objects using light, ultrasonic, or other electromagnetic or acoustic waves.
Fourier transform digital holographic adaptive optics imaging system
Liu, Changgeng; Yu, Xiao; Kim, Myung K.
2013-01-01
A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541
Optimal color image restoration: Wiener filter and quaternion Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, we consider the model of quaternion signal degradation when the signal is convoluted and an additive noise is added. The classical model of such a model leads to the solution of the optimal Wiener filter, where the optimality with respect to the mean square error. The characteristic of this filter can be found in the frequency domain by using the Fourier transform. For quaternion signals, the inverse problem is complicated by the fact that the quaternion arithmetic is not commutative. The quaternion Fourier transform does not map the convolution to the operation of multiplication. In this paper, we analyze the linear model of the signal and image degradation with an additive independent noise and the optimal filtration of the signal and images in the frequency domain and in the quaternion space.
Fourier transform spectrometer based on Fabry-Perot interferometer.
Al-Saeed, Tarek A; Khalil, Diaa A
2016-07-10
We analyze the Fourier transform spectrometer based on a symmetric/asymmetric Fabry-Perot interferometer. In this spectrometer, the interferogram is obtained by recording the intensity as a function of the interferometer length. Then, we recover the spectrum by applying the discrete Fourier transform (DFT) directly on the interferogram. This technique results in spectral harmonic overlap and fictitious wavenumber components outside the original spectral range. For this purpose, in this work, we propose a second method to recover the spectrum. This method is based on expanding the DFT of the interferogram and the spectrum by a Haar or box function. By this second method, we recovered the spectrum and got rid of the fictitious spectral components and spectral harmonic overlap. PMID:27409306
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
Spectral measurements of exhaust gases using a Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Schruefer, Elmar; Lindermeir, Erwin; Palme, Frank; Wuelbern, K.
1993-09-01
In recent years environmental issues have become increasingly important. Especially the impact of gaseous emissions on the atmosphere is of great interest. As a consequence a group of several coworkers was established at the Institute for Electrical Measurement of the Technical University of Munich, Germany) with the task to develop and investigate spectroscopic methods and instruments for the analysis of the chemical compsition of exhaust gases. This article describes the advantages of the application of Fourier transform spectroscopy against conventional gas analysis devices. Moreover results of measurements of the exhaust of a smokestack of a coal fired power plant and of an aircraft engine are presented. The last section deals with the development of a Fourier transform spectrometer which is not equipped with any moving parts. This design was made especially for applications in harsh environments.
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.
Visible Imaging Fourier Transform Spectrometer: Design and Calibration
Wishnow, E H; Wurtz, R; Blais-Ouellette, S; Cook, K H; Carr, D; Lewis, I; Grandmont, F; Stubbs, C W
2002-09-19
We present details of the design, operation and calibration of an astronomical visible-band imaging Fourier transform spectrometer (IFTS). This type of instrument produces a spectrum for every pixel in the field of view where the spectral resolution is flexible. The instrument is a dual-input/dual-output Michelson interferometer coupled to the 3.5 meter telescope at the Apache Point Observatory. Imaging performance and interferograms and spectra from calibration sources and standard stars are discussed.
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 Raman and IR spectra of snake skin
NASA Astrophysics Data System (ADS)
Barry, B. W.; Williams, A. C.; Edwards, H. G. M.
1993-06-01
The Fourier transform (FT) Raman and IR spectra of the shed dorsal skin of the snake Elaphe obsoleta (American black rat snake) are reported. Vibrational spectroscopic assignments are proposed for the first time. Although good quality Raman spectra were obtained from the hinge regions using an FT Raman microscope, the dorsal scale regions fluoresced even with 1064 nm IR excitation. This was ascribed to pigmentation markings on the scales.
Fast Fourier transformation results from gamma-ray burst profiles
NASA Technical Reports Server (NTRS)
Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.
1992-01-01
Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.
Construction of a Fourier-transform phase-modulation fluorometer
NASA Astrophysics Data System (ADS)
Shibata, Hironobu; Iwata, Tetsuo
2005-12-01
We have constructed a Fourier-transform phase-modulation fluorometer (FT-PMF) by which a fluorescence decay waveform can be obtained. In the FT-PMF, the modulation frequency of the excitation light source is swept continuously from a direct current (dc) to a high frequency f max with a time duration T. The resultant fluorescence signal waveform is Fourier-transformed to obtain its amplitude and phase spectra. The ratio of the amplitude spectrum and the difference of the phase spectrum over those of the reference spectra that are obtained from a non-fluorescent material are calculated, respectively, and the pair of both spectral data is inverse-Fourier-transformed again to obtain the fluorescence decay waveform. The light source used was an ultraviolet light emitting- diode (UV LED) whose typical operating condition was f max = 100 MHz and T = 10 μs. To demonstrate the performance of the FT-PMF, we carried out (1) measurement of a fluorescent decay waveform of YAG materials packed in a white LED, and (2) determination of fluorescence lifetime of 10 ppm quinine sulfate in 0.1N H IISO 4.
Construction of a Fourier-transform phase-modulation fluorometer
NASA Astrophysics Data System (ADS)
Iwata, Tetsuo; Shibata, Hironobu; Araki, Tsutomu
2005-11-01
We have constructed a Fourier-transform phase-modulation fluorometer (FT-PMF) by which a fluorescence decay waveform can be obtained. In the FT-PMF, the modulation frequency of the excitation light source is swept continuously from a direct current (dc) to a high frequency fmax with a time duration T. The resultant fluorescence signal waveform is Fourier transformed to obtain its amplitude and phase spectra. The ratio of the amplitude spectrum and the difference of the phase spectrum over those of the reference spectra from an excitation waveform are calculated, respectively, and the pair of both spectral data is inverse-Fourier-transformed again to obtain the fluorescence decay waveform. The light source used was an ultraviolet light-emitting diode (UV LED) whose operating condition was fmax = 50-120 MHz and T = 10 µs. To demonstrate the performance of the FT-PMF, we carried out (1) the measurement of a fluorescent decay waveform of YAG materials enclosed in a white LED and (2) determinations of fluorescence lifetimes of 10 ppm quinine sulfate in 0.1 N H2SO4 and 10 ppm rhodamine 6G in ethanol.
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
NASA Astrophysics Data System (ADS)
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.
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
Design of high-resolution Fourier transform lens
NASA Astrophysics Data System (ADS)
Zhang, Lei; Zhong, Xing; Jin, Guang
2007-12-01
With the development of optical information processing, high-resolution Fourier transform lens has often been used in holographic data storage system, spatial filtering and observation of particles. This paper studies the optical design method of high-resolution Fourier transform optical lenses system, which could be used in particles observation and holographic data storage system. According to Fourier transform relation between object and its frequency plane and the theory of geometrical optics, the system with working wavelength 532nm and resolution 3μm was designed based on ZEMAX. A multi-configuration method was adopted to optimize the system's lenses. In the optical system, a diaphragm was placed at the system's spectrum plane and the system demanded a low vacuum to cut down the influences of atmosphere and other particles. The result of finite element analysis indicated that the influences of vacuum pumping to optics spacing and mirror surface shape very minor, and the imaging quality not being affected. This system has many advantages, such as simple structure, good image quality and a high resolution of 3μm. So it has a wide application prospect and can be used both in holographic data storage system and particles observation.
Improved digital filters for evaluating Fourier and Hankel transform integrals
Anderson, Walter L.
1975-01-01
New algorithms are described for evaluating Fourier (cosine, sine) and Hankel (J0,J1) transform integrals by means of digital filters. The filters have been designed with extended lengths so that a variable convolution operation can be applied to a large class of integral transforms having the same system transfer function. A f' lagged-convolution method is also presented to significantly decrease the computation time when computing a series of like-transforms over a parameter set spaced the same as the filters. Accuracy of the new filters is comparable to Gaussian integration, provided moderate parameter ranges and well-behaved kernel functions are used. A collection of Fortran IV subprograms is included for both real and complex functions for each filter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms
Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
Santa Maria, Odilyn L.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
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.
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
The gridding method for image reconstruction by Fourier transformation
Schomberg, H.; Timmer, J.
1995-09-01
This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform {cflx f}. The method involves a window function {cflx w} and proceeds in three steps. First, the convolution {cflx g} = {cflx w} * {cflx f} is computed numerically on a Cartesian grid, using the available samples of {cflx f}. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating {cflx w} * {cflx f} is much less error prone than merely interpolating {cflx f}. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform.
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…
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.
Multinozzle supersonic expansion for Fourier transform absorption spectroscopy
NASA Astrophysics Data System (ADS)
Georges, R.; Durry, G.; Bach, M.; Pétrisse, R.; Jost, R.; Herman, M.
1995-12-01
A new supersonic expansion made of several, up to 31 aligned nozzles, on top of a set of powerful Roots blowers has been built. Adequate optics allowed the recording of infrared absorption spectra in a cell with a Fourier transform interferometer, at high spectral resolution. The system was tested with N 2O, between 2000 and 4800 cm -1. The ν1 + 2 ν2 + ν3 combination band, estimated to be some 10000 times weaker than the ν2 fundamental, could be observed among all the other expected bands, thus setting a limit for the sensitivity of the system. The formation of large N 2O clusters was observed.
Birefringent Fourier transform imaging spectrometer with a rotating retroreflector.
Bai, Caixun; Li, Jianxin; Shen, Yan; Zhou, Jianqiang
2016-08-01
A birefringent Fourier transform imaging spectrometer with a new lateral shearing interferometer is presented. The interferometer includes a Wollaston prism and a retroreflector. It splits an incident light beam into two shearing parallel parts to obtain interference fringe patterns of an imaging target, which is well established as an aid in reducing problems associated with optical alignment and manufacturing precision. Continuously rotating the retroreflector enables the spectrometer to acquire two-dimensional spectral images without spatial scanning. This technology, with a high work efficiency and low complexity, is inherently compact and robust. The effectiveness of the proposed method is demonstrated by the experimental results. PMID:27472640
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 spectrometry for fiber-optic sensor systems
NASA Technical Reports Server (NTRS)
Beheim, Glenn; Tuma, Margaret L.; Sotomayor, Jorge L.; Flatico, Joseph M.
1993-01-01
An integrated-optic Mach-Zehnder interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This type of spectrometer has an advantage over conventional grating spectrometers because it is better suited for use with time-division-multiplexed sensor networks. In addition, this spectrometer has the potential for low cost due to its use of a component that could be manufactured in large quantities for the optical communications industry.
Double passing the Kitt Peak 1-m Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Jennings, D. E.; Hubbard, R.; Brault, J. W.
1985-01-01
Attention is given to a simple technique for performing the conversion of the Kitt Peak 1-m Fourier transform spectrometer's dual input/output optical configuration to a double pass configuration that improves spectral resolution by a factor of 2. The modification is made by placing a flat mirror in the output beam from each cat's eye, retroreflecting the beams back through the cat's eyes to the first beam splitter. A single detector is placed at the second input port, which then becomes the instrument's output.
A high-resolution Fourier-transform infrared spectrometer.
NASA Technical Reports Server (NTRS)
Johnson, H. L.; Forbes, F. F.; Thompson, R. I.; Steinmetz , D. L.; Harris, O.
1973-01-01
We have developed a Fourier-transform infrared spectrometer having a resolution of 0.5/cm over the range of wavelength from 1 to 5.5 microns. It has been used to observe the sun over this wavelength range from a Lear Jet flying at an altitude of 14 km, and to observe a number of stars from the ground, using the 229-cm telescope of the Steward Observatory and the 152-cm aluminum-mirror telescope at the Observatorio Astronomico Nacional in the Sierra de San Pedro Martir, Baja California, Mexico. The solar spectrum is given here, while the ground-based spectra are being published separately.
Beam profile for the Herschel-SPIRE Fourier transform spectrometer.
Makiwa, Gibion; Naylor, David A; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H D
2013-06-01
One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile. PMID:23736346
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.
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).
Wavelength-controlled variable-order optical fractional Fourier transform.
Hennelly, Bryan; Kelly, Damian; Sheridan, John T
2004-03-01
The relationship between optical fractional Fourier transforms (OFRTs) obtained at different wavelengths is derived by use of the ABCD matrix formalism. It is shown that varying the wavelength while retaining the same optical system can be used to control the order of the OFRT. The advantage of this method of varying OFRT order is that no variation in the characteristics of the bulk optics is required. A general experimental verification of the theory is provided by showing the exact equivalence of two OFRT systems of different order when they are replayed using the same input function at different wavelengths. PMID:15005181
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.
Dispersive Fourier transform spectroscopy with gases in the visible region
NASA Astrophysics Data System (ADS)
Kerl, K.; Häusler, H.
1984-05-01
The method of dispersive Fourier transform spectroscopy (DFTS) with gases in the visible wavenumber range is described in detail and compared with the method of scanning-wavelength interferometry (SWI). Measurements of the dispersion of the complex refractive index of gases can be performed successively in several minutes using the same apparatus and gas sample conditions for both methods. In the reported experiments with CH 4 a very simple mirror drive was used. Nevertheless, reasonable results are obtained for the dispersion of the real refractive index of CH 4 in the wavenumber range 16,000 ⩽ σ ⩽ 23,000 cm -1.
Particle field holography data reduction by Fourier transform analysis
NASA Technical Reports Server (NTRS)
Hess, Cecil F.; Trolinger, James D.
1987-01-01
The size distribution of a particle field hologram is obtained with a Fourier transformation of the Fraunhofer diffraction pattern of the reconstructed hologram. Off-axis absorption holograms of particle fields with known characteristics were obtained and analyzed with a commercially available instrument. The mean particle size of the reconstructed hologram was measured with an error of + or - 5 percent, while the distribution broadening was estimated within + or - 15 percent. Small sections of a pulsed laser hologram of a synthetic fuel spray were analyzed with this method thus yielding a spatially resolved size distribution. The method yields fast and accurate automated analysis of particle field holograms.
(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.
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.
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.
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.
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
Integrated optics in an electrically scanned imaging Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Breckinridge, James B. (Inventor); Ocallaghan, Fred G. (Inventor)
1982-01-01
An efficient, lightweight and stable, Fourier transform spectrometer was developed. The mechanical slide mechanism needed to create a path difference was eliminated by the use of retro-reflecting mirrors in a monolithic interferometer assembly in which the mirrors are not at 90 degrees to the propagation vector of the radiation, but rather at a small angle. The resulting plane wave fronts create a double-sided inteferogram of the source irradiance distribution which is detected by a charge-coupled device image sensor array. The position of each CCD pixel in the array is an indication of the path difference between the two retro-reflecting mirrors in the monolithic optical structure. The Fourier transform of the signals generated by the image sensor provide the spectral irradiance distribution of the source. For imaging, the interferometer assembly scans the source of irradiation by moving the entire instrument, such as would occur if it was fixedly mounted to a moving platform, i.e., a spacecraft. During scanning, the entrace slot to the monolithic optical structure sends different pixels to corresponding interferograms detected by adjacent columns of pixels of the image sensor.
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.
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.
Versatile and Sensitive Dual Comb Fourier Transform Spectroscopy
NASA Astrophysics Data System (ADS)
Jacquey, M.; Jacquet, P.; Mandon, J.; Thon, R.; Guelachvili, G.; Hänsch, T. W.; Picqué, N.
2010-06-01
Fourier transform spectroscopy based on time-domain interferences between two slightly detuned frequency comb sources holds much promise for the real-time diagnostic of gaseous, liquid or solid-state samples. In one very recent example, cavity-enhanced absorption spectroscopy with two infrared frequency combs has demonstrated a dramatically enhanced sensitivity, compared to conventional Fourier spectroscopy, with intriguing implications for instantaneous trace gas analysis. It however remains challenging to match continuously the comb and cavity modes across a broad spectral bandwidth during the time of a measurement. An obvious alternative for reaching a long interaction path is a conventional multipass cell. Additionally, differential detection schemes may be devised to increase the dynamic range of the interferometric measurements, thus providing enhanced signal to noise ratio. Experimental demonstrations will be given in the 1.5 μm region with a dual comb set-up based on two Er-doped fiber femtosecond lasers. The versatility and performances of these solutions will be compared to the cavity-enhanced dual comb technique and other state-of-the-art alternatives. P. Jacquet, J. Mandon, B. Bernhardt, R. Holzwarth, G. Guelachvili, T. W. Hänsch, N. Picqué, Frequency Comb Fourier Transform Spectroscopy with kHz Optical Resolution, The Optical Society of America, Washington, DC 2009, paper FMB2 (2009). B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T.W. Hänsch, N. Picqué, Cavity-enhanced dual-comb spectroscopy, Nature Photonics 4, 55-57 (2010),
Coherent 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.
The Empirical Mode Decomposition algorithm via Fast Fourier Transform
NASA Astrophysics Data System (ADS)
Myakinin, Oleg O.; Zakharov, Valery P.; Bratchenko, Ivan A.; Kornilin, Dmitry V.; Artemyev, Dmitry N.; Khramov, Alexander G.
2014-09-01
In this paper we consider a problem of implementing a fast algorithm for the Empirical Mode Decomposition (EMD). EMD is one of the newest methods for decomposition of non-linear and non-stationary signals. A basis of EMD is formed "on-the-fly", i.e. it depends from a distribution of the signal and not given a priori in contrast on cases Fourier Transform (FT) or Wavelet Transform (WT). The EMD requires interpolating of local extrema sets of signal to find upper and lower envelopes. The data interpolation on an irregular lattice is a very low-performance procedure. A classical description of EMD by Huang suggests doing this through splines, i.e. through solving of a system of equations. Existence of a fast algorithm is the main advantage of the FT. A simple description of an algorithm in terms of Fast Fourier Transform (FFT) is a standard practice to reduce operation's count. We offer a fast implementation of EMD (FEMD) through FFT and some other cost-efficient algorithms. Basic two-stage interpolation algorithm for EMD is composed of a Upscale procedure through FFT and Downscale procedure through a selection procedure for signal's points. First we consider the local maxima (or minima) set without reference to the axis OX, i.e. on a regular lattice. The Upscale through the FFT change the signal's length to the Least Common Multiple (LCM) value of all distances between neighboring extremes on the axis OX. If the LCM value is too large then it is necessary to limit local set of extrema. In this case it is an analog of the spline interpolation. A demo for FEMD in noise reduction task for OCT has been shown.
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
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.
Extreme-ultraviolet lensless Fourier-transform holography.
Lee, S H; Naulleau, P; Goldberg, K A; Cho, C H; Jeong, S; Bokor, J
2001-06-01
We demonstrate 100-nm-resolution holographic aerial image monitoring based on lensless Fourier-transform holography at extreme-UV (EUV) wavelengths, using synchrotron-based illumination. This method can be used to monitor the coherent imaging performance of EUV lithographic optical systems. The system has been implemented in the EUV phase-shifting point-diffraction interferometer recently developed at Lawrence Berkeley National Laboratory. Here we introduce the idea of the holographic aerial image-recording technique and present imaging performance characterization results for a 10x Schwarzschild objective, a prototype EUV lithographic optic. The results are compared with simulations, and good agreement is obtained. Various object patterns, including phase-shift-enhanced patterns, have been studied. Finally, the application of the holographic aerial image-recording technique to EUV multilayer mask-blank defect characterization is discussed. PMID:18357280
Discrimination of different Chrysanthemums with Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Liu, Hong-xia; Zhou, Qun; Sun, Su-qin; Bao, Hong-juan
2008-07-01
Use Fourier transform infrared spectroscopy (FT-IR) to analyze simultaneously the main chemical constituents in different solvent extracts of seven kinds of Chrysanthemum samples of different regions. The findings indicate that different Chrysanthemum samples have dissimilar fingerprint characters in FT-IR spectra. Such spectral technique can provide substance structural information of the complicated test samples. According to these spectral fingerprint features, we cannot only identify the main components of different extracts, but also distinguish the origins of the Chrysanthemum samples from different regions easily, which is a troublesome work by existing analytical methods. FT-IR, with the characters of speediness, good repeatability and easy operation, can be used as an effective analytical means to study the complicated system, in our research, the tradition Chinese medicines.
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.
Control Of Cryogenic Fourier Transform Spectrometer Scanning Mirrors
NASA Astrophysics Data System (ADS)
Tripathi, S. S.; Gowrinathan, S.
1981-12-01
The Perkin-Elmer Corporation has designed and built a cryogenically cooled Fourier transform spectrometer for spaceborne applications. In operation, the spectrometer requires mirrors moving at constant velocity in both forward and reverse directions. To maintain efficiency and accuracy, the time taken to reverse direction and the vibration induced due to this reversal must be kept within low limits. This paper deals with the control system design for maintaining a constant velocity during forward and reverse scans and for smooth direction reversals. The systems aspects of the problem are described, and time-domain techniques of modern control theory are applied for optimization of turn-around profile. The analysis leads to a suboptimal design easily implemented by using analog-type components. Test results of satisfactory performance are also included.
Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)
NASA Technical Reports Server (NTRS)
Best, F. A.; Revercomb, H. E.; Bingham, G. E.; Knuteson, R. O.; Tobin, D. C.; LaPorte, D. D.; Smith, W. L.
2001-01-01
The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.
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.
Optical design of the ATMOS Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Abel, I. R.; Reynolds, B. R.; Breckinridge, J. B.; Pritchard, J.
1979-01-01
The optical system design of the ATMOS Fourier transform spectrometer to be operated from Spacelab for the measurement of stratospheric trace molecules is described. The design contains features which can achieve the required fringe contrast of 80% and spectral resolution of 0.02/cm over a spectral range of 2-16 microns. In particular, the design is based on the following features which alleviate the usual requirements for alignment precision: (1) 'cat's eye' mirror configuration in the two arms of the interferometer for retroreflection stability, (2) tilt-compensated system of beamsplitter, compensator, and fold mirrors for wavefront directional stability, (3) paraboloidal 'cat's eye' primary mirror for wavefront stability against shear, (4) rotatable compensator for matching chromatic dispersion, and (5) wedged refractive components to avoid channel spectra due to the Fabry-Perot effect.
Experimental results from an airborne static Fourier transform imaging spectrometer.
Ferrec, Yann; Taboury, Jean; Sauer, Hervé; Chavel, Pierre; Fournet, Pierre; Coudrain, Christophe; Deschamps, Joël; Primot, Jérôme
2011-10-20
A high étendue static Fourier transform spectral imager has been developed for airborne use. This imaging spectrometer, based on a Michelson interferometer with rooftop mirrors, is compact and robust and benefits from a high collection efficiency. Experimental airborne images were acquired in the visible domain. The processing chain to convert raw images to hyperspectral data is described, and airborne spectral images are presented. These experimental results show that the spectral resolution is close to the one expected, but also that the signal to noise ratio is limited by various phenomena (jitter, elevation fluctuations, and one parasitic image). We discuss the origin of those limitations and suggest solutions to circumvent them. PMID:22015418
High throughput full Stokes Fourier transform imaging spectropolarimetry.
Meng, Xin; Li, Jianxin; Xu, Tingting; Liu, Defang; Zhu, Rihong
2013-12-30
A complete full Stokes imaging spectropolarimeter is proposed. Four separate polarized spectra are fed into the Sagnac Fourier transform spectrometer without slit using different angle combinations of the polarized elements. The four polarized spectra are separated without spatial aliasing. And the system has a good performance to resist the instrument noise due to its high light throughput. The mathematical model for the approach is derived and an optimization of the retardance is discussed. For acquiring the four spectra simultaneously, an improved robust polarization modulator using aperture division is outlined. Then the system is discussed in detail including the imaging principle and spectral resolution. Lastly, two proven experiments are carried out and the experimental results in visible light are outlined. PMID:24514802
Multifunctional metasurface lens for imaging and Fourier transform
NASA Astrophysics Data System (ADS)
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-06-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping.
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.
3-D Printed Slit Nozzles for Fourier Transform Microwave Spectroscopy
NASA Astrophysics Data System (ADS)
Dewberry, Chris; Mackenzie, Becca; Green, Susan; Leopold, Ken
2015-06-01
3-D printing is a new technology whose applications are only beginning to be explored. In this report, we describe the application of 3-D printing to the facile design and construction of supersonic nozzles. The efficacy of a variety of designs is assessed by examining rotational spectra OCS and Ar-OCS using a Fourier transform microwave spectrometer with tandem cavity and chirped-pulse capabilities. This work focuses primarily on the use of slit nozzles but other designs have been tested as well. New nozzles can be created for 0.50 or less each, and the ease and low cost should facilitate the optimization of nozzle performance (e.g., jet temperature or cluster size distribution) for the needs of any particular experiment.
Fourier transform infrared phase shift cavity ring down spectrometer
NASA Astrophysics Data System (ADS)
Schundler, Elizabeth; Mansur, David J.; Vaillancourt, Robert; Benedict-Gill, Ryan; Newbry, Scott P.; Engel, James R.; Rentz Dupuis, Julia
2013-05-01
We report on our current status towards the development of a prototype Fourier transform infrared phase shift cavity ring down spectrometer (FTIR-PS-CRDS) system under a U.S. EPA SBIR contract. Our system uses the inherent wavelength-dependent modulation imposed by the FTIR on a broadband thermal source for the phase shift measurement. This spectrally-dependent phase shift is proportional to the spectrally-dependent ring down time, which is proportional to the losses of the cavity including those due to molecular absorption. Our approach is a broadband and spectral range enhancement to conventional CRDS which is typically done in the near IR at a single wavelength; at the same time our approach is a sensitivity enhancement to traditional FTIR owing to the long effective path of the resonant cavity. In this paper we present a summary of the theory including performance projections and the design details of the prototype FTIR-PS-CRDS system.
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.
Highly sensitive Fourier transform spectroscopy with LED sources
NASA Astrophysics Data System (ADS)
Serdyukov, V. I.; Sinitsa, L. N.; Vasil'chenko, S. S.
2013-08-01
It is shown that the use of high luminance LED emitters as a light source for Fourier transform spectrometers permits to enhance their threshold sensitivity in the visible range by orders of magnitude. Using a 2.5 W Edixeon EDEI-1LS3 emitter in the range of 11,350-11,700 cm-1 as a light source for the spectrometer with a 60-cm multipass cell during a 24-h measurement time, we have achieved a signal-to-noise ratio of 4.5 × 104 which corresponds to the minimal detectable absorption coefficient of 1.2 × 10-8 cm-1. Such enhanced sensitivity spectrometer has been used to measure the transition frequencies of CO2 vibrational bands 00051-00001 and 01151-01101 in the range of 11,400-11,500 cm-1.
Indirect Fourier transform in the context of statistical inference.
Muthig, Michael; Prévost, Sylvain; Orglmeister, Reinhold; Gradzielski, Michael
2016-09-01
Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments. PMID:27580204
Motion saliency detection using a temporal fourier transform
NASA Astrophysics Data System (ADS)
Chen, Zhe; Wang, Xin; Sun, Zhen; Wang, Zhijian
2016-06-01
Motion saliency detection aims at detecting the dynamic semantic regions in a video sequence. It is very important for many vision tasks. This paper proposes a new type of motion saliency detection method, Temporal Fourier Transform, for fast motion saliency detection. Different from conventional motion saliency detection methods that use complex mathematical models or features, variations in the phase spectrum of consecutive frames are identified and extracted as the key to obtaining the location of salient motion. As all the calculation is made on the temporal frequency spectrum, our model is independent of features, background models, or other forms of prior knowledge about scenes. The benefits of the proposed approach are evaluated for various videos where the number of moving objects, illumination, and background are all different. Compared with some the state of the art methods, our method achieves both good accuracy and fast computation.
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.
On the abstracted dataflow complexity of Fast Fourier Transforms
Boehm, A.P.W. . Dept. of Computer Science); Hiromoto, R.E.; Kelly, K.A. ); Ashley, J.M. . Dept. of Computer Science)
1992-01-01
In this paper we develop and analyze the simulated performance of codes for the Fast Fourier Transform written in If and targeted for execution on Motorola's dataflow machine Monsoon. The FFT application is of interest because of its computational parallelism, its requirement for global communications, and its array element data dependences. We use the parallel profiling simulator Id World to 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.
Multifunctional metasurface lens for imaging and Fourier transform
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-01-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping. PMID:27272601
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.
Universal calculation formula and calibration method in Fourier transform profilometry
Wen Yongfu; Li Sikun; Cheng Haobo; Su Xianyu; Zhang Qican
2010-12-01
We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.
A study of geometric phase topology using Fourier transform method
NASA Astrophysics Data System (ADS)
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-07-01
Topological aspect of the geometric phase (GP) due to pure polarization projection is studied using the 2D Fourier transform (2D-FT) method. Projection of orthogonal polarization state results in a phase singularity in the 2D parameter space of ellipticity and orientation of polarization ellipse. Projection of its surrounding states results in an accumulation of GP in different amount that form a spiral structure. A half wave plate–quarter wave plate combination is used to generate different polarization states which are projected using a polarizer. The accumulated phase for each orientation of the wave plate is extracted from 2D-FT of the interferogram, obtained by interfering it with a reference beam in a Mach–Zehnder like interferometer.
Multifunctional metasurface lens for imaging and Fourier transform.
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-01-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping. PMID:27272601
Gas emission analysis based on Fourier transformed infrared spectroscopy
NASA Astrophysics Data System (ADS)
Shu, Xiaowen; Zhang, Xiaofu; Lian, Xu; Jin, Hui
2014-12-01
Solar occultation flux (SOF), a new optical technology to detect the gas based on the traditional Fourier transformed infrared spectroscopy (FTIR) developed quickly recently. In this paper, the system and the data analysis is investigated. First a multilayer transmission model of solar radiation is simulated. Then the retrieval process is illustrated. In the proceeding of the data analysis, the Levenberg-Marquardt non-linear square fitting is used to obtain the gas column concentration and the related emission ratio. After the theory certification, the built up system is conducted in a fertilizer plant in Hefei city .The results show SOF is available in the practice and the retrieved gas column concentration can give important information about the pollution emission and dispersion
Denoising and deblurring of Fourier transform infrared spectroscopic imaging data
NASA Astrophysics Data System (ADS)
Nguyen, Tan H.; Reddy, Rohith K.; Walsh, Michael J.; Schulmerich, Matthew; Popescu, Gabriel; Do, Minh N.; Bhargava, Rohit
2012-03-01
Fourier transform infrared (FT-IR) spectroscopic imaging is a powerful tool to obtain chemical information from images of heterogeneous, chemically diverse samples. Significant advances in instrumentation and data processing in the recent past have led to improved instrument design and relatively widespread use of FT-IR imaging, in a variety of systems ranging from biomedical tissue to polymer composites. Various techniques for improving signal to noise ratio (SNR), data collection time and spatial resolution have been proposed previously. In this paper we present an integrated framework that addresses all these factors comprehensively. We utilize the low-rank nature of the data and model the instrument point spread function to denoise data, and then simultaneously deblurr and estimate unknown information from images, using a Bayesian variational approach. We show that more spatial detail and improved image quality can be obtained using the proposed framework. The proposed technique is validated through experiments on a standard USAF target and on prostate tissue specimens.
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.
Application of Fourier transform infrared spectroscopy to examination of documents
NASA Astrophysics Data System (ADS)
Zieba-Palus, Janina; Trzcinska, Beata
1992-03-01
Some 30 samples of writing and wrapping paper were examined using two techniques: transmission (as a KBr disc) and diffuse reflectance. About 15 blue ball pen ink samples were extracted directly from the document by means of a C2H5OH - CHCl3 mixture using an extraction apparatus which enables the separation of impurities (coming from a paper) from the extracted ball pen inks. Infrared spectra were measured on a Digilab Fourier transform spectrometer FTS-15 within the range 400 - 3800 cm-1. Statistical inference based on T2 Hotelling's test to assess the significance of differences observed in IR spectra of samples without examining the origin and essence of those differences was applied. The analysis of the spectral data was performed on a IBM-AT computer.
Sound resonance in pipes with discrete Fourier transform
NASA Astrophysics Data System (ADS)
Aljalal, Abdulaziz M.
2015-09-01
Sound resonance in pipes is investigated using a readily available setup consisting of a pipe, loudspeaker, microphone, and laptop. Discrete Fourier transform is used to extract the amplitude and phase spectra from the recorded sound enabling determination of locations and shapes of resonance peaks accurately. Either white noise signal or sharp pulse signal is used as an excited input sound signal. Both have broad frequency spectra and the difference between them is explored. The shapes of the amplitude and phase spectra are found to be well fitted to the predicted shapes. The pipe is either closed at both ends, closed at only one end, or open at both ends. The speed of sound and the effective location of reflection at the open end are in excellent agreement with theory.
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.
Parameterized Spectral Bathymetric Roughness Using the Nonequispaced Fast Fourier Transform
NASA Astrophysics Data System (ADS)
Fabre, David Hanks
The ocean and acoustic modeling community has specifically asked for roughness from bathymetry. An effort has been undertaken to provide what can be thought of as the high frequency content of bathymetry. By contrast, the low frequency content of bathymetry is the set of contours. The two-dimensional amplitude spectrum calculated with the nonequispaced fast Fourier transform (Kunis, 2006) is exploited as the statistic to provide several parameters of roughness following the method of Fox (1996). When an area is uniformly rough, it is termed isotropically rough. When an area exhibits lineation effects (like in a trough or a ridge line in the bathymetry), the term anisotropically rough is used. A predominant spatial azimuth of lineation summarizes anisotropic roughness. The power law model fit produces a roll-off parameter that also provides insight into the roughness of the area. These four parameters give rise to several derived parameters. Algorithmic accomplishments include reviving Fox's method (1985, 1996) and improving the method with the possibly geophysically more appropriate nonequispaced fast Fourier transform. A new composite parameter, simply the overall integral length of the nonlinear parameterizing function, is used to make within-dataset comparisons. A synthetic dataset and six multibeam datasets covering practically all depth regimes have been analyzed with the tools that have been developed. Data specific contributions include possibly discovering an aspect ratio isotropic cutoff level (less than 1.2), showing a range of spectral fall-off values between about -0.5 for a sandybottomed Gulf of Mexico area, to about -1.8 for a coral reef area just outside of the Saipan harbor. We also rank the targeted type of dataset, the best resolution gridded datasets, from smoothest to roughest using a factor based on the kernel dimensions, a percentage from the windowing operation, all multiplied by the overall integration length.
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.
Fourier Transform Spectroscopy Using Surface Electromagnetic Waves With Aperture Excitation
NASA Astrophysics Data System (ADS)
Gushanskaya, N. Y.; Yakovlev, V. A.; Zhizhin, G. N.; Chesters, M. A.; Parker, S. F.
1989-12-01
The surface electromagnetic wave (SEW) spectroscopy 1 with laser sources of the IR radiat on has demonstrated high sensitivity to the state of the surface. The measurements of SEW attenuation on the sample give the information about the sample conductivity, surface roughness and about the presence of oxide or adsorbate on the metal surface, especially If their absorption bands are in the spectral region where laser lines are available. High sensitivity of modern Fourier transform spectrometers allows to detect SEW excited by broadband source. We have used Fourier transform spectrometers FTS-20V (Digilab) and IFS-113 (Bruker) with liquid nitrogen cooled detectors (Hg-CD-Te). On the metal (Ag, Al, Au, Cu, V, Be) surface SEW were excited using aperture coupling. The experiment is schematically shown on the fig.1. IR radiation from interferometer was focused on the gap between the sample 3 surface and the screen 1 placed at the distance of the order of 100 μm. In such a way on the gap propagating along a metal SEW and bulk radiation above the metal are excited. SEW runs from the aperture coupler to the edge of the sample (this distance could be varied from 2 to 30 mm) and decouples into the bulk radiation on the edge. The second screen 2 above the edge cut the bulk radiation from the aperture coupler. If we change the distance between the screens it is possible to obtain SEW absorption coefficient at different frequences from the output intensity variation. Fig.2 shows SEW propagation length spectra for Au and Cu. For these metals and also for Ag 2 propagation length is proportional to the square of the wavelength as it is predicted by Drude model. For Al such dependence is valid in the oxide transperancy region, in the region 800-1000 cm -1 natural oxide film give absorption band shown on Oxide films are well recognizible also on Be and V. Thermal growth or oxide film was studied (rig.4).
Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups
Guedes, Carlos; Oriti, Daniele; Raasakka, Matti
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.
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
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.
Pulsed Fourier-transform NQR of 14N with a dc SQUID
NASA Astrophysics Data System (ADS)
Hürlimann, M. D.; Pennington, C. H.; Fan, N. Q.; Clarke, John; Pines, A.; Hahn, E. L.
1992-07-01
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 14N 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 T. The measured 14N spin-spin relaxation time is 22+/-2 ms and the spin-lattice relaxation time is 63+/-6 ms.
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
[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
Application of a nonuniform spectral resampling transform in Fourier-transform spectrometry.
Sarkissian, Edwin; Bowman, Kevin W
2003-02-20
We describe a nonuniform spectral resampling transform (NUSRT) that resamples a frequency-scaled spectrum that has been measured by a Fourier-transform spectrometer (FTS). Frequency scaling of a spectrum can arise from measurements made with off-axis detectors and Doppler shift induced by motion of a spaceborne FTS relative to an input radiation source. In addition, a spectrum may need to be rescaled in frequency to match spectral lines for applications such as the retrieval of atmospheric state parameters. The NUSRT is cast as a linear algebraic expression that relates a nonuniformly sampled interferogram to an input spectrum. A polynomial approximation is applied to this expression that reduces the inverse of the NUSRT to a series of Fourier transforms that can be implemented as fast Fourier transforms (FFTs). We show that this NUSRT algorithm requires on the order of 6N log N flops, which reduces the computational cost of rescaling by more than 1 order of magnitude compared with conventional FFT-based Shannon interpolation techniques while comparable accuracy is maintained. PMID:12617230
Single beam Fourier transform digital holographic quantitative phase microscopy
Anand, A. Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Faridian, A.; Pedrini, G.; Osten, W.; Dubey, S. K.; Javidi, B.
2014-03-10
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
Fourier Transform Microwave and Infrared Spectroscopic Investigation of Propiolactone
NASA Astrophysics Data System (ADS)
Chen, Ziqiu; van Wijngaarden, Jennifer
2009-06-01
The pure rotational spectrum of the four-membered ester ring propiolactone (C{_3}H{_4}O{_2}) has been measured in a supersonic jet between 7 and 22 GHz using Fourier transform microwave (FTMW) spectroscopy. For the normal isotopologue, a total of 19 a- and b-type transitions have been recorded. Fifteen transitions due to three different ^{13}C isotopologues have also been observed. The microwave spectrum was analyzed to obtain an improved set of ground state rotational constants in comparison to earlier microwave experiments. The new set of rotational parameters was used to predict the rovibrational band structure of the lowest frequency modes of propiolactone. A total of 12 vibrational band origins have been observed between 400 and 1500 cm^{-1} using the far infrared beamline of the Canadian Light Source coupled to a Bruker IFS125HR spectrometer. The spectra were recorded with a resolution of 0.000969 cm^{-1} and although the intensities of the bands vary, 9 bands are of sufficient quality for complete rovibrational assignment. The progress of the assignment of this rich spectrum will be discussed. D. W. Boone, C O. Britt and J. E. Boggs J. Chem. Phys. 43 (1190), 1965.
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)
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.
Californium-252 plasma desorption with Fourier transform mass spectroscopy
Loo, J.A; Williams, E.R.; Amster, I.J.; Furlong, J.J.P.; Wang, B.H.; McLafferty, F.W.; Chait, B.T.; Field, F.H.
1987-01-01
Plasma desorption (PD) such, as that induced by the 100-MeV fission products of /sup 252/Cf, is a particularly promising ionization method for large molecules, yielding molecular ion species even from trypsin, molecular weight 23,463. Further, with trypsin using nitrocellulose as the substrate, (M + 3H)/sup 3 +/ is the most abundant molecular ion species and (M + 6H)/sup 6 +/ is measurable, which greatly extends the mass values (m) observable for instruments with an upper m/z limit (z = number of charges). However, a 50-..mu..Ci /sup 252/Cf source only produces 55,000 fissions s/sup -1/, yielding ion currents that are generally much too low for scanning instruments. An instrument with unusual capabilities for these, as well as for simultaneous ion detection over a wide mass range, is the Fourier transform (FT) mass spectrometer. With FTMS, Hunt has measured (M + H)/sup +/ ions of cytochrome c, molecular weight 12,384, ionized in an exterior fast-atom-bombardment source. Here the authors describe techniques for obtaining PD/FT mass spectra for a variety of compounds with abundant molecular ion species of masses as high as 2016 (alamethicin).
Fourier transform infrared phase shift cavity ring down spectrometer
NASA Astrophysics Data System (ADS)
Schundler, Elizabeth; Mansur, David J.; Vaillancourt, Robert; Benedict-Gill, Ryan; Newbry, Scott P.; Engel, James R.; Dupuis, Julia Rentz
2014-05-01
OPTRA has developed a Fourier transform infrared phase shift cavity ring down spectrometer (FTIR-PS-CRDS) system under a U.S. EPA SBIR contract. This system uses the inherent wavelength-dependent modulation imposed by the FTIR on a broadband thermal source for the phase shift measurement. This spectrally-dependent phase shift is proportional to the spectrally-dependent ring down time. The spectral dependence of both of these values is introduced by the losses of the cavity including those due to the molecular absorption of the sample. OPTRA's approach allows broadband detection of chemicals across the feature-rich fingerprint region of the long-wave infrared. This represents a broadband and spectral range enhancement to conventional CRDS which is typically done at a single wavelength in the near IR; at the same time the approach is a sensitivity enhancement to traditional FTIR, owing to the long effective path of the resonant cavity. In previous papers1,2, OPTRA has presented a breadboard system aimed at demonstrating the feasibility of the approach and a prototype design implementing performance enhancements based on the results of breadboard testing. In this final paper in the series, we will present test results illustrating the realized performance of the fully assembled and integrated breadboard, thereby demonstrating the utility of the approach.
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.
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.
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.
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.
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.
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.
Fourier transform molecular rotational resonance spectroscopy for reprogrammable chemical sensing
NASA Astrophysics Data System (ADS)
Harris, Brent J.; Pulliam, Robin L.; Neill, Justin L.; Muckle, Matt T.; Reynolds, Roger; Pate, Brooks H.
2015-03-01
Molecular rotational resonance (MRR) spectroscopy gives spectral signatures with high chemical selectivity. At room temperature, the peak intensity of the MRR spectrum occurs in the 100 GHz - 1 THz frequency range for volatile species with mass <= 100 amu. Advances in high-power sub-mm-wave light sources has made it possible to implement time-domain Fourier transform (FT) spectroscopy techniques that are similar to FT nuclear magnetic resonance (FT-NMR) measurements. In these measurements, the gas sample is excited by a short (200 ns) excitation pulse that creates a macroscopic sample polarization. The electric field of the subsequent transient molecular emission is detected using a heterodyne receiver and a high-speed digitizer. FT-MRR spectroscopy offers speed and sensitivity improvements over absorption spectroscopy. For chemical analysis, FT-MRR spectrometers combine the benefits of broad chemical coverage typical of gas chromatography - mass spectrometry (GC-MS) instruments and the direct measurement capabilities of infrared gas sensors all in a reprogrammable platform. Pulse sequence measurements can be implemented for advanced spectroscopic analysis. Trace level quantitation of volatile species at ppbv concentration can be performed on the time scale of a minute. In cases where the sample is a complex mixture, a double-resonance pulse sequence can be used to achieve chemical selectivity even in cases where spectral overlap occurs. These measurement capabilities are illustrated using the application of FT-MRR spectroscopy to residual solvent analysis of pharmaceutical products.
Fourier transform optical profilometry using fiber optic Lloyd's mirrors.
Kart, Türkay; Kösoğlu, Gülşen; Yüksel, Heba; İnci, 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
Imaging Fourier Transform Spectro-polarimetry in the Infrared
NASA Astrophysics Data System (ADS)
Jurgenson, C. A.; Stencel, R. E.; Stout, J.
2004-12-01
Imaging spectro-polarimetry has the capability to trace polarization changes in dust grains throughout an extended region of interest. An instrument that has the capability to achieve moderately high resolution (R = 2000 at 10 microns) via a stepping Fourier transform spectrometer, while preserving imaging polarimetry capabilities (TNTCAM2, Jurgenson et al. 2003), is set to achieve first light during early 2005. Motion control of the interferometer, as well as array control/readout is accomplished via an FPGA card programmed in LabVIEW(c). Mid-IR polarization studies are useful in approximating grain shapes and sizes in dusty environments. Correlation studies between mid and near-IR features can be used to test the core-mantle arrangement of grain growth. Polarization analysis is currently only possible between 8-13 microns, but the interferometer, as well as TNTCAM2, can operate at selected bandpasses in the near-IR region. A wire grid and waveplate would need to be purchased for work in the near-IR. Laboratory calibration results, both spectral and polarization, are reported. We are seeking collaborators in shared-risk science with this instrument, so please contact the authors if interested. Sigma Xi Grants In Aid of Research as well as the estate of William Herschel Womble provided funding for this endeavor.
Fourier transform infrared spectroscopy (FTIR) of laser-irradiated cementum
NASA Astrophysics Data System (ADS)
Rechmann, Peter; White, Joel M.; Cecchini, Silvia C. M.; Hennig, Thomas
2003-06-01
Utilizing Fourier Transform Infrared Spectroscopy (FTIR) in specular reflectance mode chemical changes of root cement surfaces due to laser radiation were investigated. A total of 18 samples of root cement were analyzed, six served as controls. In this study laser energies were set to those known for removal of calculus or for disinfection of periodontal pockets. Major changes in organic as well as inorganic components of the cementum were observed following Nd:YAG laser irradiation (wavelength 1064 nm, pulse duration 250 μs, free running, pulse repetition rate 20 Hz, fiber diameter 320 μm, contact mode; Iskra Twinlight, Fontona, Slovenia). Er:YAG laser irradiation (wavelength 2.94 μm, pulse duration 250 μs, free running, pulse repetition rate 6 Hz, focus diameter 620 μm, air water cooling 30 ml/min; Iskra Twinlight, Fontona, Slovenia) significantly reduced the Amid bands due to changes in the organic components. After irradiation with a frequency doubled Alexandrite laser (wavelength 377 nm, pulse duration 200 ns, q-switched, pulse repetition rate 20 Hz, beam diameter 800 μm, contact mode, water cooling 30 ml/min; laboratory prototype) only minimal reductions in the peak intensity of the Amide-II band were detected.
SAR-based vibrometry using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Campbell, Justin B.; Wang, Qi; Ade-Bello, Jelili; Caudana, Humberto; Trujillo, Nicole B.; Bhatta, Ishwor; Dunkel, Ralf; Atwood, Thomas; Doerry, Armin; Gerstle, Walter H.; Santhanam, Balu; Hayat, Majeed M.
2015-05-01
A fundamental assumption when applying Synthetic Aperture Radar (SAR) to a ground scene is that all targets are motionless. If a target is not stationary, but instead vibrating in the scene, it will introduce a non-stationary phase modulation, termed the micro-Doppler effect, into the returned SAR signals. Previously, the authors proposed a pseudosubspace method, a modification to the Discrete Fractional Fourier Transform (DFRFT), which demonstrated success for estimating the instantaneous accelerations of vibrating objects. However, this method may not yield reliable results when clutter in the SAR image is strong. Simulations and experimental results have shown that the DFRFT method can yield reliable results when the signal-to-clutter ratio (SCR) > 8 dB. Here, we provide the capability to determine a target's frequency and amplitude in a low SCR environment by presenting two methods that can perform vibration estimations when SCR < 3 dB. The first method is a variation and continuation of the subspace approach proposed previously in conjunction with the DFRFT. In the second method, we employ the dual-beam SAR collection architecture combined with the extended Kalman filter (EKF) to extract information from the returned SAR signals about the vibrating target. We also show the potential for extending this SAR-based capability to remotely detect and classify objects housed inside buildings or other cover based on knowing the location of vibrations as well as the vibration histories of the vibrating structures that house the vibrating objects.
Fourier transform infrared spectroscopic analysis of cell differentiation
NASA Astrophysics Data System (ADS)
Ishii, Katsunori; Kimura, Akinori; Kushibiki, Toshihiro; Awazu, Kunio
2007-02-01
Stem cells and its differentiations have got a lot of attentions in regenerative medicine. The process of differentiations, the formation of tissues, has become better understood by the study using a lot of cell types progressively. These studies of cells and tissue dynamics at molecular levels are carried out through various approaches like histochemical methods, application of molecular biology and immunology. However, in case of using regenerative sources (cells, tissues and biomaterials etc.) clinically, they are measured and quality-controlled by non-invasive methods from the view point of safety. Recently, the use of Fourier Transform Infrared spectroscopy (FT-IR) has been used to monitor biochemical changes in cells, and has gained considerable importance. The objective of this study is to establish the infrared spectroscopy of cell differentiation as a quality control of cell sources for regenerative medicine. In the present study, as a basic study, we examined the adipose differentiation kinetics of preadipocyte (3T3-L1) and the osteoblast differentiation kinetics of bone marrow mesenchymal stem cells (Kusa-A1) to analyze the infrared absorption spectra. As a result, we achieved to analyze the adipose differentiation kinetics using the infrared absorption peak at 1739 cm-1 derived from ester bonds of triglyceride and osteoblast differentiation kinetics using the infrared absorption peak at 1030 cm-1 derived from phosphate groups of calcium phosphate.
Fourier transform infrared spectroscopy in physics laboratory courses
NASA Astrophysics Data System (ADS)
Möllmann, K.-P.; Vollmer, M.
2013-11-01
Infrared spectrometry is one of the most important tools in the field of spectroscopic analysis. This is due to the high information content of spectra in the so-called spectroscopic fingerprint region, which enables measurement not only of gases, but also of liquids and solids. Today, infrared spectroscopy is almost completely dominated by Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy is able to detect minute quantities in the ppm and ppb ranges, and the respective analyses are now standard tools in science as well as industry. Therefore FTIR spectroscopy should be taught within the standard curriculum at university to physicists and engineers. Here we present respective undergraduate laboratory experiments designed for students at the end of their third year. Experiments deal first with understanding the spectrometer and second with recording and analysing spectra. On the one hand, transmission spectra of gases are treated which relate to environmental analytics (being probably the most prominent and well-known examples), and on the other hand, the focus is on the transmission and reflection spectra of solids. In particular, silicon wafers are studied—as is regularly done in the microelectronics industry—in order to characterize their thickness, oxygen content and phonon modes.
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).
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.
A new hybrid algorithm for computing a fast discrete Fourier transform
NASA Technical Reports Server (NTRS)
Reed, I. S.; Truong, T. K.
1979-01-01
In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.
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
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.
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.
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.
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.
Fourier Transform Spectrometer measurements of Atmospheric Carbon Dioxide and Methane
NASA Astrophysics Data System (ADS)
Kivi, Rigel; Heikkinen, Pauli; Chen, Huilin; Hatakka, Juha; Laurila, Tuomas
2016-04-01
Ground based remote sensing measurements of column CO2 and CH4 using Fourier Transform Spectrometers (FTS) within the Total Carbon Column Observing Network (TCCON) are known for high precision and accuracy. These measurements are performed at various locations globally and they have been widely used in carbon cycle studies and validation of space born measurements. The relevant satellite missions include the Orbiting Carbon Observatory-2 (OCO-2) by the National Aeronautics and Space Administration (NASA); the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) by the European Space Agency (ESA); the Greenhouse gases Observing SATellite (GOSAT) by the Japan Aerospace Exploration Agency (JAXA) and the upcoming Sentinel-5 Precursor mission, which is an ESA mission and scheduled for launch in 2016. Results of the column CO2 and CH4 measurements at Sodankylä in northern Finland (at 67.4° N, 26.6° E) are reported in this study. The measurements have been performed on regular basis since the beginning of the program in early 2009. We also present evaluation of the data quality of the ground based measurements and comparisons with the available satellite based retrievals. In case of comparisons between the GOSAT and ground based retrievals of CO2 and CH4 no significant biases were found. Sodankylä is one of the northernmost stations in the TCCON network. However, the data coverage has been relatively good thanks to the progress towards automation of the FTS measurement system. At Sodankylä the retrievals have been also compared with the balloon borne AirCore measurements at the site. AirCore sampling system is directly related to the World Meteorological Organization in situ trace gas measurement scales. The balloon platform allows sampling in both stratosphere and troposphere, which is a benefit, compared to the aircraft in situ measurements.
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
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.
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.
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.
Dual Comb Fourier Transform Spectroscopy in the Green Region
NASA Astrophysics Data System (ADS)
Knize, R. J.; Bernhardt, B.; Picqué, N.; Hänsch, T. W.
2010-06-01
Laser combs in combination with other advancing tools of laser science, nonlinear optics, photonics, and electronic signal processing have the potential to vastly enhance the range and capabilities of molecular laser spectroscopy. The high versatility of frequency comb sources can indeed harness new techniques for ultra-rapid and ultra-sensitive recording of complex molecular spectra. The recent proof-of-principle demonstrations of dual comb Fourier transform spectroscopy have mostly been carried out in the near-infrared region, around 1.0 and 1.5 μm. The mode-locked ytterbium- or erbium-doped fiber femtosecond laser systems emitting in this range indeed require few adjustment thanks to their guided light and permit reliable unattended operation. With expanded wavelength coverage and continued improvements in speed and sensitivity, dual comb spectroscopy should find use as a novel, time-domain spectroscopic analytical tool. As far as molecular spectroscopy is concerned, the mid-infrared and visible-ultraviolet wavelength regions show both the potential for specificity and sensitivity for tracing molecules. In particular, the visible-ultraviolet region complements the mid-infrared molecular fingerprint range, as it provides access to many electronic transitions, in particular belonging to reactive species. In this contribution, we report on our progress in the implementation of dual comb spectroscopy in the 520 nm green region. We present preliminary results on a powerful new sensitive ultra-rapid tool for linear rovibronic absorption spectroscopy, based on frequency-doubled ytterbium-doped fiber lasers and we discuss its intriguing prospects for spectroscopy of short lived transient species.
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).
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.
Pisani, Marco; Zucco, Massimo
2009-05-11
An imaging spectrometer based on a Fabry-Perot interferometer is presented. The Fabry-Perot interferometer scans the mirror distance up to contact and the intensity modulated light signal is transformed using a Fourier Transform based algorithm, as the Michelson based Fourier Transform Spectrometers does. The resulting instrument has the advantage of a compact, high numerical aperture, high luminosity hyperspectral imaging device. Theory of operation is described along with one experimental realization and preliminary results. PMID:19434165
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.
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
Midwave infrared imaging Fourier transform spectrometry of combustion plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.
A midwave infrared (MWIR) imaging Fourier transform spectrometer (IFTS) was used to successfully capture and analyze hyperspectral imagery of combustion plumes. Jet engine exhaust data from a small turbojet engine burning diesel fuel at a low rate of 300 cm3/min was collected at 1 cm -1 resolution from a side-plume vantage point on a 200x64 pixel window at a range of 11.2 meters. Spectral features of H2O, CO, and CO2 were present, and showed spatial variability within the plume structure. An array of thermocouple probes was positioned within the plume to aid in temperature analysis. A single-temperature plume model was implemented to obtain spatially-varying temperatures and plume concentrations. Model-fitted temperatures of 811 +/- 1.5 K and 543 +/- 1.6 K were obtained from plume regions in close proximity to thermocouple probes measuring temperatures of 719 K and 522 K, respectively. Industrial smokestack plume data from a coal-burning stack collected at 0.25 cm-1 resolution at a range of 600 meters featured strong emission from NO, CO, CO2, SO 2, and HCl in the spectral region 1800-3000 cm-1. A simplified radiative transfer model was employed to derive temperature and concentrations for clustered regions of the 128x64 pixel scene, with corresponding statistical error bounds. The hottest region (closest to stack centerline) was 401 +/- 0.36 K, compared to an in-stack measurement of 406 K, and model-derived concentration values of NO, CO2, and SO2 were 140 +/- 1 ppmV, 110,400 +/- 950 ppmV, and 382 +/- 4 ppmV compared to in-stack measurements of 120 ppmV (NOx), 94,000 ppmV, and 382 ppmV, respectively. In-stack measurements of CO and HCl were not provided by the stack operator, but model-derived values of 19 +/- 0.2 ppmV and 111 +/- 1 ppmV are reported near stack centerline. A deployment to Dugway Proving Grounds, UT to collect hyperspectral imagery of chemical and biological threat agent simulants resulted in weak spectral signatures from several species. Plume
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
NASA Astrophysics Data System (ADS)
Grotendorst, Johannes; Otto Steinborn, E.
1985-11-01
We analyze the analytical and numerical properties of the hitherto known formulas of the Fourier transform of a two-center product of exponentially declining functions (exponential-type functions, ETFs) which are derived with the help of the Fourier convolution theorem and Feynman's identity. In detail, we consider B functions which are a special class of ETFs having advantageous properties under Fourier transformation. Other ETFs (orbitals) can be expressed in terms of B functions by linear combinations. In our derivations we use the properties of the differential operator Ylm(▽) specifying a solid harmonic whose argument is the nabla operator ∂/∂ r instead of the vector r in order to generate multicenter integrals over nonscalar functions from integrals over scalar functions. Applying the generating differential operator Ylm(Λ) we obtain a recently derived new formula for the Fourier transform of a two-center product of B functions in a much more straightforward manner. Furthermore, we present an efficient procedure to compute this new formula which is valid for arbitrary quantum numbers and exponential parameters and report various numerical test values.
Infrared Fourier transform spectroscopy of C-13 methanol
NASA Astrophysics Data System (ADS)
Predoi-Cross, Adriana
This work is a high-resolution Fourier transform infrared study of three vibrational states of C-13 methanol. We have investigated the regions from 1000-1400 cm-1 at 0.002 cm-1 resolution and from 1850-1950 cm-1 at 0.0028 cm-1 resolution. The vibrational modes covered by this study are: the CH3-Rocking band, the OH-Bending band and the first CO-Stretch overtone band. This study has led to (i) determination of excited-state molecular constants, (ii) characterization of a variety of interactions coupling the different vibrational modes, and (iii) identification of a number of reported far-infrared (FIR) lasing transitions and the prediction of new FIR laser emissions. The weak CH3-Rocking band is found to have principally a parallel character and has a double-peaked Q-branch and widely spread sub-bands due to a 28% increase in the torsional barrier height as compared to the ground state. We have assigned thirty ground torsional sub-bands and about ten sub-bands for the first excited torsional state. These sub-bands have been fitted to J(J+1) power-series expansions to obtain the sub- band origins and state-specific expansion parameters. The asymmetry splitting coefficients have also been determined. In our spectrum we have observed the effects of Coriolis coupling between rocking (K - 1) and CO- Stretching K levels for K values from 6 to 10. Other interesting interactions encountered are J-localized perturbations due to level crossing resonances with the CO-Stretch state. Two far-infrared laser emissions reported for the 10R(26) CO2 pump system are the result of a ΔK = 3 interaction. The OH-Bending band is widely spread with Q-subbranches grouped in two peaks at about 1312 cm-1 and 1338 cm-1. The OH-Bending state strongly interacts with the first excited torsional CH3-Rocking state and we have observed several 'extra' forbidden sub-bands arising from intensity borrowing from the allowed interacting sub-bands. The asymmetry splitting of the K = 2 doublet was found to
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)
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)
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).
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...
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)
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.
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,...
Forecasting performance of denoising signal by Wavelet and Fourier Transforms using SARIMA model
NASA Astrophysics Data System (ADS)
Ismail, Mohd Tahir; Mamat, Siti Salwana; Hamzah, Firdaus Mohamad; Karim, Samsul Ariffin Abdul
2014-07-01
The goal of this research is to determine the forecasting performance of denoising signal. Monthly rainfall and monthly number of raindays with duration of 20 years (1990-2009) from Bayan Lepas station are utilized as the case study. The Fast Fourier Transform (FFT) and Wavelet Transform (WT) are used in this research to find the denoise signal. The denoise data obtained by Fast Fourier Transform and Wavelet Transform are being analyze by seasonal ARIMA model. The best fitted model is determined by the minimum value of MSE. The result indicates that Wavelet Transform is an effective method in denoising the monthly rainfall and number of rain days signals compared to Fast Fourier Transform.
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
Gasoline analysis and brand identification using a static Fourier-transform ultraviolet spectrometer
NASA Astrophysics Data System (ADS)
Steers, Darren; Gerrard, Carl; Hirst, Bill; Sibbett, Wilson; Padgett, Miles J.
1999-11-01
The ultraviolet (UV) absorption spectra of several gasoline samples are measured using a compact static Fourier-transform (FT) spectrometer. The FT-UV spectrometer is constructed from crystalline quartz Wollaston prisms and polarizers fabricated from beta barium borate to form an interferogram in the spatial domain. The interferogram is recorded with a UV-sensitive detector array and Fourier transformed to yield spectra. Investigation using principal component analysis enables the identification of important gasoline properties such as origin.
Using nonequispaced fast Fourier transformation to process optical coherence tomography signals
NASA Astrophysics Data System (ADS)
Hillmann, Dierck; Hüttmann, Gereon; Koch, Peter
2009-07-01
In OCT imaging the spectra that are used for Fourier transformation are in general not acquired linearly in k-space. Therefore one needs to apply an algorithm to re-sample the data and finally do the Fourier Transformation to gain depth information. We compare three algorithms (Non-Equispaced DFT, interpolated FFT and Non-Equispaced FFT) for this purpose in terms of speed and accuracy. The optimal algorithm depends on the OCT device (speed, SNR) and the object.
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.
Time-domain surface profile imaging via a hyperspectral Fourier transform spectrometer.
Dupuis, Julia Rentz; Unlü, M Selim
2008-06-15
We describe a method for time-domain surface profile measurements via white-light reflection spectroscopy using a hyperspectral Fourier transform spectrometer (HS-FTS). This technique measures the frequency of the spectral modulation of reflected light from a multilayer optical surface and reports the spatially resolved optical thickness. Owing to the Fourier relationship, the Fourier transform spectrometer manifests this spectral modulation as temporal satellites in interferogram space. We show that measurement of the positions of these satellites can be used to reconstruct the optical thickness profile over a surface using the HS-FTS. PMID:18552962
Zheng, Y. |; Shirley, D.A.
1995-02-01
The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.
Luo, David; Kudenov, Michael W
2016-05-16
Systematic phase errors in Fourier transform spectroscopy can severely degrade the calculated spectra. Compensation of these errors is typically accomplished using post-processing techniques, such as Fourier deconvolution, linear unmixing, or iterative solvers. This results in increased computational complexity when reconstructing and calibrating many parallel interference patterns. In this paper, we describe a new method of calibrating a Fourier transform spectrometer based on the use of artificial neural networks (ANNs). In this way, it is demonstrated that a simpler and more straightforward reconstruction process can be achieved at the cost of additional calibration equipment. To this end, we provide a theoretical model for general systematic phase errors in a polarization birefringent interferometer. This is followed by a discussion of our experimental setup and a demonstration of our technique, as applied to data with and without phase error. The technique's utility is then supported by comparison to alternative reconstruction techniques using fast Fourier transforms (FFTs) and linear unmixing. PMID:27409947
Fourier Transform Methods Applied To The Analysis Of Microphotometric Images Of Histologic Sections
NASA Astrophysics Data System (ADS)
Dytch, Harvey E.; Wied, George L.
1989-06-01
Implementation of one-dimensional Fourier transform techniques for the analysis of histologic sections is discussed, as is the motivation for their use. Features of the frequency domain representation derived by such a transform are shown to be related to several important diagnostic clues. The interpretation of the Fourier magnitude spectrum in histologically relevant terms is examined by means of Fourier transforms of idealized tissue simulations. Some of the perturbations of these ideal spectra produced by biologic reality are discussed. Three classic types of cervical epithelial tissue are modeled, and their representation as Fourier magnitude spectra interpreted in the light of the previous results: characteristic frequency domain signatures are obtained for each. It is concluded that these techniques may provide diagnostically important objective measures, and may be applied to otherwise intractable histologic specimens with crowded and overlapping nuclei.
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.
NASA Astrophysics Data System (ADS)
Zhao, Chengliang; Huang, Kaikai; Lu, Xuanhui
2010-03-01
The properties of Bessel-Gaussian beams (BGBs) and Bessel beams (BBs) propagating through a fractional Fourier transform (FRT) optical system have been investigated. The analytical transformation formulae for BBs and BGBs propagation through a FRT optical system are derived based on definition of the FRT in the cylindrical coordinate system. By using the derived formula, numerical examples are illustrated.
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
Adaptive motion mapping in pancreatic SBRT patients using Fourier transforms
Jones, Bernard L.; Schefter, Tracey; Miften, Moyed
2015-01-01
Background and Purpose Recent studies suggest that 4DCT is unable to accurately measure respiratory-induced pancreatic tumor motion. In this work, we assessed the daily motion of pancreatic tumors treated with SBRT, and developed adaptive strategies to predict and account for this motion. Materials and Methods The daily motion trajectory of pancreatic tumors during CBCT acquisition was calculated using a model which reconstructs the instantaneous 3D position in each 2D CBCT projection image. We developed a metric (termed “Spectral Coherence,” SC) based on the Fourier frequency spectrum of motion in the SI direction, and analyzed the ability of SC to predict motion-based errors and classify patients according to motion characteristics. Results The amplitude of daily motion exceeded the predictions of pre-treatment 4DCT imaging by an average of 3.0 mm, 2.3 mm, and 3.5 mm in the AP/LR/SI directions. SC was correlated with daily motion differences and tumor dose coverage. In a simulated adaptive protocol, target margins were adjusted based on SC, resulting in significant increases in mean target D95, D99, and minimum dose. Conclusions Our Fourier-based approach differentiates between consistent and inconsistent motion characteristics of respiration and correlates with daily motion deviations from pre-treatment 4DCT. The feasibility of an SC-based adaptive protocol was demonstrated, and this patient-specific respiratory information was used to improve target dosimetry by expanding coverage in inconsistent breathers while shrinking treatment volumes in consistent breathers. PMID:25890573
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
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
Fourier and Hadamard transform spectrometers - A limited comparison. II
NASA Technical Reports Server (NTRS)
Harwit, M.; Tai, M. H.
1977-01-01
A mathematical approach was used to compare interferometric spectrometers and Hadamard transform spectrometers. The principle results are reported, noting that the simple Hadamard spectrometer encodes more efficiently than a Michelson interferometer which, in turn, encodes less efficiently than is usually acknowledged. Hirschfeld's (1977) major objections to these findings are discussed, although it is noted that none of his objections is supported by evidence.
Grid-Based Fourier Transform Phase Contrast Imaging
NASA Astrophysics Data System (ADS)
Tahir, Sajjad
Low contrast in x-ray attenuation imaging between different materials of low electron density is a limitation of traditional x-ray radiography. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One recently developed phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a technique recently demonstrated by Bennett et al. that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 microm spot Mo source, a CCD with 22 microm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the grid in the Fourier domain. A Matlab code was written to perform the image processing. For the first time, the effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the window function type used to separate the harmonics, and the window widths, were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and new methods investigated to form improved phase contrast images.
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
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.
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
Fast Fourier and Wavelet Transforms for Wavefront Reconstruction in Adaptive Optics
Dowla, F U; Brase, J M; Olivier, S S
2000-07-28
Wavefront reconstruction techniques using the least-squares estimators are computationally quite expensive. We compare wavelet and Fourier transforms techniques in addressing the computation issues of wavefront reconstruction in adaptive optics. It is shown that because the Fourier approach is not simply a numerical approximation technique unlike the wavelet method, the Fourier approach might have advantages in terms of numerical accuracy. However, strictly from a numerical computations viewpoint, the wavelet approximation method might have advantage in terms of speed. To optimize the wavelet method, a statistical study might be necessary to use the best basis functions or ''approximation tree.''
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){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)].
NASA Technical Reports Server (NTRS)
Munoz, R. M. (Inventor)
1974-01-01
An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. The original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications.
System design of Fourier transform imaging spectrometer using tunable lateral shearing splitter
NASA Astrophysics Data System (ADS)
Meng, Xin; Li, Jianxin; Bai, Caixun; Zhu, Rihong
2015-04-01
The Fourier transform spectrometer without slit has the advantages of high radiation throughput and high spatial resolution. It can be used for detecting more details of the spectral and spatial information. We present the initial structure of the collimator and objective based on the analysis of the principle of the Fourier transform spectrometer. Then the collimator and objective are optimized by Zemax. The MTF of the cut-off frequency is great than 0.7. The tunable lateral shearing splitter is used as the interferometer, which makes the system more compact compared with the system using Sagnac lateral shearing splitter. The method to calculate the geometric dimension of the splitter is presented. Then the complete Fourier transform spectrometer is designed. The MTF of the cut-off frequency is great than 0.6. And the largest RMS of the spot is less than 6μm.
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
Periodic artifact reduction in Fourier transforms of full field atomic resolution images.
Hovden, Robert; Jiang, Yi; Xin, Huolin L; Kourkoutis, Lena F
2015-04-01
The discrete Fourier transform is among the most routine tools used in high-resolution scanning/transmission electron microscopy (S/TEM). However, when calculating a Fourier transform, periodic boundary conditions are imposed and sharp discontinuities between the edges of an image cause a cross patterned artifact along the reciprocal space axes. This artifact can interfere with the analysis of reciprocal lattice peaks of an atomic resolution image. Here we demonstrate that the recently developed Periodic Plus Smooth Decomposition technique provides a simple, efficient method for reliable removal of artifacts caused by edge discontinuities. In this method, edge artifacts are reduced by subtracting a smooth background that solves Poisson's equation with boundary conditions set by the image's edges. Unlike the traditional windowed Fourier transforms, Periodic Plus Smooth Decomposition maintains sharp reciprocal lattice peaks from the image's entire field of view. PMID:25597865
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.
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.
NASA Astrophysics Data System (ADS)
He, Qian; Wang, Guangping; Wu, Jingli; Li, Junwei
2014-11-01
As the impact of the instrument internal error, external interference and other factors, the interferogram measured by Fourier transform spectrometer is asymmetric, result in the complex outcome after Fourier transform. Currently, most radiometric calibration method used for Fourier transform spectrometer is usually based on real spectrums, which is converted from the above complex spectrum by calculating magnitude value or make the phase correction first. Proceed from error sources and mechanisms of the Fourier transform spectrometer, we propose a multi-point radiometric calibration method based on complex spectral data to improve the processing efficiency and accuracy, which is obtained by the original interferogram via Fourier transform. We solving the instrument response function include linear gain and offset by complex spectrum above to calculate complex spectral radiance. Compared with the traditional method based on real spectrum, the present efficient method does not limited to real spectrum and the phase correction is not required. In this paper, we use BOMEM's MR304 Fourier transform infrared spectrometer and the DCN1000N3 blackbody made by HGH Infrared Systems to carry out the radiation calibration experiment in laboratory. The results show that, the amplitude of complex radiance spectrum obtained by this method has a high consistency with the theoretical value, while the extra imaginary spectrum is similar with the difference between results and theoretical value in absolute value and trends. It proved that, this multi-point radiometric calibration method by using the amplitude of complex spectral data is highly reliable; meanwhile, the imaginary spectrum can reflect the calibration error very well and offer a new technical approach for accuracy evaluation research.
Quantum Computation and Quantum Information
NASA Astrophysics Data System (ADS)
Nielsen, Michael A.; Chuang, Isaac L.
2010-12-01
Part I. Fundamental Concepts: 1. Introduction and overview; 2. Introduction to quantum mechanics; 3. Introduction to computer science; Part II. Quantum Computation: 4. Quantum circuits; 5. The quantum Fourier transform and its application; 6. Quantum search algorithms; 7. Quantum computers: physical realization; Part III. Quantum Information: 8. Quantum noise and quantum operations; 9. Distance measures for quantum information; 10. Quantum error-correction; 11. Entropy and information; 12. Quantum information theory; Appendices; References; Index.
[Research on spatially modulated Fourier transform imaging spectrometer data processing method].
Huang, Min; Xiangli, Bin; Lü, Qun-Bo; Zhou, Jin-Song; Jing, Juan-Juan; Cui, Yan
2010-03-01
Fourier transform imaging spectrometer is a new technic, and has been developed very rapidly in nearly ten years. The data catched by Fourier transform imaging spectrometer is indirect data, can not be used by user, and need to be processed by various approaches, including data pretreatment, apodization, phase correction, FFT, and spectral radicalization calibration. No paper so far has been found roundly to introduce this method. In the present paper, the author will give an effective method to process the interfering data to spectral data, and with this method we can obtain good result. PMID:20496726
NASA Astrophysics Data System (ADS)
Goda, Keisuke; Tsia, Kevin K.; Jalali, Bahram
2008-09-01
Dispersive Fourier transformation is a powerful technique in which the spectrum of an optical pulse is mapped into a time-domain waveform using chromatic dispersion. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector. This simplifies the system and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcode reader and displacement sensor that employs internally amplified dispersive Fourier transformation. This technique amplifies and simultaneously maps the spectrally encoded barcode into a temporal waveform. It achieves a record acquisition speed of 25MHz—four orders of magnitude faster than the current state of the art.
The Los Alamos Fourier-Transform Spectrometer: Applications To Molecular Spectroscopy
NASA Astrophysics Data System (ADS)
Palmer, Byron A.; McDowell, Robert S.
1989-12-01
We outline design considerations and operating characteristics of the Los Alamos Fourier-transform spectrometer, a state-of-the-art instrument operating from 200 nm to 20 μm with a resolution of 0.0026 cm-1 and very high wave number and intensity accuracy. Recent work in molecular spectroscopy carried out with this instrument will be discussed, including N2+ spectra obtained in inductively-coupled plasmas; high-temperature spectra of diatomic molecules of astrophysical interest; high-resolution rovibrational fine structure; and Fourier-transform Raman spectroscopy of species in expansion-cooled gases.
The Los Alamos Fourier-transform spectrometer: Applications to molecular spectroscopy
NASA Astrophysics Data System (ADS)
Palmer, Byron A.; McDowell, Robin S.
The design considerations and operating characteristics are outlined for the Los Alamos Fourier transform spectrometer, a state-of-the-art instrument operating from 200 nm to 20 micrometer with a resolution of 0.0026/cm and very high wave number and intensity accuracy. Recent work in molecular spectroscopy carried out with this instrument is discussed, including N2(+) spectra obtained in inductively-coupled plasmas; high-temperature spectra of diatomic molecules of astrophysical interest; high-resolution rovibrational fine structure; and Fourier transform Raman spectroscopy of species in expansion-cooled gases.
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.
Fast 3D shape measurement using Fourier transform profilometry without phase unwrapping
NASA Astrophysics Data System (ADS)
Song, Kechen; Hu, Shaopeng; Wen, Xin; Yan, Yunhui
2016-09-01
This paper presents a novel, simple, yet fast 3D shape measurement method using Fourier transform profilometry. Different from the conventional Fourier transform profilometry, this proposed method introduces the binocular stereo vision and employs two image pairs (i.e., original image pairs and fringe image pairs) to restructure 3D shape. In this proposed method, instead of phase unwrapping algorithm, a coarse disparity map is adopted as a constraint condition to realize phase matching using wrapped phase. Since the local phase matching and sub-pixel disparity refinement are proposed to obtain high measuring accuracy, high-quality phase is not required. The validity of the proposed method is verified by experiments.
Gridding and fast Fourier transformation on non-uniformly sparse sampled multidimensional NMR data.
Jiang, Bin; Jiang, Xianwang; Xiao, Nan; Zhang, Xu; Jiang, Ling; Mao, Xi-an; Liu, Maili
2010-05-01
For multidimensional NMR method, indirect dimensional non-uniform sparse sampling can dramatically shorten acquisition time of the experiments. However, the non-uniformly sampled NMR data cannot be processed directly using fast Fourier transform (FFT). We show that the non-uniformly sampled NMR data can be reconstructed to Cartesian grid with the gridding method that has been wide applied in MRI, and sequentially be processed using FFT. The proposed gridding-FFT (GFFT) method increases the processing speed sharply compared with the previously proposed non-uniform Fourier Transform, and may speed up application of the non-uniform sparse sampling approaches. PMID:20236843
Gridding and fast Fourier transformation on non-uniformly sparse sampled multidimensional NMR data
NASA Astrophysics Data System (ADS)
Jiang, Bin; Jiang, Xianwang; Xiao, Nan; Zhang, Xu; Jiang, Ling; Mao, Xi-an; Liu, Maili
2010-05-01
For multidimensional NMR method, indirect dimensional non-uniform sparse sampling can dramatically shorten acquisition time of the experiments. However, the non-uniformly sampled NMR data cannot be processed directly using fast Fourier transform (FFT). We show that the non-uniformly sampled NMR data can be reconstructed to Cartesian grid with the gridding method that has been wide applied in MRI, and sequentially be processed using FFT. The proposed gridding-FFT (GFFT) method increases the processing speed sharply compared with the previously proposed non-uniform Fourier Transform, and may speed up application of the non-uniform sparse sampling approaches.
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.
Addendum to 'A new hybrid algorithm for computing a fast discrete Fourier transform'
NASA Technical Reports Server (NTRS)
Reed, I. S.; Truong, T. K.; Benjauthrit, B.
1981-01-01
The reported investigation represents a continuation of a study conducted by Reed and Truong (1979), who proposed a hybrid algorithm for computing the discrete Fourier transform (DFT). The proposed technique employs a Winograd-type algorithm in conjunction with the Mersenne prime-number theoretic transform to perform a DFT. The implementation of the technique involves a considerable number of additions. The new investigation shows an approach which can reduce the number of additions significantly. It is proposed to use Winograd's algorithm for computing the Mersenne prime-number theoretic transform in the transform portion of the hybrid algorithm.
Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov Maxwell system
NASA Astrophysics Data System (ADS)
Eliasson, B.
2007-08-01
A problem with the solution of the Vlasov equation is its tendency to become filamented/oscillatory in velocity space, which in numerical simulations can give rise to unphysical oscillations and recurrence effects. We present a three-dimensional Vlasov-Maxwell solver (three spatial and velocity dimensions, plus time), in which the Vlasov equation is Fourier transformed in velocity space and the resulting equations solved numerically. By designing absorbing outflow boundary conditions in the Fourier transformed velocity space, the highest Fourier modes in velocity space are removed from the numerical solution. This introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced. The well-posedness of the boundary conditions is proved analytically, while the stability of the numerical implementation is assessed by long-time numerical simulations. Well-known wave-modes in magnetized plasmas are shown to be reproduced by the numerical scheme.
Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform
NASA Astrophysics Data System (ADS)
Larsson, Elisabeth; Ahlander, Krister; Hall, Andreas
2008-12-01
We show that the generalized Fourier transform can be used for reducing the computational cost and memory requirements of radial basis function methods for multi-dimensional option pricing. We derive a general algorithm, including a transformation of the Black-Scholes equation into the heat equation, that can be used in any number of dimensions. Numerical experiments in two and three dimensions show that the gain is substantial even for small problem sizes. Furthermore, the gain increases with the number of dimensions.
PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY
Open-path Fourier transform infrared (OP-FT1R) spectroscopy is an accepted technology for measuring gaseous air contaminants. OP-FT1R absorbance spectra acquired during changing aerosols conditions reveal related changes in very broad baseline features. Usually, this shearing of ...
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.
The Use of the Fourier Transform for Solving Linear Elasticity Problems
NASA Astrophysics Data System (ADS)
Kozubek, Tomas; Mocek, Lukas
2011-11-01
This paper deals with solving linear elasticity problems using a modified fictitious domain method and an effective solver based on the discrete Fourier transform and the Schur complement reduction in combination with the null space method. The main goal is to show step by step all ingredients of the numerical solution.
NASA Astrophysics Data System (ADS)
Mocek, Lukas; Kozubek, Tomas
2011-09-01
The paper deals with the numerical solution of elliptic boundary value problems for 2D linear elasticity using the fictitious domain method in combination with the discrete Fourier transform and the FETI domain decomposition. We briefly mention the theoretical background of these methods, introduce resulting solvers, and demonstrate their efficiency on model benchmarks.
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...
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)
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...
Refined Fourier-transform method of analysis of full two-dimensional digitized interferograms
NASA Astrophysics Data System (ADS)
Lovrić, Davorin; Vučić, Zlatko; Gladić, Jadranko; Demoli, Nazif; Mitrović, Slobodan; Milas, Mirko
2003-03-01
A refined Fourier-transform method of analysis of interference patterns is presented. The refinements include a method of automatic background subtraction and a way of treating the problem of heterodyning. The method proves particularly useful for analysis of long sequences of interferograms.
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
NASA Technical Reports Server (NTRS)
Wiedermann, Guenter; Jennings, D. E.; Hanel, R. H.; Kunde, V. G.; Moseley, S. H.
1989-01-01
A postdispersion system for astronomical observations with Fourier transform spectrometers in the thermal infrared has been developed which improves the sensitivity of radiation noise limited observations by reducing the spectral range incident on the detector. Special attention is given to the first-generation blocked impurity band detector. Planetary, solar, and stellar observations are reported.
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.
Gallery of Datacubes Obtained with the Livermore Imaging Fourier Transform Spectrometer
Wurtz, R; Wishnow, E H; Blais-Ouellette, S; Cook, K H; Holden, B P; Carr, D J; Stubbs, C W
2002-09-12
We have acquired spatial-spectral datacubes of astronomical objects using the Livermore visible-band imaging Fourier transform spectrometer at Apache Point Observatory. Each raw datacube contains hundreds of thousands of spectral interferograms. We present in-progress demonstrations of these observations.
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...
Several field tests of a Fourier transform infrared (FTIR) spectrometer have been conducted. he results indicate that effective use of this type of instrument in the field of continuous emissions monitoring (CEM) is possible under the proper conditions, and within limits currentl...
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 ...
As part of the Online Surface Cleanliness Project, the Naval Facilities Engineering Service Center (NFESC) conducted a study of grazing-angle reflectance Fourier Transform Infrared (FTIR) Spectroscopy as a tool for online cleanliness verification at Department of Defense (DoD) cl...
Technology Transfer Automated Retrieval System (TEKTRAN)
Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...
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 ...
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)
Amir, W.; Planchon, T. A.; Durfee, C. G.; Squier, J. A.; Gabolde, P.; Trebino, R.; Müller, M.
2006-10-01
We demonstrate the use of a simple tool to simultaneously visualize and characterize chromatic and spherical aberrations that are present in multiphoton microscopy. Using two-dimensional Fourier transform spectral interferometry, we measured these aberrations, deducing in a single shot spatiotemporal effects in high-numerical-aperture objectives.
NASA Astrophysics Data System (ADS)
Amir, W.; Planchon, T. A.; Durfee, C. G.; Squier, J. A.
2007-04-01
Spatiotemporal pulse shaping is characterized with two-dimensional Fourier transform spectral interferometry. A deformable-mirror-based bidimensional pulse shaper is used to create simple spatiotemporal structures on a femtosecond pulse, structures that are directly calculated from the measured spatiospectral phases and intensities.
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 ...
Hermann, Peter; Hoehl, Arne; Patoka, Piotr; Huth, Florian; Rühl, Eckart; Ulm, Gerhard
2013-02-11
We demonstrate scanning near-field optical microscopy with a spatial resolution below 100 nm by using low intensity broadband synchrotron radiation in the IR regime. The use of such a broadband radiation source opens up the possibility to perform nano-Fourier-transform infrared spectroscopy over a wide spectral range. PMID:23481749
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.
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…
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...
The United States Environmental Protection Agency (U.S. EPA) requires reference spectra to support its gas chromatography/Fourier transform infrared (GC/FT-IR) routine environmental monitoring program. Although on-the-fly (OTF) techniques are needed to satisfy the Agency's high s...
Technology Transfer Automated Retrieval System (TEKTRAN)
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 ...
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)
Deeley, C. M.; Spragg, R. A.; Threlfall, T. L.
Polymorphism in cortisone acetate, a synthetic adrenocortical steroid, and in a compound from a heart disease project has been studied with near-infrared Fourier transform Raman (NIR FT-Raman) spectroscopy. For cortisone acetate similar quantitative precision was obtained with both Raman and diffuse reflection IR measurements. The Raman measurements of the heart disease compound gave a calibration with a standard error of prediction of better than 2.5%. The combination of excellent precision with very convenient measurement of powders makes NIR FT-Raman spectroscopy a valuable tool for quantitative measurements of polymorphism.
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.
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.
Park, G Barratt; Field, Robert W
2016-05-28
Since its invention in 2006, the broadband chirped pulse Fourier transform spectrometer has transformed the field of microwave spectroscopy. The technique enables the collection of a ≥10 GHz bandwidth spectrum in a single shot of the spectrometer, which allows broadband, high-resolution microwave spectra to be acquired several orders of magnitude faster than what was previously possible. We discuss the advantages and challenges associated with the technique and look back on the first ten years of chirped pulse Fourier transform spectroscopy. In addition to enabling faster-than-ever structure determination of increasingly complex species, the technique has given rise to an assortment of entirely new classes of experiments, ranging from chiral sensing by three-wave mixing to microwave detection of multichannel reaction kinetics. However, this is only the beginning. Future generations of microwave experiments will make increasingly creative use of frequency-agile pulse sequences for the coherent manipulation and interrogation of molecular dynamics. PMID:27250271
Perspective: The first ten years of broadband chirped pulse Fourier transform microwave spectroscopy
NASA Astrophysics Data System (ADS)
Park, G. Barratt; Field, Robert W.
2016-05-01
Since its invention in 2006, the broadband chirped pulse Fourier transform spectrometer has transformed the field of microwave spectroscopy. The technique enables the collection of a ≥10 GHz bandwidth spectrum in a single shot of the spectrometer, which allows broadband, high-resolution microwave spectra to be acquired several orders of magnitude faster than what was previously possible. We discuss the advantages and challenges associated with the technique and look back on the first ten years of chirped pulse Fourier transform spectroscopy. In addition to enabling faster-than-ever structure determination of increasingly complex species, the technique has given rise to an assortment of entirely new classes of experiments, ranging from chiral sensing by three-wave mixing to microwave detection of multichannel reaction kinetics. However, this is only the beginning. Future generations of microwave experiments will make increasingly creative use of frequency-agile pulse sequences for the coherent manipulation and interrogation of molecular dynamics.
NASA Astrophysics Data System (ADS)
Fernandez, Sergio; Gdeisat, Munther A.; Salvi, Joaquim; Burton, David
2011-06-01
Fringe pattern analysis in coded structured light constitutes an active field of research. Techniques based on first projecting a sinusoidal pattern and then recovering the phase deviation permit the computation of the phase map and its corresponding depth map, leading to a dense acquisition of the measuring object. Among these techniques, the ones based on time-frequency analysis permit to extract the depth map from a single image, thus having potential applications measuring moving objects. The main techniques are Fourier Transform (FT), Windowed Fourier Transform (WFT) and Wavelet Transform (WT). This paper first analyzes the pros and cons of these three techniques, then a new algorithm for the automatic selection of the window size in WFT is proposed. This algorithm is compared to the traditional WT using adapted mother wavelet signals both with simulated and real objects, showing the performance results for quantitative and qualitative evaluations of the new method.
Infrared absorption of CH3OSO detected with time-resolved Fourier-transform spectroscopy.
Chen, Jin-Dah; Lee, Yuan-Pern
2011-03-01
A step-scan Fourier-transform spectrometer coupled with a multipass absorption cell was employed to detect temporally resolved infrared absorption spectra of CH(3)OSO produced upon irradiation of a flowing gaseous mixture of CH(3)OS(O)Cl in N(2) or CO(2) at 248 nm. Two intense transient features with origins near 1152 and 994 cm(-1) are assigned to syn-CH(3)OSO; the former is attributed to overlapping bands at 1154 ± 3 and 1151 ± 3 cm(-1), assigned to the S=O stretching mixed with CH(3) rocking (ν(8)) and the S=O stretching mixed with CH(3) wagging (ν(9)) modes, respectively, and the latter to the C-O stretching (ν(10)) mode at 994 ± 6 cm(-1). Two weak bands at 2991 ± 6 and 2956 ± 3 cm(-1) are assigned as the CH(3) antisymmetric stretching (ν(2)) and symmetric stretching (ν(3)) modes, respectively. Observed vibrational transition wavenumbers agree satisfactorily with those predicted with quantum-chemical calculations at level B3P86∕aug-cc-pVTZ. Based on rotational parameters predicted at that level, the simulated rotational contours of these bands agree satisfactorily with experimental results. The simulation indicates that the S=O stretching mode of anti-CH(3)OSO near 1164 cm(-1) likely makes a small contribution to the observed band near 1152 cm(-1). A simple kinetic model of self-reaction is employed to account for the decay of CH(3)OSO and yields a second-order rate coefficient k=(4 ± 2)×10(-10) cm(3)molecule(-1)s(-1). PMID:21384966
Infrared absorption of CH3OSO detected with time-resolved Fourier-transform spectroscopy
NASA Astrophysics Data System (ADS)
Chen, Jin-Dah; Lee, Yuan-Pern
2011-03-01
A step-scan Fourier-transform spectrometer coupled with a multipass absorption cell was employed to detect temporally resolved infrared absorption spectra of CH3OSO produced upon irradiation of a flowing gaseous mixture of CH3OS(O)Cl in N2 or CO2 at 248 nm. Two intense transient features with origins near 1152 and 994 cm-1 are assigned to syn-CH3OSO; the former is attributed to overlapping bands at 1154 ± 3 and 1151 ± 3 cm-1, assigned to the S=O stretching mixed with CH3 rocking (ν8) and the S=O stretching mixed with CH3 wagging (ν9) modes, respectively, and the latter to the C-O stretching (ν10) mode at 994 ± 6 cm-1. Two weak bands at 2991 ± 6 and 2956 ± 3 cm-1 are assigned as the CH3 antisymmetric stretching (ν2) and symmetric stretching (ν3) modes, respectively. Observed vibrational transition wavenumbers agree satisfactorily with those predicted with quantum-chemical calculations at level B3P86/aug-cc-pVTZ. Based on rotational parameters predicted at that level, the simulated rotational contours of these bands agree satisfactorily with experimental results. The simulation indicates that the S=O stretching mode of anti-CH3OSO near 1164 cm-1 likely makes a small contribution to the observed band near 1152 cm-1. A simple kinetic model of self-reaction is employed to account for the decay of CH3OSO and yields a second-order rate coefficient k = (4 ± 2)×10-10 cm3 molecule-1 s-1.
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
Synthesis of Arbitrary Unitary Transformations in Quantum Systems by Householder Reflections
Ivanov, P. A.; Vitanov, N. V.
2007-12-26
We demonstrate that Householder reflections emerge naturally in the propagator of a coherently driven degenerate two-level system. Such reflections are a very powerful tool for constructing arbitrary unitary transformations of an N-state quantum system. We present examples for construction of discrete Fourier transforms, superposition-to-superposition navigation between pure states, engineering of arbitrary mixed states, and entanglement of trapped ions.
A fast partial Fourier transform (FPFT) for data compression and filtering.
Smith, Mark William
2010-07-01
A discrete Fourier transform (DFT) or the closely related discrete cosine transform (DCT) is often employed as part of a data compression scheme. This paper presents a fast partial Fourier transform (FPFT) algorithm that is useful for calculating a subset of M Fourier transform coefficients for a data set comprised of N points (M < N). This algorithm reduces to the standard DFT when M = 1 and it reduces to the radix-2, decimation-in-time FFT when M = N and N is a power of 2. The DFT requires on the order of MN complex floating point multiplications to calculate M coefficients for N data points, a complete FFT requires on the order of (N/2)log{sub 2}N multiplications independent of M, and the new FPFT algorithm requires on the order of (N/2)log{sub 2}M + N multiplications. The FPFT algorithm introduced in this paper could be readily adapted to parallel processing. In addition to data compression, the FPFT algorithm described in this paper might be useful for very narrow band filter operations that pass only a small number of non-zero frequency coefficients such that M << N.
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.
Andreeva, A; Burova, M; Burov, J
2007-06-01
A metal object is computer visualized by registration of the amplitudes of the transmitted through the object short acoustic pulses. The pulses are separated by time, because of the presence of holes and internal compact components in the longitudinal section (structure along the propagation direction of acoustic wave). The acoustic field transmitted through the object is composited from a field presenting Fourier transformation of the hole shape and field, transmitted through the metal components in the longitudinal section of the object. A computer Fourier transformation of the digital data of the amplitude fields transmitted through the object components is performed instead of converging lens. The Fourier series of the object obtained as digital data after the transformation is multiplied with a term, describing the angle distribution of the field on spatial frequencies. The reconstruction of the image of the metal components is performed by reverse transformation, i.e. summing up in all spatial frequencies. 3D visualization of the transmitted through the hole acoustic field determines the hole geometry (circular, square, rectangular). It is shown that at the transmission of a short acoustic pulse through the components with different thicknesses and holes, presenting Fourier and non-Fourier transformation can be registered separately in contrast to the optics. PMID:17395232
Backlund Transformation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Burt, Philip
1996-11-01
Solutions of nonlinear field equations with polynomial nonlin earities are well known(P.B.Burt,Quantum Mechanics and Nonlinear Waves,Harwood Academic,Chur,1981).These solutions have been used to describe spin zero systems with self interactions. General- izations to systmes of fermions and bosons with various inter- actions lend themselves to description of quantum field theories with proper normalization. No ultraviolet divergences occur in such theories. The solutions themselves represent weak Backlund transformation of the nonlinear field equations and the related Klein Gordonequation(C.Rogers and W.F.Ames,Nonlinear Boundary Value Problems in Science and Engineering, Academic Press,New York,1989).
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.
Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms
NASA Astrophysics Data System (ADS)
Schmittfull, Marcel; Vlah, Zvonimir; McDonald, Patrick
2016-05-01
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. The method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.
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.
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
Li, Jianping; Chan, Robert K Y; Wang, Xuzhu
2009-11-01
An imaging Fourier transform spectrometer (IFTS) designed for fluorescence emission measurements is reported. The spectral range extension from NIR to visible of the system is realized by using a simple and low-cost optical beam-folding position-tracking technique. Spectral resolution as high as 9.78cm(-1)(0.4nm at 632.8nm) and maximum image resolution up to 300x300 pixels are proved by the system tests on its optical performances. Imaging fluorescence spectra acquisition of quantum dot clusters and single 200nm diameter fluorescent beads have demonstrated the system's potential for high throughput imaging spectroscopic measurements of fluorescent biological and chemical samples. PMID:19997347
Schrottke, L. Lü, X.; Grahn, H. T.
2015-04-21
We present a self-consistent model for carrier transport in periodic semiconductor heterostructures completely formulated in the Fourier domain. In addition to the Hamiltonian for the layer system, all expressions for the scattering rates, the applied electric field, and the carrier distribution are treated in reciprocal space. In particular, for slowly converging cases of the self-consistent solution of the Schrödinger and Poisson equations, numerous transformations between real and reciprocal space during the iterations can be avoided by using the presented method, which results in a significant reduction of computation time. Therefore, it is a promising tool for the simulation and efficient design of complex heterostructures such as terahertz quantum-cascade lasers.
Camino, Fernando E.; Nam, Chang-Yong; Pang, Yutong T.; Hoy, Jessica; Eisaman, Matthew D.; Black, Charles T.; Sfeir, Matthew Y.
2014-05-15
Here 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). Lastly, this allows for rapid fabrication of variable-pitch sub-wavelength hole arrays in metal films for use asmore » transparent electrical contacts, and evaluation of the evanescent and propagating mode coupling to resonances in the active layer.« less
Camino, Fernando E.; Nam, Chang-Yong; Pang, Yutong T.; Hoy, Jessica; Eisaman, Matthew D.; Black, Charles T.; Sfeir, Matthew Y.
2014-05-15
Here 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 mm^{2}). Lastly, 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.
Ion collision cross section measurements in Fourier transform-based mass analyzers.
Li, Dayu; Tang, Yang; Xu, Wei
2016-06-01
With the increasing demands of molecular structure analysis, several methods have been developed to measure ion collision cross sections within Fourier transform (FT) based mass analyzers. Particularly in the recent three years since 2012, the method of obtaining biomolecule collision cross sections was achieved in Fourier transform ion cyclotron resonance (FT-ICR) cells. Furthermore, similar methods have been realized or proposed for orbitraps and quadrupole ion traps. This technique adds a new ion structure analysis capability to FT-based mass analyzers. By providing complementary ion structure information, it could be used together with tandem mass spectrometry and ion mobility spectroscopy techniques. Although many questions and challenges remain, this technique potentially would greatly enhance the ion structure analysis capability of a mass spectrometer, and provide a new tool for chemists and biochemists. PMID:26788551
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.
NASA Astrophysics Data System (ADS)
Sun, Zhiwei; Zhi, Ya'nan; Liu, Liren; Sun, Jianfeng; Zhou, Yu; Hou, Peipei
2013-09-01
The synthetic aperture imaging ladar (SAIL) systems typically generate large amounts of data difficult to compress with digital method. This paper presents an optical SAIL processor based on compensation of quadratic phase of echo in azimuth direction and two dimensional Fourier transform. The optical processor mainly consists of one phase-only liquid crystal spatial modulator(LCSLM) to load the phase data of target echo and one cylindrical lens to compensate the quadratic phase and one spherical lens to fulfill the task of two dimensional Fourier transform. We show the imaging processing result of practical target echo obtained by a synthetic aperture imaging ladar demonstrator. The optical processor is compact and lightweight and could provide inherent parallel and the speed-of-light computing capability, it has a promising application future especially in onboard and satellite borne SAIL systems.
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.
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
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
de Oliveira, M E; de Oliveira, G N; de Souza, J C; dos Santos, P A M
2016-02-10
In the present paper, the method of simultaneous moiré-like fringe pattern projection for Fourier transform profilometry is described. The photorefractive holographic interferometric process produces controlled moiré-like patterns with two or more different variation directions. Each low spatial frequency fringe pattern is experimentally obtained as a result of the superposition of two high spatial frequency sinusoidal gratings, with slightly different pitches, for each fringe variation direction. These dynamic moiré-like patterns are induced due to an optical holographic beating of the sinusoidal induced gratings in the volume of the photorefractive Bi₁₂TiO₂₀ (BTO) crystal sample used as dynamic holographic medium. Two or more moiré-like fringe patterns, with at least two different variation directions, simultaneously (or not), are projected onto the object surface. Thus, this is the 2D fringe projection stage of our proposed Fourier transform procedure to determine the profile of a simple object. PMID:26906374
Fourier transform spectrometer remote sensing of O2 A-band electric quadrupole transitions
NASA Astrophysics Data System (ADS)
Miller, Charles E.; Wunch, Debra
2012-07-01
We observed electric quadrupole transitions in the O2 A-band, b1Σg+←X3Σg-(0,0), in high solar zenith angle atmospheric spectra recorded with the high-resolution solar-viewing Fourier transform spectrometer at Park Falls, WI. We identified 12 ΔN=±3 transitions for the first time, including the first detection of NO-branch transitions and extended the TS-branch observations of Brault [J Mol Spectrosc 1980;80:384-8] up to N″=23. Additionally, we observed six electric quadrupole transitions of the ΔN=-1 PO-branch. These observations demonstrate the excellent sensitivity and long-term stability of the new generation of solar-viewing Fourier transform spectrometers.
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.
Effect of the fringe visibility on spectrum SNR of Fourier transform imaging spectrometer
NASA Astrophysics Data System (ADS)
Wang, Shuang; Bin, Xiangli; Jing, Juanjuan; Pi, Haifeng
2013-08-01
The principle of Fourier transform spectrometer is based on the relationship of Fourier-Transform between interferogram and spectrum. The spectral information of Fourier transform imaging spectrometer (FTIS) reconstructed from raw interferogram by data processing. So there are two kinds of signal-to-noise ratio (SNR) to evaluate instrument performance, one regarding interferogram and the other regarding reconstructed spectrum. Because the raw interferogram is intuitive, the interferogram SNR is studied usually. On the contrary, the spectrum SNR is studied less because of the complexity of the data processing from interferogram to spectrum. The research about the effect of the interference fringe visibility on the spectrum SNR is especially few. This paper present a research work on the relations between the interference fringe visibility and the spectrum SNR. Firstly, the reduction of fringe visibility caused by imaging lens defocus was analyzed. Secondly, the changes of the average spectrum signal and noise caused by the reduction of fringe visibility were calculated. For average spectrum signal, the math deductions are done base on Fourier transform theory. The average noise with different input signal optic-electrons number are simulated. the results show that the average spectrum signal is directly proportional to the fringe visibility, and the effect of fringe visibility on the noise related to signal can be ignorable. Finally, In order to demonstrate above results, the imaging experiment was done with white-light source, using LASIS (Large aperture static imaging spectrometer) based on Sagnac Interferometer. The average spectrum SNRs under different fringe visibility are calculated and analyzed. The experimental results show that: the average spectrum SNRs increase from 42.7 to 62.4.along with the fringe visibility increasing from 0.5051 to 0.687. the reconstructed spectrum SNR is directly proportional to the fringe visibility. As a result, the interferogram
Toney, M.L.
1999-07-01
The purpose of this testing program is to obtain uncontrolled and controlled hydrogen chloride (HCl) and speciated hydrocarbon Hazardous Air Pollutants (HAPs) emissions data from lime production plants to support a national emission standard for hazardous air pollutants (NESHAP). This report presents data from the Fourier Transform Infrared Spectroscopy (FTIR) measurements. FTIR source testing was conducted for the following purposes: Quantify HCl emission levels; and Gather screening (i.e., qualitative) data on other HAP emissions.
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.
Raman spectroscopy of gases with a Fourier transform spectrometer - The spectrum of D2
NASA Technical Reports Server (NTRS)
Jennings, D. E.; Weber, A.; Brault, J. W.
1986-01-01
Fourier transform spectrometry (FTS) is presently used to record the spontaneous incoherent laser Raman spectra of gases. The high resolution, sensitivity, calibration accuracy and spectral coverage achieved demonstrate the viability of FTS for Raman spectroscopy. Attention is given to the coefficients obtained by fitting measurements obtained from the spectrum of D2, containing both v = 0-0 and 1-0 transitions, to the Dunham (1932) expansion of the vibration-rotation energy levels.
Field-of-view analysis of a polarization interference Fourier transform imaging spectrometer.
DeHoog, Edward; Xia, Xiaowei; Parfenov, Alexander; Shih, Min-Yi
2011-09-20
The Fourier transform imaging spectrometer (FTIS) is an important tool for the measurement of spectral information in a scene. Advances in electro-optic crystal systems have led to the advent of the FTIS based on polarization interference filters. The operation of these devices as spectrometers has been well characterized, but the imaging capabilities have yet to be thoroughly explored. We explore the field-of-view limitations that occur when using this particular type of FTIS. PMID:21947057
Ren, Wenyi; Zhang, Chunmin; Jia, Chenling; Mu, Tingkui; Li, Qiwei; Zhang, Lin
2013-04-15
A method was proposed to precisely reconstruct the spectrum from the interferogram taken by the Fourier transform imaging spectrometer (FTIS) based on the polarization beam splitters. Taken the FTISs based on the Savart polariscope and Wollaston prism as examples, the distorted spectrums were corrected via the proposed method effectively. The feasibility of the method was verified via simulation. The distorted spectrum, recovered from the interferogram taken by the polarization imaging spectrometer developed by us, was corrected. PMID:23595463
Isotropic Spin Trap EPR Spectra Simulation by Fast Fourier Transform (FFT)
NASA Astrophysics Data System (ADS)
Laachir, S.; Moussetad, M.; Adhiri, R.; Fahli, A.
2005-03-01
The detection and investigation of free radicals forming in living systems became possible due to the introduction of the method of spin traps. In this work, the electron spin resonance (ESR) spectra of DMPO/HO(.) and MGD-Fe-NO adducts are reproduced by simulation, based on the Fast Fourier Transform (FFT). The calculated spectral parameters as the hyperfine coupling constants, agree reasonably with the experimental data and the results are discussed.
NASA Astrophysics Data System (ADS)
Kumar, Manoj; Shakher, Chandra
2016-04-01
In this paper, moisture induced deformation and shrinkage behaviour of deodar wood during convective drying is experimentally investigated by using digital holographic interferometry. There induces dimensional changes in wood due to the moisture absorption and desorption. Lensless Fourier transform digital holographic interferometry (LLFTDH) is used to study the moisture induced deformation and strain distribution in deodar wood. The proposed technique having high sensitivity and enables the observation of deformation and strain distribution during the variations of moisture content in the deodar wood.
NASA Technical Reports Server (NTRS)
Powers, E. J.; Kim, Y. C.; Hong, J. Y.; Roth, J. R.; Krawczonek, W. M.
1978-01-01
A diagnostic, based on fast Fourier-transform spectral analysis techniques, that provides experimental insight into the relationship between the experimentally observable spectral characteristics of the fluctuations and the fluctuation-induced plasma transport is described. The model upon which the diagnostic technique is based and its experimental implementation is discussed. Some characteristic results obtained during the course of an experimental study of fluctuation-induced transport in the electric field dominated NASA Lewis bumpy torus plasma are presented.
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
Simple technique of Fourier-transform holographic microscope with compensation of phase aberration
NASA Astrophysics Data System (ADS)
Grishin, Oleg V.; Fedosov, Ivan V.; Tuchin, Valery V.
2016-04-01
In this paper, we present a novel simple technique of Fourier-transform holographic microscopy (FTHM). Simplicity of the scheme, possibility to use a small image sensor and provide compensation of aberration, enable one to construct inexpensive holographic microscopes. We experimentally compare FTHM with in-line holographic microscopy. In this paper, we present experimental scheme of FTHM, description of used algorithms and experimental results for an amplitude test object and biological samples (blood smears).
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.
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
NASA Astrophysics Data System (ADS)
Tsaur, Gin-yih; Wang, Jyhpyng
2016-07-01
The Green function method is a powerful technique for solving the initial value problem in quantum mechanics. Once the Green function is solved the whole wavefunction evolution is represented in a concise form and can be evaluated conveniently by numerical integration. We present a method for constructing the Green functions systematically which is different from the conventional methods of eigenfunction expansion or path integration. By using variable changing, function substitution, and Fourier transforms, the time dependent Schrödinger equations can be simplified and the solutions for the simplified equations can be easily derived. We then obtain the Green functions for the original equations by the reverse transforms. The method is demonstrated for the linear potential, the harmonic oscillator, the centrifugal potential, and the centripetal barrier oscillator, where the Green function for the centripetal barrier oscillator has not been solved previously by conventional methods. The method and examples illustrated in this paper can be utilised to strengthen undergraduate courses on quantum mechanics and/or partial differential equation.
High-SNR static Fourier-transform imaging spectrometer based on differential structure
NASA Astrophysics Data System (ADS)
Jin, Peng; Zhu, Shuaishuai; Zhang, Yu; Lin, Jie
2015-03-01
Fourier-transform imaging spectrometers are rapidly developed due to their extensive use in industrial monitoring, target detection, and chemical identification. Static Fourier-transform imaging spectrometer (SFIS) containing a birefringent interferometer is one of the most popular directions due to its inherent robustness. However, the SFIS suffers from its low achievable signal-to-noise ratio (SNR) because of the restriction of incident angle. Meanwhile, in applications, the SNR is perhaps the most important factor to determine the usefulness of an instrument. In this paper, we report here a Static Fourier-transform imaging spectrometer based on differential structure (SFIS-DS) in the 400-800nm wavelength range with a high SNR. As in electronic system, the differential structure can double optical efficiency and strongly restrain common mode error in the SFIS-DS. And the differential structure described here is also available for any instruments containing a birefringent interferometer. However, the drawback of the SFIS-DS is that the two images obtained by the two differential channels need precise registration which can be overcome by a sub-pixel spatial registration algorithm. The experimental results indicate the SFIS-DS can increase the SNR by no less than 40%.
Jing, Juan-Juan; Zhou, Jin-Song; Xiangli, Bin; Lü, Qun-Bo; Wei, Ru-Yi
2010-06-01
The principle of reflecting rotating Fourier transform spectrometer was introduced in the present paper. The nonlinear problem of optical path difference (OPD) of rotating Fourier transform spectrometer universally exists, produced by the rotation of rotating mirror. The nonlinear OPD will lead to fictitious recovery spectrum, so it is necessary to compensate the nonlinear OPD. Three methods of correction for the nonlinear OPD were described and compared in this paper, namely NUFFT method, OPD replace method and interferograms fitting method. The result indicates that NUFFT was the best method for the compensation of nonlinear OPD, OPD replace method was better, its precision was almost the same as NUFFT method, and their relative error are superior to 0.13%, but the computation efficiency of OPD replace method is slower than NUFFT method, while the precision and computation efficiency of interferograms fitting method are not so satisfied, because the interferograms are rapid fluctuant especially around the zero optical path difference, so it is unsuitable for polynomial fitting, and because this method needs piecewise fitting, its computation efficiency is the slowest, thus the NUFFT method is the most suited method for the nonlinear OPD compensation of reflecting rotating Fourier transform spectrometer. PMID:20707175
A compact Fourier transform imaging spectrometer employing a variable gap Fabry-Perot interferometer
NASA Astrophysics Data System (ADS)
Lucey, Paul G.; Akagi, Jason; Bingham, Adam L.; Hinrichs, John L.; Knobbe, Edward T.
2014-05-01
Fourier transform spectroscopy is a widely employed method for obtaining visible and infrared spectral imagery, with applications ranging from the desktop to remote sensing. Most fielded Fourier transform spectrometers (FTS) employ the Michelson interferometer and measure the spectrum encoded in a time-varying signal imposed by the source spectrum interaction with the interferometer. A second, less widely used form of FTS is the spatial FTS, where the spectrum is encoded in a pattern sampled by a detector array. Recently we described using a Fabry-Perot interferometer, with a deliberately wedged gap geometry and engineered surface reflectivities, to produce an imaging spatial FTS. The Fabry-Perot interferometer can be much lighter and more compact than a conventional interferometer configuration, thereby making them suitable for portable and handheld applications. This approach is suitable for use over many spectral regimes of interest, including visible and infrared regions. Primary efforts to date have focused on development and demonstration of long wave infrared (LWIR) spectral imagers. The LWIR version of the miniaturized Fabry-Perot has been shown to be effective for various applications including spectral imaging-based chemical detection. The compact LWIR spectral imager employs uncooled optics and a microbolometer camera; a handheld version is envisioned for future development. Recent advancements associated with the spatial Fourier Transform imaging spectrometer system are described.
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
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 Fourier Transform Method for Vsin i Estimations under Nonlinear Limb-darkening Laws
NASA Astrophysics Data System (ADS)
Levenhagen, R. S.
2014-12-01
Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).
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).
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
Digital watermarking algorithm research of color images based on quaternion Fourier transform
NASA Astrophysics Data System (ADS)
An, Mali; Wang, Weijiang; Zhao, Zhen
2013-10-01
A watermarking algorithm of color images based on the quaternion Fourier Transform (QFFT) and improved quantization index algorithm (QIM) is proposed in this paper. The original image is transformed by QFFT, the watermark image is processed by compression and quantization coding, and then the processed watermark image is embedded into the components of the transformed original image. It achieves embedding and blind extraction of the watermark image. The experimental results show that the watermarking algorithm based on the improved QIM algorithm with distortion compensation achieves a good tradeoff between invisibility and robustness, and better robustness for the attacks of Gaussian noises, salt and pepper noises, JPEG compression, cropping, filtering and image enhancement than the traditional QIM algorithm.
Precise measurement of the resolution in light microscopy using Fourier transform.
Vainrub, Arnold
2008-04-01
The resolution power of light microscope has been accurately measured (+/-5%) by Fourier transform of various object images and further evaluation of the highest spatial frequency in Fourier spectrum. Any unknown shape plane object with a shape feature's size smaller than the resolution to be measured was shown to provide a reliable resolution test. This simple method gives a direct measurement of the resolution power as defined by Abbe [Archiv. F. Mikroskopische Anat. 9, 413 (1873)]. The results have been justified by comparison to a standard resolution measurement by using calibrated periodic line patterns. Notably, the approach is applicable in super-resolution light microscopy (transmission, reflection, and fluorescence), where calibrated resolution targets do not occur. It was conveniently implemented by using a compact disk as a test object and free IMAGEJ imaging software. PMID:18447570
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.
Precise measurement of the resolution in light microscopy using Fourier transform
Vainrub, Arnold
2008-04-15
The resolution power of light microscope has been accurately measured ({+-}5%) by Fourier transform of various object images and further evaluation of the highest spatial frequency in Fourier spectrum. Any unknown shape plane object with a shape feature's size smaller than the resolution to be measured was shown to provide a reliable resolution test. This simple method gives a direct measurement of the resolution power as defined by Abbe [Archiv. F. Mikroskopische Anat. 9, 413 (1873)]. The results have been justified by comparison to a standard resolution measurement by using calibrated periodic line patterns. Notably, the approach is applicable in super-resolution light microscopy (transmission, reflection, and fluorescence), where calibrated resolution targets do not occur. It was conveniently implemented by using a compact disk as a test object and free IMAGEJ imaging software.
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.
Suzuki, M.; Isogami, S.; Tsunoda, M.; Takahashi, S.; Ishio, S.
2011-09-09
We present a fabrication method for a reference source that is efficient when used for lensless Fourier transform holography. This method produces a reference source that yields high spatial resolution and enhanced signal-to-noise ratio in a Fourier-transformed real-space image, and is particularly useful for Fourier transform holography experiments in the hard x-ray region.
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...
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-01
In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption. PMID:27505799
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
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…
Rice, S.B.; Freund, H.; Huang, W.L.; Clouse, J.A.; Isaacs, C.M.
1995-10-02
An important goal in silica diagenesis research is to understand the kinetics of opal transformation from noncrystalline opal-A to the disordered silica polymorph opal-CT. Because the conventional technique for monitoring the transformation, powder X-ray diffraction (XRD), is applicable only to phases with long-range order, the authors used Fourier transform infrared spectroscopy (FTIR) to monitor the transformation. They applied this technique, combined with XRD and TEM, to experimental run products and natural opals from the Monterey Formation and from siliceous deposits in the western Pacific Ocean. Using a ratio of two infrared absorption intensities ({omega} = I{sub 472 cm{sup {minus}1}}/I{sub 500 cm{sup {minus}1}}), the relative proportions of opal-A and opal-CT can be determined. The progress of the transformation is marked by changes in slope of {omega} vs. depth or time when a sufficient stratigraphic profile is available. There are three stages in the opal-A to opal-CT reaction: (1) opal-A dissolution; (2) opal-CT precipitation, whose end point is marked by completion of opal-A dissolution; and (3) opal-CT ordering, during which tridymite stacking is eliminated in favor of crystobalite stacking.
Slit Function Measurement of An Imaging Spectrograph Using Fourier Transform Techniques
NASA Technical Reports Server (NTRS)
Park, Hongwoo; Swimyard, Bruce; Jakobsen, Peter; Moseley, Harvey; Greenhouse, Matthew
2004-01-01
Knowledge of a spectrograph slit function is necessary to interpret the unresolved lines in an observed spectrum. A theoretical slit function can be calculated from the sizes of the entrance slit, the detector aperture when it functions as an exit slit, the dispersion characteristic of the disperser, and the point spread function of the spectrograph. A measured slit function is preferred to the theoretical one for the correct interpretation of the spectral data. In a scanning spectrometer with a single exit slit, the slit function is easily measured. In a fixed grating/or disperser spectrograph, illuminating the entrance slit with a near monochromatic light from a pre-monochrmator or a tunable laser and varying the wavelength of the incident light can measure the slit function. Even though the latter technique had been used successfully for the slit function measurements, it had been very laborious and it would be prohibitive to an imaging spectrograph or a multi-object spectrograph that has a large field of view. We explore an alternative technique that is manageable for the measurements. In the proposed technique, the imaging spectrograph is used as a detector of a Fourier transform spectrometer. This method can be applied not only to an IR spectrograph but also has a potential to a visible/UV spectrograph including a wedge filter spectrograph. This technique will require a blackbody source of known temperature and a bolometer to characterize the interferometer part of the Fourier Transform spectrometer. This pa?er will describe the alternative slit function measurement technique using a Fourier transform spectrometer.
Image Reconstruction from Under sampled Fourier Data Using the Polynomial Annihilation Transform
Archibald, Richard K.; Gelb, Anne; Platte, Rodrigo
2015-09-09
Fourier samples are collected in a variety of applications including magnetic resonance imaging and synthetic aperture radar. The data are typically under-sampled and noisy. In recent years, l1 regularization has received considerable attention in designing image reconstruction algorithms from under-sampled and noisy Fourier data. The underlying image is assumed to have some sparsity features, that is, some measurable features of the image have sparse representation. The reconstruction algorithm is typically designed to solve a convex optimization problem, which consists of a fidelity term penalized by one or more l1 regularization terms. The Split Bregman Algorithm provides a fast explicit solutionmore » for the case when TV is used for the l1l1 regularization terms. Due to its numerical efficiency, it has been widely adopted for a variety of applications. A well known drawback in using TV as an l1 regularization term is that the reconstructed image will tend to default to a piecewise constant image. This issue has been addressed in several ways. Recently, the polynomial annihilation edge detection method was used to generate a higher order sparsifying transform, and was coined the “polynomial annihilation (PA) transform.” This paper adapts the Split Bregman Algorithm for the case when the PA transform is used as the l1 regularization term. In so doing, we achieve a more accurate image reconstruction method from under-sampled and noisy Fourier data. Our new method compares favorably to the TV Split Bregman Algorithm, as well as to the popular TGV combined with shearlet approach.« less
Image Reconstruction from Under sampled Fourier Data Using the Polynomial Annihilation Transform
Archibald, Richard K.; Gelb, Anne; Platte, Rodrigo
2015-09-09
Fourier samples are collected in a variety of applications including magnetic resonance imaging and synthetic aperture radar. The data are typically under-sampled and noisy. In recent years, l^{1} regularization has received considerable attention in designing image reconstruction algorithms from under-sampled and noisy Fourier data. The underlying image is assumed to have some sparsity features, that is, some measurable features of the image have sparse representation. The reconstruction algorithm is typically designed to solve a convex optimization problem, which consists of a fidelity term penalized by one or more l^{1} regularization terms. The Split Bregman Algorithm provides a fast explicit solution for the case when TV is used for the l1l1 regularization terms. Due to its numerical efficiency, it has been widely adopted for a variety of applications. A well known drawback in using TV as an l^{1} regularization term is that the reconstructed image will tend to default to a piecewise constant image. This issue has been addressed in several ways. Recently, the polynomial annihilation edge detection method was used to generate a higher order sparsifying transform, and was coined the “polynomial annihilation (PA) transform.” This paper adapts the Split Bregman Algorithm for the case when the PA transform is used as the l^{1} regularization term. In so doing, we achieve a more accurate image reconstruction method from under-sampled and noisy Fourier data. Our new method compares favorably to the TV Split Bregman Algorithm, as well as to the popular TGV combined with shearlet approach.
NASA Astrophysics Data System (ADS)
Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua
2016-07-01
On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.
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 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)
Townley-Smith, Keeley; Nave, Gillian; Pickering, Juliet C.; Blackwell-Whitehead, Richard J.
2016-09-01
We expand on the comprehensive study of hyperfine structure (HFS) in Mn II conducted by Holt et al. (1999) by verifying hyperfine magnetic dipole constants (A) for 20 levels previously measured by Holt et al. (1999) and deriving A constants for 47 previously unstudied levels. The HFS patterns were measured in archival spectra from Fourier transform (FT) spectrometers at Imperial College London and the National Institute of Standards and Technology. Analysis of the FT spectra was carried out in XGREMLIN. Our A constant for the ground level has a lower uncertainty by a factor of 6 than that of Blackwell-Whitehead et al.
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.
A compact, high numerical aperture imaging Fourier transform spectrometer and its application
NASA Astrophysics Data System (ADS)
Alcock, R. D.; Coupland, J. M.
2006-11-01
This paper describes a compact imaging Fourier transform spectrometer with high numerical aperture. In comparison with other optical arrangements in which extended interferometer paths are required for the inclusion of dispersion compensation optics, this technique utilizes a rudimentary cubic beam splitter based Michelson interferometer with minimal optical path so that the numerical aperture of the system is maximized. Mathematical modelling is presented showing that the fringe distortions caused by the dispersion in the cubic beam splitter can be entirely removed without any loss of the spectral information. An illustration of the power of the technique is given classifying between different plant foliage performed using a Fisher discriminant function based optimal linear filtering.
Imaging open-path Fourier transform infrared spectrometer for 3D cloud profiling
NASA Astrophysics Data System (ADS)
Rentz Dupuis, Julia; Mansur, David J.; Vaillancourt, Robert; Carlson, David; Evans, Thomas; Schundler, Elizabeth; Todd, Lori; Mottus, Kathleen
2009-05-01
OPTRA is developing an imaging open-path Fourier transform infrared (I-OP-FTIR) spectrometer for 3D profiling of chemical and biological agent simulant plumes released into test ranges and chambers. An array of I-OP-FTIR instruments positioned around the perimeter of the test site, in concert with advanced spectroscopic algorithms, enables real time tomographic reconstruction of the plume. The approach is intended as a referee measurement for test ranges and chambers. This Small Business Technology Transfer (STTR) effort combines the instrumentation and spectroscopic capabilities of OPTRA, Inc. with the computed tomographic expertise of the University of North Carolina, Chapel Hill.
Radar cross-section reduction based on an iterative fast Fourier transform optimized metasurface
NASA Astrophysics Data System (ADS)
Song, Yi-Chuan; Ding, Jun; Guo, Chen-Jiang; Ren, Yu-Hui; Zhang, Jia-Kai
2016-07-01
A novel polarization insensitive metasurface with over 25 dB monostatic radar cross-section (RCS) reduction is introduced. The proposed metasurface is comprised of carefully arranged unit cells with spatially varied dimension, which enables approximate uniform diffusion of incoming electromagnetic (EM) energy and reduces the threat from bistatic radar system. An iterative fast Fourier transform (FFT) method for conventional antenna array pattern synthesis is innovatively applied to find the best unit cell geometry parameter arrangement. Finally, a metasurface sample is fabricated and tested to validate RCS reduction behavior predicted by full wave simulation software Ansys HFSSTM and marvelous agreement is observed.
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.
Application of numerical Fourier transformation on measurements made on board rotating spacecraft
NASA Astrophysics Data System (ADS)
Grabowski, R.; Boesch, B.; Wolf, H.
Use of a Fast Fourier Transform algorithm to perform digital evaluation of signals from spacecraft featuring spin modulation and nutational effects is described. The case of a rotating spacecraft without nutation is modeled, with account taken of demodulation performed simultaneously with respect to amplitude and phase. Applying the demodulation technique twice removes the nutational effects. Assumptions are made that the spectral functions do not vary as fast as the spin modulation, and the signal variance independent of spacecraft rotation occurs at a rate significantly less than the spin rate. A demodulation example is given for a signal received from a probe on the Porcupine 2 rocket.
Vilkov, Andrey N.; Gamage, Chaminda M.; Misharin, Alexander S.; Doroshenko, Vladimir M.; Tolmachev, Dmitry A.; Tarasova, Irina A.; Kharybin, Oleg N.; Novoselov, Konstantin P.; Gorshkov, Michael V.
2007-01-01
A new Fourier Transform Ion Cyclotron Resonance mass spectrometer based on a permanent magnet with an atmospheric pressure ionization source was designed and constructed. A mass resolving power (full-width-at-half-maximum) of up to 80,000 in the electron ionization mode and 25,000 in the electrospray mode was obtained. Also, a mass measurement accuracy at low-ppm level has been demonstrated for peptide mixtures in a mass range of up to 1,200 m/z in the isotopically resolved mass spectra. PMID:17587594
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.
Schoonover, J R; Steckle, Jr., W P; Elliot, N; Ebey, P S; Nobile, A; Nikroo, A; Cook, R C; Letts, S A
2005-06-16
Planar samples of varying thicknesses of both CH and CD glow discharge polymer have been measured with Fourier transform infrared (FTIR) spectroscopy before and after exposure to deuterium-tritium (DT) gas at elevated temperature and pressure. Planar samples of polyimide films made from both hydrogenated and deuterated precursors have also been examined by FTIR before and after DT exposure. The post-exposure FTIR spectra demonstrated no measurable exchange of hydrogen with deuterium or tritium for either polymer. Evidence for oxidation of the glow discharge polymer due to atmospheric oxygen was the only chemical change indicated by the FTIR data.
Mao, Zhuoxiong; McIntosh, M.J.; Demirgian, J.C.
1992-01-01
Incineration of chlorobenzene in a small laboratory incinerator was monitored by using Fourier transform infrared spectroscopy (FTIR) coupled with a heated long-path cell (LPC) to analyze and quantify flue gas emissions in near real time. The effects of operating conditions under stable and decreasing incineration temperatures on the destruction of chlorobenzene were studied. The results from the decreasing temperature experiments were found to be consistent with those from experiments at stable temperatures. This finding demonstrates that the FTIR/LPC, as a continuous emissions monitor, can effectively detect dynamic changes in the incinerator emissions and can contribute significantly to the safety of incinerators.
Mao, Zhuoxiong; McIntosh, M.J.; Demirgian, J.C.
1992-06-01
Incineration of chlorobenzene in a small laboratory incinerator was monitored by using Fourier transform infrared spectroscopy (FTIR) coupled with a heated long-path cell (LPC) to analyze and quantify flue gas emissions in near real time. The effects of operating conditions under stable and decreasing incineration temperatures on the destruction of chlorobenzene were studied. The results from the decreasing temperature experiments were found to be consistent with those from experiments at stable temperatures. This finding demonstrates that the FTIR/LPC, as a continuous emissions monitor, can effectively detect dynamic changes in the incinerator emissions and can contribute significantly to the safety of incinerators.
Fourier transform spectroscopy of the nu3 band of the N3 radical
NASA Technical Reports Server (NTRS)
Brazier, C. R.; Bernath, P. F.; Burkholder, James B.; Howard, Carleton J.
1988-01-01
The nu3 transitions of N3 radicals produced by HN3-Cl reactions in a multipass cell (effective path length 100 m) are investigated experimentally using a Fourier-transform spectrometer with maximum resolution 0.004/cm. A total of 176 rotation-vibration lines are listed in a table and used, in combination with published data on 240 optical lines (Douglas and Jones, 1965), to determine the nu3 molecular constants. The lower-than-expected value of the nu3 fundamental frequency (1644.6784/cm) is attributed to the vibronic interaction discussed by Kawaguchi et al. (1981).
A High Precision Scanning Control System For A VUV Fourier Transform Spectrometer
De Oliveira, N.; Nahon, L.; Polack, F.; Joyeux, D.; Phalippou, D.; Rodier, J. C.; Vervloeet, M.
2007-01-19
A VUV Fourier transform spectrometer based on a wavefront division interferometer has been built. Our ultimate goal is to provide a high resolution absorption spectrometer in the 140 - 40 nm range using the new third generation French synchrotron source Soleil as the background continuum. Here, we present the design and latest performance of the instrument scanning control system. It is based on multiple reflections of a monomode, frequency-stabilized HeNe laser between two plane mirrors allowing the required sensitivity on the displacement of the interferometer mobile arm. The experimental results on the sampling precision show an rms error below 5 nm for a travel length of 7.5 mm.
Design of spatio-temporally modulated static infrared imaging Fourier transform spectrometer.
Wang, WenCong; Liang, JingQiu; Liang, ZhongZhu; Lü, JinGuang; Qin, YuXin; Tian, Chao; Wang, WeiBiao
2014-08-15
A novel static medium wave infrared (MWIR) imaging Fourier transform spectrometer (IFTS) is conceptually proposed and experimentally demonstrated. In this system, the moving mirror in traditional temporally modulated IFTS is replaced by multi-step micro-mirrors to realize the static design. Compared with the traditional spatially modulated IFTS, they have no slit system and are superior with larger luminous flux and higher energy efficiency. The use of the multi-step micro-mirrors can also make the system compact and light. PMID:25121906
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.
Lin, Yu; Liao, Ning-fang; Luo, Yong-dao; Cui, De-qi; Tan, Bo-neng; Wu, Wen-min
2010-08-01
In the present paper, the authors will introduce our research on spectral reconstruction of Fourier transform computed tomography imaging spectrometer by means of the algebraic reconstruction technology. A simulation experiment was carried out to demonstrate the algorithm. The spatial similarities and spectral similarities were evaluated using the normalized correlation coefficient. The performance of ART was evaluated when the quantity of projection is 45. In that case, filter back projection can't work well. Actual spectral slices were reconstructed by using ART in the last part of this paper. PMID:20939312
NASA Astrophysics Data System (ADS)
Osowiecki, Gaël. D.; Madi, Mohammad; Shorubalko, Ivan; Philipoussis, Irène; Alberti, Edoardo; Scharf, Toralf; Herzig, Hans P.
2015-09-01
We show the miniaturization and parallelization of a scanning standing wave spectrometer with a long term goal of creating a compact imaging spectrometer. In our standing wave integrated Fourier transform spectrometer, light is injected with micro-lenses into several optical polymer waveguides. A piezo actuated mirror located at the waveguide end-facet can shift the interferogram to increase its sampling frequency. The spatial distribution of the standing wave intensity inside the waveguide is partially scattered out of the plane by a periodic metallic grating and recorded by a CCD camera. We present spectra acquisition for six adjacent waveguides simultaneously at a wavelength of 632.8 nm.
Remote Fourier transform-infrared spectral imaging system with hollow-optical fiber bundle.
Huang, Chenhui; Kino, Saiko; Katagiri, Takashi; Matsuura, Yuji
2012-10-10
A spectral imaging system consisting of a Fourier transform-infrared spectrometer, a high-speed infrared camera, and a bundle of hollow-optical fibers transmitting infrared radiation images was constructed. Infrared transmission spectra were obtained by carefully processing multiple interferograms taken by high-speed photography. Infrared spectral images of a variety of samples captured by the system were measured. We successfully detected existence maps of the oil and fat of biological samples by mapping the transmission of specific wavelengths in the spectrum. PMID:23052066
Automated turbulences jitters correction with a dual ports imaging Fourier-transform spectrometer
NASA Astrophysics Data System (ADS)
Prel, Florent; Lantagne, Stéphane; Moreau, Louis; Roy, Claude
2015-05-01
When the scene observed by an imaging Fourier-Transform Spectrometer is not stable in amplitude or in position during the time it takes to acquire to spectrum, spectro-radiometric artifacts are generated. These artifacts reduce the radiometric accuracy and may also damage the spectral line shape. The displacements of the scene in the field of view can be due to air turbulence, platform jitters or scene jitters. We describe an automated correction process based on the information provided by the second output port of a two-port imaging FTS. Corrected and uncorrected data will be compared.
MTI Thermal Bands Calibration at Ivanpah Playa with a Fourier Transform Infrared Spectrometer
Villa-Aleman, E.
2001-06-27
The Savannah River Technology Center (SRTC) is currently calibrating the Multispectral Thermal Imager (MTI) satellite sponsored by the Department of Energy. The reflective bands of the MTI satellite are calibrated in desert playas such as Ivanpah Playa in the Nevada/California border. The five MTI thermal bands are calibrated with targets of known emissivity and temperature such as power plant heated lakes. In order to accomplish a full calibration at the desert playas, a Fourier transform infrared spectrometer was used to measure soil surface radiance and temperature during the satellite overpass. The results obtained with the mobile FTIR during the ground truth campaign at Ivanpah Playa will be presented.
Research on algorithm for infrared hyperspectral imaging Fourier transform spectrometer technology
NASA Astrophysics Data System (ADS)
Wan, Lifang; Chen, Yan; Liao, Ningfang; Lv, Hang; He, Shufang; Li, Yasheng
2015-08-01
This paper reported the algorithm for Infrared Hyperspectral Imaging Radiometric Spectrometer Technology. Six different apodization functions are been used and compared, and the phase corrected technologies of Forman is researched and improved, fast fourier transform(FFT)is been used in this paper instead of the linear convolution to reduce the quantity of computation.The interferograms is achieved by the Infrared Hyperspectral Imaging Radiometric Spectrometer which are corrected and rebuilded by the improved algorithm, this algorithm reduce the noise and accelerate the computing speed with the higher accuracy of spectrometers.
Measurements of solar magnetic fields by Fourier transform techniques. I - Unsaturated lines
NASA Technical Reports Server (NTRS)
Title, A. M.; Tarbell, T. D.
1975-01-01
If the basic profile shapes of the normal Zeeman triplet do not have zeros in their Fourier transform, the magnetic field splitting can be determined independent of the profile shape. When the ratio of the splitting of the components is greater than the intrinsic FWHM of the component profiles, the magnetic splitting can be determined with significantly greater accuracy than the measurement accuracy of the original profile. For Gaussian shaped components and a ratio of magnetic splitting to FWHM of 1.5, the noise reduction factor is 25.
Application of micro-Fourier transform infrared spectroscopy to the examination of paint samples
NASA Astrophysics Data System (ADS)
Zięba-Palus, J.
1999-11-01
The examination and identification of automobile paints is an important problem in road accidents investigations. Since the real sample available is very small, only sensitive microtechniques can be applied. The methods of optical microscopy and micro-Fourier transform infrared spectroscopy (MK-FTIR) supported by scanning electron microscopy together with X-ray microanalysis (SEM-EDX) allow one to carry out the examination of each paint layer without any separation procedure. In this paper an attempt is made to discriminate between different automobile paints of the same colour by the use of these methods for criminalistic investigations.
Eyring, E.M.
1980-12-01
A description of visible Fourier transform photoacoustic spectroscopy (PAS) has been published in two places. Application of PAS to a zirconium phosphate inorganic system has also been described. The use of visible synchrotron radiation in quantitative high frequency PAS has been attempted, and a theoretical modeling of such experiments is nearing completion. A Nicolet FTIR spectrometer is being used to perform mid-infrared PA spectroscopy on carbon samples with a view to determining the best means of ratioing out variations with wavelength in infrared source intensity.
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 Astrophysics Data System (ADS)
Simonis, G. J.; Sattler, J. P.; Worchesky, T. L.; Leavitt, R. P.
1984-01-01
Nondispersive Fourier-transform-spectroscopic techniques are used to measure the complex indices of refraction of materials between frequencies of 120 and 550 GHz. Results are presented for crystal quartz, cross-linked polystyrene (Rexolite 1422), glass-loaded polytetrafluoroethylene (Duroid 5880) and a nickel ferrite (Trans-Tech 2-111). These results are compared with other data on these materials in this frequency range. The accuracy of these measurements yields a considerable improvement in the near-millimeter-wave characterization of several of these materials. For materials other than crystal quartz, the results are the first measurements of their properties over the entire frequency range studied.
Strehl ratio as the Fourier transform of a probability density of error differences.
Alonso, Miguel A; Forbes, G W
2016-08-15
To give useful insight into the impact of mid-spatial frequency structure on optical performance, the Strehl ratio is shown to correspond to the Fourier transform of a simple statistical characterization of the aberration in the exit pupil. This statistical description is found simply by autocorrelating a histogram of the aberration values. In practice, the histogram itself can often be approximated by a convolution of underlying histograms associated with fabrication steps and, together with the final autocorrelation, it follows from the central limit theorem that the Strehl ratio as a function of the scale of the phase error is generally approximated well by a Gaussian. PMID:27519076
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
Simple atmospheric transmittance calculation based on a Fourier-transformed Voigt profile.
Kobayashi, Hirokazu
2002-11-20
A method of line-by-line transmission calculation for a homogeneous atmospheric layer that uses the Fourier-transformed Voigt profile is presented. The method is based on a pure Voigt function with no approximation and an interference term that takes into account the line-mixing effect. One can use the method to calculate transmittance, considering each line shape as it is affected by temperature and pressure, with a line database with an arbitrary wave-number range and resolution. To show that the method is feasible for practical model development, we compared the calculated transmittance with that obtained with a conventional model, and good consistency was observed. PMID:12463237
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.
Aizikov, Konstantin; Mathur, Raman; O’Connor, Peter B.
2009-01-01
The spontaneous loss of coherence catastrophe (SLCC) is a frequently observed, yet poorly studied, space-charge related effect in Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS). This manuscript presents an application of the filter diagonalization method (FDM) in the analysis of this phenomenon. The temporal frequency behavior reproduced by frequency shift analysis using the FDM shows the complex nature of the SLCC, which can be explained by a combination of factors occurring concurrently, governed by electrostatics and ion packet trajectories inside the ICR cell. PMID:19013078
NASA Technical Reports Server (NTRS)
Smillie, D. G.; Pickering, J. C.; Blackwell-Whitehead, R. J.; Smith, Peter L.; Nave, G.
2006-01-01
We report new measurements of doubly ionized iron group element spectra, important in the analysis of B-type (hot) stars whose spectra they dominate. These measurements include Co III and Cr III taken with the Imperial College VUV Fourier transform (FT) spectrometer and measurements of Co III taken with the normal incidence vacuum spectrograph at NIST, below 135 nm. We report new Fe III grating spectra measurements to complement our FT spectra. Work towards transition wavelengths, energy levels and branching ratios (which, combined with lifetimes, produce oscillator strengths) for these ions is underway.
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
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.
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.
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.
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
NASA Astrophysics Data System (ADS)
Han, Yanong; Sonnenberg, Wendi; Short, Kurt W.; Spangler, Lee H.
1999-10-01
We have developed methods of measuring absorption of transient species utilizing stepped-scan Fourier transform interferometry that allows a combination of broad spectral coverage (10,000 - 15,000 cm-1 per spectrum), good spectral resolution, and up to ns temporal resolution with possibilities of extension to the ps domain. Nanosecond, psec or fsec laser systems, tunable from UV to IR can be used as the pump source to prepare the transient species. The absorption of that species is measured with broadband, incoherent light and can be simultaneously time and frequency resolved.
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.
Fourier transform C-13 NMR analysis of some free and potassium-ion complexed antibiotics.
NASA Technical Reports Server (NTRS)
Ohnishi, M.; Fedarko, M.-C.; Baldeschwieler, J. D.; Johnson, L. F.
1972-01-01
Fourier transforms of the noise-decoupled, natural abundance C-13 NMR free induction decays of the cyclic antibiotic valinomycin and its potassium-ion complex have been obtained at 25.2 MHz. Comparisons are made with C-13 NMR spectra taken at 22.6 MHz of the cyclic antibiotic nonactin and the synthetic polyether dicyclohexyl-18-crown-6 and their potassium complexes. The results obtained suggest that conformational rearrangements of the molecule as a whole can compete with direct interactions between carbons and the potassium ion in determining C-13 chemical shift differences between the free and complexed species.
NASA Astrophysics Data System (ADS)
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.
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>
Blackford, Jennifer Urbano; Salomon, Ronald M.; Waller, Niels G.
2009-01-01
Treatment-related changes in neurobiological rhythms are of increasing interest to psychologists, psychiatrists, and biological rhythms researchers. New methods for analyzing change in rhythms are needed, as most common methods disregard the rich complexity of biological processes. Large time series data sets reflect the intricacies of underlying neurobiological processes, but can be difficult to analyze. We propose the use of Fourier methods with multivariate permutation test (MPT) methods for analyzing change in rhythms from time series data. To validate the use of MPT for Fourier-transformed data, we performed Monte Carlo simulations and compared statistical power and family-wise error for MPT to Bonferroni-corrected and uncorrected methods. Results show that MPT provides greater statistical power than Bonferroni-corrected tests, while appropriately controlling family-wise error. We applied this method to human, pre-and post-treatment, serially-sampled neurotransmitter data to confirm the utility of this method using real data. Together, Fourier with MPT methods provides a statistically powerful approach for detecting change in biological rhythms from time series data. PMID:19212840
Reconstruction of piecewise homogeneous images from partial knowledge of their Fourier Transform
NASA Astrophysics Data System (ADS)
Féron, Olivier; Chama, Zouaoui; Mohammad-Djafari, Ali
2004-11-01
Fourier synthesis (FS) inverse problem consists in reconstructing a multi-variable function from the measured data which correspond to partial and uncertain knowledge of its Fourier Transform (FT). By partial knowledge we mean either partial support and/or the knowledge of only the module and by uncertain we mean both uncertainty of the model and noisy data. This inverse problem arises in many applications such as : optical imaging, radio astronomy, magnetic resonance imaging (MRI) and diffraction scattering (ultrasounds or microwave imaging). Most classical methods of inversion are based on interpolation of the data and fast inverse FT. But when the data do not fill uniformly the Fourier domain or when the phase of the signal is lacking as in optical interferometry, the results obtained by such methods are not satisfactory, because these inverse problems are ill-posed. The Bayesian estimation approach, via an appropriate modeling of the unknown functions gives the possibility of compensating the lack of information in the data, thus giving satisfactory results. In this paper we study the case where the observations are a part of the FT modulus of objects which are composed of a few number of homogeneous materials. To model such objects we use a Hierarchical Hidden Markov Modeling (HMM) and propose a Bayesian inversion method using appropriate Markov Chain Monte Carlo (MCMC) algorithms.
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.
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.
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
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.
Rebagay, T.V.; Dodd, D.A.
1989-07-01
The effective immobilization of low-level radioactive liquid wastes in the form of grout depends on the quality of the dry cementitious blends used in the grout formulation. Variation in the mix ratios of the components of the blend can cause detrimental effects on the processing behavior of the grout slurry and the final properties of the cured grout. Thus the blends require thorough chemical characterization and monitoring by strict quality control protocols. In an earlier work at our laboratories, Fourier transform infrared- transmission method has been successfully applied in the analysis of blends of cement, fly ash, and clays. However, this method involved time-consuming sample preparation resulting in slow turnaround for repetitive sampling. A practical approach to quality control required a fast and simple method for the analysis of the blends. This paper describes a diffuse reflectance infrared Fourier transform (DRIFT) spectrometric procedure for the routine examination of neat blends consisting of cement, fly ash, clays and/or blast furnace slags. (1 ref., 10 figs., 4 tabs.)
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 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)
Wang, Guangjun; Wang, Huaying; Wang, Dayong; Xie, Jianjun; Zhao, Jie
2007-12-01
A simple holographic high-resolution imaging system without pre-magnification, which is based on off-axis lensless Fourier transform configuration, has been developed. Experimental investigations are performed on USAF resolution test target. The method based on angular spectrum theory for reconstructing lensless Fourier hologram is given. The reconstructed results of the same hologram at different reconstructing distances are presented for what is to our knowledge the first time. Approximate diffraction limited lateral resolution is achieved. The results show that the angular spectrum method has several advantages over more commonly used Fresnel transform method. Lossless reconstruction can be achieved for any numerical aperture holograms as long as the wave field is calculated at a special reconstructing distance, which is determined by the light wavelength and the chip size and the pixel size of the CCD sensor. This is very important for reconstructing an extremely large numerical aperture hologram. Frequency-domain spectrum filtering can be applied conveniently to remove the disturbance of zero-order. The reconstructed image wave field is accurate so long as the sampling theorem is not violated. The experimental results also demonstrate that for a high quality hologram, special image processing is unnecessary to obtain a high quality image.
NASA Astrophysics Data System (ADS)
Otten, Leonard John, III; Butler, Eugene W.; Rafert, Bruce; Sellar, R. Glenn
1995-06-01
Kestrel Corporation and the Florida Institute of Technology have designed, and are now manufacturing, a Fourier transform visible hyperspectral imager system for use in a single engine light aircraft. The system is composed of a Sagnac-based interferometer optical subsystem, a data management system, and an aircraft attitude and current position sybsystem. The system is designed to have better than 5 nm spectral resolution at 450 nm, operates over the 440 nm to 1150 nm spectral band and has a 2D spatial resolution of 0.8 mrad. An internal calibration source is recorded with every frame of data to retain radiometric accuracy. The entire system fits into a Cessna 206 and uses a conventional downward looking view port located in the baggage compartment. During operation, data are collected at a rate of 15 Mbytes per second and stored direct to a disk array. Data storage has been sized to accommodate 56 minutes of observations. Designed for environmental mapping, this Fourier transform imager has uses in emergency response and military operations.
Gorzsás, András; Sundberg, Björn
2014-01-01
Fourier transform infrared (FT-IR) spectroscopy is a fast, sensitive, inexpensive, and nondestructive technique for chemical profiling of plant materials. In this chapter we discuss the instrumental setup, the basic principles of analysis, and the possibilities for and limitations of obtaining qualitative and semiquantitative information by FT-IR spectroscopy. We provide detailed protocols for four fully customizable techniques: (1) Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS): a sensitive and high-throughput technique for powders; (2) attenuated total reflectance (ATR) spectroscopy: a technique that requires no sample preparation and can be used for solid samples as well as for cell cultures; (3) microspectroscopy using a single element (SE) detector: a technique used for analyzing sections at low spatial resolution; and (4) microspectroscopy using a focal plane array (FPA) detector: a technique for rapid chemical profiling of plant sections at cellular resolution. Sample preparation, measurement, and data analysis steps are listed for each of the techniques to help the user collect the best quality spectra and prepare them for subsequent multivariate analysis. PMID:24057375
Algorithm, applications and evaluation for protein comparison by Ramanujan Fourier transform.
Zhao, Jian; Wang, Jiasong; Hua, Wei; Ouyang, Pingkai
2015-12-01
The amino acid sequence of a protein determines its chemical properties, chain conformation and biological functions. Protein sequence comparison is of great importance to identify similarities of protein structures and infer their functions. Many properties of a protein correspond to the low-frequency signals within the sequence. Low frequency modes in protein sequences are linked to the secondary structures, membrane protein types, and sub-cellular localizations of the proteins. In this paper, we present Ramanujan Fourier transform (RFT) with a fast algorithm to analyze the low-frequency signals of protein sequences. The RFT method is applied to similarity analysis of protein sequences with the Resonant Recognition Model (RRM). The results show that the proposed fast RFT method on protein comparison is more efficient than commonly used discrete Fourier transform (DFT). RFT can detect common frequencies as significant feature for specific protein families, and the RFT spectrum heat-map of protein sequences demonstrates the information conservation in the sequence comparison. The proposed method offers a new tool for pattern recognition, feature extraction and structural analysis on protein sequences. PMID:26325081
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.
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.
Binary encoding method to encrypt Fourier-transformed information of digital images
NASA Astrophysics Data System (ADS)
Lin, Kuang Tsan
2009-02-01
An encoding method is used to encrypt the Fourier-transformed information of a hidden (covert) digital image in an overt image, while the Fourier-transformed information must be encoded with binary codes. All of the pixels in an overt image are classified into five groups that are called identification, type, tracing, dimension, and information codes. Identification codes are used to judge if the overt image contains codes that belong to the proposed encoding method or not; type codes are used to judge the encoding type; tracing codes are used to judge the encoding trace; dimension codes are used to judge the size of the hidden information; and information codes are used to decode the hidden information. Applying the proposed encoding method is rather easy, and host images corresponding to overt images are not needed for decoding work. The experiment has demonstrated four types of encoding for the proposed encoding method to reconstruct covert images without any distortion or only with a little distortion.
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
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.
Fourier Transform Infrared Emission Spectroscopy and AB Initio Study of Hbo and BO
NASA Astrophysics Data System (ADS)
Li, G.; Hargreaves, R. J.; Bernath, P. F.
2010-06-01
The Fourier-transform infrared emission spectra of HBO and BO were recorded using a Bruker IFS-125HR Fourier transform spectrometer. HBO molecules were synthesized using a high temperature tube furnace at 1450 °C. Our spectra of the HBO molecule in the 1200-4000 cm-1 region contain the v1 and v3 fundamental vibrational modes plus numerous hot bands. An accurate potential energy surface using the MRCI method with correlation consistent core-valence basis sets aug-cc-PCVnZ (n=3, 4, 5) is being calculated and a vibrational configuration interaction (VCI) calculation based on this surface will be performed to assist in the assignment of the HBO hot bands. BO molecules were produced by applying a DC discharge to the furnace containing HBO. Our spectrum of BO in the 1200-2100 cm-1 region contains the fundamental bands of both isotopic species, 11BO, 10BO, and one hot band of the main isotopologue 11BO. The fundamental band of 11BO contains 95 lines roughly equally distributed between the P and R branches. A combined least-squares fit with ground state microwave data was performed to determine the spectroscopic constants. Further results on this ongoing project will be presented.
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.
NASA Astrophysics Data System (ADS)
Wu, Xuebin; Yan, Zhiyuan; Lin, Jun
2012-07-01
Long Reed-Solomon (RS) codes are desirable for digital communication and storage systems due to their improved error performance, but the high computational complexity of their decoders is a key obstacle to their adoption in practice. As discrete Fourier transforms (DFTs) can evaluate a polynomial at multiple points, efficient DFT algorithms are promising in reducing the computational complexities of syndrome based decoders for long RS codes. In this paper, we first propose partial composite cyclotomic Fourier transforms (CCFTs) and then devise syndrome based decoders for long RS codes over large finite fields based on partial CCFTs. The new decoders based on partial CCFTs achieve a significant saving of computational complexities for long RS codes. Since partial CCFTs have modular and regular structures, the new decoders are suitable for hardware implementations. To further verify and demonstrate the advantages of partial CCFTs, we implement in hardware the syndrome computation block for a $(2720, 2550)$ shortened RS code over GF$(2^{12})$. In comparison to previous results based on Horner's rule, our hardware implementation not only has a smaller gate count, but also achieves much higher throughputs.
NASA Astrophysics Data System (ADS)
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
Instrumental phase-based method for Fourier transform spectrometer measurements processing
Saggin, Bortolino; Scaccabarozzi, Diego; Tarabini, Marco
2011-04-20
Phase correction is a critical procedure for most space-borne Fourier transform spectrometers (FTSs) whose accuracy (owing to often poor signal-to-noise ratio, SNR) can be jeopardized from many uncontrollable environmental conditions. This work considers the phase correction in an FTS working under significant temperature change during the measurement and affected by mechanical disturbances. The implemented method is based on the identification of an instrumental phase that is dependent on the interferometer temperature and on the extraction of a linear phase component through a least-squares approach. The use of an instrumental phase parameterized with the interferometer temperature eases the determination of the linear phase that can be extracted using only a narrow spectral region selected to be immune from disturbances. The procedure, in this way, is made robust against phase errors arising from instrumental effects, a key feature to reduce the disturbances through spectra averaging. The method was specifically developed for the Mars IR Mapper spectrometer, that was designed for operation onboard a rover on the Mars surface; the validation was performed using ground and in-flight measurements of the Fourier transform IR spectrometer planetary Fourier spectrometer, onboard the MarsExpress mission. The symmetrization has been exploited also for the spectra calibration, highlighting the issues deriving from the cases of relevant beamsplitter emission. The applicability of this procedure to other instruments is conditional to the presence in the spectra of at least one spectral region with a large SNR along with a negligible (or known) beamsplitter emission. For the PFS instrument, the processing of data with relevant beamsplitter emission has been performed exploiting the absorption carbon dioxide bands present in Martian spectra.
Instrumental phase-based method for Fourier transform spectrometer measurements processing.
Saggin, Bortolino; Scaccabarozzi, Diego; Tarabini, Marco
2011-04-20
Phase correction is a critical procedure for most space-borne Fourier transform spectrometers (FTSs) whose accuracy (owing to often poor signal-to-noise ratio, SNR) can be jeopardized from many uncontrollable environmental conditions. This work considers the phase correction in an FTS working under significant temperature change during the measurement and affected by mechanical disturbances. The implemented method is based on the identification of an instrumental phase that is dependent on the interferometer temperature and on the extraction of a linear phase component through a least-squares approach. The use of an instrumental phase parameterized with the interferometer temperature eases the determination of the linear phase that can be extracted using only a narrow spectral region selected to be immune from disturbances. The procedure, in this way, is made robust against phase errors arising from instrumental effects, a key feature to reduce the disturbances through spectra averaging. The method was specifically developed for the Mars IR Mapper spectrometer, that was designed for operation onboard a rover on the Mars surface; the validation was performed using ground and in-flight measurements of the Fourier transform IR spectrometer planetary Fourier spectrometer, onboard the MarsExpress mission. The symmetrization has been exploited also for the spectra calibration, highlighting the issues deriving from the cases of relevant beamsplitter emission. The applicability of this procedure to other instruments is conditional to the presence in the spectra of at least one spectral region with a large SNR along with a negligible (or known) beamsplitter emission. For the PFS instrument, the processing of data with relevant beamsplitter emission has been performed exploiting the absorption carbon dioxide bands present in Martian spectra. PMID:21509063
Real-time 2D floating-point fast Fourier transforms for seeker simulation
NASA Astrophysics Data System (ADS)
Chamberlain, Richard; Lord, Eric; Shand, David J.
2002-07-01
The floating point Fast Fourier Transform (FFT) is one of the most useful basic functions available to the image and signal processing engineer allowing many complex and detailed special functions to be implemented more simply in the frequency domain. In the Hardware-in-the-Loop field an image transformed using FFT would allow the designer to think about accurate frequency based simulation of seeker lens effects, motion blur, detector transfer functions and much more. Unfortunately, the transform requires many hundreds of thousands or millions of floating point operations on a single modest sized image making it impractical for realtime Hardware-in-the-Loop systems. .until now. This paper outlines the development, by Nallatech, of an FPGA based IEEE floating point core. It traces the subsequent use of this core to develop a full 256 X 256 FFT and filter process implemented on COTS hardware at frame rates up to 150Hz. This transform can be demonstrated to model optical transfer functions at a far greater accuracy than the current spatial models. Other applications and extensions of this technique will be discussed such as filtering for image tracking algorithms and in the simulation of radar processing in the frequency domain.
Chen, Li; Yap, Yee Leng
2008-01-01
This study describes a new algorithm for charge state determination of complex isotope-resolved mass spectra. This algorithm is based on peak-target Fourier transform (PTFT) of isotope packets. It is modified from the widely used Fourier transform method because Fourier transform may give ambiguous charge state assignment for low signal-to-noise ratio (S/N) or overlapping isotopic clusters. The PTFT algorithm applies a novel "folding" strategy to enhance peaks that are symmetrically spaced about the targeted peak before applying the FT. The "folding" strategy multiplies each point to the high-m/z side of the targeted peak by its counterpart on the low-m/z side. A Fourier transform of this "folded" spectrum is thus simplified, emphasizing the charge state of the "chosen" ion, whereas ions of other charge states contribute less to the transformed data. An intensity-dependent technique is also proposed for charge state determination from frequency signals. The performance of PTFT is demonstrated using experimental electrospray ionization Fourier transform ion cyclotron resonance mass spectra. The results show that PTFT is robust for charge state determination of low S/N and overlapping isotopic clusters, and also useful for manual verification of potential hidden isotopic clusters that may be missed by the current analysis algorithms, i.e., AID-MS or THRASH. PMID:18293485
NASA Technical Reports Server (NTRS)
Klimas, A. J.
1983-01-01
A numerical method is presented for studying one-dimensional electron plasma evolution under typical interplanetary conditions. The method applies the Fourier-Fourier transform approach to a plasma model that is a generalization of the electrostatic Vlasov-Poisson system of equations. Conservation laws that are modified to include the plasma model generalization and also the boundary effects of nonperiodic solutions are given. A new conservation law for entropy in the transformed space is then introduced. These conservation laws are used to verify the numerical solutions. A discretization error analysis is presented. Two numerical instabilities and the methods used for their suppression are treated. It is shown that in interplanetary plasma conditions, the bump-on-tail instability produces significant excitation of plasma oscillations at the Bohm-Gross frequency and its second harmonic. An explanation of the second harmonic excitation is given in terms of wave-wave coupling during the growth phase of the instability.