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.
Fourier transform spectra of quantum dots
NASA Astrophysics Data System (ADS)
Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.
2010-05-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
Fourier transform spectra of quantum dots
NASA Astrophysics Data System (ADS)
Damian, V.; Ardelean, I.; Armăşelu, Anca; Apostol, D.
2009-09-01
Semiconductor quantum dots are nanometer-sized crystals with unique photochemical and photophysical properties that are not available from either isolated molecules or bulk solids. These nanocrystals absorb light over a very broad spectral range as compared to molecular fluorophores which have very narrow excitation spectra. High-quality QDs are proper to be use in different biological and medical applications (as fluorescent labels, the cancer treatment and the drug delivery). In this article, we discuss Fourier transform visible spectroscopy of commercial quantum dots. We reveal that QDs produced by Evident Technologies when are enlightened by laser or luminescent diode light provides a spectral shift of their fluorescence spectra correlated to exciting emission wavelengths, as shown by the ARCspectroNIR Fourier Transform Spectrometer. In the final part of this paper we show an important biological application of CdSe/ZnS core-shell ODs as microbial labeling both for pure cultures of cyanobacteria (Synechocystis PCC 6803) and for mixed cultures of phototrophic and heterotrophic microorganisms.
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.
Quantum Fourier transform performance scaling; defective rotation gates
NASA Astrophysics Data System (ADS)
Nam, Yunseong; Blumel, Reinhold
2015-03-01
We investigate analytically and numerically the quantum Fourier transform (QFT) with defective controlled rotation (CROT) gates. We find that the QFT can tolerate systematic and random defects up to 30 % and still perform its function. Analytical scaling laws of QFT performance are derived with respect to the number of qubits n, the size δ of systematic defects, and size ɛ of random defects. Our analytical results are in excellent agreement with numerical simulations. In addition, we present an unexpected result: The performance of the defective QFT does not deteriorate with increasing n, but approaches a constant that scales in ɛ. We derive an analytical formula that accurately reproduces the ɛ scaling of the performance plateaus. The extraordinary robustness of the QFT with respect to static gate defects displayed in our numerical and analytical calculations should be a welcome boon for laboratory and industrial realizations of quantum circuitry.
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.
NASA Astrophysics Data System (ADS)
Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong
2016-09-01
To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.
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
2016-02-04
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms.
Suppression law of quantum states in a 3D photonic fast Fourier transform chip
Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio
2016-01-01
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135
Song, Xinbing; Sun, Yifan; Li, Pengyun; Qin, Hongwei; Zhang, Xiangdong
2015-09-15
We perform Bell's measurement for the non-separable correlation between polarization and orbital angular momentum from the same classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally.
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.
Robustness of the quantum Fourier transform with respect to static gate defects
NASA Astrophysics Data System (ADS)
Nam, Y. S.; Blümel, R.
2014-04-01
The quantum Fourier transform (QFT) is one of the most widely used quantum algorithms, ranging from its primary role in finding the periodicity hidden in a quantum state to its use in constructing a quantum adder. Testing how the QFT performs under more realistic conditions, we find that the QFT, when used for period finding, shows extraordinary robustness with respect to static gate defects. For instance, replacing all rotation angles π /2j of the controlled rotation gates in the QFT circuit by π(1+r )/2j, where r is a uniformly distributed random variable taking values in the range [-1,1], effectively resulting in a QFT with random gates, the QFT performs well above the expected random result. However, it is important to keep the 2j terms in the denominators of the rotation angles, resulting in random, but hierarchically random, gates. Relaxing this hierarchical structure of the QFT circuit, we find that the performance of the QFT deteriorates significantly. This observation indicates that the hierarchical structure of the quantum circuit of the QFT is more important for the observed robustness in performance than the precise actions of individual gates. In addition to the specific example of the QFT circuit studied here, this observation also corroborates our experience with more general and more complex quantum circuits. Thus, backed by our detailed numerical and analytical results, we may condense the results of our research into the following general principle: The topology of a quantum circuit is more important than the precise actions of its gates.
Fourier transform infrared spectroscopy
Ferraro, J.R.; Basile, L.J.
1985-01-01
The final and largest volume to complete this four-volume treatise is published in response to the intense commercial and research interest in Fourier Transform Interferometry. Volume 4 introduces new information on, for example, applications of Diffuse Reflectance Spectroscopy in the Far-infrared Region. The editors place emphasis on surface studies and address advances in Capillary Gas Chromatography-Fourier Transform Interferometry.
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 mass spectrometry.
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-07-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.
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
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.
Submillimeter Fourier transform spectroscopy
NASA Astrophysics Data System (ADS)
Serabyn, Eugene
1998-07-01
At submillimeter wavelengths, broadband spectroscopy is currently possible only with a Fourier transform spectrometer (FTS). As a result, FTSes are quite useful for observations of objects in which spectral lines either cover a large frequency range, or where lines are broadened either by pressure or kinematics. Sources matching these descriptions include galaxies, hot, dense cores in interstellar molecular clouds, and planetary atmospheres. In the following, a tour of the classes of observations enabled by broadband spectroscopy is presented. As meaningful results call for attention to calibration, relevant calibration issues are discussed in the context of these observations.
NASA Technical Reports Server (NTRS)
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Fast Fourier transform telescope
Tegmark, Max; Zaldarriaga, Matias
2009-04-15
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore's law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog{sub 2}N rather than N{sup 2}) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Imaging Fourier Transform Spectrometer
Bennett, C.L.; Carter, M.R.; Fields, D.J.; Hernandez, J.
1993-04-14
The operating principles of an Imaging Fourier Transform Spectrometer (IFTS) are discussed. The advantages and disadvantages of such instruments with respect to alternative imaging spectrometers are discussed. The primary advantages of the IFTS are the capacity to acquire more than an order of magnitude more spectral channels than alternative systems with more than an order of magnitude greater etendue than for alternative systems. The primary disadvantage of IFTS, or FTS in general, is the sensitivity to temporal fluctuations, either random or periodic. Data from the IRIFTS (ir IFTS) prototype instrument, sensitive in the infrared, are presented having a spectral sensitivity of 0.01 absorbance units, a spectral resolution of 6 cm{sup {minus}1} over the range 0 to 7899 cm{sup {minus}1}, and a spatial resolution of 2.5 mr.
Fourier Transform Spectrometer System
NASA Technical Reports Server (NTRS)
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
NASA Astrophysics Data System (ADS)
Ermilov, A. S.; Zobov, V. E.
2007-12-01
To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3-10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.
NASA Astrophysics Data System (ADS)
Snehalatha, M.; Sekar, N.; Jayakumar, V. S.; Joe, I. Hubert
2008-01-01
Fourier transform infrared (FTIR) spectrum of a well-known food dye sunset yellow FCF (E110) has been recorded and analysed. Assignments of the vibrational spectrum has been facilitated by density functional theory (DFT) calculations. The results of the optimized molecular structure obtained on the basis of B3LYP with 6-31G(d) along with the 'LANL2DZ' basis sets give clear evidence for the intramolecular charge transfer (ICT) and strong hydrogen bonding enhancing the optical nonlinearity of the molecule. The first hyperpolarizability of the acidic monoazo dye 'E110' is computed. Azo stretching frequencies have been lowered due to conjugation and π-electron delocalization. Hydroxyl vibrations with intramolecular H-bonding are analyzed, supported by the computed results. The natural bond orbitals (NBO) analysis confirms this strong hydrogen bond between the hydrogen of the hydroxyl group and nitrogen of the azo group of the molecule. Assignments of benzene and naphthalene ring vibrations are found to agree well with the theoretical wave numbers.
Multiple fractional Fourier transform holography
NASA Astrophysics Data System (ADS)
Zeng, Yangsu; Zhang, Yixiao; Gao, Feng; Gao, Fuhua; Huang, Xiaoyang; Guo, Yongkang
2002-04-01
In this paper, we introduce the recording and reconstruction theories of the multiple fractional Fourier transform hologram (M-FRTH). We fabricated a multiple fractional Fourier transform hologram, and obtained satisfying reconstruction results. The experimental result shows that the M-FRTH has a high anti-counterfeiting capacity and can be used in the fabrication of the trademark, ID, and the notes.
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.
Fourier transform of confining potentials
Heiss, W.D.; Welke, G.M.
1986-04-01
The precise meaning of the Fourier transform of Vertical BarxVertical Bar/sup ..nu../ is examined. A general expression is given for real positive ..nu... For odd ..nu.., derivatives of principal value integrals are obtained, while even ..nu.. gives rise to derivatives of the delta function.
ERIC Educational Resources Information Center
Debnath, Lokenath
2012-01-01
This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…
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.
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.
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 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.
Faraggi, A.E.; Matone, M.
1998-01-09
We show that the quantum Hamilton-Jacobi equation can be written in the classical form with the spatial derivative {partial_derivative}{sub q} replaced by {partial_derivative}{sub q} with dq = dq/{radical}1{minus}{beta}{sup 2}(q), where {beta}{sup 2}(q) is strictly related to the quantum potential. This can be seen as the opposite of the problem of finding the wave function representation of classical mechanics as formulated by Schiller and Rosen. The structure of the above {open_quotes}quantum transformation{close_quotes}, related to the recently formulated equivalence principle, indicates that the potential deforms space geometry. In particular, a result by Flanders implies that both W(q) = V(q) {minus} E and the quantum potential Q are proportional to the curvatures {kappa}{sub W} and {kappa}{sub Q} which arise as natural invariants in an equivalence problem for curves in the projective line. In this formulation the Schroedinger equation takes the geometrical form ({partial_derivative}{sub q}{sup 2} + {kappa}{sub W}){psi} = 0.
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 Analysis and Structure Determination: Part I: Fourier Transforms.
ERIC Educational Resources Information Center
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
Fourier transform and related integral transforms in superspace
NASA Astrophysics Data System (ADS)
de Bie, H.
2008-09-01
In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to superspace are studied. Previously, a Fourier transform in superspace was already studied, but with a different kernel. In this work, the fermionic part of the Fourier kernel has a natural symplectic structure, derived using a Clifford analysis approach. Several basic properties of these three transforms are studied. Using suitable generalizations of the Hermite polynomials to superspace (see [H. De Bie, F. Sommen, Hermite and Gegenbauer polynomials in superspace using Clifford analysis, J. Phys. A 40 (2007) 10441-10456]) an eigenfunction basis for the Fourier transform is constructed.
NASA Astrophysics Data System (ADS)
Neeman, Elias M.; Dréan, Pascal; Huet, T. R.
2016-06-01
The emission of volatile organic compounds, from plants has strong revelance for plant physiology, plant ecology and atmospheric chemistry. Camphene (C10H16) is a bicyclic monoterpene which is emitted in the atmosphere by biogenic sources. 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. A magnetic hyperfine structure associated with the pairs of hydrogen nuclei in the methylene groups was observed and modeled.The rotational constants coupled to the equilibrium structure calculations were used to determine the r_0 and the r_m(1) gas-phase geometries of the carbon skeleton. The present work provides the first spectroscopic characterization of camphene in the gas phase and these results are also relevant for ozonolysis kinetics study through Criegee intermediates. R. Baraldi, F. Rapparini, O. Facini, D. Spano and P. Duce, Journal of Mediterranean Ecology, Vol.6, No.1, (2005). A. Bracho-Nunez, N. M. Knothe, S. Welter, M. Staudt, W. R. Costa, M. A. R. Liberato, M. T. F. Piedade, and J. Kesselmeier Biogeosciences, 10, 5855-5873, (2013). Minna Kivimäenpää, Narantsetseg Magsarjav, Rajendra Ghimire, Juha-Matti Markkanen, Juha Heijari, Martti Vuorinen and Jarmo K. Holopainen, Atmospheric Environment, 60, 477-485, (2012). R.C. de M. Oliveira and G. F. Bauerfeldt, J. Phys. Chem. A, 119 2802-2812 (2015)
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.
NASA Astrophysics Data System (ADS)
Furue, Shigenori; Nakayama, Kazuyuki; Kohmoto, Toshiro; Kunitomo, Masakazu; Fukuda, Yukio
2004-05-01
The fast-spin dynamics of transition-metal ions in an aqueous solution at room temperature has been directly observed in the subnanosecond region by polarization spectroscopy using the pump-probe technique. The time evolution of the optically induced magnetization is monitored through the change in the polarization of the probe pulse. Quantum-beat free-induction decay signals in the ground state of copper ions in an aqueous solution of copper sulfate are observed in transverse magnetic fields. The Fourier transform of the observed signals gives the ESR spectra. From the magnetic-field dependence of the beat frequency, the g-value of copper ions is g=2.20± 0.05. The observed line shape of the ESR spectra suggests that the hydrated copper complex rotates in the picosecond region. This all-optical method can be a powerful tool for the study of fast-spin dynamics in solutions.
NASA Astrophysics Data System (ADS)
Heo, Jino; Kang, Min-Sung; Hong, Chang-Ho; Yang, Hyeon; Choi, Seong-Gon
2016-09-01
We present a scheme for implementing discrete quantum Fourier transform (DQFT) with robustness against the decoherence effect using weak cross-Kerr nonlinearities (XKNLs). The multi-photon DQFT scheme can be achieved by operating the controlled path and merging path gates that are formed with weak XKNLs and linear optical devices. To enhance feasibility under the decoherence effect, in practice, we utilize a displacement operator and photon-number-resolving measurement in the optical gate using XKNLs. Consequently, when there is a strong amplitude of the coherent state, we demonstrate that it is possible to experimentally implement the DQFT scheme, utilizing current technology, with a certain probability of success under the decoherence effect.
Demystification of the geometric Fourier transforms
NASA Astrophysics Data System (ADS)
Bujack, Roxana; Scheuermann, Gerik; Hitzer, Eckhard
2013-10-01
As it will turn out in this paper, the recent hype about most of the Clifford Fourier transforms is not thoroughly worth the pain. Almost every one that has a real application is separable and these transforms can be decomposed into a sum of real valued transforms with constant multivecor factors. This fact makes their interpretation, their analysis, and their implementation almost trivial.
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.
ERIC Educational Resources Information Center
Glasser, L.
1987-01-01
This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…
Image processing and the Arithmetic Fourier Transform
Tufts, D.W.; Fan, Z.; Cao, Z.
1989-01-01
A new Fourier technique, the Arithmetic Fourier Transform (AFT) was recently developed for signal processing. This approach is based on the number-theoretic method of Mobius inversion. The AFT needs only additions except for a small amount of multiplications by prescribed scale factors. This new algorithm is also well suited to parallel processing. And there is no accumulation of rounding errors in the AFT algorithm. In this reprint, the AFT is used to compute the discrete cosine transform and is also extended to 2-D cases for image processing. A 2-D Mobius inversion formula is proved. It is then applied to the computation of Fourier coefficients of a periodic 2-D function. It is shown that the output of an array of delay-line (or transversal) filters is the Mobius transform of the input harmonic terms. The 2-D Fourier coefficients can therefore be obtained through Mobius inversion of the output of the filter array.
NASA Astrophysics Data System (ADS)
Liu, Shu-Guang; Fan, Hong-Yi
2009-12-01
We find that constructing the two mutually-conjugate tripartite entangled state representations naturally leads to the entangled Fourier transformation. We then derive the convolution theorem for the threedimensional entangled fractional Fourier transformation in the context of quantum mechanics.
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 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.
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.
Fourier transform infrared imaging of bone.
Paschalis, Eleftherios P
2012-01-01
Fourier transform infrared imaging (FTIRI) is a technique that can be used to analyze the material properties of bone using tissue sections. In this chapter I describe the basic principles of FTIR and the methods for capturing and analyzing FTIR images in bone sections.
Pseudochromatic encoding fractional Fourier transform rainbow hologram
NASA Astrophysics Data System (ADS)
Guo, Yongkang; Huang, Qizhong; Du, Jinglei
1998-08-01
The FRTH is presented in this paper and its properties are discussed. Then we make a pseudo chromatic encoding fractional Fourier transform rainbow hologram, based on its specialty in its reconstruction and that the encoding color has relationship with the order of the reconstruction FRT system, a new type of anti-counterfeiting hologram is introduced.
Fourier transform infrared spectrometery: an undergraduate experiment
NASA Astrophysics Data System (ADS)
Lerner, L.
2016-11-01
Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory.
Livermore Imaging Fourier Transform Infrared Spectrometer (LIFTIRS)
Carter, M.R.; Bennett, C.L.; Fields, D.J.; Lee, F.D.
1995-05-10
Lawrence Livermore National Laboratory is currently operating a hyperspectral imager, the Livermore Imaging Fourier Transform Infrared Spectrometer (LIFTIRS). This instrument is capable of operating throughout the infrared spectrum from 3 to 12.5 {mu}m with controllable spectral resolution. In this presentation we report on it`s operating characteristics, current capabilities, data throughput and calibration issues.
Fourier Transform and Reflective Imaging Pyrometry
Stevens, G. D.
2011-07-01
A stationary Fourier transform pyrometer was used to record mid-wavelength IR spectra in dynamic shock experiments. The gated-IR camera used with this system was also used to record images of light produced and light reflected from shocked metals in order to constrain the dynamic emissivity and provide temperature estimates. This technique will be referred to as reflective imaging pyrometry.
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.
Discrete Fourier transforms of nonuniformly spaced data
NASA Technical Reports Server (NTRS)
Swan, P. R.
1982-01-01
Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.
Electro-optic imaging Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm
NASA Astrophysics Data System (ADS)
García, Javier; Mas, David; Dorsch, Rainer G.
1996-12-01
A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT s in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from 1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT are discussed.
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.
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
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.
Fourier transform infrared spectroscopy of deuterated proteins
NASA Astrophysics Data System (ADS)
Marcano O., A.; Markushin, Y.; Melikechi, N.; Connolly, D.
2008-08-01
We report on Fourier transform spectra of deuterated proteins: Bovine Serum Albumin, Leptin, Insulin-like Growth Factor II, monoclonal antibody to ovarian cancer antigen CA125 and Osteopontin. The spectra exhibit changes in the relative amplitude and spectral width of certain peaks. New peaks not present in the non-deuterated sample are also observed. Ways for improving the deuteration of proteins by varying the temperature and dilution time are discussed. We propose the use of deuterated proteins to increase the sensitivity of immunoassays aimed for early diagnostic of diseases most notably cancer.
Advanced Techniques for Fourier Transform Wavefront Reconstruction
Poyneer, L A
2002-08-05
The performance of Fourier transform (FT) reconstructors in large adaptive optics systems with Shack-Hartmann sensors and a deformable mirror is analyzed. FT methods, which are derived for point-based geometries, are adapted for use on the continuous systems. Analysis and simulation show how to compensate for effects such as misalignment of the deformable mirror and wavefront sensor gain. Further filtering methods to reduce noise and improve performance are presented. All these modifications can be implemented at the filtering stage, preserving the speed of FT reconstruction. Simulation of a large system shows how compensated FT methods can have equivalent or better performance to slower vector-matrix-multiply reconstructions.
The quantum Arnold transformation
NASA Astrophysics Data System (ADS)
Aldaya, V.; Cossío, F.; Guerrero, J.; López-Ruiz, F. F.
2011-02-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with friction linear in velocity, can be related to the quantum free-particle dynamical system. This transformation provides a basic (Heisenberg-Weyl) algebra of quantum operators, along with well-defined Hermitian operators which can be chosen as evolution-like observables and complete the entire Schrödinger algebra. It also proves to be very helpful in performing certain computations quickly, to obtain, for example, wavefunctions and closed analytic expressions for time-evolution operators.
An implementation problem for boson fields and quantum Girsanov transform
NASA Astrophysics Data System (ADS)
Ji, Un Cig; Obata, Nobuaki
2016-08-01
We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier-Gauss and Fourier-Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.
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.
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2016-10-25
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 transform spectrometer optimal design considerations
NASA Astrophysics Data System (ADS)
Macoy, Norman H.
1999-10-01
The systems engineering aspects of evolving and developing the optimal design for Fourier transform interferometers are presented in this paper. A Fourier transform spectrometer (FTS) is a versatile electro-optical sensor for remote sensing, hyperspectral imaging, and laboratory chemical kinetics. Principal features include broad spectral coverage and high spectral resolution (Fellgate advantage) and high throughput (Jacquinot advantage). Due to its versatility, across various requirements, e.g. (resolution, bandwidth and aperture) sensor architecture contains an N-dimensional parametric trade matrix that needs to be readily assessed. Specifically considered are the logical steps utilized to flow down primary (customer) requirements and specifications to secondary (derived) requirements. Configurational aspects, generic trades, and parametric selections are emphasized for non-imagers as well as for imaging FTS. With an appropriately designed robust sensor, the noise equivalent spectral radiance or NE(Delta) N performance will be largely dictated by the scene and the instrument background flux. The performance will not be dictated by noise terms associated with interferogram encoding and signal handling. The mathematical formalism of interferometric error source types and photon limited design expressions are presented. The composition of these expressions are examined from the points of view of optical band limiting and some useful trade rules parametrically relating scan time and S/N to spectral resolution. For a well designed and executed interferometer, typical performance data are presented in terms of modulation index, calibrated radiometric atmospheric spectral signatures, and atmospheric spectral signatures for two spectral resolutions.
Lacunary Fourier Series for Compact Quantum Groups
NASA Astrophysics Data System (ADS)
Wang, Simeng
2016-05-01
This paper is devoted to the study of Sidon sets, {Λ(p)} -sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, {Λ(p)} -sets and lacunarities for L p -Fourier multipliers, generalizing a previous work by Blendek and Michalic̆ek. We also prove the existence of {Λ(p)} -sets for orthogonal systems in noncommutative L p -spaces, and deduce the corresponding properties for compact quantum groups. Central Sidon sets are also discussed, and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central Sidon sets. Several examples are also included.
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",…
Surface Inspection using fourier transform infrared spectroscopy
Powell, G.L.; Smyrl, N.R.; Williams, D.M.; Meyers, H.M. III; Barber, T.E.; Marrero-Rivera, M.
1994-08-08
The use of reflectance Fourier transform infrared (FTIR) spectroscopy as a tool for surface inspection is described. Laboratory instruments and portable instruments can support remote sensing probes that can map chemical contaminants on surfaces. Detection limits under the best of conditions are in the subnanometer range (i.e., near absolute cleanliness), excellent performance is obtained in the submicrometer range, and useful performance may exist for films tens of microns thick. Identifying and quantifying contamination such as mineral oils and greases, vegetable oils, and silicone oils on aluminum foil, galvanized sheet steel, smooth aluminum tubing, and gritblasted 7075 aluminum alloy and D6AC steel are described. The ability to map in time and space the distribution of oil stains on metals is demonstrated. Techniques for quantitatively applying oils to metals, subsequently verifying the application, and nonlinear relationships between reflectance and the quantity of oil are discussed.
Fourier transform 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.
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
Puzzarini, Cristina; Cazzoli, Gabriele; López, Juan Carlos; Alonso, José Luis; Baldacci, Agostino; Baldan, Alessandro; Stopkowicz, Stella; Cheng, Lan; Gauss, Jürgen
2011-05-01
Guided by theoretical predictions, the rotational spectrum of fluoroiodomethane, CH(2)FI, has been recorded and assigned. Accurate values are reported for the ground-state rotational constants, all quartic, sextic, and two octic centrifugal-distortion constants. The hyperfine structure of the rotational spectrum was thoroughly investigated using a Fourier-transform microwave spectrometer and the Lamb-dip technique in the millimeter-/submillimeter-wave region, thus allowing the accurate determination of the complete iodine quadrupole-coupling tensor and of the diagonal elements of the iodine spin-rotation tensor. Relativistic effects turned out to be essential for the accurate theoretical prediction of the dipole moment and quadrupole-coupling constants and were accounted for by direct perturbation theory and a spin-free four-component treatment based on the Dirac-Coulomb Hamiltonian. The relativistic corrections to the dipole moment amount to up to 34% and to the iodine quadrupole-coupling tensor to about 15-16% of the total values.
Imaging Fourier transform spectrometry of chemical plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.; Gross, Kevin C.; Perram, Glen P.
2009-05-01
A midwave infrared (MWIR) imaging Fourier transform spectrometer (FTS), the Telops FIRST-MWE (Field-portable Imaging Radiometric Spectrometer Technology - Midwave Extended) has been utilized for the standoff detection and characterization of chemical plumes. Successful collection and analysis of MWIR hyperspectral imagery of jet engine exhaust has allowed us to produce spatial profiles of both temperature and chemical constituent concentrations of exhaust plumes. Successful characterization of this high temperature combustion event has led to the collection and analysis of hyperspectral imagery of lower temperature emissions from industrial smokestacks. This paper presents MWIR data from remote collection of hyperspectral imagery of methyl salicilate (MeS), a chemical warfare agent simulant, during the Chemical Biological Distributed Early Warning System (CBDEWS) test at Dugway Proving Grounds, UT in 2008. The data did not contain spectral lines associated with emission of MeS. However, a few broad spectral features were present in the background-subtracted plume spectra. Further analysis will be required to assign these features, and determine the utility of MWIR hyperspectral imagery for analysis of chemical warfare agent plumes.
Fourier transform spectroscopy for future planetary missions
NASA Astrophysics Data System (ADS)
Brasunas, John C.; Hewagama, Tilak; Kolasinski, John R.; Kostiuk, Theodor
2015-11-01
Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system.Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, NASA Goddard was funded via the Planetary Instrument Definition and Development Progrem (PIDDP) to develop CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. Following the initial validation of CIRS-lite operation in the laboratory, we have been acquiring atmospheric data in the 8-12 micron window at the 1.2 m telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) in Greenbelt, MD. Targets so far have included Earth's atmosphere (in emission, and in absorption against the moon), and Venus.We will present the roadmap for making CIRS-lite a viable candidate for future planetary missions.
Vdovenko, Sergey I; Gerus, Igor I; Fedorenko, Elena A
2009-12-01
IR Fourier and (1)H NMR spectra of beta-dimethylaminoacrolein (DMAA) were investigated in various pure solvents. Quantum chemical calculations by the method AM1 also was carried out to evaluate relative energy and dipole moment of each conformer. On the basis of NMR and IR-spectra we showed that the (DMAA) presented in solutions as equilibrium of two conformers, (E-s-Z) <==> (E-s-E). Constant of this equilibrium, K(eq) = C(E-s-E)/C(E-s-Z), depended strongly on the total (DMAA) concentration: ln K(eq) = ln K(eq0) + a(1 - e(-bC) total). Besides, (E-s-Z) conformer of the (DMAA) was more polar and more stable than the (E-s-E) conformer. Correlation of the out-of-phase nu(C=O) and in-phase nu(C=C) vibrations with solvatochromic parameters of Kamlet, Abbot, and Taft (KAT) revealed that the main contribution to the shift of the out-of-phase nu(C=O) vibrations of the both conformers made solvent's hydrogen bond acceptor (HBA) (beta) term, whereas hydrogen bond donor (HBD) acidity (alpha) term influenced predominantly on the shift of the in-phase nu(C=C) vibrations of the conformers. Moreover, influence of these dominated terms was more pronounced for the (E-s-Z) conformer in comparison with the (E-s-E) conformer, hence the first conformer was more polarized than the last. Investigations of the enthalpies of the (E-s-Z) <==> (E-s-E) equilibrium in carbon tetrachloride, 1,4-dioxane and their mixtures showed that these enthalpies depended predominantly on the solvent's atomic and electronic polarization and dispersive interactions.
Chiral Analysis of Isopulegol by Fourier Transform Molecular Rotational Spectroscopy
NASA Astrophysics Data System (ADS)
Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks
2016-06-01
Chiral analysis on molecules with multiple chiral centers can be performed using pulsed-jet Fourier transform rotational spectroscopy. This analysis includes quantitative measurement of diastereomer products and, with the three wave mixing methods developed by Patterson, Schnell, and Doyle (Nature 497, 475-477 (2013)), quantitative determination of the enantiomeric excess of each diastereomer. The high resolution features enable to perform the analysis directly on complex samples without the need for chromatographic separation. Isopulegol has been chosen to show the capabilities of Fourier transform rotational spectroscopy for chiral analysis. Broadband rotational spectroscopy produces spectra with signal-to-noise ratio exceeding 1000:1. The ability to identify low-abundance (0.1-1%) diastereomers in the sample will be described. Methods to rapidly identify rotational spectra from isotopologues at natural abundance will be shown and the molecular structures obtained from this analysis will be compared to theory. The role that quantum chemistry calculations play in identifying structural minima and estimating their spectroscopic properties to aid spectral analysis will be described. Finally, the implementation of three wave mixing techniques to measure the enantiomeric excess of each diastereomer and determine the absolute configuration of the enantiomer in excess will be described.
NASA Astrophysics Data System (ADS)
Neeman, Elias M.; Aviles Moreno, Juan-Ramon; Huet, T. R.
2016-06-01
Several monoterpenes and terpenoids are biogenic volatile organic compounds which are emitted in the atmosphere, where they react with OH, O_3 and NO_x etc. to give rise to several oxidation and degradation products. Their decomposition products are a major source of secondray organic aerosol (SOA). Spectroscopic information on these atmospheric species is still very scarce. The rotational spectrum of nopinone (C_9H14O) one of the major oxidation products of β-pinene, and of its water complexes were recorded in a supersonic jet expansion with a Fourier transform microwave spectrometer over the range 2-20 GHz. The structure of the unique stable conformer of the nopinone was optimized using density functional theory and ab initio calculations. Signals from the parent species and from the 13C and 18O isotopomers were observed in natural abundance. A magnetic hyperfine structure associated with the pairs of hydrogen nuclei in the methylene groups was observed and modeled. The structures of several conformers of the nopinone-water complexes with up to three molecules of water were optimized using density functional theory and ab initio calculations. The energetically most stable of calculated conformers were observed and anlyzed. The rotational and centrifugal distortion parameters were fitted to a Watson's Hamiltonian in the A-reduction. The present work provides the first spectroscopic characterization of nopinone and its water complexes in the gas phase. A. Calogirou, B.R. Larsen, and D. Kotzias, Atmospheric Environment, 33, 1423-1439, (1999) P. Paasonen et al., Nat. Geosci., 6, 438-442 (2013) D. Zhang and R. Zhang The Journal of Chemical Physics, 122, 114308, (2005) R. Winterhalter et al. Journal of Atmospheric Chemistry, 35, 165-197, (2000)
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
Principle and application of multiple fractional Fourier transform holography
NASA Astrophysics Data System (ADS)
Zeng, Yangsu; Guo, Yongkang; Gao, Fuhua; Zhu, Jianhua
2003-01-01
In this paper, the principle of multiple fractional Fourier transform hologram (FRTH) is presented, and its characteristics based on the particularity in recording and reconstruction are analyzed. With this method, a multiple FRTH of several objects with different fractional transform orders is fabricated on one holographic plate. It requires a matched multiple fractional Fourier transform system to reconstruct the recorded images correctly. The potential application of multiple FRTH in optical security or anti-counterfeiting system is also discussed.
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.
Embolic Doppler ultrasound signal detection via fractional Fourier transform.
Gençer, Merve; Bilgin, Gökhan; Aydın, Nizamettin
2013-01-01
Computerized analysis of Doppler ultrasound signals can aid early detection of asymptomatic circulating emboli. For analysis, physicians use informative features extracted from Doppler ultrasound signals. Time -frequency analysis methods are useful tools to exploit the transient like signals such as Embolic signals. Detection of discriminative features would be the first step toward automated analysis of embolic Doppler ultrasound signals. The most problematic part of setting up emboli detection system is to differentiate embolic signals from confusing similar wave-like patterns such as Doppler speckle and artifacts caused by tissue movement, probe tapping, speaking etc. In this study, discrete version of fractional Fourier transform is presented as a solution in the detection of emboli in digitized Doppler ultrasound signals. An accurate set of parameters are extracted using short time Fourier transform and fractional Fourier transform and the results are compared to reveal detection quality. Experimental results prove the efficiency of fractional Fourier transform in which discriminative features becomes more evident.
Fourier transform techniques for the inference of cloud motion
NASA Technical Reports Server (NTRS)
Lo, R. C.; Rosenfeld, A.
1974-01-01
The development and evaluation are reported of phase shift techniques based on the Fourier transform for the estimation of cloud motion from geosynchronous meteorological satellite photographs. An alternative approach to cloud motion estimation, involving thresholding, was proposed and studied.
Xgremlin: Interferograms and spectra from Fourier transform spectrometers analysis
NASA Astrophysics Data System (ADS)
Nave, G.; Griesmann, U.; Brault, J. W.; Abrams, M. C.
2015-11-01
Xgremlin is a hardware and operating system independent version of the data analysis program Gremlin used for Fourier transform spectrometry. Xgremlin runs on PCs and workstations that use the X11 window system, including cygwin in Windows. It is used to Fourier transform interferograms, plot spectra, perform phase corrections, perform intensity and wavenumber calibration, and find and fit spectral lines. It can also be used to construct synthetic spectra, subtract continua, compare several different spectra, and eliminate ringing around lines.
Automatic Fourier transform and self-Fourier beams due to parabolic potential
NASA Astrophysics Data System (ADS)
Zhang, Yiqi; Liu, Xing; Belić, Milivoj R.; Zhong, Weiping; Petrović, Milan S.; Zhang, Yanpeng
2015-12-01
We investigate the propagation of light beams including Hermite-Gauss, Bessel-Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. In addition to oscillation, the finite-energy Airy beams exhibit periodic inversion during propagation. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. Based on the propagation in parabolic potential, we introduce a class of optically-interesting beams that are self-Fourier beams-that is, the beams whose Fourier transforms are the beams themselves.
The efficient computation of Fourier transforms on the symmetric group
NASA Astrophysics Data System (ADS)
Maslen, D. K.
1998-07-01
This paper introduces new techniques for the efficient computation of Fourier transforms on symmetric groups and their homogeneous spaces. We replace the matrix multiplications in Clausen's algorithm with sums indexed by combinatorial objects that generalize Young tableaux, and write the result in a form similar to Horner's rule. The algorithm we obtain computes the Fourier transform of a function on S-n in no more than 3/4n(n - 1)S-n multiplications and the same number of additions. Analysis of our algorithm leads to several combinatorial problems that generalize path counting. We prove corresponding results for inverse transforms and transforms on homogeneous spaces.
Rotation-invariant texture analysis using Radon and Fourier transforms
NASA Astrophysics Data System (ADS)
Xiao, Songshan; Wu, Yongxing
2007-09-01
Texture analysis is a basic issue in image processing and computer vision, and how to attain the rotation-invariant texture characterization is a key problem. This paper proposes a rotation-invariant texture analysis technique using Radon and Fourier transforms. This method uses Radon transform to convert rotation to translation, then utilizes Fourier transform and takes the moduli of the Fourier transform of these functions to make the translation invariant. A k-nearest-neighbor rule is employed to classify texture images. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. Experiment results show the feasibility of the proposed method and its robustness to additive white noise.
Rotation-invariant texture analysis using Radon and Fourier transforms
NASA Astrophysics Data System (ADS)
Xiao, Song-Shan; Wu, Yong-Xing
2007-07-01
Texture analysis is a basic issue in image processing and computer vision, and how to attain the Rotation-invariant texture characterization is a key problem. This paper proposes a rotation-invariant texture analysis technique using Radon and Fourier transform. This method uses Radon transform to convert rotation to translation, then utilizes the Fourier transform and takes the modules of the Fourier transform of these functions to make the translation invariant. A k-nearest-neighbor rule is employed to classify textures images. The proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the Radon transform step. To test and evaluate the method, several different kinds of experiments are employed. Experiments results show the feasibility of the proposed method and its robustness to additive white noise.
Dynamic measurement of deformation using Fourier transform digital holographic interferometry
NASA Astrophysics Data System (ADS)
Gao, Xinya; Wu, Sijin; Yang, Lianxiang
2013-10-01
Digital holographic interferometry (DHI) is a well-established optical technique for measurement of nano-scale deformations. It has become more and more important due to the rapid development of applications in aerospace engineering and biomedicine. Traditionally, phase shift technique is used to quantitatively measure the deformations in DHI. However, it cannot be applied in dynamic measurement. Fourier transform phase extraction method, which can determine the phase distribution from only a single hologram, becomes a promising method to extract transient phases in DHI. This paper introduces a digital holographic interferometric system based on 2D Fourier transform phase extraction method, with which deformations of objects can be measured quickly. In the optical setup, the object beam strikes a CCD via a lens and aperture, and the reference beam is projected on the CCD through a single-mode fiber. A small inclination angle between the diverging reference beam and optical axial is introduced in order to physically separate the Fourier components in frequency domain. Phase maps are then obtained by the utilization of Fourier transform and windowed inverse Fourier transform. The capability of the Fourier transform DHI is discussed by theoretical discussion as well as experiments.
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.
Practical Algorithm For Computing The 2-D Arithmetic Fourier Transform
NASA Astrophysics Data System (ADS)
Reed, Irving S.; Choi, Y. Y.; Yu, Xiaoli
1989-05-01
Recently, Tufts and Sadasiv [10] exposed a method for computing the coefficients of a Fourier series of a periodic function using the Mobius inversion of series. They called this method of analysis the Arithmetic Fourier Transform(AFT). The advantage of the AFT over the FN 1' is that this method of Fourier analysis needs only addition operations except for multiplications by scale factors at one stage of the computation. The disadvantage of the AFT as they expressed it originally is that it could be used effectively only to compute finite Fourier coefficients of a real even function. To remedy this the AFT developed in [10] is extended in [11] to compute the Fourier coefficients of both the even and odd components of a periodic function. In this paper, the improved AFT [11] is extended to a two-dimensional(2-D) Arithmetic Fourier Transform for calculating the Fourier Transform of two-dimensional discrete signals. This new algorithm is based on both the number-theoretic method of Mobius inversion of double series and the complex conjugate property of Fourier coefficients. The advantage of this algorithm over the conventional 2-D FFT is that the corner-turning problem needed in a conventional 2-D Discrete Fourier Transform(DFT) can be avoided. Therefore, this new 2-D algorithm is readily suitable for VLSI implementation as a parallel architecture. Comparing the operations of 2-D AFT of a MxM 2-D data array with the conventional 2-D FFT, the number of multiplications is significantly reduced from (2log2M)M2 to (9/4)M2. Hence, this new algorithm is faster than the FFT algorithm. Finally, two simulation results of this new 2-D AFT algorithm for 2-D artificial and real images are given in this paper.
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
2D hexagonal quaternion Fourier transform in color image processing
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2016-05-01
In this paper, we present a novel concept of the quaternion discrete Fourier transform on the two-dimensional hexagonal lattice, which we call the two-dimensional hexagonal quaternion discrete Fourier transform (2-D HQDFT). The concept of the right-side 2D HQDFT is described and the left-side 2-D HQDFT is similarly considered. To calculate the transform, the image on the hexagonal lattice is described in the tensor representation when the image is presented by a set of 1-D signals, or splitting-signals which can be separately processed in the frequency domain. The 2-D HQDFT can be calculated by a set of 1-D quaternion discrete Fourier transforms (QDFT) of the splitting-signals.
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.
Two-dimensional chirped-pulse Fourier transform microwave spectroscopy.
Wilcox, David S; Hotopp, Kelly M; Dian, Brian C
2011-08-18
Two-dimensional (2D) correlation techniques are developed for chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy. The broadband nature of the spectrometer coupled with fast digital electronics permits the generation of arbitrary pulse sequences and simultaneous detection of the 8-18 GHz region of the microwave spectrum. This significantly increases the number of rotation transitions that can be simultaneously probed, as well as the bandwidth in both frequency dimensions. We theoretically and experimentally evaluate coherence transfer of three- and four-level systems to relate the method with previous studies. We then extend the principles of single-quantum and autocorrelation to incorporate broadband excitation and detection. Global connectivity of the rotational energy level structure is demonstrated through the transfer of multiple coherences in a single 2D experiment. Additionally, open-system effects are observed from irradiating many-level systems. Quadrature detection in the indirectly measured frequency dimension and phase cycling are also adapted for 2D CP-FTMW spectroscopy.
Large Molecule Structures by Broadband Fourier Transform Molecular Rotational Spectroscopy
NASA Astrophysics Data System (ADS)
Evangelisti, Luca; Seifert, Nathan A.; Spada, Lorenzo; Pate, Brooks
2016-06-01
Fourier transform molecular rotational resonance spectroscopy (FT-MRR) using pulsed jet molecular beam sources is a high-resolution spectroscopy technique that can be used for chiral analysis of molecules with multiple chiral centers. The sensitivity of the molecular rotational spectrum pattern to small changes in the three dimensional structure makes it possible to identify diastereomers without prior chemical separation. For larger molecules, there is the additional challenge that different conformations of each diastereomer may be present and these need to be differentiated from the diastereomers in the spectral analysis. Broadband rotational spectra of several larger molecules have been measured using a chirped-pulse FT-MRR spectrometer. Measurements of nootkatone (C15H22O), cedrol (C15H26O), ambroxide (C16H28O) and sclareolide (C16H26O2) are presented. These spectra are measured with high sensitivity (signal-to-noise ratio near 1,000:1) and permit structure determination of the most populated isomers using isotopic analysis of the 13C and 18O isotopologues in natural abundance. The accuracy of quantum chemistry calculations to identify diastereomers and conformers and to predict the dipole moment properties needed for three wave mixing measurements is examined.
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.
Fourier-transform and global contrast interferometer alignment methods
Goldberg, Kenneth A.
2001-01-01
Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.
Fractional Fourier transform in temporal ghost imaging with classical light
Setaelae, Tero; Shirai, Tomohiro; Friberg, Ari T.
2010-10-15
We investigate temporal, second-order classical ghost imaging with long, incoherent, scalar plane-wave pulses. We prove that in rather general conditions, the intensity correlation function at the output of the setup is given by the fractional Fourier transform of the temporal object. In special cases, the correlation function is shown to reduce to the ordinary Fourier transform and the temporal image of the object. Effects influencing the visibility and the resolution are considered. This work extends certain known results on spatial ghost imaging into the time domain and could find applications in temporal tomography of pulses.
Modulated Fourier Transform Raman Fiber-Optic Spectroscopy
NASA Technical Reports Server (NTRS)
Jensen, Brian J. (Inventor); Cooper, John B. (Inventor); Wise, Kent L. (Inventor)
2000-01-01
A modification to a commercial Fourier Transform (FT) Raman spectrometer is presented for the elimination of thermal backgrounds in the FT Raman spectra. The modification involves the use of a mechanical optical chopper to modulate the continuous wave laser, remote collection of the signal via fiber optics, and connection of a dual-phase digital-signal-processor (DSP) lock-in amplifier between the detector and the spectrometer's collection electronics to demodulate and filter the optical signals. The resulting Modulated Fourier Transform Raman Fiber-Optic Spectrometer is capable of completely eliminating thermal backgrounds at temperatures exceeding 300 C.
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.
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.
Absorption mode Fourier transform electrostatic linear ion trap mass spectrometry.
Hilger, Ryan T; Wyss, Phillip J; Santini, Robert E; McLuckey, Scott A
2013-09-01
In Fourier transform mass spectrometry, it is well-known that plotting the spectrum in absorption mode rather than magnitude mode has several advantages. However, magnitude spectra remain commonplace due to difficulties associated with determining the phase of each frequency at the onset of data acquisition, which is required for generating absorption spectra. The phasing problem for electrostatic traps is much simpler than for Fourier transform ion cyclotron resonance (FTICR) instruments, which greatly simplifies the generation of absorption spectra. Here, we present a simple method for generating absorption spectra from a Fourier transform electrostatic linear ion trap mass spectrometer. The method involves time shifting the data prior to Fourier transformation in order to synchronize the onset of data acquisition with the moment of ion acceleration into the electrostatic trap. Under these conditions, the initial phase of each frequency at the onset of data acquisition is zero. We demonstrate that absorption mode provides a 1.7-fold increase in resolution (full width at half maximum, fwhm) as well as reduced peak tailing. We also discuss methodology that may be applied to unsynchronized data in order to determine the time shift required to generate an absorption spectrum.
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.
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
Calculating Fourier transforms of long-tailed functions
Lyness, J.N.; Kaper, T.J.
1987-11-01
In this paper, the authors describe a method for evaluating Fourier Transform functions numerically when function values f(chi) are available for any value of chi. Their method is based on the Mobius inversion of the Poisson summation formula, and employs a nonlinear series acceleration technique. Numerical evidence suggests that, for relatively smooth functions having long tails, this approach may be very useful.
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.
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.
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
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…
Ultrafast ranging lidar based on real-time Fourier transformation.
Xia, Haiyun; Zhang, Chunxi
2009-07-15
Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the time delay between the two signals. The temporal interferograms are transformed from the time domain into the frequency domain using a time-to-frequency conversion function obtained in the calibration process. The Fourier transform is used in the data processing. A range resolution of 334 nm at a sampling rate of 48.6 MHz over a distance of 16 cm is demonstrated in the laboratory.
Ultrafast ranging lidar based on real-time Fourier transformation.
Xia, Haiyun; Zhang, Chunxi
2009-07-15
Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the time delay between the two signals. The temporal interferograms are transformed from the time domain into the frequency domain using a time-to-frequency conversion function obtained in the calibration process. The Fourier transform is used in the data processing. A range resolution of 334 nm at a sampling rate of 48.6 MHz over a distance of 16 cm is demonstrated in the laboratory. PMID:19823517
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
Transfer Functions Via Laplace- And Fourier-Borel Transforms
NASA Technical Reports Server (NTRS)
Can, Sumer; Unal, Aynur
1991-01-01
Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.
A 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.
Fourier transform approach in modulation technique of experimental measurements.
Khazimullin, M V; Lebedev, Yu A
2010-04-01
An application of Fourier transform approach in modulation technique of experimental studies is considered. This method has obvious advantages compared with traditional lock-in amplifiers technique--simple experimental setup, a quickly available information on all the required harmonics, high speed of data processing using fast Fourier transform algorithm. A computationally simple, fast and accurate Fourier coefficients interpolation (FCI) method has been implemented to obtain a useful information from harmonics of a multimode signal. Our analysis shows that in this case FCI method has a systematical error (bias) of a signal parameters estimation, which became essential for the short data sets. Hence, a new differential Fourier coefficients interpolation (DFCI) method has been suggested, which is less sensitive to a presence of several modes in a signal. The analysis has been confirmed by simulations and measurements of a quartz wedge birefringence by means of the photoelastic modulator. The obtained bias, noise level, and measuring speed are comparable and even better than in lock-in amplifier technique. Moreover, presented DFCI method is expected to be promised candidate for using in actively developing imaging systems based on the modulation technique requiring fast digital signal processing of large data sets.
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.
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.
Matrix-Vector Based Fast Fourier Transformations on SDR Architectures
NASA Astrophysics Data System (ADS)
He, Y.; Hueske, K.; Götze, J.; Coersmeier, E.
2008-05-01
Today Discrete Fourier Transforms (DFTs) are applied in various radio standards based on OFDM (Orthogonal Frequency Division Multiplex). It is important to gain a fast computational speed for the DFT, which is usually achieved by using specialized Fast Fourier Transform (FFT) engines. However, in face of the Software Defined Radio (SDR) development, more general (parallel) processor architectures are often desirable, which are not tailored to FFT computations. Therefore, alternative approaches are required to reduce the complexity of the DFT. Starting from a matrix-vector based description of the FFT idea, we will present different factorizations of the DFT matrix, which allow a reduction of the complexity that lies between the original DFT and the minimum FFT complexity. The computational complexities of these factorizations and their suitability for implementation on different processor architectures are investigated.
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.
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
Time-frequency representation measurement based on temporal Fourier transformation
NASA Astrophysics Data System (ADS)
Suen, Yifan; Xiao, Shaoqiu; Hao, Sumin; Zhao, Xiaoxiang; Xiong, Yigao; Liu, Shenye
2016-10-01
We propose a new scheme to physically realize the short-time Fourier transform (STFT) of chirped optical pulse using time-lens array that enables us to get time-frequency representation without using FFT algorithm. The time-lens based upon the four-wave mixing is used to perform the process of temporal Fourier transformation. Pump pulse is used for both providing the quadratic phase and being the window function of STFT. The idea of STFT is physically realized in our scheme. Simulations have been done to investigate performance of the time-frequency representation scheme (TFRS) in comparison with STFT using FFT algorithm. Optimal measurement of resolution in time and frequency has been discussed.
A simple scanning mirror mechanism for a Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Brasunas, John C.; Cushman, G. Mark
1998-04-01
We present a simple scanning mirror mechanism for a Fourier transform spectrometer, consisting of a voice coil actuator, a ball-bearing slide, and a single cube corner mirror or retroreflector. The use of a single cube corner reduces significantly the sensitivity of the Fourier transform spectrometer to the tilt of its moving mirror, enabling the simple mechanism. With simple velocity feedback using a linear velocity transducer, we achieve a scan speed stability of 2%-5% (root-mean-square) for scan speeds from 40 to 440 μm/s for a travel of 2.2 cm, corresponding to a spectral resolution of 0.06 cm-1. Fringe amplitude stability is about 5%. This scan mechanism was operated at standard temperature and pressure, but the relatively minute amount of lubricant in the ball-bearing slide may indicate possible operation under vacuum and/or cryogenic conditions.
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.
Fourier spectroscopy with a one-million-point transformation
NASA Technical Reports Server (NTRS)
Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.
1972-01-01
A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.
Apparatus and methods for continuous beam fourier transform mass spectrometry
McLuckey, Scott A.; Goeringer, Douglas E.
2002-01-01
A continuous beam Fourier transform mass spectrometer in which a sample of ions to be analyzed is trapped in a trapping field, and the ions in the range of the mass-to-charge ratios to be analyzed are excited at their characteristic frequencies of motion by a continuous excitation signal. The excited ions in resonant motions generate real or image currents continuously which can be detected and processed to provide a mass spectrum.
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.
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)
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.
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.
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.
Mass spectral peak distortion due to Fourier transform signal processing.
Rockwood, Alan L; Erve, John C L
2014-12-01
Distortions of peaks can occur when one uses the standard method of signal processing of data from the Orbitrap and other FT-based methods of mass spectrometry. These distortions arise because the standard method of signal processing is not a linear process. If one adds two or more functions, such as time-dependent signals from a Fourier transform mass spectrometer and performs a linear operation on the sum, the result is the same as if the operation was performed on separate functions and the results added. If this relationship is not valid, the operation is non-linear and can produce unexpected and/or distorted results. Although the Fourier transform itself is a linear operator, the standard algorithm for processing spectra in Fourier transform-based methods include non-linear mathematical operators such that spectra processed by the standard algorithm may become distorted. The most serious consequence is that apparent abundances of the peaks in the spectrum may be incorrect. In light of these considerations, we performed theoretical modeling studies to illustrate several distortion effects that can be observed, including abundance distortions. In addition, we discuss experimental systems where these effects may manifest, including suggested systems for study that should demonstrate these peak distortions. Finally, we point to several examples in the literature where peak distortions may be rationalized by the phenomena presented here.
Experimental considerations and scaling property of the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Lohmann, Adolf W.; Zalevsky, Zeev; Dorsch, Rainer G.; Mendlovic, David
1998-01-01
The fractional Fourier transform (FRT) is a mathematical operation which is useful in several branches of physics and signal processing. The FRT can be performed by a simple optical experiment. The FRT reacts in a somewhat complicated manner to a shift or to a scale change of the input. Likewise, a scaling change of the experimental parameters (wavelength, focal lengths) means a non-trivial change of the associated FRT. We study the scaling behavior of the FRT mainly from the experimentalists point of view. Some computer simulations illustrate our conclusions. A theoretical comment: The FRT is a two-parameter family of transformations.
Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
Santa Maria, Odilyn L.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
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…
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
IR spectral depth profiling using Fourier transform photothermal beam deflection
NASA Astrophysics Data System (ADS)
Varlashkin, P. G.; Low, M. J. D.
1986-05-01
Fourier transform IR photothermal beam-deflection spectroscopy (PBDS) was used to make spectral depth-profiling measurements with synthetic bilayer samples of polyethylene/nitrocellulose, with a commercial plastic having surface printing and with a single human hair. An interferometer modified to operate at several scan speeds was used to record the spectra, without the cell-resonance problems found with photoacoustic spectroscopy (PAS). The utility of spectral depth profiling is discussed; significant S/N improvements seem to be needed and, with either PBDS or PAS, a wider range of modulation frequencies is required for the methods to be useful.
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.
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.
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
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.
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.
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.
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.
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.
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.
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 for Fermionic Systems and the Spectral Tensor Network
NASA Astrophysics Data System (ADS)
Ferris, Andrew J.
2014-07-01
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.
Voigt line infrared atmospheric transmittance calculations by Fourier transform
NASA Astrophysics Data System (ADS)
Neuendorffer, A. C.
1980-04-01
The absorption coefficient space of an IR atmospheric path contains the linear superposition of many Voigt spectral lines. This paper discusses the practical application of Karp's method to the simulation of satellite transmittance and radiance observations by using fast Fourier transforms on the recursively generated Voigt transforms. Although the procedure is physically straightforward, it is nonetheless computationally demanding and suited primarily to narrow isolated Q-branch regions. Performing the calculation on a 2.4/cm wide 15-micron CO2 Q-branch region demonstrates that 4% of the total absorption takes place above 0.1 mb. This absorption is in the cold mesopause and results in a 1-2% radiation deficit with its inclusion in a satellite radiation calculation.
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.
Fourier transform for fermionic systems and the spectral tensor network.
Ferris, Andrew J
2014-07-01
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law. Translationally invariant systems of free fermions in arbitrary dimensions as well as 1D systems solved by the Jordan-Wigner transformation are shown to be exactly represented in this class. Further, it is proposed that these tensor networks be used as generic structures to variationally describe more complicated systems, such as interacting fermions. This class shares some similarities with the Evenbly-Vidal branching multiscale entanglement renormalization ansatz, but with some important differences and greatly reduced computational demands.
Fast Fourier Transform Co-processor (FFTC), towards embedded GFLOPs
NASA Astrophysics Data System (ADS)
Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Witte, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland; Kopp, Nicholas
2012-10-01
Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co-Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment. In frame of the ESA activity "Fast Fourier Transform DSP Co-processor (FFTC)" (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following: • Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP. • The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance. The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 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.
Fast Fourier Transform Co-Processor (FFTC)- Towards Embedded GFLOPs
NASA Astrophysics Data System (ADS)
Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Wite, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland
2012-08-01
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 presentation will give and overview on the project, including the results of the validation of the FFTC ASIC prototypes.
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.
Fourier-Transform Ghost Imaging with Hard X Rays.
Yu, Hong; Lu, Ronghua; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming
2016-09-01
Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available.
Ultrafast and versatile spectroscopy by temporal Fourier transform.
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E; Wong, Kenneth K Y
2014-06-18
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.
[Fourier Transform Spectrometer Based on Rotating Parallel-Mirror-Pair].
Zhao, Bao-wei; Xiangli, Bin; Cai, Qi-sheng; Lü, Qun-bo; Zhou, Jin-song
2015-11-01
In the temporally-modulated Fourier transform spectroscopy, the translational moving mirror is difficult to drive accurately, causing tilt and shear problems. While, a rotational moving mirror can solve these problems. A rotary Fourier transform spectrometer is recommanded in this paper. Its principle is analyzed and the optical path difference is deduced. Also, the constrains for engineering realization are presented. This spectrometer consists of one beamsplitter, two fixed mirrors, one rotating parallel mirror pair, a collimating lens, a collecting lens, and one detector. From it's principle, this spectrometer show a simple structure, and it is assembled and adjustmented easily because the two split light are interfered with each other after reflected through the same plane mirror; By calculating the expression of it's optical path difference, the spectrometer is easy to realize large optical path difference, meaning high spectral resolution; Through analyzing it's engineering design constraints and computer simulation, it is known that the spectrometer should get the high resolution sample by high-speed spinning motor, so it is easy to achieve precise motion control, good stability, fast measurement speed.
Fourier-Transform Ghost Imaging with Hard X Rays
NASA Astrophysics Data System (ADS)
Yu, Hong; Lu, Ronghua; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming
2016-09-01
Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available.
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.
Fourier-Transform Ghost Imaging with Hard X Rays.
Yu, Hong; Lu, Ronghua; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming
2016-09-01
Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available. PMID:27661686
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.
Fourier Analytic Approach to Quantum Estimation of Group Action
NASA Astrophysics Data System (ADS)
Hayashi, Masahito
2016-10-01
This article proposes a unified method to estimation of group action by using the inverse Fourier transform of the input state. The method provides optimal estimation for commutative and non-commutative groups with and without energy constraint. The proposed method can be applied to projective representations of non-compact groups as well as of compact groups. This paper addresses the optimal estimation of R, U(1), SU(2), SO(3), and R^2 with Heisenberg representation under a suitable energy constraint.
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.
Fourier's law for quasi-one-dimensional chaotic quantum systems
NASA Astrophysics Data System (ADS)
Seligman, Thomas H.; Weidenmüller, Hans A.
2011-05-01
We derive Fourier's law for a completely coherent quasi-one-dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.
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.
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.
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.
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
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.
Generation of Fourier-transform-limited heralded single photons
U'Ren, Alfred B.; Jeronimo-Moreno, Yasser; Garcia-Gracia, Hipolito
2007-02-15
In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets.
A 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.
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.
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.
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.
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
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.
Data processing in Fourier transform ion cyclotron resonance mass spectrometry.
Qi, Yulin; O'Connor, Peter B
2014-01-01
The Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer intricately couples advanced physics, instrumentation, and electronics with chemical and particularly biochemical research. However, general understanding of the data processing methodologies used lags instrumentation, and most data processing algorithms we are familiar with in FT-ICR are not well studied; thus, professional skill and training in FT-ICR operation and data analysis is still the key to achieve high performance in FT-ICR. This review article is focused on FT-ICR data processing, and explains the procedures step-by-step for users with the goal of maximizing spectral features, such as mass accuracy, resolving power, dynamic range, and detection limits.
[Influence of collimation system on static Fourier transform spectrometer].
Jiang, Cheng-Zhi; Liang, Jing-Qiu; Liang, Zhong-Zhu; Sun, Qiang; Wang, Wei-Biao
2014-01-01
Collimation system provides collimated light for the static Fourier-transform spectroscopy (SFTS). Its quality is crucial to the signal to noise ratio (SNR) of SFTS. In the present paper, the physical model of SFTS was established based on the Fresnel diffraction theory by means of numerical software. The influence of collimation system on the SFTS was discussed in detail focusing on the aberrations of collimation lens and the quality of extended source. The results of simulation show that the influences of different kinds of aberrations on SNR take on obvious regularity, and in particular, the influences of off-axis aberrations on SNR are closely related to the location of off-axis point source. Finally the extended source's maximum radius allowed was obtained by simulation, which equals to 0.65 mm. The discussion results will be used for the design of collimation system.
Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)
NASA Technical Reports Server (NTRS)
Best, F. A.; Revercomb, H. E.; Bingham, G. E.; Knuteson, R. O.; Tobin, D. C.; LaPorte, D. D.; Smith, W. L.
2001-01-01
The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.
Optical design of the ATMOS Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Abel, I. R.; Reynolds, B. R.; Breckinridge, J. B.; Pritchard, J.
1979-01-01
The optical system design of the ATMOS Fourier transform spectrometer to be operated from Spacelab for the measurement of stratospheric trace molecules is described. The design contains features which can achieve the required fringe contrast of 80% and spectral resolution of 0.02/cm over a spectral range of 2-16 microns. In particular, the design is based on the following features which alleviate the usual requirements for alignment precision: (1) 'cat's eye' mirror configuration in the two arms of the interferometer for retroreflection stability, (2) tilt-compensated system of beamsplitter, compensator, and fold mirrors for wavefront directional stability, (3) paraboloidal 'cat's eye' primary mirror for wavefront stability against shear, (4) rotatable compensator for matching chromatic dispersion, and (5) wedged refractive components to avoid channel spectra due to the Fabry-Perot effect.
Molecular Structure and Chirality Detection by Fourier Transform Microwave Spectroscopy.
Lobsiger, Simon; Perez, Cristobal; Evangelisti, Luca; Lehmann, Kevin K; Pate, Brooks H
2015-01-01
We describe a three-wave mixing experiment using time-separated microwave pulses to detect the enantiomer-specific emission signal of the chiral molecule using Fourier transform microwave (FTMW) spectroscopy. A chirped-pulse FTMW spectrometer operating in the 2-8 GHz frequency range is used to determine the heavy-atom substitution structure of solketal (2,2-dimethyl-1,3-dioxolan-4-yl-methanol) through analysis of the singly substituted (13)C and (18)O isotopologue rotational spectra in natural abundance. A second set of microwave horn antennas is added to the instrument design to permit three-wave mixing experiments where an enantiomer-specific phase of the signal is observed. Using samples of R-, S-, and racemic solketal, the properties of the three-wave mixing experiment are presented, including the measurement of the corresponding nutation curves to demonstrate the optimal pulse sequence.
How to tickle spins with a fourier transform NMR spectrometer.
Segawa, Takuya F; Carnevale, Diego; Bodenhausen, Geoffrey
2013-02-01
In the long bygone days of continuous-wave nuclear magnetic resonance (NMR) spectroscopy, a selected transition within a multiplet of a high-resolution spectrum could be irradiated by a highly selective continuous-wave (CW) radio-frequency (rf) field with a very weak amplitude ω(2)/(2π)≤J. This causes splittings of connected transitions, allowing one to map the connectivities of all transitions within the energy-level diagram of the spin system. Such "tickling" experiments stimulated the invention of two-dimensional spectroscopy, but seem to have been forgotten for nearly 50 years. We show that tickling can readily be achieved in homonuclear systems with Fourier transform spectrometers by applying short pulses in the intervals between the sampling points. Extensions to heteronuclear systems are even more straightforward since they can be carried out using very weak CW rf fields.
A direct digital synthesis chirped pulse Fourier transform microwave spectrometer.
Finneran, Ian A; Holland, Daniel B; Carroll, P Brandon; Blake, Geoffrey A
2013-08-01
Chirped pulse Fourier transform microwave (CP-FTMW) spectrometers have become the instrument of choice for acquiring rotational spectra, due to their high sensitivity, fast acquisition rate, and large bandwidth. Here we present the design and capabilities of a recently constructed CP-FTMW spectrometer using direct digital synthesis (DDS) as a new method for chirped pulse generation, through both a suite of extensive microwave characterizations and deep averaging of the 10-14 GHz spectrum of jet-cooled acetone. The use of DDS is more suited for in situ applications of CP-FTMW spectroscopy, as it reduces the size, weight, and power consumption of the chirp generation segment of the spectrometer all by more than an order of magnitude, while matching the performance of traditional designs. The performance of the instrument was further improved by the use of a high speed digitizer with dedicated signal averaging electronics, which facilitates a data acquisition rate of 2.1 kHz.
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.
Dual-frequency fringe Fourier transform profilometry based on defocusing
NASA Astrophysics Data System (ADS)
Fu, Yanjun; Wang, Yonglong; Wu, Jianfeng; Jiang, Guangyu
2013-05-01
Dual-frequency fringe Fourier transform profilometry (FTP) is used to measure steep objects. The dual-frequency fringe can easily be obtained through software programming. However, due to the nonlinear gamma of the projector, the second harmonic generated by the nonlinear response of the camera and the presence of noise, digital filtering becomes difficult and measurement errors are introduced, thus reducing measurement accuracy. Therefore a novel method to generate dual-frequency fringe is presented in this study to solve the aforementioned problems. A binary square wave is projected onto the measured objects. By properly defocusing, the fundamental frequency and the third harmonic components can be preserved. The generated dual-frequency fringe is used to measure the 3-D profile of a computer mouse. The experimental results verify the feasibility of this method. The proposed method has higher measurement accuracy compared with the traditional dual-frequency fringe FTP.
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
Fourier domain target transformation analysis in the thermal infrared
NASA Technical Reports Server (NTRS)
Anderson, D. L.
1993-01-01
Remote sensing uses of principal component analysis (PCA) of multispectral images include band selection and optimal color selection for display of information content. PCA has also been used for quantitative determination of mineral types and abundances given end member spectra. The preliminary results of the investigation of target transformation PCA (TTPCA) in the fourier domain to both identify end member spectra in an unknown spectrum, and to then calculate the relative concentrations of these selected end members are presented. Identification of endmember spectra in an unknown sample has previously been performed through bandmatching, expert systems, and binary classifiers. Both bandmatching and expert system techniques require the analyst to select bands or combinations of bands unique to each endmember. Thermal infrared mineral spectra have broad spectral features which vary subtly with composition. This makes identification of unique features difficult. Alternatively, whole spectra can be used in the classification process, in which case there is not need for an expert to identify unique spectra. Use of binary classifiers on whole spectra to identify endmember components has met with some success. These techniques can be used, along with a least squares fit approach on the endmembers identified, to derive compositional information. An alternative to the approach outlined above usese target transformation in conjunction with PCA to both identify and quantify the composition of unknown spectra. Preprocessing of the library and unknown spectra into the fourier domain, and using only a specific number of the components, allows for significant data volume reduction while maintaining a linear relationship in a Beer's Law sense. The approach taken here is to iteratively calculate concentrations, reducing the number of endmember components until only non-negative concentrations remain.
Adaptive Controller for Compact Fourier Transform Spectrometer with Space Applications
NASA Astrophysics Data System (ADS)
Keymeulen, D.; Yiu, P.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.; Conroy, M.
2014-12-01
Here we present noise mitigation techniques developed as part of an adaptive controller for a very compact Compositional InfraRed Interferometric Spectrometer (CIRIS) implemented on a stand-alone field programmable gate array (FPGA) architecture with emphasis on space applications in high radiation environments such as Europa. CIRIS is a novel take on traditional Fourier Transform Spectrometers (FTS) and replaces linearly moving mirrors (characteristic of Michelson interferometers) with a constant-velocity rotating refractor to variably phase shift and alter the path length of incoming light. The design eschews a monochromatic reference laser typically used for sampling clock generation and instead utilizes constant time-sampling via internally generated clocks. This allows for a compact and robust device, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 µm) on planetary exploration missions. The instrument's embedded microcontroller is implemented on a VIRTEX-5 FPGA and a PowerPC with the aim of sampling the instrument's detector and optical rotary encoder in order to construct interferograms. Subsequent onboard signal processing provides spectral immunity from the noise effects introduced by the compact design's removal of a reference laser and by the radiation encountered during space flight to destinations such as Europa. A variety of signal processing techniques including resampling, radiation peak removal, Fast Fourier Transform (FFT), spectral feature alignment, dispersion correction and calibration processes are applied to compose the sample spectrum in real-time with signal-to-noise-ratio (SNR) performance comparable to laser-based FTS designs in radiation-free environments. The instrument's FPGA controller is demonstrated with the FTS to characterize its noise mitigation techniques and highlight its suitability for implementation in space systems.
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 the 2DFT spectra suggest the presence of excitation induced dephasing and excitation induced shift.
Phase cycling for optical two-dimensional Fourier-transform spectroscopy
NASA Astrophysics Data System (ADS)
Autry, Travis; Moody, Galan; Li, Hebin; Siemens, Mark; Cundiff, Steven
2011-03-01
Phase-cycling has been implemented in optical two-dimensional Fourier-transform spectroscopy to extract signals from quantum wells and quantum dots and to eliminate noise such as pump scatter co-propagating with the four-wave mixing signal. Experiments using actively phase-stabilized interferometers to cycle the excitation pulse optical phases suffer from partial noise cancellation because excitation and phase-control laser wavelengths are incommensurate. To obtain full noise elimination, we have incorporated liquid crystal variable retarders capable of imposing a π phase shift for wavelengths 650-950 nm. We present non-rephasing spectra of potassium vapor contained in a ~ 20 μ m transmission cell and show that this phase cycling method removes all noise from pump scatter while drastically reducing the data acquisition time compared to mechanical phase-delay techniques. This work was supported by an NSF-REU grant at the University of Colorado- Boulder.
Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy
Paul, J.; Dey, P.; Tokumoto, T.; Reno, J. L.; Hilton, D. J.; Karaiskaj, D.
2014-10-07
The dephasing of excitons in a modulation doped single quantum well was carefully measured using time integrated four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. These are the first 2DFT measurements performed on a modulation doped single quantum well. The inhomogeneous and homogeneous excitonic line widths were obtained from the diagonal and cross-diagonal profiles of the 2DFT spectra. The laser excitation density and temperature were varied and 2DFT spectra were collected. A very rapid increase of the dephasing decay, and as a result, an increase in the cross-diagonal 2DFT linewidths with temperature was observed. Furthermore, the lineshapes of themore » 2DFT spectra suggest the presence of excitation induced dephasing and excitation induced shift.« less
Identification of formation interfaces by using wavelet and Fourier transforms
NASA Astrophysics Data System (ADS)
Mukherjee, Bappa; Srivardhan, V.; Roy, P. N. S.
2016-05-01
The identification of formation interfaces is of prime importance from well log data. The interfaces are not clearly discernible due to the presence of high and low frequency noise in the log response. Accurate bed boundary information is very crucial in hydrocarbon exploration and the problem has received considerable attention and many techniques have been proposed. Frequency spectrum based filtering techniques aids us in interpretation, but usually leads to inaccurate amplification of unwanted components of the log response. Wavelet transform is very effective in denoising the log response and can be carried out to filter low and high frequency components of signal. The use of Fourier and Wavelet transform in denoising the log data for obtaining formation interfaces is demonstrated in this work. The feasibility of the proposed technique is tested so that it can be used in the industry to decipher formation interfaces. The work flow is demonstrated by testing on wells belonging to the Upper Assam Basin, which are self-potential, gamma ray, and resistivity log responses.
The use of Fourier reverse transforms in crystallographic phase refinement
Ringrose, S.
1997-10-08
Often a crystallographer obtains an electron density map which shows only part of the structure. In such cases, the phasing of the trial model is poor enough that the electron density map may show peaks in some of the atomic positions, but other atomic positions are not visible. There may also be extraneous peaks present which are not due to atomic positions. A method for determination of crystal structures that have resisted solution through normal crystallographic methods has been developed. PHASER is a series of FORTRAN programs which aids in the structure solution of poorly phased electron density maps by refining the crystallographic phases. It facilitates the refinement of such poorly phased electron density maps for difficult structures which might otherwise not be solvable. The trial model, which serves as the starting point for the phase refinement, may be acquired by several routes such as direct methods or Patterson methods. Modifications are made to the reverse transform process based on several assumptions. First, the starting electron density map is modified based on the fact that physically the electron density map must be non-negative at all points. In practice a small positive cutoff is used. A reverse Fourier transform is computed based on the modified electron density map. Secondly, the authors assume that a better electron density map will result by using the observed magnitudes of the structure factors combined with the phases calculated in the reverse transform. After convergence has been reached, more atomic positions and less extraneous peaks are observed in the refined electron density map. The starting model need not be very large to achieve success with PHASER; successful phase refinement has been achieved with a starting model that consists of only 5% of the total scattering power of the full molecule. The second part of the thesis discusses three crystal structure determinations.
[Biological Process Oriented Online Fourier Transform Infrared Spectrometer].
Xie, Fei; Wu, Qiong-shui; Zeng, Li-bo
2015-08-01
An online Fourier Transform Infrared Spectrometer and an ATR (Attenuated Total Reflection) probe, specifically at the application of real time measurement of the reaction substrate concentration in biological processes, were designed. (1) The spectrometer combined the theories of double cube-corner reflectors and flat mirror, which created a kind of high performance interferometer system. The light path folding way was utilized to makes the interferometer compact structure. Adopting double cube-corner reflectors, greatly reduces the influence of factors in the process of moving mirror movement such as rotation, tilt, etc. The parallelogram oscillation flexible support device was utilized to support the moving mirror moves. It cancelled the friction and vibration during mirror moving, and ensures the smooth operation. The ZnSe splitter significantly improved the hardware reliability in high moisture environment. The method of 60° entrance to light splitter improves the luminous flux. (2) An ATR in situ measuring probe with simple structure, large-flux, economical and practical character was designed in this article. The transmission of incident light and the light output utilized the infrared pipe with large diameter and innerplanted-high plating membrane, which conducted for the infrared transmission media of ATR probe. It greatly reduced the energy loss of infrared light after multiple reflection on the inner wall of the light pipe. Therefore, the ATR probe obtained high flux, improved the signal strength, which make the signal detected easily. Finally, the high sensitivity of MCT (Mercury Cadmium Telluride) detector was utilized to realize infrared interference signal collection, and improved the data quality of detection. The test results showed that the system yields the advantages of perfect moisture-proof performance, luminous flux, online measurement, etc. The designed online Fourier infrared spectrometer can real-time measured common reactant substrates
[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
Single beam Fourier transform digital holographic quantitative phase microscopy
Anand, A. Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Faridian, A.; Pedrini, G.; Osten, W.; Dubey, S. K.; Javidi, B.
2014-03-10
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
External Second Gate-Fourier Transform Ion Mobility Spectrometry.
Tarver, Edward E., III
2005-01-01
Ion mobility spectrometry (IMS) is recognized as one of the most sensitive and versatile techniques for the detection of trace levels of organic vapors. IMS is widely used for detecting contraband narcotics, explosives, toxic industrial compounds and chemical warfare agents. Increasing threat of terrorist attacks, the proliferation of narcotics, Chemical Weapons Convention treaty verification as well as humanitarian de-mining efforts has mandated that equal importance be placed on the analysis time as well as the quality of the analytical data. (1) IMS is unrivaled when both speed of response and sensitivity has to be considered. (2) With conventional (signal averaging) IMS systems the number of available ions contributing to the measured signal to less than 1%. Furthermore, the signal averaging process incorporates scan-to-scan variations decreasing resolution. With external second gate Fourier Transform ion mobility spectrometry (FT-IMS), the entrance gate frequency is variable and can be altered in conjunction with other data acquisition parameters to increase the spectral resolution. The FT-IMS entrance gate operates with a 50% duty cycle and so affords a 7 to 10-fold increase in sensitivity. Recent data on high explosives are presented to demonstrate the parametric optimization in sensitivity and resolution of our system.
Liquid chromatography/Fourier transform IR spectrometry interface flow cell
Johnson, Charles C.; 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.
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.
Fourier transform ion cyclotron resonance mass spectrometry: a primer.
Marshall, A G; Hendrickson, C L; Jackson, G S
1998-01-01
This review offers an introduction to the principles and generic applications of FT-ICR mass spectrometry, directed to readers with no prior experience with the technique. We are able to explain the fundamental FT-ICR phenomena from a simplified theoretical treatment of ion behavior in idealized magnetic and electric fields. The effects of trapping voltage, trap size and shape, and other nonidealities are manifested mainly as perturbations that preserve the idealized ion behavior modified by appropriate numerical correction factors. Topics include: effect of ion mass, charge, magnetic field, and trapping voltage on ion cyclotron frequency; excitation and detection of ICR signals; mass calibration; mass resolving power and mass accuracy; upper mass limit(s); dynamic range; detection limit, strategies for mass and energy selection for MSn; ion axialization, cooling, and remeasurement; and means for guiding externally formed ions into the ion trap. The relation of FT-ICR MS to other types of Fourier transform spectroscopy and to the Paul (quadrupole) ion trap is described. The article concludes with selected applications, an appendix listing accurate fundamental constants needed for ultrahigh-precision analysis, and an annotated list of selected reviews and primary source publications that describe in further detail various FT-ICR MS techniques and applications.
Diagnostic ultrasound tooth imaging using fractional Fourier transform.
Harput, Sevan; Evans, Tony; Bubb, Nigel; Freear, Steven
2011-10-01
An ultrasound contact imaging method is proposed to measure the enamel thickness in the human tooth. A delay-line transducer with a working frequency of 15 MHz is chosen to achieve a minimum resolvable distance of 400 μm in human enamel. To confirm the contact between the tooth and the transducer, a verification technique based on the phase shift upon reflection is used. Because of the high attenuation in human teeth, linear frequency-modulated chirp excitation and pulse compression are exploited to increase the penetration depth and improve the SNR. Preliminary measurements show that the enamel-dentin boundary creates numerous internal reflections, which cause the applied chirp signals to interfere arbitrarily. In this work, the fractional Fourier transform (FrFT) is employed for the first time in dental imaging to separate chirp signals overlapping in both time and frequency domains. The overlapped chirps are compressed using the FrFT and matched filter techniques. Micro-computed tomography is used for validation of the ultrasound measurements for both techniques. For a human molar, the thickness of the enamel layer is measured with an average error of 5.5% after compressing with the FrFT and 13.4% after compressing with the matched filter based on the average speed of sound in human teeth.
Picolinic and isonicotinic acids: a Fourier transform microwave spectroscopy study.
Peña, Isabel; Varela, Marcelino; Franco, Vanina G; López, Juan C; Cabezas, Carlos; Alonso, José L
2014-12-01
The rotational spectra of laser ablated picolinic and isonicotinic acids have been studied using broadband chirped pulse (CP-FTMW) and narrowband molecular beam (MB-FTMW) Fourier transform microwave spectroscopies. Two conformers of picolinic acid, s-cis-I and s-cis-II, and one conformer of isonicotinic acid have been identified through the analysis of their rotational spectra. The values of the inertial defect and the quadrupole coupling constants obtained for the most stable s-cis-I conformer of picolinic acid, evidence the formation of an O-H···N hydrogen bond between the acid group and the endocyclic N atom. The stabilization provided by this hydrogen bond compensates the destabilization energy due to the adoption of a -COOH trans configuration in this conformer. Its rs structure has been derived from the rotational spectra of several (13)C, (15)N, and (18)O species observed in their natural abundances. Mesomeric effects have been revealed by comparing the experimental values of the (14)N nuclear quadrupole coupling constants in the isomeric series of picolinic, isonicotinic, and nicotinic acids.
Fourier transform spectrometer for Greenhouse Gases Observing Satellite (GOSAT)
NASA Astrophysics Data System (ADS)
Hamazaki, Takashi; Kaneko, Yutaka; Kuze, Akihiko; Kondo, Kayoko
2005-01-01
Global warming has become a very serious issue for human beings. In 1997, the Kyoto Protocol was adopted at the Third Session of the Conference of the Parties to the United Nations Framework Convention on Climate Change (COP3), making it mandatory for developed nations to reduce carbon dioxide emissions by six (6) to eight (8) per cent of their total emissions in 1990, and to meet this goal sometime between 2008 and 2012. The Greenhouse gases Observing SATellite (GOSAT) is designed to monitor the global distribution of carbon dioxide (CO2) from the space. GOSAT is a joint project of Japan Aerospace Exploration Agency (JAXA), the Ministry of Environment (MOE), and the National Institute for Environmental Studies (NIES). JAXA is responsible for the satellite and instrument development, MOE is involved in the instrument development, and NIES is responsible for the satellite data retrieval. The satellite is scheduled to be launched in 2008. In order to detect the CO2 variation of boundary layers, both the technique to measure the column density and the retrieval algorithm to remove cloud and aerosol contamination are investigated. Main mission sensor of the GOSAT is a Fourier Transform Spectrometer with high optical throughput, spectral resolution and wide spectral coverage, and a cloud-aerosol detecting imager attached to the satellite. The paper presents the mission sensor system of the GOSAT together with the results of performance demonstration with proto-type instrument aboard an aircraft.
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)
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.
Understanding coal using thermal decomposition and fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Solomon, P. R.; Hamblen, D. G.
1981-02-01
Fourier Transform Infrared Spectroscopy (FTIR) is being used to provide understanding of the organic structure of coals and coal thermal decomposition products. The research has developed a relationship between the coal organic structure and the products of thermal decomposition. The work has also led to the discovery that many of the coal structural elements are preserved in the heavy molecular weight products (tar) released in thermal decomposition and that careful analysis of these products in relation to the parent coal can supply clues to the original structure. Quantitative FTIR spectra for coals, tars and chars are used to determine concentrations of the hydroxyl, aliphatic and aromatic hydrogen. Concentrations of aliphatic carbon are computed using an assumed aliphatic stoichiometry; aromatic carbon concentrations are determined by difference. The values are in good agreement with date determined by 13C and proton NMR. Analysis of the solid produ ts produced by successive stages in the thermal decomposition provides information on the changes in the chemical bonds occurring during the process. Time resolved infrared scans (129 msec/scan) taken during the thermal decomposition provide data on the amount, composition and rate of evolution of light gas species. The relationship between the evolved light species and their sources in the coal is developed by comparing the rate of evolution with the rate of change in the chemical bonds. With the application of these techniques, a general kinetic model has been developed which relates the products of thermal decomposition to the organic structure of the parent coal.
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.
Fourier Transform Power Spectra Analysis of Dwarf Irregular Galaxies
NASA Astrophysics Data System (ADS)
Zhang, Hongxin; Hunter, D. A.; LITTLE THINGS Team
2012-01-01
The LITTLE THINGS survey has obtained deep HI emission line maps with the data from VLA B, C and D array configurations for a representative sample of nearby dwarf irregular galaxies, and supplemented this with images from the FUV to the NIR. We present the fourier transform power spectra of the HI maps, FUV and NIR images for a subsample of nearly face-on (minor-to-major axis ratio > 0.8) LITTLE THINGS galaxies in order to examine structures within the galaxies' gas and stellar disks.The radial variations of the power spectra will be compared with global properties. We will also compare the relationship between the gas, star formation and stellar mass on different physical scales and at different radii, and discuss the possibility of using breaks in power-law power spectra to constrain the disk thickness. The LITTLE THINGS team is grateful to the National Science Foundation for funding through grants AST-0707563, AST-0707426, AST-0707468, and AST-0707835 to DAH, BGE, CES, and LMY. HZ was partly supported by NSF of China through grants \\#10425313, \\#10833006 and \\#10621303 to Professor Yu Gao.
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.
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.
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.
Quantitative analysis of polyethylene blends by Fourier transform infrared spectroscopy.
Cran, Marlene J; Bigger, Stephen W
2003-08-01
The quantitative analysis of binary polyethylene (PE) blends by Fourier transform infrared (FT-IR) spectroscopy has been achieved based on the ratio of two absorbance peaks in an FT-IR spectrum. The frequencies for the absorbance ratio are selected based on structural entities of the PE components in the blend. A linear relationship between the absorbance ratio and the blend composition was found to exist if one of the absorbance peaks is distinct to one of the components and the other peak is common to both components. It was also found that any peak resulting from short-chain branching in copolymers (such as linear low-density polyethylene (LLDPE) or metallocene-catalyzed LLDPE (mLLDPE)), is suitable for use as the peak that is designated as being distinct to that component. In order to optimize the linearity of the equation, however, the selection of the second common peak is the most important and depends on the blend system studied. Indeed, under certain circumstances peaks that are not spectrally distinct can be used successfully to apply the method. The method exhibits potential for the routine analysis of PE blends that have been calibrated prior to its application.
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.
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.
Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS)
NASA Technical Reports Server (NTRS)
Sromovsky, L. A.
2002-01-01
This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).
Fourier Transform Infrared Spectroscopy and Photoacoustic Spectroscopy for Saliva Analysis.
Mikkonen, Jopi J W; Raittila, Jussi; Rieppo, Lassi; Lappalainen, Reijo; Kullaa, Arja M; Myllymaa, Sami
2016-09-01
Saliva provides a valuable tool for assessing oral and systemic diseases, but concentrations of salivary components are very small, calling the need for precise analysis methods. In this work, Fourier transform infrared (FT-IR) spectroscopy using transmission and photoacoustic (PA) modes were compared for quantitative analysis of saliva. The performance of these techniques was compared with a calibration series. The linearity of spectrum output was verified by using albumin-thiocyanate (SCN(-)) solution at different SCN(-) concentrations. Saliva samples used as a comparison were obtained from healthy subjects. Saliva droplets of 15 µL were applied on the silicon sample substrate, 6 drops for each specimen, and dried at 37 ℃ overnight. The measurements were carried out using an FT-IR spectrometer in conjunction with an accessory unit for PA measurements. The findings with both transmission and PA modes mirror each other. The major bands presented were 1500-1750 cm(-1) for proteins and 1050-1200 cm(-1) for carbohydrates. In addition, the distinct spectral band at 2050 cm(-1) derives from SCN(-) anions, which is converted by salivary peroxidases to hypothiocyanate (OSCN(-)). The correlation between the spectroscopic data with SCN(-) concentration (r > 0.990 for transmission and r = 0.967 for PA mode) was found to be significant (P < 0.01), thus promising to be utilized in future applications.
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 studies in hypergolic ignition of ionic liquids.
Chambreau, Steven D; Schneider, Stefan; Rosander, Michael; Hawkins, Tom; Gallegos, Christopher J; Pastewait, Matthew F; Vaghjiani, Ghanshyam L
2008-08-28
A class of room-temperature ionic liquids (RTILs) that exhibit hypergolic activity toward fuming nitric acid is reported. Fast ignition of dicyanamide ionic liquids when mixed with nitric acid is contrasted with the reactivity of the ionic liquid azides, which show high reactivity with nitric acid, but do not ignite. The reactivity of other potential salt fuels is assessed here. Rapid-scan, Fourier transform infrared (FTIR) spectroscopy of the preignition phase indicates the evolution of N 2O from both the dicyanamide and azide RTILs. Evidence for the evolution of CO 2 and isocyanic acid (HNCO) with similar temporal behavior to N 2O from reaction of the dicyanamide ionic liquids with nitric acid is presented. Evolution of HN 3 is detected from the azides. No evolution of HCN from the dicyanamide reactions was detected. From the FTIR observations, biuret reaction tests, and initial ab initio calculations, a mechanism is proposed for the formation of N 2O, CO 2, and HNCO from the dicyanamide reactions during preignition. PMID:18681416
Ribosomal DNA nanoprobes studied by Fourier transform infrared spectroscopy.
Fagundes, Jaciara; Castilho, Maiara L; Téllez Soto, Claudio A; Vieira, Laís de Souza; Canevari, Renata A; Fávero, Priscila P; Martin, Airton A; Raniero, Leandro
2014-01-24
Paracoccidioides brasiliensis (P. brasiliensis) is a thermo-dimorphic fungus that causes paracoccidioidomycosis. Brazil epidemiological data shows that endemic areas are the subtropical regions, especially where agricultural activities predominate such as the Southeast, South, and Midwest. There are several tests to diagnose paracoccidioidomycosis, but they have many limitations such as low sensitivity, high cost, and a cross-reacting problem. In this work, gold nanoprobes were used to identify P. brasiliensis as an alternative diagnostic technique, which is easier to apply, costs less, and has great potential for application. The specific Ribosomal sequence of P. brasiliensis DNA was amplified and used to design the nanoprobes using a thiol-modified oligonucleotide. The results of positive and negative tests were done by UV-visible and Fourier Transform Infrared (FT-IR) measurements. The deconvolution of FT-IR sample spectra showed differences in the vibrational modes from the hydrogen bridge NHN and NHO bands that form the double helix DNA for samples matching the DNA sequence of nanoprobes that could be used to classify the samples.
Optical Fourier transform scatterometry for LER and LWR metrology
NASA Astrophysics Data System (ADS)
Boher, P.; Petit, J.; Leroux, T.; Foucher, J.; Desieres, Y.; Hazart, J.; Chaton, P.
2005-05-01
We present an innovating instrument based on optical Fourier transform (OFT) capable to measure simultaneously the specular and non specular diffraction pattern of sub-micronic periodic structures. The sample is illuminated at fixed wavelength (green laser) versus a large angular aperture both in incidence (0 to 80°) and azimuth (0 to 180°). In the present paper we focus on the possibility to measure line edge roughness (LER) and line width roughness (LWR) using this new technique. To understand the problem, different gratings with artificial periodic LER and LWR roughness have been fabricated and characterized precisely by atomic force microscopy (AFM). Different light scattering measurements have been performed using the OFT instrument with different illuminations in order to understand precisely the optical behavior of these systems. We show that we can distinguish LER and LWR by measuring simultaneously the diffracted contributions coming from the grating and from the periodic roughness. In phase LER with small LWR does not give first order diffraction contribution for the periodic roughness. In contrast, LER in opposite phase with large LWR gives a strong contribution for the first order of diffraction of the periodic roughness. In any case, the sensitivity to LER and LWR is better than 5nm for 500nm period gratings measured at 532nm. This result can be extended to samples with real LER and LWR. It shows without ambiguity that simultaneous measurement of the specular and diffracted light diffraction patterns is necessary to extract separately the two parameters.
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.
An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.
ERIC Educational Resources Information Center
Eastman, M. P.; And Others
1986-01-01
Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.
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
Precise and fast spatial-frequency analysis using the iterative local Fourier transform.
Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook
2016-09-19
The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 2^{10} times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.
Precise and fast spatial-frequency analysis using the iterative local Fourier transform.
Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook
2016-09-19
The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 2^{10} times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source. PMID:27661946
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 Raman spectroscopy of synthetic and biological calcium phosphates.
Sauer, G R; Zunic, W B; Durig, J R; Wuthier, R E
1994-05-01
Fourier-transform (FT) Raman spectroscopy was used to characterize the organic and mineral components of biological and synthetic calcium phosphate minerals. Raman spectroscopy provides information on biological minerals that is complimentary to more widely used infrared methodologies as some infrared-inactive vibrational modes are Raman-active. The application of FT-Raman technology has, for the first time, enabled the problems of high sample fluorescence and low signal-to-noise that are inherent in calcified tissues to be overcome. Raman spectra of calcium phosphates are dominated by a very strong band near 960 cm-1 that arises from the symmetric stretching mode (v1) of the phosphate group. Other Raman-active phosphate vibrational bands are seen at approximately 1075 (v3), 590 (v4), and 435 cm-1 (v2). Minerals containing acidic phosphate groups show additional vibrational modes. The different calcium phosphate mineral phases can be distinguished from one another by the relative positions and shapes of these bands in the Raman spectra. FT-Raman spectra of nascent, nonmineralized matrix vesicles (MV) show a distinct absence of the phosphate v1 band even though these structures are rich in calcium and phosphate. Similar results were seen with milk casein and synthetic Ca-phosphatidyl-serine-PO4 complexes. Hence, the phosphate and/or acidic phosphate ions in these noncrystalline biological calcium phosphates is in a molecular environment that differs from that in synthetic amorphous calcium phosphate. In MV, the first distinct mineral phase to form contained acidic phosphate bands similar to those seen in octacalcium phosphate. The mineral phase present in fully mineralized MV was much more apatitic, resembling that found in bones and teeth.(ABSTRACT TRUNCATED AT 250 WORDS)
Air quality monitoring based on Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Zheng, Wei; Wang, Yan; Wang, Rui
2006-09-01
The use of optical techniques to identify and quantify atmospheric pollutants has been focused within the past two decades. Fourier Transform Infrared (FTIR) spectroscopy has proven to be a powerful tool for multi-component analysis of air quality monitoring. The technique has been used for gaseous samples by extractive sampling as well as in the open-path configuration. The present contribution has described the application of FTIR to analyze gaseous pollutants in ambient air in detail. The study for the detection limits of the interested gas, the design of the multipass White mirror system, and the experimental results are described. The White cell is employed to increase the absorbance relative to noise in the absorbance spectrum by increasing the path length without proportional loss of signal. A classical least squares (CLS) fit is used to match the scaled standards or previously measured absorption profiles to those of the observed spectrum in the specified spectral analysis regions for simultaneous quantification of the compounds of interest, plus several other ambient air constituents. The regions were chosen carefully to provide optimum detection of the compounds of interest with minimum interference by other compounds. Specially, spectrum subtraction and differential absorption concepts are introduced into FTIR data analysis. The optimal window for CO, S0 II, NO II, NO and CO II would be the region at 2250-2020 cm -1, 1230-1070 cm -1, 2940-2840 cm -1, 1965-1775 cm -1, and around 668.24 cm -1 respectively. Deviations from traditional measured results for all approaches are in 10%.
Fourier Transform 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.
Fourier transform Raman lidar for trace gas detection and quantification
Sentell, J.C.
1994-12-31
The Raman technique, while a valuable tool in chemical and combustion research, is limited in many remote sensing applications because of the low Raman scattering cross-section, which may be three to five orders of magnitude below the Rayleigh (elastic) values. Two concepts for increasing the signal level are discussed. First, use a range-gated Fourier transform spectrometer to increase the system throughput and allow multiplexing advantages. The spectrum is obtained by performing a FFT on the resulting interferogram. Second, since the cross section goes as the fourth power of the optical frequency, use ultra-violet laser illumination, and separate the resulting fluorescence radiation by placing a known dispersion on the transmitted waveform. The techniques for achieving this function, and the mathematical formulation for the phase-modulated auto-correlation which result, are not evaluated in this paper. However, the approach does not appreciably lower the available resolution because the limits are imposed by the sampling function inherent to the finite-duration Michelson mirror scan. A conceptual design using a long-pulse, flashlamp-pumped dye laser is shown, and typical performance equations in the detection of Freon 12, CCl{sub 2}F{sub 2}, are presented. For a one joule laser and a thirty (30) cm aperture operating in darkness, a concentration of 10{sup 23} molecules/m{sup 3} can be detected in a 60 km visibility at a range of 3.4 km. Much greater performance is obtained against molecules exhibiting the resonance Raman effect, such as nitrogen dioxide.
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).
Continuously tunable optical multidimensional Fourier-transform spectrometer.
Dey, P; Paul, J; Bylsma, J; Deminico, S; Karaiskaj, D
2013-02-01
A multidimensional optical nonlinear spectrometer (MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. The MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delays between them while maintaining phase stability. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy. The present work reports on overcoming some important limitations on the original design of the MONSTR apparatus. One important advantage of the MONSTR is the fact that it is a closed platform, which provides the high stability. Once the optical alignment is performed, it is desirable to maintain the alignment over long periods of time. The previous design of the MONSTR was limited to a narrow spectral range defined by the optical coating of the beam splitters. In order to achieve tunability over a broad spectral range the internal optics needed to be changed. By using broadband coated and wedged beam splitters and compensator plates, combined with modifications of the beam paths, continuous tunability can be achieved from 520 nm to 1100 nm without changing any optics or performing alignment of the internal components of the MONSTR. Furthermore, in order to achieve continuous tunability in the spectral region between 520 nm and 720 nm, crucially important for studies on numerous biological molecules, a single longitudinal mode laser at 488.5 nm was identified and used as a metrology laser. The shorter wavelength of the metrology laser as compared to the usual HeNe laser has also increased the phase stability of the system. Finally, in order to perform experiments in the reflection geometry, a simple method to achieve active phase stabilization
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.
A Study of Two Dimensional Electron Gas Using 2D Fourier Transform Spectroscopy
NASA Astrophysics Data System (ADS)
McIntyre, Carl; Paul, Jagannath; Karaiskaj, Denis
2015-03-01
The dephasing of FES was measured in a symmetrically modulation doped 12 nm single quantum well GaAs/AlGaAs two dimensional electron gas system using time integrated four wave mixing (TIFWM) and a two dimensional Fourier transform spectroscopy (2DFTS). At high in-well carrier densities of ~4 x 1011 cm-2, many body effects that are prevalent and measurable with non-linear optical spectroscopy. Effects of exciton-exciton and exciton-phonon scattering events, exciton populations, and biexciton formation are detectable at these carrier concentrations. Homogeneous linewidths obtained from 2DFT and TIFWM yield a zero Kelvin linewidth of 1.42 meV and an acoustic phonon scattering coefficient of 158 μ eV/K. These observations indicate a rapid increase in homogeneous linewidth with increased temperature. NSF REU Grant # DMR-1263066: REU Site in Applied Physics at USF.
Grating Sagnac Fourier transform spectrometer and its applications
NASA Astrophysics Data System (ADS)
Ma, Huan
The Active Hyperspectral Imaging (AHI) project at University of Hawaii uses the multi-color laser induced fluorescence to detect the low concentration molecules in the atmosphere. A high throughput, high spectral and time resolution receiver is required by this application. The stationary Fourier transform spectrometer (FTS) is one candidate for this purpose. Compared to the traditional FTS, the stationary FTS has the advantage of high time resolution. However, the spectral resolution of the stationary FTS has been relatively low in the past two decades. We have invented and developed a novel stationary FTS based on a modified Sagnac interferometer. The use of multiple diffraction gratings greatly improves the spectral resolution of the interferometer. A prototype of two-grating Sagnac ITS is built. The theoretical resolving power of the prototype is 0.957 x 106 at HeNe wavelength, which corresponds to the resolution of 495 MHz in frequency. The 700--1000 MHz (<0.03 cm-1) resolution is obtained at 633 nm experimentally for the prototype. This is in full agreement with the theory and numerical simulation. The free spectral range of the prototype is more than 0.5 THz (>16.68 cm-1). The time resolution of the grating Sagnac FTS is transform-limited. The pulsed laser experiment demonstrates the 2 ˜ 3 nsec time resolution for the prototype of the two-grating Sagnac FTS. The grating Sagnac FTS has wide tuning range. The same setup can cover the full visible spectral range by simply rotating the gratings. Although only visible spectrum is demonstrated, the grating Sagnac ITS can be used for UV and IR spectral measurement when different materials and detectors are used. The general theory on optimum N-grating Sagnac FTS is developed. The higher spectral resolution is possible when more gratings are used. A successful computer model is built up to help us design the system. The characteristic of high spectral resolution and high time resolution makes the grating Sagnac FTS
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 Astrophysics Data System (ADS)
Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.
2012-06-01
By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H_2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct. Q. Ma, R. H. Tipping, and N. N. Lavrentieva, JQSRT dio:10.1016/j.jqsrt.2012.02.012 (2012).
NASA Technical Reports Server (NTRS)
Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.
2012-01-01
By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.
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.
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
Polymer standards for testing Fourier transform infrared spectrometers
NASA Astrophysics Data System (ADS)
Bowie, Bryan T.; Griffiths, Peter R.
1998-06-01
An ideal sample for monitoring the photometric accuracy of Fourier transform infrared (FT-IR) spectrometers should be a self-supporting solid that is stable over a period of several years. Ideally, the spectrum of this sample should also have no interference fringes and the bands of interest should be stable over a wide temperature range. Two differently processed isotactic polypropylene samples, one stress-relieved and the other extruded, mounted between two BaF2˙ windows were investigated for this purpose. The 841-cm-1 band of polypropylene has been investigated as a possible wavenumber and photometric standard, because it is sharp, is not overlapped by neighboring bands and absorbs in an atmospheric window. When measured at 2 cm-1 resolution, the band centers (as calculated by their center of mass) are 841.68 cm-1 and 840.08 cm-1 for the stress-relieved and extruded polymer respectively. When the sample temperature changes from 10 °C to 50 °C, the band shifts by 0.03 cm-1 and 0.014 cm-1 for the stress-relieved and extruded polymer respectively. The full width at half height (FWHH) of the band increases by 0.33 cm-1 for both films when the temperature is increased from 10 °C to 50 °C. Conversely, the absorbance decreases by 0.085 and 0.058 for the stress-relieved and extruded film respectively when the temperature is increased from 10 °C to 50 °C. The percent deviation of the band area is 4.69 and 2.96 for the stress-relieved and extruded polymer respectively. Another possible issue to be concerned with when using a polymer as a standard is the effect of dichroism. The intensity of the 841-cm-1 band of the stress relieved polymer varies by 4.5% when the orientation of incident polarized radiation is varied by 90° about an axis normal to the plane of the polymer sample. When two layers of the polymer are overlaid such that the backbone chains of each layer are oriented orthogonally, the intensity of the analogous band for the extruded polymer changes by
Quantum decoration transformation for spin models
NASA Astrophysics Data System (ADS)
Braz, F. F.; Rodrigues, F. C.; de Souza, S. M.; Rojas, Onofre
2016-09-01
It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the "classical" limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising-Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.
Barshan, Billur; Ayrulu, Birsel
2002-01-01
This study investigates fractional Fourier transform pre-processing of input signals to neural networks. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a. Judicious choice of this parameter can lead to overall improvement of the neural network performance. As an illustrative example, we consider recognition and position estimation of different types of objects based on their sonar returns. Raw amplitude and time-of-flight patterns acquired from a real sonar system are processed, demonstrating reduced error in both recognition and position estimation of objects.
Phase demodulation using adaptive windowed Fourier transform based on Hilbert-Huang transform.
Wang, Chenxing; Da, Feipeng
2012-07-30
The phase demodulation method of adaptive windowed Fourier transform (AWFT) is proposed based on Hilbert-Huang transform (HHT). HHT is analyzed and performed on fringe pattern to obtain instantaneous frequencies firstly. These instantaneous frequencies are further analyzed based on the condition of AWFT to locate local stationary areas where the fundamental spectrum will not be interfered by high-order spectrum. Within each local stationary area, the fundamental spectrum can be extracted accurately and adaptively by using AWFT with the background, which has been determined previously with the presented criterion during HHT, being eliminated to remove the zero-spectrum. This method is adaptive and unconstrained by any precondition for the measured phase. Experiments demonstrate its robustness and effectiveness for measuring the object with discontinuities or complex surface.
A Novel Approach for the Fourier Transform of Photoreflectance Spectra
NASA Astrophysics Data System (ADS)
Hwang, Jenn-Shyong; Chang, Chung-Chih; Chen, Mei-Fei; Kuo, Chia-Wei; Lu, Yan-Ten
2002-12-01
In a surface-intrinsic-n+ (SIN+) structure, the strong electric field in the intrinsic layer gives rise to level splitting (˜20 meV) between heavy-hole (HH) and light-hole (LH) bands. This causes inaccuracy in the traditional scaling Fourier analysis of photoreflectance (PR). In this work, we present a novel technique for obtaining the valence-band split from the Fourier spectrum of PR of GaAs. A linear combination of the FKO spectra of HH and LH is adopted as a trial function. Besides two linear coefficients, the band gaps for HH and LH are also treated as adjusted parameters. We develop an efficient algorithm for fitting the trial function to the PR spectrum in Fourier space. The field-induced splits are observed in PR spectra obtained under various pump beam intensities.
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)
Fourier transform of delayed fluorescence as an indicator of herbicide concentration.
Guo, Ya; Tan, Jinglu
2014-12-21
It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method.
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,...
NASA Technical Reports Server (NTRS)
Bowman, K.; Worden, H.; Beer, R.
1999-01-01
Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.
NASA Technical Reports Server (NTRS)
Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.
2000-01-01
A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).
NASA Astrophysics Data System (ADS)
D'Astous, Y.; Blanchard, M.
1982-05-01
In the past years, the Journal has published a number of articles1-5 devoted to the introduction of Fourier transform spectroscopy in the undergraduate labs. In most papers, the proposed experimental setup consists of a Michelson interferometer, a light source, a light detector, and a chart recorder. The student uses this setup to record an interferogram which is then Fourier transformed to obtain the spectrogram of the light source. Although attempts have been made to ease the task of performing the required Fourier transform,6 the use of computers and Cooley-Tukey's fast Fourier transform (FFT) algorithm7 is by far the simplest method to use. However, to be able to use FFT, one has to get a number of samples of the interferogram, a tedious job which should be kept to a minimum. (AIP)
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)
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: • The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms. • The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform. • The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.
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.
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.
Wang, Ruhang; Huang, Jianguo; Ma, Tian; Zhang, Qunfei
2010-12-01
This letter presents an improved space time prewhitening method for linear frequency modulation (LFM) reverberation. The proposed method transforms the reverberation to fractional Fourier domain to whiten using fractional Fourier transform. The linear varying frequency in LFM reverberation is focused on a stationary frequency, and the adjacent block signal is used as the reference signal of prewhitening. Finally, experiment results with real reverberation data verify that the proposed method improves the detection performance of active sonar in shallow sea significantly.
Plane-wave ultrasound beamforming using a nonuniform fast Fourier transform.
Kruizinga, Pieter; Mastik, Frits; de Jong, Nico; van der Steen, Antonius F W; van Soest, Gijs
2012-12-01
Beamforming of plane-wave ultrasound echo signals in the Fourier domain provides fast and accurate image reconstruction. Conventional implementations perform a k-space interpolation from the uniform sampled grid to a nonuniform acoustic dispersion grid. In this paper, we demonstrate that this step can be replaced by a nonuniform Fourier transform. We study the performance of the nonuniform fast Fourier transform (NUFFT) in terms of signal-to-noise ratio and computational cost, and show that the NUFFT offers an advantage in the trade-off between speed and accuracy, compared with other frequency-domain beamforming strategies.
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}.
Parallel Methods for Solving Time-Dependent Problems Using the Fourier-Laplace Transformation
NASA Astrophysics Data System (ADS)
Sheen, Dongwoo
In this paper we summarize recent progresses on the parallel method for solving time-dependent problems using the Fourier-Laplace transformation. These problems arise in the study of elastic wave equations with absorbing boundary conditions, for example. Instead of solving the time-dependent problems in the space-time domain, we solve them as follows. First, take the Fourier-Laplace transformation of given problems originally set in the space-time domain, and consider the corresponding problems in the space-frequency domain which form a set of indefinite, complex-valued elliptic problems. Such problems are solved in a natural parallel manner since each problem is independent of others. The Fourier-Laplace inversion formula will then recover the solution in the space-time domain. Keywords: parallel method, Fourier-Laplace transform, parabolic and hyperbolic problems
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.
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
Quantum simulation of noncausal kinematic transformations.
Alvarez-Rodriguez, U; Casanova, J; Lamata, L; Solano, E
2013-08-30
We propose the implementation of Galileo group symmetry operations or, in general, linear coordinate transformations in a quantum simulator. With an appropriate encoding, unitary gates applied to our quantum system give rise to Galilean boosts or spatial and time parity operations in the simulated dynamics. This framework provides us with a flexible toolbox that enhances the versatility of quantum simulation theory, allowing the direct access to dynamical quantities that would otherwise require full tomography. Furthermore, this method enables the study of noncausal kinematics and phenomena beyond special relativity in a quantum controllable system. PMID:24033011
Quantum simulation of noncausal kinematic transformations.
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.
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.
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
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.
Locke, Jonathan; White, Paul R
2011-10-01
The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species.
A faster method to reconstruct seismic data using anti-leakage Fourier transform
NASA Astrophysics Data System (ADS)
Jahanjooy, Saber; Nikrouz, Ramin; Mohammed, Nematullah
2016-02-01
Despite the simplicity of the anti-leakage Fourier transform (ALFT), and its ability to regularize pure non-uniform data sets and handle higher dimension seismic data, ALFT still remains less appealing because of its iterative algorithm and so its costly computation. During this study a set of parameters and techniques were studied to reduce needed computation and speed up ALFT. Having a good weighting function and cautiously selecting more Fourier coefficients at each iteration could improve the resolution of each iteration and subsequently enhance the converge speed of ALFT. Here a precomputed matrix by exponential term of Fourier transform is used to compute Fourier components at each iteration of the ALFT. This proposed matrix dramatically reduces the needed complex multiplication and speeds up the ALFT. By merging this process with a proper weighting function, the fast-ALFT will be quicker than the original ALFT, while it will have almost the same output.
Locke, Jonathan; White, Paul R
2011-10-01
The analysis of cetacean vocalizations is considered using Fourier-based techniques that employ chirp functions in their decomposition. In particular, the paper considers a short-time methods based on the fractional Fourier transform for detecting frequency modulated narrow-band signals, such as dolphin whistles, and compares this to the classical short-time Fourier methods. The fractional Fourier technique explored computes transforms associated with a range of chirp rates and automatically selects the rate for the final analysis. This avoids the need for prior knowledge of signal's chirp rate. An analysis is presented that details the performance of both methods as signal detectors and allows one to determine their detection thresholds. These thresholds are then used to measure the detectability of synthetic signals. This principle is then extended to measure performance on a set of recordings of narrow-band vocalizations from a range of cetacean species. PMID:21973352
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.
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)].
Grid-Based Fourier Transform Phase Contrast Imaging
NASA Astrophysics Data System (ADS)
Tahir, Sajjad
Low contrast in x-ray attenuation imaging between different materials of low electron density is a limitation of traditional x-ray radiography. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One recently developed phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a technique recently demonstrated by Bennett et al. that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 microm spot Mo source, a CCD with 22 microm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the grid in the Fourier domain. A Matlab code was written to perform the image processing. For the first time, the effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the window function type used to separate the harmonics, and the window widths, were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and new methods investigated to form improved phase contrast images.
Fourier-transform spectroscopy: new methods and applications: introduction by the feature editors.
Traub, W A; Winkel, R J; Goldman, A
1996-06-01
We are pleased to introduce this special issue of papers on Fourier-transform spectroscopy, which grew out of a recent topical meeting sponsored by the Optical Society of America. The topical meeting welcomed all researchers who practice the art of Fourier-transform spectroscopy in the laboratory, in the atmosphere, and in space. The power and the wide applicability of Fourier-transform spectroscopy unite these fields with a common mathematical and instrumental bond. The meeting probed each of these areas in depth, bringing out new ideas for instrumentation, analysis, and applications. There was a strong sentiment at the meeting that the quality of papers and posters was exceptionally high and that it would be important for future progress in the field to have the results of this meeting captured in print. This special issue is the fruit of that effort.
Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform
NASA Astrophysics Data System (ADS)
Lang, Jun
2012-05-01
In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by using the fractional Fourier transform, but most of their encryptions are complex values and need digital hologram technique to record information, which is inconvenient for digital transmission. In this paper, we propose a new approach for image encryption based on the real-valuedness and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission. In the proposed scheme, the original and encrypted images are respectively in the spatial domain and the reality-preserving multiple-parameter fractional Fourier transformed domain determined by the encryption keys. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.
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.
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.
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.
Quantum corrections of Abelian duality transformations
NASA Astrophysics Data System (ADS)
Balog, J.; Forgács, P.; Horváth, Z.; Palla, L.
1996-02-01
A modification of the Abelian duality transformations is proposed guaranteeing that a (not necessarily conformally invariant) σ-model be quantum equivalent (at least up to two loops in perturbation theory) to its dual. This requires a somewhat nonstandard perturbative treatment of the dual σ-model. Explicit formulae of the modified duality transformation are presented for a special class of block diagonal purely metric σ-models.
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.
Simple geometry to record fractional Fourier transform hologram with holographic lens
NASA Astrophysics Data System (ADS)
Gao, Feng; Zhang, Yixiao; Zeng, Yangsu; Yang, Jing; Xie, Shiwei; Gao, Fuhua; Huang, Xiaoyang; Yao, Jun; Du, Jinglei; Guo, Yongkang
2002-06-01
FRTH is a new kind of hologram, which is different form common Fresnel holograms and Fourier transform holograms. It can be applied for fractional Fourier transform filtering and anti-counterfeiting, etc. Due to the flexibility of holographic lens, we present a method that uses the -1 diffraction wave of holographic lens as the object wave and the 0 diffraction wave as the reference wave to record FRTH. It provides a new simple way to record FRTH. In this paper, the theory of achieving FRT and recording FRTH with holographic lens has been discussed, and the experimental results are also presented.
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.
CGH calculation with the ray tracing method for the Fourier transform optical system.
Ichikawa, Tsubasa; Yoneyama, Takuo; Sakamoto, Yuji
2013-12-30
Computer-generated holograms (CGHs) are usually displayed on electronic devices. However, the resolution of current output devices is not high enough to display CGHs, so the visual field is very narrow. A method using a Fourier transform optical system has been proposed, to enlarge the size of reconstructed images. This paper describes a method of CGH calculations for the Fourier transform optical system to enlarge the visual field and reconstruct realistic images by using the ray tracing method. This method reconstructs images at arbitrary depths and also eliminates unnecessary light including zero-th order light.
A broadband configuration for static Fourier transform spectroscopy with bandpass sampling
NASA Astrophysics Data System (ADS)
Sardari, Behzad; Davoli, Federico; Özcan, Meriç
2016-10-01
In this work a new broadband static Fourier transform spectrometer (static-FTS) configuration based on the division of the spectrum into multiple narrow-bands is proposed. This configuration not only decreases the spectrometer size but also allows operation in the traditional spectrometer wavelength range, namely, 400 nm-1100 nm with 1 cm-1 or better resolution. This technique solves the Nyquist sampling rate issue and enables us to record high resolution spectrums with regular CCDs. An algorithm is developed to process the signal and calculate the Fourier transform of the recorded interferograms on the CCD camera.
Interferometric time delay correction for Fourier transform spectroscopy in the extreme ultraviolet
NASA Astrophysics Data System (ADS)
Meng, Yijian; Zhang, Chunmei; Marceau, Claude; Naumov, A. Yu.; Corkum, P. B.; Villeneuve, D. M.
2016-09-01
We demonstrate a Fourier transform spectrometer in the extreme ultraviolet (XUV) spectrum using a high-harmonic source, with wavelengths as short as 32 nm. The femtosecond infrared laser source is divided into two separate foci in the same gas jet to create two synchronized XUV sources. An interferometric method to determine the relative delay between the two sources is shown to improve the accuracy of the delay time, with corrections of up to 200 asec required. By correcting the time base before the Fourier transform, the frequency resolution is improved by up to an order of magnitude.
Security of image encryption scheme based on multi-parameter fractional Fourier transform
NASA Astrophysics Data System (ADS)
Zhao, Tieyu; Ran, Qiwen; Yuan, Lin; Chi, Yingying; Ma, Jing
2016-10-01
Recently, multi-parameter fractional Fourier transform (MPFRFT) has been widely applied in the optics cryptosystem, which has attracted more and more researchers' attention. However, in further study we find a serious security problem on the MPFRFT which is the multi-choice of decryption key corresponding to an encryption key. The existence of multi-decryption-key hinders the application of this algorithm. We present a new generalized fractional Fourier transform, which can overcome the problem and enlarge the key space. The simulation results show that the proposed algorithm has higher security and key sensitivity.
Local structure information by EXAFS analysis using two algorithms for Fourier transform calculation
NASA Astrophysics Data System (ADS)
Aldea, N.; Pintea, S.; Rednic, V.; Matei, F.; Tiandou, Hu; Yaning, Xie
2009-08-01
The present work is a comparison study between different algorithms of Fourier transform for obtaining very accurate local structure results using Extended X-ray Absorption Fine Structure technique. In this paper we focus on the local structural characteristics of supported nickel catalysts and Fe3O4 core-shell nanocomposites. The radial distribution function could be efficiently calculated by the fast Fourier transform when the coordination shells are well separated while the Filon quadrature gave remarkable results for close-shell coordination.
Progress Towards Chirped-Pulse Fourier Transform Thz Spectroscopy
NASA Astrophysics Data System (ADS)
Douglass, Kevin O.; Plusquellic, David F.; Gerecht, Eyal
2010-06-01
New opportunities are provided by the development of higher power THz frequency multiplier sources, the development of a broadband Chirped-Pulse FTMW spectroscopy technique at microwave and mm Wave frequencies, and recently demonstrated heterodyne hot electron bolometer detection technology in the THz frequency region with near quantum noise-limited performance and high spectral resolution. Combining these three technologies and extending the chirped-pulse technique to 0.85 THz enables a host of new applications. NIST is currently pursing applications as a point sensor for greenhouse gases, volatile organic compounds, and potentially human breath. The generation and detection of phase stable chirped pulses at 850 GHz will be demonstrated. A description of the experimental setup and preliminary data will be presented for nitrous oxide. G.G. Brown, B.C. Dian, K.O. Douglass, S.M. Geyer, S. Shipman and B.H. Pate, Rev.Sci.Instrum. 79 (2008) 053103. E. Gerecht, D. Gu, L. You, K.S. Yngvesson, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES. 56, (2008) 1083.
Fourier Transform Near Infrared Spectrometry: Using Interferograms To Determine Chemical Composition
NASA Astrophysics Data System (ADS)
Hoy, R. M.; McClure, W. Fred
1989-12-01
Previous research conducted in this laboratory has demonstrated several advantages accrued by transforming near infrared spectra from the wavelength domain to the Fourier domain. Those advantages include: [1] smoothing wavelength domain data without loss of end points, [2] correcting for particle size phenomena encountered in solid sample analyses by simply omitting the mean term Fourier coefficient from the "retransformation process", [3] minimizing the multicollinearity problem prevalent in wavelength space, [4] generating wavelength-space derivatives from Fourier space without loss of end points, [5] performing band enhancements via Fourier self-deconvolution, [6] identifying sample type using Fourier vectors, [7] estimating chemical composition using only the first few Fourier coefficients, [8] cutting of computer storage requirements by more than 96%, [9] cutting of calibration time by more than 96%, hence [10] reducing the drudgery of maintaining calibrations. That the first 12 Fourier coefficients contain sufficient information to determine chemical constituents in many products has turned out to be a major advantage leading us to understand that the chemical absorption information in the wavelength spectrum of a sample obtained with an interferometer was also present in the interferogram.
Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
NASA Astrophysics Data System (ADS)
Aerts, Diederik; Czachor, Marek; Kuna, Maciej
2016-10-01
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the expected basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
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.
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.
High Speed Countercurrent Chromatography/Fourier Transform Infrared (HSCCC/FT-IR) Spectrometry
NASA Astrophysics Data System (ADS)
Romanach, Rodolfo J.; de Haseth, James A.
1985-12-01
High Speed Countercurrent Chromatography/Fourier transform infrared (HSCCC/FT-IR) spectrometry is present-ed. High solute-to-solvent ratios can be obtained in separations performed using HSCCC. At these high solute concentrations it is possible to obtain spectra of solutes without solvent elimination, even in the presence of polar solvents, such as water and methanol.
Fourier-Borel Transforms in Clifford Analysis and the Dual Fischer Decomposition
Sommen, Franciscus C.
2008-09-01
In this presentation we introduce several generalizations to Clifford analysis of the classical Fourier-Borel transform for analytic of holomorphic functionals. We also prove that every analytic or holomorphic functional admits a unique decomposition as a series of Dirac derivatives of monogenic functionals, a result which is dual to the Fischer decomposition.
Two-dimensional ultrafast fourier transform spectroscopy in the deep ultraviolet.
Tseng, Chien-hung; Matsika, Spiridoula; Weinacht, Thomas C
2009-10-12
We demonstrate two-dimensional ultrafast fourier transform spectroscopy in the deep ultraviolet (approximately 260 nm) using an acousto-optic modulator based pulse shaper. The use of a pulse shaper in the ultraviolet allows for rapid scanning, high phase (time) stability (approximately 0.017 rad) and phase cycling. We present measurements on the DNA nucleobase Adenine.
Alpha-rooting method of color image enhancement by discrete quaternion Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2014-02-01
This paper presents a novel method for color image enhancement based on the discrete quaternion Fourier transform. We choose the quaternion Fourier transform, because it well-suited for color image processing applications, it processes all 3 color components (R,G,B) simultaneously, it capture the inherent correlation between the components, it does not generate color artifacts or blending , finally it does not need an additional color restoration process. Also we introduce a new CEME measure to evaluate the quality of the enhanced color images. Preliminary results show that the α-rooting based on the quaternion Fourier transform enhancement method out-performs other enhancement methods such as the Fourier transform based α-rooting algorithm and the Multi scale Retinex. On top, the new method not only provides true color fidelity for poor quality images but also averages the color components to gray value for balancing colors. It can be used to enhance edge information and sharp features in images, as well as for enhancing even low contrast images. The proposed algorithms are simple to apply and design, which makes them very practical in image enhancement.
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…
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.
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)
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.
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.
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...
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-...
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 ...
Technology Transfer Automated Retrieval System (TEKTRAN)
This study deals with transferring the near-infrared (NIR) calibration models for quality assessment of barley between two instruments with different resolutions and number of data points, a Fourier transform instrument (master) and a dispersive instrument (slave). A file of spectra from 206 ground ...
The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.
ERIC Educational Resources Information Center
Suslick, Kenneth S.; And Others
1987-01-01
Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)
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...
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.
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.
Fourier transforms with rotations on circles or ellipses in signal and image processing
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.
2015-03-01
Fast unitary transforms are widely used in different areas such as data compression, pattern recognition and image reconstruction, interpolation, linear filtering, and spectral analysis. In this paper, we analyze the general concept of rotation and processing of data around not only circles but ellipses, in general. For that, we describe and analyze the general concept of the elliptic Fourier transform which was developed by Grigoryan in 2009. The block-wise representation of the discrete Fourier transform is considered in the real space, which is effective and that can be generalized to obtain new methods in spectral analysis. The N-point Elliptic discrete Fourier transform (EDFT) uses as a basic 2 × 2 transformation the rotations around ellipses. The EDFT distinguishes well from the carrying frequencies of the signal in both real and imaginary parts. It also has a simple inverse matrix. It is parameterized and includes also the DFT. Our preliminary results show that by using different parameters, the EDFT can be used effectively for solving many problems in signal and image processing field, in which includes problems such as image enhancement, filtration, encryption and many others.
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.
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.
Application of the fractional Fourier transform to image reconstruction in MRI.
Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo
2012-07-01
The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding.
Sene, CFB.; McCann, M. C.; Wilson, R. H.; Grinter, R.
1994-01-01
Infrared and Raman spectra of sequentially extracted primary cell walls and their pectic polymers were obtained from five angiosperm plants. Fourier-transform Raman spectrometry was shown to be a powerful tool for the investigation of primary cell-wall architecture at a molecular level, providing complementary information to that obtained by Fourier-transform infrared microspectroscopy. The use of an extraction procedure using imidazole instead of cyclohexane trans-1,2-N,N,N[prime],N[prime]-diaminotetraacetate allows the extension of the infrared spectral window for data interpretation from 1300 to 800 cm-1, to 2000 to 800 cm-1, and allows us to obtain Raman spectra from extracted cell-wall material. Wall constituents such as pectins, proteins, aromatic phenolics, cellulose, and hemicellulose have characteristic spectral features that can be used to identify and/or fingerprint these polymers without, in most cases, the need for any physical separation. The Gramineae (rice [Oryza sativa], polypogon [Polypogon fugax steud], and sweet corn [Zea mays]) are spectroscopically very different from the nongraminaceous monocotyledon (onion [Allium cepa]) and the dicotyledon (carrot [Daucus carota]); this reflects differences in chemical composition and cross-linking of the walls. The possibility of a taxonomic classification of plant cell walls based on infrared and Raman spectroscopies and the use of spectral fingerprinting for authentication and detection of adulteration of products rich in cell-wall materials are discussed. PMID:12232436
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).
Program for the analysis of time series. [by means of fast Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Brown, T. J.; Brown, C. G.; Hardin, J. C.
1974-01-01
A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.
A Study of Derivative Filters Using the Discrete Fourier Transform. Final Report M. S. Thesis
NASA Technical Reports Server (NTRS)
Ioup, G. E.
1980-01-01
Important properties of derivative (difference) filters using the discrete Fourier transform are investigated. The filters are designed using the derivative theorem of Fourier analysis. Because physical data are generally degraded by noise, the derivative filter is modified to diminish the effects of the noise, especially the noise amplification which normally occurs while differencing. The basis for these modifications is the reduction of those Fourier components for which the noise most dominates the data. The various filters are tested by applying them to find differences of two-dimensional data to which various amounts of signal dependent noise, as measured by a root mean square value, have been added. The modifications, circular and square ideal low-pass filters and a cut-off pyramid filter, are all found to reduce noise in the derivative without significantly degrading the result.
Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan
2016-01-01
Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods. PMID:27512636
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.
Niida, Chisato; Nakajima, Masakazu; Endo, Yasuki; Sumiyoshi, Yoshihiro; Ohshima, Yasuhiro; Kohguchi, Hiroshi
2014-03-14
Pure rotational transitions of the Ar–CS van der Waals complex have been observed by Fourier Transform Microwave (FTMW) and FTMW-millimeter wave double resonance spectroscopy. Rotational transitions of v{sub s} = 0, 1, and 2 were able to be observed for normal CS, together with those of C{sup 34}S in v{sub s} = 0, where v{sub s} stands for the quantum number of the CS stretching vibration. The observed transition frequencies were analyzed by a free rotor model Hamiltonian, where rovibrational energies were calculated as dynamical motions of the three nuclei on a three-dimensional potential energy surface, expressed by analytical functions with 57 parameters. Initial values for the potential parameters were obtained by high-level ab initio calculations. Fifteen parameters were adjusted among the 57 parameters to reproduce all the observed transition frequencies with the standard deviation of the fit to be 0.028 MHz.
NASA Astrophysics Data System (ADS)
Schrottke, L.; Lü, X.; Grahn, H. T.
2015-04-01
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
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 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.
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.
Tropical Forest Biomass Estimation from Vertical Fourier Transforms of Lidar and InSAR Profiles
NASA Astrophysics Data System (ADS)
Treuhaft, R. N.; Goncalves, F.; Drake, J.; Hensley, S.; Chapman, B. D.; Michel, T.; Dos Santos, J. R.; Dutra, L.; Graca, P. A.
2010-12-01
Structural forest biomass estimation from lidar or interferometric SAR (InSAR) has demonstrated better performance than radar-power-based approaches for the higher biomasses (>150 Mg/ha) found in tropical forests. Structural biomass estimation frequently regresses field biomass to some function of forest height. With airborne, 25-m footprint lidar data and fixed-baseline C-band InSAR data over tropical wet forests of La Selva Biological Station, Costa Rica, we compare the use of Fourier transforms of vertical profiles at a few frequencies to the intrinsically low-frequency “average height”. RMS scatters of Fourier-estimated biomass about field-measured biomass improved by 40% and 20% over estimates base on average height from lidar and fixed-baseline InSAR, respectively. Vertical wavelengths between 14 and 100 m were found to best estimate biomass. The same airborne data acquisition over La Selva was used to generate many 10’s of repeat-track L-band InSAR baselines with time delays of 1-72 hours, and vertical wavelengths of 5-100 m. We will estimate biomass from the Fourier transforms of L-band radar power profiles (InSAR complex coherence). The effects of temporal decorrelation will be modeled in the Fourier domain to try to model and reduce their impact. Using L-band polarimetric interferometry, average heights will be estimated as well and biomass regression performance compared to the Fourier transform approach. The more traditional approach of using L-band radar polarimetry will also be compared to structural biomass estimation.
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.
Fast Fourier transformation resampling algorithm and its application in satellite image processing
NASA Astrophysics Data System (ADS)
Li, Zhenping
2014-01-01
The image resampling algorithm, fast Fourier transformation resampling (FFTR), is introduced. The FFTR uses a global function in the Fourier expansion form to represent an image, and the image resampling is achieved by the introduction of a phase shift in the Fourier expansion. The comparison with the cubic spline interpolation approach in the image resampling is presented, which shows that FFTR is more accurate in the satellite image resampling. The FFTR algorithm is also generally reversible, because both the resampled and its original images share the same Fourier spectrum. The resampling for the images with hot spots is discussed. The hot spots in an image are the pixels with the second-order derivatives that are order of magnitude larger than the average value. The images with the hot spots are resampled with the introduction of a local Gaussian function to model the hot spot data, so that the remaining data for the Fourier expansion are continuous. Its application to the infrared channel image of Geostationary Operational Environmental Satellite Imager, to mitigate a diurnally changing band co-registration, is presented.
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.
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.
NASA Astrophysics Data System (ADS)
Preses, Jack M.; Hall, Gregory E.; Muckerman, James T.; Sears, Trevor J.; Weston, Ralph E., Jr.; Guyot, Christian; Hanson, Jonathan C.; Flynn, George W.; Bernstein, Herbert J.
1993-01-01
An infrared time-resolved Fourier-transform emission spectrophotometer was constructed and its use demonstrated. The instrument is based on a commercial interferometer combined with a data acquisition system. Operation in a smooth scan mode and the use of a transient digitizer provides good time efficiency for data acquisition and reduces the need to maintain constant energy pulses for long periods of time. An entire 100-point time history of a single point of an interferogram is obtained from a single laser pulse and usable data can be obtained from 10 to 50 mirror scans. The experimental apparatus, data acquisition program, and data evaluation are reviewed. Time-resolved Fourier-transform spectroscopy is an efficient method of determining the dynamics of molecular reactions and relaxation.
Seismology with a Fourier-transform spectrometer: applications to giant planets and stars.
Maillard, J P
1996-06-01
A method to detect the acoustic oscillation spectrum of giant planets and stars exploits the multiplex properties of a Fourier-transform spectrometer (FTS). It is based on measurement of the small Doppler shift related to the oscillation of the atmosphere measured from all the lines in a portion of the planetary or the stellar spectrum directly from the interferogram. The resulting amplitude modulation of the output signal is recorded continuously over several consecutive nights at a fixed path difference selected from criteria of optimum efficiency. Hence the Fourier transform of this signal yields the pressure-mode spectrum of the object. Applications to Jupiter, Saturn, and Procyon, observed in this mode with the step-scan FTS installed in the Canada-France-Hawaii Telescope, are presented. Future projects are discussed.
MightySat II.1 Fourier-transform hyperspectral imager payload performance
NASA Astrophysics Data System (ADS)
Otten, Leonard J.; Sellar, R. Glenn; Rafert, J. Bruce
1995-12-01
Using a new microsat called MightySat II as a platform, Kestrel Corporation is designing and building the first Fourier transform hyperspectral imager (FTHSI) to be operated from a spacecraft. This payload will also be the first to fly on the Phillips Laboratory MightySat II spacecraft series, a new, innovative approach, to affordable space testing of high risk, high payoff technologies. Performance enhancements offered by the Fourier transform approach have shown it to be one of the more promising spaceborne hyperspectral concepts. Simulations of the payload's performance have shown that the instrument is capable of separating a wide range of subtle spectral differences. Variations in the return from the Georges Bank and shoals are discernible and various types of coastal grasses (sea oats and spartina) can be isolated against a sand background.
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.
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.
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.
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.
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)
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 Astrophysics Data System (ADS)
Kikuchi, Kazuyoshi
2014-09-01
Convectively coupled equatorial waves (CCEWs) are major sources of tropical day-to-day variability. The majority of CCEWs-related studies for the past decade or so have based their analyses, in one form or another, on the Fourier-based space-time spectral analysis method developed by Wheeler and Kiladis (WK). Like other atmospheric and oceanic phenomena, however, CCEWs exhibit pronounced nonstationarity, which the conventional Fourier-based method has difficulty elucidating. The purpose of this study is to introduce an analysis method that is able to describe the time-varying spectral features of CCEWs. The method is based on a transform, referred to as the combined Fourier-wavelet transform (CFWT), defined as a combination of the Fourier transform in space (longitude) and wavelet transform in time, providing an instantaneous space-time spectrum at any given time. The elaboration made on how to display the CFWT spectrum in a manner analogous to the conventional method (i.e., as a function of zonal wavenumber and frequency) and how to estimate the background noise spectrum renders the method more practically feasible. As a practical example, this study analyzes 3-hourly cloud archive user service (CLAUS) cloudiness data for 23 years. The CFWT and WK methods exhibit a remarkable level of agreement in the distributions of climatological-mean space-time spectra over a wide range of space-time scales ranging in time from several hours to several tens of days, indicating the instantaneous CFWT spectrum provides a reasonable snapshot. The usefulness of the capability to localize space-time spectra in time is demonstrated through examinations of the annual cycle, interannual variability, and a case study.
NASA Astrophysics Data System (ADS)
Mossoulina, O. A.; Kirilenko, M. S.; Khonina, S. N.
2016-08-01
We use radial Fractional Fourier transform to model vortex laser beams propagation in optical waveguides with parabolic dependence of the refractive index. To overcome calculation difficulties at distances proportional to a quarter of the period we use varied calculation step. Numerical results for vortex modes superposition propagation in a parabolic optical fiber show that the transverse beam structure can be changed significantly during the propagation. To provide stable transverse distribution input scale modes should be in accordance with fiber parameters.
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
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.
LETTER TO THE EDITOR: The fractional Fourier transform and ISAR imaging
NASA Astrophysics Data System (ADS)
Borden, Brett
2000-04-01
We comment on a connection between the fractional Fourier transform and inverse synthetic aperture radar imaging (ISAR). The results help illuminate older constructions due to Bernfeld (Bernfeld M 1984 Chirp Doppler radar Proc. IEEE Lett. 72 540) and Feig and Grünbaum (Feig E and Grünbaum A 1986 Tomographic methods in range-Doppler radar Inverse Problems 2 185-95) and suggest a fast scheme for eliminating the polar data reformatting step in (ordinary) ISAR imaging.
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.
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.
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.
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.
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.
Quantum control of a molecular ionization process by using Fourier-synthesized laser fields
NASA Astrophysics Data System (ADS)
Ohmura, Hideki; Saito, Naoaki
2015-11-01
In photoexcitation processes, if the motion of excited electrons can be precisely steered by the instantaneous electric field of an arbitrary waveform of a Fourier-synthesized laser field, the resultant matter response can be achieved within one optical cycle, usually within the attosecond (1 as =10-18s) regime. Fourier synthesis of laser fields has been achieved in various ways. However, the general use of Fourier-synthesized laser fields for the control of matter is extremely limited. Here, we report the quantum control of a nonlinear response of a molecular ionization process by using Fourier-synthesized laser fields. The directionally asymmetric molecular tunneling ionization induced by intense (5.0 ×1012W /c m2) Fourier-synthesized laser fields consisting of fundamental, second-, third-, and fourth-harmonic light achieves the orientation-selective ionization; we utilized the orientation-selective ionization for measurement of the relative phase differences between the fundamental and each harmonic light. Our findings impact not only light-wave engineering but also the control of matter, possibly triggering the creation and establishment of a new methodology that uses Fourier-synthesized laser fields.
High-resolution and high-speed rotary Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Yang, Xiaoxu; Zhou, Sizhong; Lu, Qunbo; Xiangli, Bin; Zhou, Renkui
2006-02-01
Rotary Fourier Transform Spectrometer (RFTS) contains a rotary refractor, which produces continuous variational optical path difference (OPD). This specialty makes RFTS suitable to high speed spectrum measuring. Maximal OPD can increase so easily through increasing maximal sampling angle from which the system can get high resolution reconstructed spectrum also. Depending on rotating refractor to produce OPD brings some important advantages such as good immunity to outside influences, light weight, small size, etc. The basic theory of this new kind of spectrogram measuring instrument is introduced. OPD is the most important aspect to be considered in studying or designing a Fourier Transform spectrometer(FTS) system. OPD formulas of RFTS are deduced. RFTS has nonlinearity of OPD, which brings interferogram periodicity drifting and reconstructed spectrum noise. The index of OPD nonlinearity is defined and important aspects of nonlinearity are analyzed, including relationships with the refractor's refractive index and the rotating angle. Replacing OPD in Fourier Transform with nonlinear OPD of RFTS can buck the error of nonlinear OPD in reconstructed spectrum, and computer simulation shows the method effective.
Infrared small target enhancement via phase spectrum of Quaternion Fourier Transform
NASA Astrophysics Data System (ADS)
Qi, Shengxiang; Ma, Jie; Li, Hang; Zhang, Shuiping; Tian, Jinwen
2014-01-01
Small target enhancement is one of the crucial stages in infrared small target detection. In this paper, we propose a new method using phase spectrum of Quaternion Fourier Transform to enhance small targets while suppressing backgrounds for infrared images. This is inspired by the property that regularly Gaussian-like shape small targets could be considered as attractively salient signal in infrared images and the location information of such signal is implicitly contained in the phase spectrum from frequency domain. Formally, in the proposed method, we adopt the phase spectrum of Quaternion Fourier Transform instead of using traditional Fourier Transform to enhance the targets since the quaternion provides at most four data channels than only one for the latter, which could be helpful to broad types of background clutters by adding more information. For the construction of the quaternion, we present a second-order directional derivative filter via facet model to compute four second order directional derivative maps from four directions respectively as the four data channels. This filter is used to suppress noises and distinguish the targets and backgrounds into separably different textures so that it would boost the robustness of small target enhancement. In experiments, some typical infrared images with various scenes are tested to validate the effectiveness of the proposed method. The results demonstrate that our method actually has good performance and outperforms several state-of-the-art methods, which can be further used for infrared small target detection and tracking.
[A novel spatial modulation Fourier transform spectrometer with adjustable spectral resolution].
Lian, Yu-Sheng; Liao, Ning-Fang; Lü, Hang; Wu, Wen-Min; Dong, Zhi-Gang
2014-11-01
In the premise of fulfilling the application requirement, the adjustment of spectral resolution can improve efficiency of data acquisition, data processing and data saving. So, by adjusting the spectral resolution, the performance of spectrometer can be improved, and its application range can be extended. To avoid the problems of the fixed spectral resolution of classical Fourier transform spectrometer, a novel type of spatial modulation Fourier transform spectrometer with adjustable spectral resolution is proposed in this paper. The principle of the novel spectrometer and its interferometer is described. The general expressions of the optical path difference and the lateral shear are induced by a ray tracing procedure. The equivalent model of the novel interferometer is analyzed. Meanwhile, the principle of the adjustment of spectral resolution is analyzed. The result shows that the novel spectrometer has the merits of adjustable spectral resolution, high stability, easy assemblage and adjustment etc. This theoretical study will provide the theoretical basis for the design of the spectrometer with adjustable spectral resolution and expand the application range of Fourier transform spectrometer.
Grainger, J.; Reddy, V.V.; Patterson, D.G. Jr. )
1988-09-01
Analysis of polychlorinated dibenzo-p-dioxin (PCDD) isomers has been the focus of a number of recent investigations due to the extreme toxicities of specific laterally tetrachlorinated isomers. These investigations have primarily been directed toward 2,3,7,8-tetrachlorodibenzo-p-dioxin (2,3,7,8-TCDD), the most toxic PCDD isomer and toward isomer differentiation of TCDD isomers as a group. With the exception of pentachlorodibenzo-p-dioxin (PnCDD) isomer specific determinations based on calculated retention indices, isomer differentiation of the 14 PnCDD isomers has not been reported although 1,2,3,7,8-PnCDD is nearly as toxic as 2,3,7,8-TCDD. Chromatographically independent methods for PCDD isomer assignment have been reported by x-ray powder diffraction, proton nuclear magnetic resonance ({sup 1}H NMR), gas chromatography/matrix isolation Fourier transform infrared (MI/FTIR) spectroscopy, diffuse reflectance infrared Fourier transformation (DRIFT) spectroscopy and gas chromatography/Fourier transform infrared (GC/FTIR) spectroscopy. Although TCDD isomer assignments by the various methods are substantially in agreement, some differences are yet to be resolved. Vapor-phase reference infrared spectra are presented for the 14 PnCDD isomers. These spectra were recorded from low (< 10) microgram quantities for each isomer. The spectrum of each isomer is unique, allowing for positive isomer identification and individual group frequency absorption characteristics as a function of isomer structure.
[The principle and analysis of micro-Fourier transform spectrometer based on MEMS micro-mirror].
Chen, Jian-Jun; Zhu, Yong; Liu, Bo; Wei, Wei; Zhang, Jie; Wang, Ning
2012-11-01
The present paper puts forward a novel micro-Fourier transform infrared spectrometer based on programmable MEMS micro-mirror. This design uses a MEMS micro-mirror and a slantwise reflector to replace the moving mirror system on traditional spectrometer. This paper analyzes the operating principle of this spectrometer and gives the simulation result to prove the feasibility of this method. The results show that the spectral resolution is less than 5 nm in near-infrared wave band, the wave-length accuracy is approximately 1 nm and the sampling period of this spectrometer is approximately 50 ms. This method can use Hadamard transform to improve the SNR.
The parallel implementation of the one-dimensional Fourier transformed Vlasov Poisson system
NASA Astrophysics Data System (ADS)
Eliasson, Bengt
2005-08-01
A parallel implementation of an algorithm for solving the one-dimensional, Fourier transformed Vlasov-Poisson system of equations is documented, together with the code structure, file formats and settings to run the code. The properties of the Fourier transformed Vlasov-Poisson system is discussed in connection with the numerical solution of the system. The Fourier method in velocity space is used to treat numerical problems arising due the filamentation of the solution in velocity space. Outflow boundary conditions in the Fourier transformed velocity space removes the highest oscillations in velocity space. A fourth-order compact Padé scheme is used to calculate derivatives in the Fourier transformed velocity space, and spatial derivatives are calculated with a pseudo-spectral method. The parallel algorithms used are described in more detail, in particular the parallel solver of the tri-diagonal systems occurring in the Padé scheme. Program summaryTitle of program:vlasov Catalogue identifier:ADVQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating system under which the program has been tested: Sun Solaris; HP-UX; Read Hat Linux Programming language used: FORTRAN 90 with Message Passing Interface (MPI) Computers: Sun Ultra Sparc; HP 9000/785; HP IPF (Itanium Processor Family) ia64 Cluster; PCs cluster Number of lines in distributed program, including test data, etc.:3737 Number of bytes in distributed program, including test data, etc.:18 772 Distribution format: tar.gz Nature of physical problem: Kinetic simulations of collisionless electron-ion plasmas. Method of solution: A Fourier method in velocity space, a pseudo-spectral method in space and a fourth-order Runge-Kutta scheme in time. Memory required to execute with typical data: Uses typically of the order 10 5-10 6 double precision numbers. Restriction on the complexity of the problem: The program uses
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…
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
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>
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).
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.
Optimal quantum learning of a unitary transformation
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; Chiribella, Giulio; D'Ariano, Giacomo Mauro; Facchini, Stefano; Perinotti, Paolo
2010-03-01
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.
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.
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.
Digital watermarking algorithm research of color images based on quaternion Fourier transform
NASA Astrophysics Data System (ADS)
An, Mali; Wang, Weijiang; Zhao, Zhen
2013-10-01
A watermarking algorithm of color images based on the quaternion Fourier Transform (QFFT) and improved quantization index algorithm (QIM) is proposed in this paper. The original image is transformed by QFFT, the watermark image is processed by compression and quantization coding, and then the processed watermark image is embedded into the components of the transformed original image. It achieves embedding and blind extraction of the watermark image. The experimental results show that the watermarking algorithm based on the improved QIM algorithm with distortion compensation achieves a good tradeoff between invisibility and robustness, and better robustness for the attacks of Gaussian noises, salt and pepper noises, JPEG compression, cropping, filtering and image enhancement than the traditional QIM algorithm.
NASA Astrophysics Data System (ADS)
García, Javier; Dorsch, Rainer G.; Lohmann, Adolf W.; Ferreira, Carlos; Zalevsky, Zeev
1997-02-01
Recently, in the field of fractional Fourier transforms (FRT) an operation coined "fractional correlation" has been proposed and investigated experimentally. In this paper we propose a new setup for obtaining the fractional correlation, which presents several advantages from the experimental point of view. The fractional filter plane can be adjusted accurately with the help of converging beam illumination and using an adjusting device consisting of a combination of Fresnel zone plates. Moreover the scaling factor between the input pattern and the filter can be adjusted at will. This degree of freedom is of special interest when using SLMs. In addition we present a configuration, based on this setup, for spatial filtering of chirp noise in the fractional Fourier domain.
Vurpillot, F; De Geuser, F; Da Costa, G; Blavette, D
2004-12-01
Because of the increasing number of collected atoms (up to millions) in the three-dimensional atom probe, derivation of chemical or structural information from the direct observation of three-dimensional images is becoming more and more difficult. New data analysis tools are thus required. Application of a discrete Fourier transform algorithm to three-dimensional atom probe datasets provides information that is not easily accessible in real space. Derivation of mean particle size from Fourier intensities or from three-dimensional autocorrelation is an example. These powerful methods can be used to detect and image nano-segregations. Using three-dimensional 'bright-field' imaging, single nano-segregations were isolated from the surrounding matrix of an iron-copper alloy. Measurement of the inner concentration within clusters is, therefore, straightforward. Theoretical aspects related to filtering in reciprocal space are developed.
Asymmetric multiple-image encryption based on the cascaded fractional Fourier transform
NASA Astrophysics Data System (ADS)
Li, Yanbin; Zhang, Feng; Li, Yuanchao; Tao, Ran
2015-09-01
A multiple-image cryptosystem is proposed based on the cascaded fractional Fourier transform. During an encryption procedure, each of the original images is directly separated into two phase masks. A portion of the masks is subsequently modulated into an interim mask, which is encrypted into the ciphertext image; the others are used as the encryption keys. Using phase truncation in the fractional Fourier domain, one can use an asymmetric cryptosystem to produce a real-valued noise-like ciphertext, while a legal user can reconstruct all of the original images using a different group of phase masks. The encryption key is an indivisible part of the corresponding original image and is still useful during decryption. The proposed system has high resistance to various potential attacks, including the chosen-plaintext attack. Numerical simulations also demonstrate the security and feasibility of the proposed scheme.
Precise measurement of the resolution in light microscopy using Fourier transform
Vainrub, Arnold
2008-04-15
The resolution power of light microscope has been accurately measured ({+-}5%) by Fourier transform of various object images and further evaluation of the highest spatial frequency in Fourier spectrum. Any unknown shape plane object with a shape feature's size smaller than the resolution to be measured was shown to provide a reliable resolution test. This simple method gives a direct measurement of the resolution power as defined by Abbe [Archiv. F. Mikroskopische Anat. 9, 413 (1873)]. The results have been justified by comparison to a standard resolution measurement by using calibrated periodic line patterns. Notably, the approach is applicable in super-resolution light microscopy (transmission, reflection, and fluorescence), where calibrated resolution targets do not occur. It was conveniently implemented by using a compact disk as a test object and free IMAGEJ imaging software.
Technology Transfer Automated Retrieval System (TEKTRAN)
Analysis of DNA samples of Salmonella serotypes (Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky) were performed using Fourier transform infrared spectroscopy (FT-IR) spectrometer by placing directly in contact with a diamond attenua...
A portable Fourier transform infrared gas analyzer with a photoacoustic detector performed reliably during pollution prevention research at two industrial facilities. It exhibited good agreement (within approximately 6%) with other analytical instruments (dispersive infrared and ...
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
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.
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
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.
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.
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.
Applications of asynoptic space - Time Fourier transform methods to scanning satellite measurements
NASA Technical Reports Server (NTRS)
Lait, Leslie R.; Stanford, John L.
1988-01-01
A method proposed by Salby (1982) for computing the zonal space-time Fourier transform of asynoptically acquired satellite data is discussed. The method and its relationship to other techniques are briefly described, and possible problems in applying it to real data are outlined. Examples of results obtained using this technique are given which demonstrate its sensitivity to small-amplitude signals. A number of waves are found which have previously been observed as well as two not heretofore reported. A possible extension of the method which could increase temporal and longitudinal resolution is described.
Fourier transform acousto-optic imaging with a custom-designed CMOS smart-pixels array.
Barjean, Kinia; Contreras, Kevin; Laudereau, Jean-Baptiste; Tinet, Éric; Ettori, Dominique; Ramaz, François; Tualle, Jean-Michel
2015-03-01
We report acousto-optic imaging (AOI) into a scattering medium using a Fourier Transform (FT) analysis to achieve axial resolution. The measurement system was implemented using a CMOS smart-pixels sensor dedicated to the real-time analysis of speckle patterns. This first proof-of-principle of FT-AOI demonstrates some of its potential advantages, with a signal-to-noise ratio comparable to the one obtained without axial resolution, and with an acquisition rate compatible with a use on living biological tissue.
NASA Astrophysics Data System (ADS)
Hanafi, Abdelmalek; Gharbi, Tijani; Cornu, Jean-Yves
2005-07-01
We explore the potential use of the Fourier-transform profilometry technique in in vivo studies of muscular contractions through the variation of muscle-group cross sections. Thanks to a tensorial analysis of the technique, a general expression of its sensitivity vector is established. It allows derivation of the expression of the resolution and the limit condition imposed by the spatial sampling of the fringe pattern. Key parameters that maximize the sensitivity are then simulated. A measurement system is accordingly built up and characterized. It is then successfully applied to the evaluation of the deformation of the forearm muscles during grasping exertions.
Two-dimensional Fourier transform spectroscopy of exciton-polaritons and their interactions
NASA Astrophysics Data System (ADS)
Takemura, N.; Trebaol, S.; Anderson, M. D.; Kohnle, V.; Léger, Y.; Oberli, D. Y.; Portella-Oberli, M. T.; Deveaud, B.
2015-09-01
We investigate polariton-polariton interactions in a semiconductor microcavity through two-dimensional Fourier transform (2DFT) spectroscopy. We observe, in addition to the lower-lower and the upper-upper polariton self-interactions, a lower-upper cross interaction. This appears as separated peaks in the on-diagonal and off-diagonal parts of 2DFT spectra. Moreover, we elucidate the role of the polariton dispersion through a fine structure in the 2DFT spectrum. Simulations, based on lower-upper polariton basis Gross-Pitaevskii equations including both self- and cross interactions, result in a 2DFT spectra in qualitative agreement with experiments.
Universal and special keys based on phase-truncated Fourier transform
Qin, Wan; Peng, Xiang; Meng, Xiangfeng; Gao, Bruce
2013-01-01
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 de cryption keys. PMID:25339784
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.
Chelliah, Pandian; Sahoo, Trilochan; Singh, Sheela; Sujatha, Annie
2015-10-20
A Fourier transform spectrometer (FTS) used for interrogating a fiber Bragg grating (FBG) consists of a scanning-type interferometer. The FTS has a broad wavelength range of operation and good multiplexing capability. However, it has poor wavelength resolution and interrogation speed. We propose a modification to the FTS using path delay multiplexing to improve the same. Using this method, spatial resolution and interrogation time can be improved by n times by using n path delays. In this paper, simulation results for n=2, 5 are shown.
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.
NASA Astrophysics Data System (ADS)
Serfas, Ottmar; Naumann, Dieter; Standfuss, Gabriele; Brueggemann, Lutz; Flemming, Ingeborg
1992-03-01
The Fourier-transform infrared spectra of intact procaryotic cells (bacteria) have already been used in the past to characterize (differentiate, classify and identify) a variety of bacterial strains and taxa. In this paper the essential features of a methodology are described which extend the FT-IR pattern recognition approach to intact eucaryotic cells (yeasts/fungi). Basically, the characteristic information pertaining to microbial FT-IR patterns is explored by applying multivariate statistics and cluster analysis to both the time and frequency domain of the mid-ir spectral data.
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
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)
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.
Côté, Alex; Levasseur, Simon; Boudreau, Sylvain; Genest, Jérôme
2014-07-01
This paper presents a concept using field cameras in combination with Fourier transform spectrometers. The device can produce five-dimensional (position-angle-spectra) data cubes. This can lead to accurate measurements in both spectrum and distance and allows a thorough characterization of the interferometer, as well as adds passive ranging information to hyperspectral images. Shear and tilt fringes are simultaneously observed in a fixed optical path difference interferometer, and a passive spectral ranging demonstration is done in both absorption and emission for the 500-900 nm spectral bands.
Trousson, P.; Lion, Y.
1985-05-09
A study of long-range proton coupling in nitroxide radicals has been performed with a numerical analysis program using the Fourier transform technique. The present method provides a means for further identification of radicals which is particularly useful for species that are otherwise indistinguishable. The superhyperfine structure of piperidine and pyrrolidine-1-oxyl derivatives, showing ..gamma..-nuclei coupling constants as small as 0.2 G, has been brought out. The results are in good agreement with those obtained by other resolution-enhancement methods. 17 references, 7 figures, 3 tables.
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.
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.
HIGH-RESOLUTION FOURIER TRANSFORM SPECTROSCOPY OF Nb i IN THE NEAR-INFRARED
Er, A.; Güzelçimen, F.; Başar, Gö.; Öztürk, I. K.; Tamanis, M.; Ferber, R.; Kröger, S. E-mail: sophie.kroeger@htw-berlin.de
2015-11-15
In this study, a Fourier Transform spectrum of Niobium (Nb) is investigated in the near-infrared spectral range from 6000 to 12,000 cm{sup −1} (830–1660 nm). The Nb spectrum is produced using a hollow cathode discharge lamp in an argon atmosphere. Both Nb and Ar spectral lines are visible in the spectrum. A total of 110 spectral lines are assigned to the element Nb. Of these lines, 90 could be classified as transitions between known levels of atomic Nb. From these classified Nb i transitions, 27 have not been listed in literature previously. Additionally, 8 lines are classified for the first time.
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.
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.
High Throughput Proteomics Using Fourier Transform Ion Cyclotron Resonance Mass Spectrometry
Qian, Weijun; Camp, David G.; Smith, Richard D.
2004-06-01
The advent of high throughput proteomics technology for global detection and quantitation of proteins creates new opportunities and challenges for those seeking to gain greater understanding of cellular machinery. Here, we review recent advances in high-resolution capillary liquid chromatography coupled to Fourier transform ion cyclotron resonance (FTICR) mass spectrometry along with its potential application to high throughput proteomics. These technological advances combined with quantitative stable isotope labeling methodologies provide powerful tools for expanding our understanding of biology at the system-level.
NASA 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.
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.
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.
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.
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.
Zheng, Ying; Liang, Jingqiu; Liang, Zhongzhu
2013-01-14
A model of miniaturized space-modulated Fourier transform infrared spectrometer (FTIR) is given. The two step mirrors as the key components are designed and a lithography-electroplating technique used to fabricate the small step mirror is proposed. We analyze the effect of the experiment results resulted from fabricating technics on the recovery spectrum in theory, and demonstrate that the lithography-electroplating technique is an effective method to fabricate the step mirror, which make miniaturized FTIR realized. We believe that the performances of FTIR can be better realized by optimizing experimental conditions to make this fabricating method more attractive.
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.
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.
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
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
Imaging the in-plane magnetization in a Co microstructure by Fourier transform holography.
Tieg, C; Frömter, R; Stickler, D; Hankemeier, S; Kobs, A; Streit-Nierobisch, S; Gutt, C; Grübel, G; Oepen, H P
2010-12-20
We report on experiments using Fourier transform holography to image the in-plane magnetization of a magnetic microstructure. Magnetic sensitivity is achieved via the x-ray magnetic circular dichroism effect by recording holograms in transmission at off-normal incidence. The reference beam is defined by a narrow hole milled at an inclined angle into the opaque mask. We present magnetic domain images of an in-plane magnetized cobalt element with a size of 2 μm × 2 μm× 20 nm. The domain pattern shows a multi-vortex state that deviates from the simple Landau ground state.
Niece, Krista L; Akers, Kevin S
2015-09-01
Colistin use has increased in response to the advent of infections caused by multidrug-resistant organisms. It is administered parenterally as an inactive prodrug, colistin methanesulfonate (CMS). Various formulations of CMS and labeling conventions can lead to confusion about colistin dosing, and questions remain about the pharmacokinetics of CMS. Since CMS does not have strong UV absorbance, current methods employ a laborious process of chemical conversion to colistin followed by precolumn derivatization to detect formed colistin by high-performance liquid chromatography. Here, we report a method for direct quantification of colistin methanesulfonate by attenuated total reflectance Fourier transform infrared spectroscopy (ATR FTIR).
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
Solouki, T; Russell, D H
1992-01-01
Matrix-assisted laser desorption ionization is used to obtain Fourier-transform ion cyclotron resonance mass spectra of model peptides (e.g., gramicidin S, angiotensin I, renin substrate, melittin, and bovine insulin). Matrix-assisted laser desorption ionization yields ions having appreciable kinetic energies. Two methods for trapping the high kinetic energy ions are described: (i) the ion signal for [M+H]+ ions is shown to increase with increasing trapping voltages, and (ii) collisional relaxation is used for the detection of [M+H]+ ions of bovine insulin. Images PMID:1378614
High-throughput proteomics using Fourier transform ion cyclotron resonance mass spectrometry.
Qian, Wei-Jun; Camp, David G; Smith, Richard D
2004-06-01
The advent of high-throughput proteomic technologies for global detection and quantitation of proteins creates new opportunities and challenges for those seeking to gain greater understanding of the cellular machinery. Here, recent advances in high-resolution capillary liquid chromatography coupled to Fourier transform ion cyclotron resonance mass spectrometry are reviewed 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.
Chemical imaging with Fourier transform coherent anti-Stokes Raman scattering microscopy.
Cui, Meng; Skodack, Joshua; Ogilvie, Jennifer P
2008-11-01
We report chemical imaging using Fourier transform coherent anti-Stokes Raman scattering (FTCARS) microscopy. Adding a passively phase-stable local field to amplify the weak FTCARS signal, we also demonstrate interferometric FTCARS microscopy, permitting reduced incident power to be used for imaging. We discuss signal-to-noise considerations and the conditions necessary to effectively suppress background noise, allowing FTCARS microscopy that is limited by the shot noise of the detector. We also discuss differences between the signal-to-noise obtainable by time and frequency domain coherent anti-Stokes Raman scattering (CARS) methods. PMID:19122721
Opto-digital image encryption by using Baker mapping and 1-D fractional Fourier transform
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Li, She; Liu, Wei; Liu, Shutian
2013-03-01
We present an optical encryption method based on the Baker mapping in one-dimensional fractional Fourier transform (1D FrFT) domains. A thin cylinder lens is controlled by computer for implementing 1D FrFT at horizontal direction or vertical direction. The Baker mapping is introduced to scramble the amplitude distribution of complex function. The amplitude and phase of the output of encryption system are regarded as encrypted image and key. Numerical simulation has been performed for testing the validity of this encryption scheme.
Laser desorption/Fourier transform mass spectra of glycoalkaloids and steroid glycosides.
Coates, M L; Wilkins, C L
1986-04-01
Positive- and negative-ion mass spectra of five glycoconjugates were obtained using laser desorption/Fourier transform mass spectrometry. These were the glycoalkaloids alpha-solanine and alpha-tomatine and the steroid glycosides gitoxin, lanatoside A and digitonin. Doping with KCl yielded both potassium- and chloride-attachment ions. Few fragment ions were observed for these species, with the exception of digitonin, although the negative-ion spectra showed relatively more fragmentation than the positive-ion spectra. All major fragments appeared to arise from losses of sugar groups due to cleavages at the glycosidic linkages. This contrasted sharply with the behavior of the malto-oligosaccharides studied in this laboratory.
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.
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
Testing and data path redesign of a high speed, 16-point Winograd Fourier transform processor
NASA Astrophysics Data System (ADS)
Pavick, Steven W.
1989-12-01
A prototype 16-point, 70 MHz Fourier transform processor using 1.2 micron minimum feature sizes was tested using a Tektronix DAS 9200, digital analysis system. The results showed that it is possible to operate an Air Force Institute of Technology (AFIT) WFT16 chip at 70 MHz. The results also showed a great deal of variation among the individual packaged chips. Using the WFT16's built in testing circuitry, portions of the main data and control circuitry were tested. The AFIT XROM address generator and control circuitry proved to be the most reliable chip subsection, followed by the arithmetic and register control system. The parallel-in serial-out input data register was also tested and showed consistent results even though the results were not as expected. The variation among chips was shown when attempts at trivial transforms were done. The attempted transforms consisted of dc data values of zero and minus one. Two of 16 tested chips showed correct transform values, but for only a limited, nonrepeated sequence. In later testing, two chips were found that gave repeatable results which closely approximated the expected results for both trivial and nontrivial transform attempts. Test procedures and input to output relationships were determine to aid further testing of the AFIT WFT16 circuit.
Witte, H; Rother, M
1992-03-01
The multiple possibilities for the application of Fast Fourier Transformation (FFT) in the cardiorespirography of neonates are shown as a summary of our own results. The basis is the power spectral analysis of instantaneous heart rate and respiratory movements, which can be complemented by a coherence analysis of both parameters. A model-aided method for quantification of respiratory sinus arrhythmia (RSA) as an additional application for power spectral and coherence analysis is discussed. The realization of Hilbert transformation by FFT makes possible the interval-related calculation of respiration rate. The necessity of this supplementation, as well as the resulting strategies of additional processing steps are emphasized. The results is a concept of signal processing which increases the efficiency of previously employed methods in computer-aided cardiorespirography.
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.
Real-time Fourier transform spectrometry for fluorescence imaging and flow cytometry
Buican, T.N.
1990-01-01
We present a Fourier transform (FT) spectrometer that is suitable for real-time spectral analysis in fluorescence imaging and flow cytometry. The instrument consists of a novel type of interferometer that can be modulated at frequencies of up to 100 kHz and has a high light throughput; and a dedicated, parallel array processor for the real-time computation of spectral parameters. The data acquisition array processor can be programmed by a host computer to perform any desired linear transform on the interferogram and can thus separate contributions from multiple fluorescence microscopy. The integration of a flow cytometer and a spectral imaging fluorescence microscope is discussed, and the concepts of direct and reversed virtual sorting'' are introduced. 9 refs., 8 figs.
Iterative Fourier transform algorithm: different approaches to diffractive optical element design
NASA Astrophysics Data System (ADS)
Skeren, Marek; Richter, Ivan; Fiala, Pavel
2002-10-01
This contribution focuses on the study and comparison of different design approaches for designing phase-only diffractive optical elements (PDOEs) for different possible applications in laser beam shaping. Especially, new results and approaches, concerning the iterative Fourier transform algorithm, are analyzed, implemented, and compared. Namely, various approaches within the iterative Fourier transform algorithm (IFTA) are analyzed for the case of phase-only diffractive optical elements with quantizied phase levels (either binary or multilevel structures). First, the general scheme of the IFTA iterative approach with partial quantization is briefly presented and discussed. Then, the special assortment of the general IFTA scheme is given with respect to quantization constraint strategies. Based on such a special classification, the three practically interesting approaches are chosen, further-analyzed, and compared to eachother. The performance of these algorithms is compared in detail in terms of the signal-to-noise ratio characteristic developments with respect to the numberof iterations, for various input diffusive-type objects chose. Also, the performance is documented on the complex spectra developments for typical computer reconstruction results. The advantages and drawbacks of all approaches are discussed, and a brief guide on the choice of a particular approach for typical design tasks is given. Finally, the two ways of amplitude elimination within the design procedure are considered, namely the direct elimination and partial elimination of the amplitude of the complex hologram function.
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.
A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp.
Barlow, Euan; Mulholland, Anthony J
2011-11-01
The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.
Ipsen, Andreas
2014-06-01
The isotope patterns of unknown analytes provide information that can be of great value in their identification as part of a mass spectrometry experiment. Determining the range of compounds that are consistent with an empirically observed isotope pattern requires, as an initial step, the calculation of the theoretical isotope patterns of all feasible candidate formulas, and this is not a trivial mathematical task. While algorithms based on the Fourier transform have been used for almost two decades to perform such calculation efficiently, they have hitherto not been able to provide the exact sets of masses and abundances that constitute the fundamental isotope pattern. This article presents a new approach to the treatment of such calculations, which involves arranging and manipulating the isotope patterns of distinct elements as multidimensional data structures. This enables the use of the multidimensional Fourier transform to calculate isotope patterns with an accuracy that is limited only by the errors of floating point arithmetic. The algorithm is both highly efficient and very easy to implement in many programming environments. An open-source implementation of the algorithm in the R programming language will be made publicly available and is also available upon request.
Azizian, Hormoz; Kramer, John K G; Phillips, Stuart M
2014-01-01
Currently, there are no direct and reliable methods to measure the body fat content of women during pregnancy. Estimates of fat accretion can significantly affect calculations of energy requirements. We report here the first direct measurement of determining the body fat content of two women during pregnancy using the Fourier transform near-infrared spectroscopy (FT-NIR) method. Fourier transform near-infrared spectroscopy was shown to provide comparable results to dual-energy X-ray absorptiometry and magnetic resonance imaging. These latter methods, even though very reliable to measure body fat levels, cannot be used to measure the body fat of women during pregnancy because of health concerns, while FT-NIR poses no health risk. The FT-NIR results showed the percent body fat remained relatively constant throughout pregnancy, but fat mass and fat free mass increased. Fat mass followed an S curve with a maximum increase between 15 to 25 weeks of gestation that was only detected by repeated measurements using the FT-NIR technique. These results demonstrate the value of the FT-NIR method to directly measure the fat content of pregnant women in minutes instead of relying on indirect calculations or taking measurements before and after pregnancy to track gestational fat mass accretion.
Yang, Xin; Jenkins, Gareth; Franzke, Joachim; Manz, Andreas
2005-07-01
A circular, shear-driven pumping system combined with Fourier Transform detection has been developed for the application of chip based cyclic chromatography. Using this system, it is possible to perform an injection of a sample plug into a circular micro-channel and then drive the sample through the channel, using shear flow induced by a rotation stage. High pumping rates at uniform speeds are attainable with this system with very little heat production. Typical pumping rates of up to 1.423 mm s(-1) +/- 2 microm s(-1) were used in experiments although much higher rates >14 mm s(-1) are also possible with this system. Fluorescence detection was used to detect a sample plug of Coumarin dyes, flowing around the channel. A coating of porous polymethacrylate was used to immobilise RP-HPLC beads onto the glass surface and was applied to the glass micro-channel by selective photopolymerisation. This coating acted as a stationary phase and differences in retention time were observed for an injection of Coumarin dyes for different methanol-water, mobile phase ratios. Full sample retention occurred for 30 : 70 (v/v) methanol-water whereas no retention occurred for 92 : 8 (v/v) methanol-water which can be expected for such a reverse phase, open tubular system. Fourier transform detection applied to the fully retained and non-retained cases showed frequency domain data from a single detection point corresponding to that which may be expected from shear flow theory.
Source brightness fluctuation correction of solar absorption fourier transform mid infrared spectra
NASA Astrophysics Data System (ADS)
Ridder, T.; Warneke, T.; Notholt, J.
2011-06-01
The precision and accuracy of trace gas observations using solar absorption Fourier Transform infrared spectrometry depend on the stability of the light source. Fluctuations in the source brightness, however, cannot always be avoided. Current correction schemes, which calculate a corrected interferogram as the ratio of the raw DC interferogram and a smoothed DC interferogram, are applicable only to near infrared measurements. Spectra in the mid infrared spectral region below 2000 cm-1 are generally considered uncorrectable, if they are measured with a MCT detector. Such measurements introduce an unknown offset to MCT interferograms, which prevents the established source brightness fluctuation correction. This problem can be overcome by a determination of the offset using the modulation efficiency of the instrument. With known modulation efficiency the offset can be calculated, and the source brightness correction can be performed on the basis of offset-corrected interferograms. We present a source brightness fluctuation correction method which performs the smoothing of the raw DC interferogram in the interferogram domain by an application of a running mean instead of high-pass filtering the corresponding spectrum after Fourier transformation of the raw DC interferogram. This smoothing can be performed with the onboard software of commercial instruments. The improvement of MCT spectra and subsequent ozone profile and total column retrievals is demonstrated. Application to InSb interferograms in the near infrared spectral region proves the equivalence with the established correction scheme.
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.
Identification of Earthquake Induced Damage Areas Using Fourier Transform and SPOT HRVIR Pan Images.
Sertel, Elif
2009-01-01
A devastating earthquake with a magnitude of Mw 7.4 occurred on the North Anatolian Fault Zone (NAFZ) of Turkey on August 17, 1999 at 00:01:39 UTC (3:01 a.m. local time). The aim of this study is to propose a new approach to automatically identify earthquake induced damage areas which can provide valuable information to support emergency response and recovery assessment procedures. This research was conducted in the Adapazari inner city, covering a 3 × 3 km area, where 11,373 buildings collapsed as a result of the earthquake. SPOT high resolution visible infrared (HRVIR) Pan images obtained before (25 June 1999) and after (4 October 1999) the earthquake were used in the study. Five steps were employed to conduct the research and these are: (i) geometric and radiometric correction of satellite images, (ii) Fast Fourier Transform (FFT) of pre- and post-earthquake images and filtering the images in frequency domain, (iii) generating difference image using Inverse Fast Fourier Transform (IFFT) pre- and post- earthquake images, (iv) application of level slicing to difference image to identify the earthquake-induced damages, (v) accuracy assessment of the method using ground truth obtained from a 1/5,000 scale damage map. The total accuracy obtained in the research is 80.19 %, illustrating that the proposed method can be successfully used to automatically identify earthquake-induced damage areas.
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.
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.)
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.
[A phase error correction method for the new Fourier transforms spectrometer].
Wang, Ning; Gong, Tian-Cheng; Chen, Jian-Jun; Li, Yang; Yang, Yi-Ning; Zhu, Yong; Zhang, Jie; Chen, Wei-Min
2014-11-01
To decrease the distortion of the recovered spectrum, improve the quantity of the recovered spectrum and decrease the influence of the phase error of the new spectrum detection system based on MEMS (micro-electro-mechanical systems) micro-mirrors, a new phase error correction method for this system is proposed in the present paper. The source of phase error of the spectrum detection system based on MEMS micro-mirrors is analyzed firstly. The analyzed result indicated that the phase error of the new spectral Fourier transform detection system is the zero drift of the optical path difference, and the phase error can be corrected by Zero-crossing sampling which is realized by improving the structure of the interferometer system and Mertz product The spectrum detection system is set up and the phase error correction method is verified by this system. The experiment result is show that the quantity of the recovered spectrum of the spectrum detection is improved obviously by using the improved interferometer system and Mertz product, and the recovered spectrum has no negative peaks and the side lobes is suppressed markedly. This correction method can reduce the influence caused by phase error to the system performance well and improve the spectral detection performance effectively. In this paper, the origin of the system phase error based on the new MEMS micromirror Fourier transform spectroscopy detection system is analyzed, and the phase error correction method is proposed. This method can improve the performance of the spectrum detection system.
3D-printed slit nozzles for Fourier transform microwave spectroscopy.
Dewberry, Christopher T; Mackenzie, Rebecca B; Green, Susan; Leopold, Kenneth R
2015-06-01
3D printing is a new technology whose applications are only beginning to be explored. In this report, we describe the application of 3D printing to the design and construction of supersonic nozzles. Nozzles can be created for $0.50 or less, and the ease and low cost can facilitate the optimization of nozzle performance for the needs of any particular experiment. The efficacy of a variety of designs is assessed by examining rotational spectra of OCS (carbonyl sulfide) and Ar-OCS using a Fourier transform microwave spectrometer with tandem cavity and chirped-pulse capabilities. A slit geometry which, to the best of our knowledge has not been used in conjunction with Fourier transform microwave spectrometers, was found to increase the signal-to-noise ratio for the J = 1←0 transition of OCS, by a factor of three to four compared with that obtained using our standard circular nozzle. Corresponding gains for the Ar-OCS complex were marginal, at best, but further optimization of nozzle geometry should be possible. The spectrometer itself is designed to allow rapid switching between cavity and chirped-pulse modes of operation without the need to break vacuum. This feature, as well as the newly incorporated chirped-pulse capability, is described in detail.
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.
[The study of photo-elastic modulator-based Fourier transform spectroscopy].
Chen, You-hua; Wang, Zhao-ba; Wang, Zhi-bin; Wang, Yan-chao; Li, Yong-shuai; Zhang, Yu-han
2014-06-01
In order to enhance the spectrum resolution of current photo-elastic modulator-based Fourier transform spectrometer, a multi-reflected photo-elastic modulator-based interferometer structure was proposed in the present paper. Through coating reflecting film alternatingly on the photo-elastic crystal and light oblique incidence, and allowing the incident ray to have the multi-reflection in the crystal and exit from the other side of the crystal, the authors increased the light propagation distance in the crystal and enhanced the optical path difference at last. Based on this, the function of interference-spectrum retrieval was established, the optical system matched to the multi-reflected PEM-based interferometer was designed, and finally, the experimental system of multi-reflected PEM-based Fourier transform spectroscopy for telemetry was established. The principle of verification tests by using 671 nm laser and xenon lamp shows that the interferogram was clear and stable, and the feasibility of the principle of the system was verified. The expected result shows that the spectrum resolution of the designed PEM-FTs with multi-reflection achieved 13 cm(-1), and its luminous flux just didn't reduce too much, which ensured the SNR. Through spectral inversion of the interference fringes, the technical feasibility of the spectrum system developed was verified. This work established the basic condition of prototype fabrication, radiation precise calibration, spectral calibration and instrument signal-to-noise ratio test and so on.
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.
The design of ROM-type holographic memory with iterative Fourier transform algorithm
NASA Astrophysics Data System (ADS)
Akamatsu, Hideki; Yamada, Kai; Unno, Noriyuki; Yoshida, Shuhei; Taniguchi, Jun; Yamamoto, Manabu
2013-03-01
The research and development of the holographic data storage (HDS) is advanced, as one of the high-speed, mass storage systems of the next generation. Recently, along the development of the write-once system that uses photopolymer media, large capacity ROM type HDS which can replace conventional optical discs becomes important. In this study, we develop the ROM type HDS using a diffractive optical element (DOE), and verify the effectiveness of our approach. In order to design DOE, iterative Fourier transform algorithm was adopted, and DOE is fabricated with electron beam (EB) cutting and nanoimprint lithography. We optimize the phase distribution of the hologram by iterative Fourier transform algorithm known as Gerchberg-Saxton (GS) algorithm with the angular spectrum method. In the fabrication process, the phase distribution of the hologram is implicated as the concavity and convexity structure by the EB cutting and transcribed with nanoimprint lithography. At this time, the mold is formed as multiple-stage concavity and convexity. The purpose of multiple-stage concavity and convexity is to obtain high diffraction efficiency and signal-to-noise ratio (SNR). Fabricated trial model DOE is evaluated by the experiment.
Ground-based high resolution Fourier transform spectrometer and its application in Beijing
NASA Astrophysics Data System (ADS)
Fan, Dongdong
2013-10-01
The B3M-FTS instrument, inherited from ACE-FTS and PARIS, is built by Canadian ABB and Beijing Vision Sky Aerospace Co., Ltd. The B3M is a complete stand-alone spectrometer designed to operate from the ground in moderate environment. It can acquire atmospheric spectra with the Sun as back illumination. This instrument is an adapted version of the classical Michelson interferometer using an optimized optical layout, and it is a high-resolution infrared Fourier transform spectrometer operating in the 750 to 4100cm-1 spectral range. In this paper, the instrument concept of a compact, portable, high-resolution Fourier transform spectrometer is introduced. Some test results of the instrument such as ILS and SNR are presented, and the spectral resolution of 0.028cm-1 @ 750cm-1 and SNR over 100:1 are achieved. Sample atmospheric absorption spectra and corresponding retrieval results measured by the FTS are given. The B3M-FTS, with its high performance, provides the capability to monitor the atmospheric composition changes by measuring the atmospheric absorption spectra of solar radiance. Lots of measurements have been acquired at the Olympics atmospheric observation super-station. Up to now, the VMRs of near 10 trace gases have been retrieved. The success of atmospheric composition profile retrieval using the FTS measurements makes the further application of FTS type payload possible in China.
A fractional Fourier transform analysis of the scattering of ultrasonic waves
Tant, Katherine M.M.; Mulholland, Anthony J.; Langer, Matthias; Gachagan, Anthony
2015-01-01
Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time–frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excitation, as well as establishing a time–frequency domain framework to assist in flaw identification and classification. PMID:25792967
Identification of Earthquake Induced Damage Areas Using Fourier Transform and SPOT HRVIR Pan Images
Sertel, Elif
2009-01-01
A devastating earthquake with a magnitude of Mw 7.4 occurred on the North Anatolian Fault Zone (NAFZ) of Turkey on August 17, 1999 at 00:01:39 UTC (3:01 a.m. local time). The aim of this study is to propose a new approach to automatically identify earthquake induced damage areas which can provide valuable information to support emergency response and recovery assessment procedures. This research was conducted in the Adapazari inner city, covering a 3 × 3 km area, where 11,373 buildings collapsed as a result of the earthquake. SPOT high resolution visible infrared (HRVIR) Pan images obtained before (25 June 1999) and after (4 October 1999) the earthquake were used in the study. Five steps were employed to conduct the research and these are: (i) geometric and radiometric correction of satellite images, (ii) Fast Fourier Transform (FFT) of pre- and post-earthquake images and filtering the images in frequency domain, (iii) generating difference image using Inverse Fast Fourier Transform (IFFT) pre- and post- earthquake images, (iv) application of level slicing to difference image to identify the earthquake-induced damages, (v) accuracy assessment of the method using ground truth obtained from a 1/5,000 scale damage map. The total accuracy obtained in the research is 80.19 %, illustrating that the proposed method can be successfully used to automatically identify earthquake-induced damage areas. PMID:22573966
Dziuba, B
2013-01-01
Fourier transform infrared spectroscopy (FTIR) and artificial neural networks (ANN's) were used to identify species of Propionibacteria strains. The aim of the study was to improve the methodology to identify species of Propionibacteria strains, in which the differentiation index D, calculated based on Pearson's correlation and cluster analyses were used to describe the correlation between the Fourier transform infrared spectra and bacteria as molecular systems brought unsatisfactory results. More advanced statistical methods of identification of the FTIR spectra with application of artificial neural networks (ANN's) were used. In this experiment, the FTIR spectra of Propionibacteria strains stored in the library were used to develop artificial neural networks for their identification. Several multilayer perceptrons (MLP) and probabilistic neural networks (PNN) were tested. The practical value of selected artificial neural networks was assessed based on identification results of spectra of 9 reference strains and 28 isolates. To verify results of isolates identification, the PCR based method with the pairs of species-specific primers was used. The use of artificial neural networks in FTIR spectral analyses as the most advanced chemometric method supported correct identification of 93% bacteria of the genus Propionibacterium to the species level.
Arithmetic Fourier transform and adaptive delta modulation: A symbiosis for high speed computation
Tufts, D.W.; Sadasiv, G.
1988-01-01
This report presents preliminary results on the VLSI design and implementation of a novel and promising algorithm for accurate high-speed Fourier analysis and synthesis. The Arithmetic Fourier Transform is based on the number -theoretic method of Mobius inversion. Its computations proceed in parallel and the individual operations are very simple. Except for a small number of scalings in one stage of the computation, only multiplications by 0, +1, and -1 are required. If the input samples were not quantized and if deal real-number operations were used internally, then the results would be exact. The accuracy of the computation is limited only by the input A/D conversion process, any constraints on the word lengths of internal accumulating registers, and the implementation of the few scaling operations. Motivated by the goal of efficient, effective, high-speed realization of the algorithm in an integrated circuit, we introduce further simplicities by the use of delta modulation to represent the input function in digital form. The result is that only binary (or preferably, ternary) sequences need to be processed in the parallel computations. And the required accumulations can be replaced by up/down counters. The dynamic range of the resulting transformation can be increased by the use of adaptive delta modulation.
[A phase error correction method for the new Fourier transforms spectrometer].
Wang, Ning; Gong, Tian-Cheng; Chen, Jian-Jun; Li, Yang; Yang, Yi-Ning; Zhu, Yong; Zhang, Jie; Chen, Wei-Min
2014-11-01
To decrease the distortion of the recovered spectrum, improve the quantity of the recovered spectrum and decrease the influence of the phase error of the new spectrum detection system based on MEMS (micro-electro-mechanical systems) micro-mirrors, a new phase error correction method for this system is proposed in the present paper. The source of phase error of the spectrum detection system based on MEMS micro-mirrors is analyzed firstly. The analyzed result indicated that the phase error of the new spectral Fourier transform detection system is the zero drift of the optical path difference, and the phase error can be corrected by Zero-crossing sampling which is realized by improving the structure of the interferometer system and Mertz product The spectrum detection system is set up and the phase error correction method is verified by this system. The experiment result is show that the quantity of the recovered spectrum of the spectrum detection is improved obviously by using the improved interferometer system and Mertz product, and the recovered spectrum has no negative peaks and the side lobes is suppressed markedly. This correction method can reduce the influence caused by phase error to the system performance well and improve the spectral detection performance effectively. In this paper, the origin of the system phase error based on the new MEMS micromirror Fourier transform spectroscopy detection system is analyzed, and the phase error correction method is proposed. This method can improve the performance of the spectrum detection system. PMID:25752034
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
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.
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.
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.
NASA Astrophysics Data System (ADS)
Ma, Q.; Boulet, C.; Tipping, R. H.
2014-03-01
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the {hat S} operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
Ma, Q.; Tipping, R. H.
2014-03-14
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS{sub 1} − S{sub 2} introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the S-circumflex operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters’ two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
NASA Technical Reports Server (NTRS)
Ma, Q.; Boulet, C.; Tipping, R. H.
2014-01-01
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
NASA Astrophysics Data System (ADS)
Graf, Robert N.; Chen, Xiaoxin; Brown, William; Wax, Adam
2008-02-01
Fourier Domain Low Coherence Interferometry (fLCI) is a promising technique which combines the depth resolution of low coherence interferometry with the sensitivity of light scattering spectroscopy for probing the health of epithelial tissue layers. Our new fLCI system configuration utilizes a white light Xe arc lamp source and a 4-f interferometer which re-images light scattered from the sample onto the detection plane. The system employs an imaging spectrometer at the detection plane to acquire depth resolved profiles from 252 adjacent spatial points without the need for any scanning. The limited spatial coherence of the light source requires the resolution of adjacent spatial points for the generation of depth information. Depth-resolved spectral information is recovered by performing a short-time Fourier transform on the detected spectra, similar to spectroscopic optical coherence tomography. Wavelength dependent variations in scattering intensity are analyzed as a function of depth to obtain information about the neoplastic transformation of the probed cells. Previous studies have demonstrated fLCI as an excellent technique for probing the scatterer morphology of simple phantoms and of in vitro cancer cell monolayers. We now seek to assess the ability of the new fLCI system to measure the health of subsurface tissue layers using the hamster cheek pouch model. Seven hamsters will have one cheek pouch treated with the known carcinogen DMBA. At the conclusion of the 24 week treatment period the animals will be anesthetized and the cheek pouches will be extracted. We will use the fLCI optical system to measure the neoplastic transformation of the in situ subsurface tissue layers in both the normal and DMBA-treated cheek pouches. Traditional histological analysis will be used to verify the fLCI measurements. We expect our results to establish the feasibility of fLCI to distinguish between healthy and dysplastic epithelial tissues in the hamster cheek pouch.
NASA Astrophysics Data System (ADS)
Monge, Josue Roberto
The goal of our scattering experiments is to derive the distribution the differential cross-section and elucidate the dynamics of a bimolecular collision via pure rotational spectroscopy. We have explored the use of a data reduction model to directly transform rotational line shapes into the differential cross section and speed distribution of a reactive bimolecular collision. This inversion technique, known as Fourier Transform Doppler Spectroscopy (FTDS), initially developed by James Kinsey, deconvolves the velocity information contained in one-dimensional Doppler Profiles to construct the non-thermal, state-selective three-dimensional velocity distribution. By employing an expansion in classical orthogonal polynomials, the integral transform in FTDS can be simplified into a set of purely algebraic expressions technique; i.e. the Taatjes method. In this investigation, we extend the Taatjes method for general use in recovering asymmetric velocity distributions. We have also constructed a hypothetical asymmetric distribution from adiabatic scattering in Argon-Argon to test the general method. The angle- and speed-components of the sample distribution were derived classically from a Lennard-Jones 6-12 potential, with collisions at 60 meV, and mapped onto Radon space to generate a set of discrete Doppler profiles. The sample distribution was reconstructed from these profiles using FTDS. Both distributions were compared along with derived total cross sections for the Argon--Argon system. This study serves as a template for constructing velocity distributions from bimolecular scattering experiments using the FTDS inversion technique.
A two-phase approach to Fourier transform ion mobility time-of-flight mass spectrometry.
Clowers, Brian H; Siems, William F; Yu, Zhihao; Davis, Austen L
2015-10-21
It is well known that the duty cycle of common drift-tube ion mobility experiments is often below 1%. However, multiplexing approaches such as Fourier and Hadamard pulsing schemes have been shown to independently enhance the throughput of ion mobility spectrometry (IMS) experiments to levels that approach 50%. While challenges remain to their broad scale implementation we describe a new Fourier transform (FT) IMS experiment that is directly compatible with standard drift tube ion mobility mass spectrometers (DT-IMMS). Compared to previous FT-IMS experiments, our new approach requires only a single gate and circumvents the need for signal apodization by combining data from two frequency pulsing sequences 180° out of phase. Assessment of our initial results highlights an increase in signal-to-noise (SNR) relative to both previous implementations FT-IMS experiments and signal averaged (SA) experiments. For select tetraalkylammonium salts SNR improvements of more than one order of magnitude are routinely possible. To explore the performance metrics associated with the technique a number of experimental variables were systematically altered including frequency sweep range, sweep time, and data acquisition time. Using this experimental design we present the key aspects, considerations, and minimum resources necessary for other IMS researchers to incorporate this operational mode into their research. The two-phase FT-IMMS technique offers a tractable mechanism to enhance sensitivity for IMMS measurements and its broad-scale adoption by IMMS researchers promises to enhance the acquisition speed for mobility measurements using hybrid instrumentation.
Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.
Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José
2015-12-14
We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme.
Bangalore, Arjun S.; Demirgian, Jack C.; Boparai, Amrit S.; Small, Gary W.
1999-11-01
The Fourier transform infrared (FT-IR) spectral data of two nerve agent simulants, diisopropyl methyl phosphonate (DIMP) and dimethyl methyl phosphonate (DMMP), are used as test cases to determine the spectral resolution that gives optimal pattern recognition performance. DIMP is used as the target analyte for detection, while DMMP is used to test the ability of the automated pattern recognition methodology to detect the analyte selectively. Interferogram data are collected by using a Midac passive FT-IR instrument. The methodology is based on the application of pattern recognition techniques to short segments of single-beam spectra obtained by Fourier processing the collected interferogram data. The work described in this article evaluates the effect of varying spectral resolution on the pattern recognition results. The objective is to determine the optimal spectral resolution to be used for data collection. The results of this study indicate that the data with a nominal spectral resolution of 16 cm{sup -1} provide sufficient selectivity to give pattern recognition results comparable to that obtained by using higher resolution data. We found that, while higher resolution does not increase selectivity sufficiently to provide better pattern recognition results, lower resolution decreases selectivity and degrades the pattern recognition results. These results can be used as guidelines to maximize detection sensitivity, to minimize the time needed for data collection, and to reduce data storage requirements. (c) 2000 Society for Applied Spectroscopy.
Structural analyses in three-dimensional atom probe: a Fourier transform approach.
Vurpillot, F; Da Costa, G; Menand, A; Blavette, D
2001-09-01
The three-dimensional atom probe (3DAP) technique gives the elemental identities and the position of atoms within the small volume analysed (on the order of 10 x 10 x 100 nm(3)). The large number of atoms collected (up to two million) and the excellent spatial resolution of this instrument allows the observation of some crystallographic features of phases chemically identified. This paper shows that the application of a discrete Fourier transform algorithm to a 3DAP dataset provides information that is not easily accessible in real space. The derivation of the mean size of particles from Fourier intensities is an example. Using 3D 'dark-field' imaging, single ordered grains were isolated from the disordered matrix of a ternary alloy. Moreover, the intrinsic spatial resolution of the instrument was evaluated by this method for pure metal; the resolution reaches 0.2 nm laterally and 0.06 nm in depth. This excellent resolution is shown to be sufficient to give access to the crystalline lattice. The use of image filtering in the reciprocal space enables for atomic columns to be imaged the first time from 3DAP data.
Binding balls: fast detection of binding sites using a property of spherical Fourier transform.
Comin, Matteo; Guerra, Concettina; Dellaert, Frank
2009-11-01
The functional prediction of proteins is one of the most challenging problems in modern biology. An established computational technique involves the identification of three-dimensional local similarities in proteins. In this article, we present a novel method to quickly identify promising binding sites. Our aim is to efficiently detect putative binding sites without explicitly aligning them. Using the theory of Spherical Harmonics, a candidate binding site is modeled as a Binding Ball. The Binding Ball signature, offered by the Spherical Fourier coefficients, can be efficiently used for a fast detection of putative regions. Our contribution includes the Binding Ball modeling and the definition of a scoring function that does not require aligning candidate regions. Our scoring function can be computed efficiently using a property of Spherical Fourier transform (SFT) that avoids the evaluation of all alignments. Experiments on different ligands show good discrimination power when searching for known binding sites. Moreover, we prove that this method can save up to 40% in time compared with traditional approaches.
Liu, Derek Sloboda, Ron S.
2014-05-15
Purpose: Boyer and Mok proposed a fast calculation method employing the Fourier transform (FT), for which calculation time is independent of the number of seeds but seed placement is restricted to calculation grid points. Here an interpolation method is described enabling unrestricted seed placement while preserving the computational efficiency of the original method. Methods: The Iodine-125 seed dose kernel was sampled and selected values were modified to optimize interpolation accuracy for clinically relevant doses. For each seed, the kernel was shifted to the nearest grid point via convolution with a unit impulse, implemented in the Fourier domain. The remaining fractional shift was performed using a piecewise third-order Lagrange filter. Results: Implementation of the interpolation method greatly improved FT-based dose calculation accuracy. The dose distribution was accurate to within 2% beyond 3 mm from each seed. Isodose contours were indistinguishable from explicit TG-43 calculation. Dose-volume metric errors were negligible. Computation time for the FT interpolation method was essentially the same as Boyer's method. Conclusions: A FT interpolation method for permanent prostate brachytherapy TG-43 dose calculation was developed which expands upon Boyer's original method and enables unrestricted seed placement. The proposed method substantially improves the clinically relevant dose accuracy with negligible additional computation cost, preserving the efficiency of the original method.
Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.
Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José
2015-12-14
We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme. PMID:26699041
NASA Astrophysics Data System (ADS)
Thorwirth, Sven; Lattanzi, Valerio; McCarthy, Michael C.
2014-06-01
By means of Fourier transform microwave spectroscopy of a supersonic jet, the pure rotational spectra of two second-row analogs to isocyanic acid, HNCO, have been observed for the first time. The phosphorus and silicon analogs HPCO and HNSiO, respectively, were observed by their fundamental a-type rotational transitions (μa(HPCO)= 0.45 D, μa(HNSiO)= 2.10 D) in the centimeter wave range from 10 to 32 GHz through discharges of appropriate precursor gases highly diluted in neon. Spectroscopic searches and identification were based on predictions from high-level quantum-chemical calculations at the CCSD(T) level of theory in combination with large basis sets. Excellent agreement between experimental and calculated molecular parameters is found. In case of HPCO, the 13C isotopic species was also observed. Since both the stem compound HNCO and its sulphur analog HNCS are known to be present in space, and because also a sizable number of phosphorus and silicon-bearing species were detected there, both compounds are plausible targets for future radio astronomical searches using sensitive radio astronomical instrumentation.
Evangelisti, Luca; Sedo, Galen; van Wijngaarden, Jennifer
2011-02-10
The pure rotational spectra of 1,1,1-trifluoro-2-butanone and its four (13)C isotopologues have been studied using the new chirped-pulsed Fourier transform microwave spectrometer at the University of Manitoba in combination with a conventional Balle-Flygare-type instrument. Quantum chemical calculations, at the MP2/6-311++G(d,p) level, were carried out to obtain information about the structure, relative stability, and difference in populations of the three lowest energy conformers corresponding to dihedral angles of 0°, 82.8°, and 119.2° along the carbon backbone. The observed spectra are that of conformer I (dihedral angle 0°), and, based on analysis of the observed splitting, the V(3) barrier to internal rotation of the methyl group has been determined to be 9.380(5) kJ mol(-1). The spectroscopic constants of the five isotopologues were used to precisely derive the r(s) and partial r(0) geometries of this conformer based on an assumed planar carbon backbone (as supported by the spectra and ab initio calculations).
Fourier transform spectroscopy of CO2 isotopologues at 1.6 μm: Line positions and intensities
NASA Astrophysics Data System (ADS)
Jacquemart, D.; Borkov, Yu. G.; Lyulin, O. M.; Tashkun, S. A.; Perevalov, V. I.
2015-07-01
The line positions and intensities of carbon dioxide isotopologues have been retrieved between 5900 and 6400 cm-1 region from Fourier transform spectra of 17O- and 18O-enriched carbon dioxide recorded in LADIR (Paris, France) with the Bruker IFS 125-HR. In total 1634 line positions and intensities of 20 bands of the 5 major CO2 isotopologues present in our sample 16O12C17O (39.48%), 17O12C17O (27.73%), 16O12C16O (15.20%), 16O12C18O (7.32%) and 17O12C18O (8.25%) are retrieved. All studied bands belong to the ΔP=8 (only for asymmetric species) and 9 series of transitions, where P = 2V1 +V2 + 3V3 is the polyad number (Vi are vibrational quantum numbers). The accuracy of the line position determination is about 0.3×10-3 cm-1 for the unblended and not very weak lines and the accuracy for the line intensities varies from 4% to 30% depending on the intensity of the line and on the extent of the line overlapping. For the 16O12C17O, 17O12C17O, 16O12C18O and 17O12C18O isotopologues the systematic comparisons have been performed with the recent CRDS measurements.
Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode
Goncharov, Vasily; Hall, Gregory
2016-08-25
Here, we have developed phase-sensitive signal detection and processing algorithms for Fourier transform spectrometers fitted with supercontinuum sources for applications requiring ultimate sensitivity. Similar to well-established approach of source noise cancellation through balanced detection of monochromatic light, our method is capable of reducing the relative intensity noise of polychromatic light by 40 dB. Unlike conventional balanced detection, which relies on differential absorption measured with a well matched pair of photo-detectors, our algorithm utilizes phase-sensitive differential detection on a single photodiode and is capable of the real-time correction for instabilities in supercontinuum spectral structure over a broad range of wavelengths. Inmore » the resulting method is universal in terms of applicable wavelengths and compatible with commercial spectrometers. We present a proof-of-principle experimental« less
NASA Astrophysics Data System (ADS)
Castilho, Maiara L.; Campos, Claudia B. L.; Matos, Tatiana G. F.; de Abreu, Geraldo M. A.; Martin, Airton A.; Raniero, Leandro
2012-01-01
Paracoccidioides brasiliensis the etiological agent of paracoccidioidomycosis, is a dimorphic fungus existing as mycelia in the environment (or at 25 °C in vitro) and as yeast cells in the human host (or at 37°C in vitro). The most prominent difference between both forms is probably the cell wall polysaccharide, being 1,3-β-glucan usually found in mycelia and 1,3-α-glucan found in yeasts, but a plethora of other differences have already been described. In this work, we performed a Fourier Transform Infrared Spectroscopy analysis to compare the yeast and mycelia forms of P. brasiliensis and found additional biochemical differences. The analysis of the spectra showed that differences were distributed in chemical bonds of proteins, lipids and carbohydrates.
Authentication of canned fish packing oils by means of Fourier transform infrared spectroscopy.
Dominguez-Vidal, Ana; Pantoja-de la Rosa, Jaime; Cuadros-Rodríguez, Luis; Ayora-Cañada, María José
2016-01-01
The authentication of packing oil from commercial canned tuna and other tuna-like fish species was examined by means of attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) and chemometrics. Using partial least squares discriminant analysis (PLS-DA), it was possible to differentiate olive oil from seed oils. Discrimination of olive oil from high-oleic sunflower oil was possible, despite the latter having a degree of unsaturation more similar to olive oil than to sunflower oil. However, in the samples analyzed, sunflower oil could not be differentiated clearly from those labeled with the generic term "vegetable oil". Furthermore, the authentication of extra virgin olive oil, although more difficult, could be achieved using ATR-FTIR spectroscopy. The method could be applied regardless of fish type, without interference from fish lipids.
Almeida, Francylaine S; Lima, Sandro M; Andrade, Luis H C; Súarez, Yzel R
2012-07-01
Fourier transform infrared photoacoustic spectroscopy (FTIR-PAS) was applied to nineteen fish species in Brazil's Upper Paraná River basin to identify differences in the structural composition of their scales. To differentiate the species, a canonical discriminant analysis was used to indicate the most important absorption peaks in the mid-infrared region. Significant differences were found in the chemical composition of scales among the studied fish species, with Wilk's lambda = 5.2 × 10(-6), F((13,18,394)) = 37.57, and P < 0.001, indicating that O-CH(2) wag at 1396 cm(-1) can be used as a biomarker of this species group. The species could be categorized into four groups according to phylogenetic similarity, suggesting that the O-CH(2) 1396 cm(-1) absorbance is related to the biological traits of each species. This procedure can also be used to complement evolutionary studies.
Largo-Gosens, Asier; Hernández-Altamirano, Mabel; García-Calvo, Laura; Alonso-Simón, Ana; Álvarez, Jesús; Acebes, José L.
2014-01-01
Fourier transform mid-infrared (FT-MIR) spectroscopy has been extensively used as a potent, fast and non-destructive procedure for analyzing cell wall architectures, with the capacity to provide abundant information about their polymers, functional groups, and in muro entanglement. In conjunction with multivariate analyses, this method has proved to be a valuable tool for tracking alterations in cell walls. The present review examines recent progress in the use of FT-MIR spectroscopy to monitor cell wall changes occurring in muro as a result of various factors, such as growth and development processes, genetic modifications, exposition or habituation to cellulose biosynthesis inhibitors and responses to other abiotic or biotic stresses, as well as its biotechnological applications. PMID:25071791
Amirfattahi, Rassoul
2013-10-01
Owing to its simplicity radix-2 is a popular algorithm to implement fast fourier transform. Radix-2(p) algorithms have the same order of computational complexity as higher radices algorithms, but still retain the simplicity of radix-2. By defining a new concept, twiddle factor template, in this paper, we propose a method for exact calculation of multiplicative complexity for radix-2(p) algorithms. The methodology is described for radix-2, radix-2 (2) and radix-2 (3) algorithms. Results show that radix-2 (2) and radix-2 (3) have significantly less computational complexity compared with radix-2. Another interesting result is that while the number of complex multiplications in radix-2 (3) algorithm is slightly more than radix-2 (2), the number of real multiplications for radix-2 (3) is less than radix-2 (2). This is because of the twiddle factors in the form of which need less number of real multiplications and are more frequent in radix-2 (3) algorithm.
NASA Astrophysics Data System (ADS)
Titus, E.; Ali, N.; Cabral, G.; Gracio, J.; Ramesh Babu, P.; Jackson, M. J.
2006-04-01
This article reports key findings on the chemical functionalization of carbon nanotubes (CNT). The functionalization of chemical vapor-deposited CNT was carried out by treating tubes with polyvinyl alcohol through ultrasonication in water with the aid of a surfactant. The surfactant is expected to promote the unbundling of aggregated CNT. The characterization of functionalized samples using thermogravimetric analysis, Fourier transform infrared spectroscopy, and Raman spectroscopy revealed that the CNT were functionalized by the interaction of carboxylic acid and hydroxyl groups. From the characterization studies, it is apparent that there is a strong interaction between these functional groups and the covalently bonded carbon in the CNT network. The functionalization process enabled good CNT dispersion in the solution, and the CNT remained in suspension for many days. To support the effective functionalization of the tubes, the interaction of functionalized CNT with Ni ions is also demonstrated.
Singular Spectrum Analysis: A Note on Data Processing for Fourier Transform Hyperspectral Imagers.
Rafert, J Bruce; Zabalza, Jaime; Marshall, Stephen; Ren, Jinchang
2016-09-01
Hyperspectral remote sensing is experiencing a dazzling proliferation of new sensors, platforms, systems, and applications with the introduction of novel, low-cost, low-weight sensors. Curiously, relatively little development is now occurring in the use of Fourier transform (FT) systems, which have the potential to operate at extremely high throughput without use of a slit or reductions in both spatial and spectral resolution that thin film based mosaic sensors introduce. This study introduces a new physics-based analytical framework called singular spectrum analysis (SSA) to process raw hyperspectral imagery collected with FT imagers that addresses some of the data processing issues associated with the use of the inverse FT. Synthetic interferogram data are analyzed using SSA, which adaptively decomposes the original synthetic interferogram into several independent components associated with the signal, photon and system noise, and the field illumination pattern.