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.
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.
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.
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
2010-04-01
OPTRA has developed 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. In this paper, we summarize the design and build and detail system characterization and test of a prototype I-OP-FTIR instrument. System characterization includes radiometric performance and spectral resolution. Results from a series of tomographic reconstructions of sulfur hexafluoride plumes in a laboratory setting are also presented.
Imaging open-path Fourier transform infrared spectrometer for 3D cloud profiling
NASA Astrophysics Data System (ADS)
Rentz Dupuis, Julia; Mansur, David J.; Engel, James R.; Vaillancourt, Robert; Todd, Lori; Mottus, Kathleen
2008-04-01
OPTRA and University of North Carolina are 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 will be considered as a candidate 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. In this paper, we summarize progress to date and overall system performance projections based on the instrument, spectroscopy, and tomographic reconstruction accuracy. We then present a preliminary optical design of the I-OP-FTIR.
NASA Astrophysics Data System (ADS)
Fernandez, Sergio; Gdeisat, Munther A.; Salvi, Joaquim; Burton, David
2011-06-01
Fringe pattern analysis in coded structured light constitutes an active field of research. Techniques based on first projecting a sinusoidal pattern and then recovering the phase deviation permit the computation of the phase map and its corresponding depth map, leading to a dense acquisition of the measuring object. Among these techniques, the ones based on time-frequency analysis permit to extract the depth map from a single image, thus having potential applications measuring moving objects. The main techniques are Fourier Transform (FT), Windowed Fourier Transform (WFT) and Wavelet Transform (WT). This paper first analyzes the pros and cons of these three techniques, then a new algorithm for the automatic selection of the window size in WFT is proposed. This algorithm is compared to the traditional WT using adapted mother wavelet signals both with simulated and real objects, showing the performance results for quantitative and qualitative evaluations of the new method.
Suppression law of quantum states in a 3D photonic fast Fourier transform chip.
Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio
2016-01-01
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135
Suppression law of quantum states in a 3D photonic fast Fourier transform chip
Crespi, Andrea; Osellame, Roberto; Ramponi, Roberta; Bentivegna, Marco; Flamini, Fulvio; Spagnolo, Nicolò; Viggianiello, Niko; Innocenti, Luca; Mataloni, Paolo; Sciarrino, Fabio
2016-01-01
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong–Ou–Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms. PMID:26843135
NASA Astrophysics Data System (ADS)
Windhari, Ayuty; Handayani, Gunawan
2015-04-01
The 3D inversion gravity anomaly to estimate topographical density using a matlab source code from gridded data provided by Parker Oldenburg algorithm based on fast Fourier transform was computed. We extend and improved the source code of 3DINVERT.M invented by Gomez Ortiz and Agarwal (2005) using the relationship between Fourier transform of the gravity anomaly and the sum of the Fourier transform from the topography density. We gave density contrast between the two media to apply the inversion. FFT routine was implemented to construct amplitude spectrum to the given mean depth. The results were presented as new graphics of inverted topography density, the gravity anomaly due to the inverted topography and the difference between the input gravity data and the computed ones. It terminates when the RMS error is lower than pre-assigned value used as convergence criterion or until maximum of iterations is reached. As an example, we used the matlab program on gravity data of Banten region, Indonesia.
Trillo, Cristina; Doval, Angel F; Mendoza-Santoyo, Fernando; Pérez-López, Carlos; de la Torre-Ibarra, Manuel; Deán, J Luis
2009-09-28
The combination of a high-speed TV holography system and a 3D Fourier-transform data processing is proposed for the analysis of multimode vibrations in plates. The out-of-plane displacement of the object under generic vibrational excitation is resolved in time by the fast acquisition rate of a high-speed camera, and recorded in a sequence of interferograms with spatial carrier. A full-field temporal history of the multimode vibration is thus obtained. The optical phase of the interferograms is extracted and subtracted from the phase of a reference state to yield a sequence of optical phase-change maps. Each map represents the change undergone by the object between any given state and the reference state. The sequence of maps is a 3D array of data (two spatial dimensions plus time) that is processed with a 3D Fourier-transform algorithm. The individual vibration modes are separated in the 3D frequency space due to their different vibration frequencies and, to a lesser extent, to the different spatial frequencies of the mode shapes. The contribution of each individual mode (or indeed the superposition of several modes) to the dynamic behaviour of the object can then be separated by means of a bandpass filter (or filters). The final output is a sequence of complex-valued maps that contain the full-field temporal history of the selected mode (or modes) in terms of its mechanical amplitude and phase. The proof-of-principle of the technique is demonstrated with a rectangular, fully clamped, thin metal plate vibrating simultaneously in several of its natural resonant frequencies under white-noise excitation. PMID:19907591
NASA Astrophysics Data System (ADS)
Chang, Chenliang; Xia, Jun; Lei, Wei
2015-03-01
We proposed a new method to calculate the color computer generated hologram of three-dimensional object in holographic display. The three-dimensional object is composed of several tilted planes which are tilted from the hologram. The diffraction from each tilted plane to the hologram plane is calculated based on the coordinate rotation in Fourier spectrum domains. We used the nonuniform fast Fourier transformation (NUFFT) to calculate the nonuniform sampled Fourier spectrum on the tilted plane after coordinate rotation. By using the NUFFT, the diffraction calculation from tilted plane to the hologram plane with variable sampling rates can be achieved, which overcomes the sampling restriction of FFT in the conventional angular spectrum based method. The holograms of red, green and blue component of the polygon-based object are calculated separately by using our NUFFT based method. Then the color hologram is synthesized by placing the red, green and blue component hologram in sequence. The chromatic aberration caused by the wavelength difference can be solved effectively by restricting the sampling rate of the object in the calculation of each wavelength component. The computer simulation shows the feasibility of our method in calculating the color hologram of polygon-based object. The 3D object can be displayed in color with adjustable size and no chromatic aberration in holographic display system, which can be considered as an important application in the colorful holographic three-dimensional display.
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.
Fourier Transform Mass Spectrometry.
ERIC Educational Resources Information Center
Gross, Michael L.; Rempel, Don L.
1984-01-01
Discusses the nature of Fourier transform mass spectrometry and its unique combination of high mass resolution, high upper mass limit, and multichannel advantage. Examines its operation, capabilities and limitations, applications (ion storage, ion manipulation, ion chemistry), and future applications and developments. (JN)
NASA Technical Reports Server (NTRS)
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Imaging Fourier Transform Spectrometer
Bennett, C.L.; Carter, M.R.; Fields, D.J.; Hernandez, J.
1993-04-14
The operating principles of an Imaging Fourier Transform Spectrometer (IFTS) are discussed. The advantages and disadvantages of such instruments with respect to alternative imaging spectrometers are discussed. The primary advantages of the IFTS are the capacity to acquire more than an order of magnitude more spectral channels than alternative systems with more than an order of magnitude greater etendue than for alternative systems. The primary disadvantage of IFTS, or FTS in general, is the sensitivity to temporal fluctuations, either random or periodic. Data from the IRIFTS (ir IFTS) prototype instrument, sensitive in the infrared, are presented having a spectral sensitivity of 0.01 absorbance units, a spectral resolution of 6 cm{sup {minus}1} over the range 0 to 7899 cm{sup {minus}1}, and a spatial resolution of 2.5 mr.
Fourier Transform Spectrometer System
NASA Technical Reports Server (NTRS)
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
Fourier transform interferometer alignment method.
Goldberg, Kenneth A; Naulleau, Patrick; Bokor, Jeffrey
2002-08-01
A rapid and convenient method has been developed to facilitate the alignment of the image-plane components of point-diffraction interferometers, including the phase-shifting point-diffraction interferometer. In real time, the Fourier transform of the detected image is used to calculate a pseudoimage of the electric field in the image plane of the test optic where thecritical alignment o f variousoptical components is performed. Reconstruction of the pseudoimage is similar to off-axis, Fourier transform holography. Intermediate steps in the alignment procedure are described. Fine alignment is aided by the introduction and optimization of a global-contrast parameter that is easily calculated from the Fourier transform. Additional applications include the alignment of image-plane apertures in general optical systems, the rapid identification of patterned image-plane alignment marks, and the probing of important image-plane field properties. PMID:12153074
Static Fourier transform infrared spectrometer.
Schardt, Michael; Murr, Patrik J; Rauscher, Markus S; Tremmel, Anton J; Wiesent, Benjamin R; Koch, Alexander W
2016-04-01
Fourier transform spectroscopy has established itself as the standard method for spectral analysis of infrared light. Here we present a robust and compact novel static Fourier transform spectrometer design without any moving parts. The design is well suited for measurements in the infrared as it works with extended light sources independent of their size. The design is experimentally evaluated in the mid-infrared wavelength region between 7.2 μm and 16 μm. Due to its large etendue, its low internal light loss, and its static design it enables high speed spectral analysis in the mid-infrared. PMID:27137061
ERIC Educational Resources Information Center
Debnath, Lokenath
2012-01-01
This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…
Fourier-transform optical microsystems
NASA Technical Reports Server (NTRS)
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
JPL Fourier transform ultraviolet spectrometer
NASA Technical Reports Server (NTRS)
Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.
1994-01-01
The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.
Fourier-Transform Infrared Spectrometer
NASA Technical Reports Server (NTRS)
Schindler, R. A.
1986-01-01
Fourier-transform spectrometer provides approximately hundredfold increase in luminosity at detector plane over that achievable with older instruments of this type. Used to analyze such weak sources as pollutants and other low-concentration substances in atmosphere. Interferometer creates fringe patterns on two distinct arrays of light detectors, which observe different wavelength bands. Objective lens focuses scene on image plane, which contains optical chopper. To make instrument less susceptible to variations in scene under observation, field and detector lenses focus entrance aperture, rather that image, onto detector array.
Improved Fourier-transform profilometry
Mao Xianfu; Chen Wenjing; Su Xianyu
2007-02-10
An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object.
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.
Automatic needle segmentation in 3D ultrasound images using 3D Hough transform
NASA Astrophysics Data System (ADS)
Zhou, Hua; Qiu, Wu; Ding, Mingyue; Zhang, Songgeng
2007-12-01
3D ultrasound (US) is a new technology that can be used for a variety of diagnostic applications, such as obstetrical, vascular, and urological imaging, and has been explored greatly potential in the applications of image-guided surgery and therapy. Uterine adenoma and uterine bleeding are the two most prevalent diseases in Chinese woman, and a minimally invasive ablation system using an RF button electrode which is needle-like is being used to destroy tumor cells or stop bleeding currently. Now a 3D US guidance system has been developed to avoid accidents or death of the patient by inaccurate localizations of the electrode and the tumor position during treatment. In this paper, we described two automated techniques, the 3D Hough Transform (3DHT) and the 3D Randomized Hough Transform (3DRHT), which is potentially fast, accurate, and robust to provide needle segmentation in 3D US image for use of 3D US imaging guidance. Based on the representation (Φ , θ , ρ , α ) of straight lines in 3D space, we used the 3DHT algorithm to segment needles successfully assumed that the approximate needle position and orientation are known in priori. The 3DRHT algorithm was developed to detect needles quickly without any information of the 3D US images. The needle segmentation techniques were evaluated using the 3D US images acquired by scanning water phantoms. The experiments demonstrated the feasibility of two 3D needle segmentation algorithms described in this paper.
Fourier transform infrared (FTIR) spectroscopy.
Berthomieu, Catherine; Hienerwadel, Rainer
2009-01-01
Fourier transform infrared (FTIR) spectroscopy probes the vibrational properties of amino acids and cofactors, which are sensitive to minute structural changes. The lack of specificity of this technique, on the one hand, permits us to probe directly the vibrational properties of almost all the cofactors, amino acid side chains, and of water molecules. On the other hand, we can use reaction-induced FTIR difference spectroscopy to select vibrations corresponding to single chemical groups involved in a specific reaction. Various strategies are used to identify the IR signatures of each residue of interest in the resulting reaction-induced FTIR difference spectra. (Specific) Isotope labeling, site-directed mutagenesis, hydrogen/deuterium exchange are often used to identify the chemical groups. Studies on model compounds and the increasing use of theoretical chemistry for normal modes calculations allow us to interpret the IR frequencies in terms of specific structural characteristics of the chemical group or molecule of interest. This review presents basics of FTIR spectroscopy technique and provides specific important structural and functional information obtained from the analysis of the data from the photosystems, using this method. PMID:19513810
The fractional Fourier transform and applications
NASA Technical Reports Server (NTRS)
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
The Geostationary Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Key, Richard; Sander, Stanley; Eldering, Annmarie; Miller, Charles; Frankenberg, Christian; Natra, Vijay; Rider, David; Blavier, Jean-Francois; Bekker, Dmitriy; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for an earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. The GeoFTS instrument is a half meter cube size instrument designed to operate in geostationary orbit as a secondary "hosted" payload on a commercial geostationary satellite mission. The advantage of GEO is the ability to continuously stare at a region of the earth, enabling frequent sampling to capture the diurnal variability of biogenic fluxes and anthropogenic emissions from city to continental scales. The science goal is to obtain a process-based understanding of the carbon cycle from simultaneous high spatial resolution measurements of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) many times per day in the near infrared spectral region to capture their spatial and temporal variations on diurnal, synoptic, seasonal and interannual time scales. The GeoFTS instrument is based on a Michelson interferometer design with a number of advanced features incorporated. Two of the most important advanced features are the focal plane arrays and the optical path difference mechanism. A breadboard GeoFTS instrument has demonstrated functionality for simultaneous measurements in the visible and IR in the laboratory and subsequently in the field at the California Laboratory for Atmospheric Remote Sensing (CLARS) observatory on Mt. Wilson overlooking the Los Angeles basin. A GeoFTS engineering model instrument is being developed which will make simultaneous visible and IR measurements under space flight like environmental conditions (thermal-vacuum at 180 K). This will demonstrate critical instrument capabilities such as optical alignment stability, interferometer modulation efficiency, and high throughput FPA signal processing. This will reduce flight instrument development risk and show that the Geo
The Geostationary Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
An efficient and robust 3D mesh compression based on 3D watermarking and wavelet transform
NASA Astrophysics Data System (ADS)
Zagrouba, Ezzeddine; Ben Jabra, Saoussen; Didi, Yosra
2011-06-01
The compression and watermarking of 3D meshes are very important in many areas of activity including digital cinematography, virtual reality as well as CAD design. However, most studies on 3D watermarking and 3D compression are done independently. To verify a good trade-off between protection and a fast transfer of 3D meshes, this paper proposes a new approach which combines 3D mesh compression with mesh watermarking. This combination is based on a wavelet transformation. In fact, the used compression method is decomposed to two stages: geometric encoding and topologic encoding. The proposed approach consists to insert a signature between these two stages. First, the wavelet transformation is applied to the original mesh to obtain two components: wavelets coefficients and a coarse mesh. Then, the geometric encoding is done on these two components. The obtained coarse mesh will be marked using a robust mesh watermarking scheme. This insertion into coarse mesh allows obtaining high robustness to several attacks. Finally, the topologic encoding is applied to the marked coarse mesh to obtain the compressed mesh. The combination of compression and watermarking permits to detect the presence of signature after a compression of the marked mesh. In plus, it allows transferring protected 3D meshes with the minimum size. The experiments and evaluations show that the proposed approach presents efficient results in terms of compression gain, invisibility and robustness of the signature against of many attacks.
Automatic needle segmentation in 3D ultrasound images using 3D improved Hough transform
NASA Astrophysics Data System (ADS)
Zhou, Hua; Qiu, Wu; Ding, Mingyue; Zhang, Songgen
2008-03-01
3D ultrasound (US) is a new technology that can be used for a variety of diagnostic applications, such as obstetrical, vascular, and urological imaging, and has been explored greatly potential in the applications of image-guided surgery and therapy. Uterine adenoma and uterine bleeding are the two most prevalent diseases in Chinese woman, and a minimally invasive ablation system using a needle-like RF button electrode is widely used to destroy tumor cells or stop bleeding. To avoid accidents or death of the patient by inaccurate localizations of the electrode and the tumor position during treatment, 3D US guidance system was developed. In this paper, a new automated technique, the 3D Improved Hough Transform (3DIHT) algorithm, which is potentially fast, accurate, and robust to provide needle segmentation in 3D US image for use of 3D US imaging guidance, was presented. Based on the coarse-fine search strategy and a four parameter representation of lines in 3D space, 3DIHT algorithm can segment needles quickly, accurately and robustly. The technique was evaluated using the 3D US images acquired by scanning a water phantom. The segmentation position deviation of the line was less than 2mm and angular deviation was much less than 2°. The average computational time measured on a Pentium IV 2.80GHz PC computer with a 381×381×250 image was less than 2s.
FOURIER TRANSFORM INFRARED SPECTROMETRY OF AMBIENT AEROSOLS
Fourier transform infrared (FTIR) spectrometry has been evaluated as a method for determining the concentration of selected species present in ambient aerosols collected on Teflon filters. The filters are analyzed by transmission measurements after collection of the fine fraction...
Plasma Spectrochemistry with a Fourier Transform Spectrometer.
NASA Astrophysics Data System (ADS)
Manning, Thomas Joseph John
1990-01-01
This dissertation can be interpreted as being two-dimensional. The first dimension uses the Los Alamos Fourier Transform Spectrometer to uncover various physical aspects of a Inductively Coupled Plasma. The limits of wavenumber accuracy and resolution are pushed to measure line shifts and line profiles in an Inductively Coupled Argon Plasma. This is new physical information that the plasma spectroscopy community has been seeking for several years. Other plasma spectroscopy carried out includes line profile studies, plasma diagnostics, and exact identification of diatomic molecular spectra. The second aspect of the dissertation involves studies of light sources for Fourier Transform Spectroscopy. Sources developed use an inductively coupled plasma (ICP) power supply. New sources (neon ICP, closed cell ICP, and helium ICP) were developed and new methods to enhance the performance and understand a Fourier Transform Spectrometer were studied including a novel optical filter, a spectrum analyzer to study noises, and a standard to calibrate and evaluate a Fourier Transform Spectrometer.
Electronically-Scanned Fourier-Transform Spectrometer
NASA Technical Reports Server (NTRS)
Breckinridge, J. B.; Ocallaghan, F. G.
1984-01-01
Instrument efficient, lightweight, and stable. Fourier-transform spectrometer configuration uses electronic, instead of mechanical, scanning. Configuration insensitive to vibration-induced sampling errors introduced into mechanically scanned systems.
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
A Primer of Fourier Transform NMR.
ERIC Educational Resources Information Center
Macomber, Roger S.
1985-01-01
Fourier transform nuclear magnetic resonance (NMR) is a new spectroscopic technique that is often omitted from undergraduate curricula because of lack of instructional materials. Therefore, information is provided to introduce students to the technique of data collection and transformation into the frequency domain. (JN)
3D entangled fractional squeezing transformation and its quantum mechanical correspondence
NASA Astrophysics Data System (ADS)
Jia, Fang; Xu, Shuang; Deng, Cheng-Zhi; Liu, Cun-Jin; Hu, Li-Yun
2016-06-01
A new type of entangled fractional squeezing transformation (EFrST) has been theoretically proposed for 2D entanglement [ Front. Phys. 10, 100302 (2015)]. In this paper, we shall extend this case to that of 3D entanglement by introducing a type of three-mode entangled state representation, which is not the product of three 1D cases. Using the technique of integration within an ordered product of operators, we derive a compact unitary operator corresponding to the 3D fractional entangling transformation, which is an entangling operator that presents a clear transformation relation. We also verified that the additivity property of the novel 3D EFrST is of a Fourier character by using its quantum mechanical description. As an application of this representation, the EFrST of the three-mode number state is calculated using the quantum description of the EFrST.
Needle segmentation using 3D Hough transform in 3D TRUS guided prostate transperineal therapy
Qiu Wu; Yuchi Ming; Ding Mingyue; Tessier, David; Fenster, Aaron
2013-04-15
Purpose: Prostate adenocarcinoma is the most common noncutaneous malignancy in American men with over 200 000 new cases diagnosed each year. Prostate interventional therapy, such as cryotherapy and brachytherapy, is an effective treatment for prostate cancer. Its success relies on the correct needle implant position. This paper proposes a robust and efficient needle segmentation method, which acts as an aid to localize the needle in three-dimensional (3D) transrectal ultrasound (TRUS) guided prostate therapy. Methods: The procedure of locating the needle in a 3D TRUS image is a three-step process. First, the original 3D ultrasound image containing a needle is cropped; the cropped image is then converted to a binary format based on its histogram. Second, a 3D Hough transform based needle segmentation method is applied to the 3D binary image in order to locate the needle axis. The position of the needle endpoint is finally determined by an optimal threshold based analysis of the intensity probability distribution. The overall efficiency is improved through implementing a coarse-fine searching strategy. The proposed method was validated in tissue-mimicking agar phantoms, chicken breast phantoms, and 3D TRUS patient images from prostate brachytherapy and cryotherapy procedures by comparison to the manual segmentation. The robustness of the proposed approach was tested by means of varying parameters such as needle insertion angle, needle insertion length, binarization threshold level, and cropping size. Results: The validation results indicate that the proposed Hough transform based method is accurate and robust, with an achieved endpoint localization accuracy of 0.5 mm for agar phantom images, 0.7 mm for chicken breast phantom images, and 1 mm for in vivo patient cryotherapy and brachytherapy images. The mean execution time of needle segmentation algorithm was 2 s for a 3D TRUS image with size of 264 Multiplication-Sign 376 Multiplication-Sign 630 voxels. Conclusions
Fast Fourier Transforms of Piecewise Constant Functions
NASA Astrophysics Data System (ADS)
Sorets, Eugene
1995-02-01
We present an algorithm for the evaluation of the Fourier transform of piecewise constant functions of two variables. The algorithm overcomes the accuracy problems associated with computing the Fourier transform of discontinuous functions; in fact, its time complexity is O (N2 logN + NP log2 (1/ε) + V log3 (1/ε)), where ε is the accuracy, N is the size of the problem, P is the perimeter of the set of discontinuities, and V is its number of vertices. The algorithm is based on the Lagrange interpolation formula and the Green's theorem, which are used to preprocess the data before applying the fast Fourier transform. It readily generalizes to higher dimensions and to piecewise smooth functions.
High order generalized permutational fractional Fourier transforms
NASA Astrophysics Data System (ADS)
Ran, Qi-Wen; Yuan, Lin; Tan, Li-Ying; Ma, Jing; Wang, Qi
2004-02-01
We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M = +infty, M = 4k (k is a natural number) and M = 4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
Fast Fourier Transform algorithm design and tradeoffs
NASA Technical Reports Server (NTRS)
Kamin, Ray A., III; Adams, George B., III
1988-01-01
The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space. PMID:16138556
Holographic display of real existing objects from their 3D Fourier spectrum
NASA Astrophysics Data System (ADS)
Yatagai, Toyohiko; Sando, Yusuke
2005-02-01
A method for synthesizing computer-generated holograms of real-existing objects is described. A series of projection images are recorded both vertically and horizontally with an incoherent light source and a color CCD camera. According to the principle of computer tomography(CT), the 3-D Fourier spectrum is calculated from several projection images of objects and the Fresnel computer-generated hologram(CGH) is synthesized using a part of the 3-D Fourier spectrum. This method has following advantages. At first, no-blur reconstructed images in any direction are obtained owing to two-dimensionally scanning in recording. Secondarily, since not interference fringes but simple projection images of objects are recorded, a coherent light source is not necessary for recording. The use of a color CCD in recording enables us to record and reconstruct colorful objects. Finally, we demonstrate color reconstruction of objects both numerically and optically.
Ultrafast Fourier-transform parallel processor
Greenberg, W.L.
1980-04-01
A new, flexible, parallel-processing architecture is developed for a high-speed, high-precision Fourier transform processor. The processor is intended for use in 2-D signal processing including spatial filtering, matched filtering and image reconstruction from projections.
REMOTE FOURIER TRANSFORM INFRARED AIR POLLUTION STUDIES
A commercial Fourier transform infrared interferometer system has been installed in a van and used to make longpath absorption and single-ended emission measurements of gaseous pollutant concentrations at a variety of pollutant sources. The interferometer system is described and ...
Livermore Imaging Fourier Transform Infrared Spectrometer (LIFTIRS)
Carter, M.R.; Bennett, C.L.; Fields, D.J.; Lee, F.D.
1995-05-10
Lawrence Livermore National Laboratory is currently operating a hyperspectral imager, the Livermore Imaging Fourier Transform Infrared Spectrometer (LIFTIRS). This instrument is capable of operating throughout the infrared spectrum from 3 to 12.5 {mu}m with controllable spectral resolution. In this presentation we report on it`s operating characteristics, current capabilities, data throughput and calibration issues.
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.
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.
Electro-optic Imaging Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin
2005-01-01
JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-O IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 micron (1000-4000/cm) to allow high-resolution, high-speed hyperspectral imaging applications. One application will be the remote sensing of the measurement of a large number of different atmospheric gases simultaneously in the same airmass. Due to the use of a combination of birefringent phase retarders and multiple achromatic phase switches to achieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventional Fourier transform spectrometer but without any moving parts. In this paper, the principle of operations, system architecture and recent experimental progress will be presented.
Electro-optic Imaging Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Chao, Tien-Hsin
2005-01-01
JPL is developing an innovative compact, low mass, Electro-Optic Imaging Fourier Transform Spectrometer (E-0IFTS) for hyperspectral imaging applications. The spectral region of this spectrometer will be 1 - 2.5 pm (1000 -4000 cm-') to allow high-resolution, high-speed hyperspectral imaging applications [l-51. One application will be theremote sensing of the measurement of a large number of different atmospheric gases simultaneously in the sameairmass. Due to the use of a combination of birefiingent phase retarders and multiple achromatic phase switches toachieve phase delay, this spectrometer is capable of hyperspectral measurements similar to that of the conventionalFourier transform spectrometer but without any moving parts. In this paper, the principle of operations, systemarchitecture and recent experimental progress will be presen.
Miniaturization of holographic Fourier-transform spectrometers.
Agladze, Nikolay I; Sievers, Albert J
2004-12-20
Wave propagation equations in the stationary-phase approximation have been used to identify the theoretical bounds of a miniature holographic Fourier-transform spectrometer (HFTS). It is demonstrated that the HFTS throughput can be larger than for a scanning Fourier-transform spectrometer. Given room- or a higher-temperature constraint, a small HFTS has the potential to outperform a small multichannel dispersive spectrograph with the same resolving power because of the size dependence of the signal-to-noise ratio. These predictions are used to analyze the performance of a miniature HFTS made from simple optical components covering a broad spectral range from the UV to the near IR. The importance of specific primary aberrations in limiting the HFTS performance has been both identified and verified. PMID:15646777
Microholography by Numerical Wavefront Reconstruction in the Fourier Transform Geometry.
NASA Astrophysics Data System (ADS)
Haddad, Waleed Sami
New techniques for pulsed holographic microimaging with x-rays and visible light based on the Fourier transform geometry are presented. A charge-coupled device (CCD) is used to record the holographic information. Images are reconstructed numerically by fast Fourier transform (FFT) and by a novel "stigmatic" aberration-free technique. It is shown by numerical simulation that reconstruction by FFT inherently suffers from coma. An innovative design for a Fourier transform x -ray holographic microscope incorporating a metallic microsphere as the reference wave producing element is presented. The design is optimized for use with an x-ray laser source operating in the range lambda~eq43 A; nickel is found to be the best material for the reference sphere in this range. A visible light analog of the x-ray microscope was built and tested yielding an image of Ascaris larva. Two unique visible light Fourier transform holographic microscopes are also presented. The first incorporates a glycerol microdrop reference lens. This microscope was operated at N.A. ~ 0.25 with an argon ion laser at lambda = 514.5 nm. The transverse point spread function of the system was measured to be 1.40 mum, near the theoretical diffraction limit of 1.29 mu m. The second is a design based on a Mach-Zehnder interferometer. This Fourier Mach Zehnder holographic microscope (FMZHM) offers great flexibility and many advantages. The FMZHM was operated at N.A. _sp{~ }{>} 0.25 with lambda = 514.5 nm and yielded many 2-D and 3-D images of biological samples. A study of potential biological applications of visible and x-ray holographic microscopy is also presented.
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.
3D homogeneity study in PMMA layers using a Fourier domain OCT system
NASA Astrophysics Data System (ADS)
Briones-R., Manuel de J.; Torre-Ibarra, Manuel H. De La; Tavera, Cesar G.; Luna H., Juan M.; Mendoza-Santoyo, Fernando
2016-11-01
Micro-metallic particles embedded in polymers are now widely used in several industrial applications in order to modify the mechanical properties of the bulk. A uniform distribution of these particles inside the polymers is highly desired for instance, when a biological backscattering is simulated or a bio-framework is designed. A 3D Fourier domain optical coherence tomography system to detect the polymer's internal homogeneity is proposed. This optical system has a 2D camera sensor array that records a fringe pattern used to reconstruct with a single shot the tomographic image of the sample. The system gathers the full 3D tomographic and optical phase information during a controlled deformation by means of a motion linear stage. This stage avoids the use of expensive tilting stages, which in addition are commonly controlled by piezo drivers. As proof of principle, a series of different deformations were proposed to detect the uniform or non-uniform internal deposition of copper micro particles. The results are presented as images coming from the 3D tomographic micro reconstruction of the samples, and the 3D optical phase information that identifies the in-homogeneity regions within the Poly methyl methacrylate (PMMA) volume.
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.
Wavelet transform analysis of truncated fringe patterns in 3-D surface profilometry
NASA Astrophysics Data System (ADS)
Gorthi, Sai Siva; Lolla, Kameswara R.
2005-06-01
Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe images do not satisfy periodicity. Three specific cases that give raise to non-periodicity of fringe image are simulated and leakage effects caused by each one of them are analyzed with continuous complex Morlet wavelet transform. Same images are analyzed with FFT method to make a comparison of the reconstructed profiles with both methods. Simulation results revealed a significant advantage of wavelet transform profilometry (WTP), that the distortions that arise due to leakage are confined to the locations of discontinuity and do not spread out over the entire projection as in the case of Fourier transform profilometry (FTP).
Reconstruction for 3D PET Based on Total Variation Constrained Direct Fourier Method
Yu, Haiqing; Chen, Zhi; Zhang, Heye; Loong Wong, Kelvin Kian; Chen, Yunmei; Liu, Huafeng
2015-01-01
This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF). PMID:26398232
NASA Astrophysics Data System (ADS)
Debnath, Lokenath
2012-07-01
Optical image encryption based on multifractional Fourier transforms.
Zhu, B; Liu, S; Ran, Q
2000-08-15
We propose a new image encryption algorithm based on a generalized fractional Fourier transform, to which we refer as a multifractional Fourier transform. We encrypt the input image simply by performing the multifractional Fourier transform with two keys. Numerical simulation results are given to verify the algorithm, and an optical implementation setup is also suggested. PMID:18066153
The PROSAIC Laplace and Fourier Transform
Smith, G.A.
1994-11-01
Integral Transform methods play an extremely important role in many branches of science and engineering. The ease with which many problems may be solved using these techniques is well known. In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to provide alternate representations of signals and data. These techniques, while seemingly overshadowed by today`s emphasis on digital analysis, still form an invaluable basis in the understanding of systems and circuits. A firm grasp of the practical aspects of these subjects provides valuable conceptual tools. This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications. The interrelationship of the time and frequency domains will be stressed, in an attempt to comfort those who, after living so much of their lives in the time domain, find thinking in the frequency domain disquieting.
Secret sharing based on quantum Fourier transform
NASA Astrophysics Data System (ADS)
Yang, Wei; Huang, Liusheng; Shi, Runhua; He, Libao
2013-07-01
Secret sharing plays a fundamental role in both secure multi-party computation and modern cryptography. We present a new quantum secret sharing scheme based on quantum Fourier transform. This scheme enjoys the property that each share of a secret is disguised with true randomness, rather than classical pseudorandomness. Moreover, under the only assumption that a top priority for all participants (secret sharers and recovers) is to obtain the right result, our scheme is able to achieve provable security against a computationally unbounded attacker.
Phase amplitude conformal symmetry in Fourier transforms
NASA Astrophysics Data System (ADS)
Kuwata, S.
2015-04-01
For the Fourier transform ℑ : L2(R) → L2(R) of a complex-valued even or odd function ψ, it is found that the amplitude invariance |ℑψ| = |ψ| leads to a phase invariance or inversion as arg(ℑψ) = ±argψ + θ (θ = constant). The converse holds unless arg ψ = constant. The condition |ψ| = |ℑψ| is required in dealing with, for example, the minimum uncertainty relation between position and momentum. Without the evenness or oddness of ψ, |ℑψ| = |ψ| does not necessarily imply arg(ℑψ) = ±argψ + θ, nor is the converse.
Noise figure of amplified dispersive Fourier transformation
Goda, Keisuke; Jalali, Bahram
2010-09-15
Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.
Advanced Techniques for Fourier Transform Wavefront Reconstruction
Poyneer, L A
2002-08-05
The performance of Fourier transform (FT) reconstructors in large adaptive optics systems with Shack-Hartmann sensors and a deformable mirror is analyzed. FT methods, which are derived for point-based geometries, are adapted for use on the continuous systems. Analysis and simulation show how to compensate for effects such as misalignment of the deformable mirror and wavefront sensor gain. Further filtering methods to reduce noise and improve performance are presented. All these modifications can be implemented at the filtering stage, preserving the speed of FT reconstruction. Simulation of a large system shows how compensated FT methods can have equivalent or better performance to slower vector-matrix-multiply reconstructions.
Fourier transform infrared spectroscopy of deuterated proteins
NASA Astrophysics Data System (ADS)
Marcano O., A.; Markushin, Y.; Melikechi, N.; Connolly, D.
2008-08-01
We report on Fourier transform spectra of deuterated proteins: Bovine Serum Albumin, Leptin, Insulin-like Growth Factor II, monoclonal antibody to ovarian cancer antigen CA125 and Osteopontin. The spectra exhibit changes in the relative amplitude and spectral width of certain peaks. New peaks not present in the non-deuterated sample are also observed. Ways for improving the deuteration of proteins by varying the temperature and dilution time are discussed. We propose the use of deuterated proteins to increase the sensitivity of immunoassays aimed for early diagnostic of diseases most notably cancer.
Anisotropic magnification distortion of the 3D galaxy correlation. II. Fourier and redshift space
Hui Lam; Gaztanaga, Enrique; LoVerde, Marilena
2008-03-15
In paper I of this series we discuss how magnification bias distorts the 3D correlation function by enhancing the observed correlation in the line-of-sight (LOS) orientation, especially on large scales. This lensing anisotropy is distinctive, making it possible to separately measure the galaxy-galaxy, galaxy-magnification and magnification-magnification correlations. Here we extend the discussion to the power spectrum and also to redshift space. In real space, pairs oriented close to the LOS direction are not protected against nonlinearity even if the pair separation is large; this is because nonlinear fluctuations can enter through gravitational lensing at a small transverse separation (or i.e. impact parameter). The situation in Fourier space is different: by focusing on a small wave number k, as is usually done, linearity is guaranteed because both the LOS and transverse wave numbers must be small. This is why magnification distortion of the galaxy correlation appears less severe in Fourier space. Nonetheless, the effect is non-negligible, especially for the transverse Fourier modes, and should be taken into account in interpreting precision measurements of the galaxy power spectrum, for instance those that focus on the baryon oscillations. The lensing induced anisotropy of the power spectrum has a shape that is distinct from the more well-known redshift space anisotropies due to peculiar motions and the Alcock-Paczynski effect. The lensing anisotropy is highly localized in Fourier space while redshift space distortions are more spread out. This means that one could separate the magnification bias component in real observations, implying that potentially it is possible to perform a gravitational lensing measurement without measuring galaxy shapes.
Coherent Fourier transform electrical pulse shaping.
Xiao, Shijun; Weiner, Andrew M
2006-04-01
Fourier synthesis pulse shaping methods allowing generation of programmable, user defined femtosecond optical waveforms have been widely applied in ultrafast optical science and technology. In the electrical domain, arbitrary waveform generation is well established at frequencies below approximately 1 GHz, but is difficult at higher frequencies due to limitations in digital-to-analog converter technology. In this paper we demonstrate a method for electrical waveform synthesis at substantially higher frequencies (approximately 20 GHz electrical bandwidth) by combining Fourier optical pulse shaping (extended to hyperfine frequency resolution) and heterodyne optical to electrical conversion. Our scheme relies on coherent manipulation of fields and phases at all stages, both for processing in the optical domain and for conversion from the optical to the electrical domain. We illustrate this technique through a number of examples, including programmable retardation or advancement of short electrical pulses in time over a range exceeding ten pulse durations. Such optically implemented, coherent Fourier transform electrical pulse shaping should open new prospects in ultrawideband electromagnetics. PMID:19516448
Fourier transform optical profilometry using fiber optic Lloyd's mirrors.
Kart, Türkay; Kösoğlu, Gülşen; Yüksel, Heba; İnci, Mehmet Naci
2014-12-10
A fiber optic Lloyd's mirror assembly is used to obtain various optical interference patterns for the detection of 3D rigid body shapes. Two types of fiber optic Lloyd's systems are used in this work. The first consists of a single-mode optical fiber and a highly reflecting flat mirror to produce bright and dark strips. The second is constructed by locating a single-mode optical fiber in a v-groove, which is formed by two orthogonal flat mirrors to allow the generation of square-type interference patterns for the desired applications. The structured light patterns formed by these two fiber Lloyd's techniques are projected onto 3D objects. Fringe patterns are deformed due to the object's surface topography, which are captured by a digital CCD camera and processed with a Fourier transform technique to accomplish 3D surface topography of the object. It is demonstrated that the fiber-optic Lloyd's technique proposed in this work is more compact, more stable, and easier to configure than other existing surface profilometry systems, since it does not include any high-cost optical tools such as aligners, couplers, or 3D stages. The fringe patterns are observed to be more robust against environmental disturbances such as ambient temperature and vibrations. PMID:25608057
Optical interpretation of a complex-order Fourier transform.
Shih, C C
1995-05-15
It is demonstrated that the definition of a fractional-order Fourier transform can be extended into the complexorder regime. A complex-order Fourier transform deals with the imaginary part as well as the real part of the exponential function in the integral. As a result, while the optical implementation of fractional-order Fourier transform involves gradient-index media or spherical lenses, the optical interpretation of complex-order Fourier transform is practically based on the convolution operation and Gaussian apertures. The beam width of a Gaussian beam subjected to the complex-order Fourier transform is obtained analytically with the ABCD matrix approach. PMID:19859464
Alternating multivariate trigonometric functions and corresponding Fourier transforms
NASA Astrophysics Data System (ADS)
Klimyk, A. U.; Patera, J.
2008-04-01
We define and study multivariate sine and cosine functions, symmetric with respect to the alternating group An, which is a subgroup of the permutation (symmetric) group Sn. These functions are eigenfunctions of the Laplace operator. They determine Fourier-type transforms. There exist three types of such transforms: expansions into corresponding sine-Fourier and cosine-Fourier series, integral sine-Fourier and cosine-Fourier transforms, and multivariate finite sine and cosine transforms. In all these transforms, alternating multivariate sine and cosine functions are used as a kernel.
FFTW: Fastest Fourier Transform in the West
NASA Astrophysics Data System (ADS)
Frigo, Matteo; Johnson, Steven G.
2012-01-01
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST). Benchmarks performed on a variety of platforms show that FFTW's performance is typically superior to that of other publicly available FFT software, and is even competitive with vendor-tuned codes. In contrast to vendor-tuned codes, however, FFTW's performance is portable: the same program will perform well on most architectures without modification. The FFTW library is required by other codes such as StarCrash and Hammurabi.
Two-dimensional fourier transform spectrometer
DeFlores, Lauren; Tokmakoff, Andrei
2013-09-03
The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.
Compact Fourier transform spectrometer without moving parts
NASA Astrophysics Data System (ADS)
Huang, Chu-Yu; Estroff, B.; Wang, Wei-Chih
2012-04-01
Fourier transform spectroscopy (FTS) is a potent analytical tool for chemical and biological analysis, but is limited by system size, expense, and robustness. To make FTS technology more accessible, we present a compact, inexpensive FTS system based on a novel liquid crystal (LC) interferometer. This design is unique because the optical path difference (OPD) is controlled by voltage applied to the LC cell. The OPD is further improved by reflecting the polarized incident light through the LC several times before reaching the second polarizer and measurement. This paper presents the theoretical model and numerical simulations for the liquid crystal Fourier transform spectrometer (LCFTS), and experimental results from the prototype. Based on the experimental results, the LCFTS performs in accordance with the theoretical predictions, achieving a maximum OPD of 210μm and a resolution of 1nm at a wavelength of 630nm. The instrumental response refresh rate is just under 1 second. Absorbance measurements were conducted for single and mixed solutions of deionized water and isopropyl alcohol, demonstrating agreement with a commercial system and literature values. We also present the LCFTS transmission spectra for varying concentrations of potassium permanganate to show system sensitivity.
Fourier Transforms Simplified: Computing an Infrared Spectrum from an Interferogram
ERIC Educational Resources Information Center
Hanley, Quentin S.
2012-01-01
Fourier transforms are used widely in chemistry and allied sciences. Examples include infrared, nuclear magnetic resonance, and mass spectroscopies. A thorough understanding of Fourier methods assists the understanding of microscopy, X-ray diffraction, and diffraction gratings. The theory of Fourier transforms has been presented in this "Journal",…
Interior Reconstruction Using the 3d Hough Transform
NASA Astrophysics Data System (ADS)
Dumitru, R.-C.; Borrmann, D.; Nüchter, A.
2013-02-01
Laser scanners are often used to create accurate 3D models of buildings for civil engineering purposes, but the process of manually vectorizing a 3D point cloud is time consuming and error-prone (Adan and Huber, 2011). Therefore, the need to characterize and quantify complex environments in an automatic fashion arises, posing challenges for data analysis. This paper presents a system for 3D modeling by detecting planes in 3D point clouds, based on which the scene is reconstructed at a high architectural level through removing automatically clutter and foreground data. The implemented software detects openings, such as windows and doors and completes the 3D model by inpainting.
Fourier transform spectrometer controller for partitioned architectures
NASA Astrophysics Data System (ADS)
Tamas-Selicean, D.; Keymeulen, D.; Berisford, D.; Carlson, R.; Hand, K.; Pop, P.; Wadsworth, W.; Levy, R.
The current trend in spacecraft computing is to integrate applications of different criticality levels on the same platform using no separation. This approach increases the complexity of the development, verification and integration processes, with an impact on the whole system life cycle. Researchers at ESA and NASA advocated for the use of partitioned architecture to reduce this complexity. Partitioned architectures rely on platform mechanisms to provide robust temporal and spatial separation between applications. Such architectures have been successfully implemented in several industries, such as avionics and automotive. In this paper we investigate the challenges of developing and the benefits of integrating a scientific instrument, namely a Fourier Transform Spectrometer, in such a partitioned architecture.
Compact snapshot birefringent imaging Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Kudenov, Michael W.; Dereniak, Eustace L.
2010-08-01
The design and implementation of a compact multiple-image Fourier transform spectrometer (FTS) is presented. Based on the multiple-image FTS originally developed by A. Hirai, the presented device offers significant advantages over his original implementation. Namely, its birefringent nature results in a common-path interferometer which makes the spectrometer insensitive to vibration. Furthermore, it enables the potential of making the instrument ultra-compact, thereby improving the portability of the sensor. The theory of the birefringent FTS is provided, followed by details of its specific embodiment. A laboratory proof of concept of the sensor, designed and developed at the Optical Detection Lab, is also presented. Spectral measurements of laboratory sources are provided, including measurements of light-emitting diodes and gas-discharge lamps. These spectra are verified against a calibrated Ocean Optics USB2000 spectrometer. Other data were collected outdoors, demonstrating the sensor's ability to resolve spectral signatures in standard outdoor lighting and environmental conditions.
Surface Inspection using fourier transform infrared spectroscopy
Powell, G.L.; Smyrl, N.R.; Williams, D.M.; Meyers, H.M. III; Barber, T.E.; Marrero-Rivera, M.
1994-08-08
The use of reflectance Fourier transform infrared (FTIR) spectroscopy as a tool for surface inspection is described. Laboratory instruments and portable instruments can support remote sensing probes that can map chemical contaminants on surfaces. Detection limits under the best of conditions are in the subnanometer range (i.e., near absolute cleanliness), excellent performance is obtained in the submicrometer range, and useful performance may exist for films tens of microns thick. Identifying and quantifying contamination such as mineral oils and greases, vegetable oils, and silicone oils on aluminum foil, galvanized sheet steel, smooth aluminum tubing, and gritblasted 7075 aluminum alloy and D6AC steel are described. The ability to map in time and space the distribution of oil stains on metals is demonstrated. Techniques for quantitatively applying oils to metals, subsequently verifying the application, and nonlinear relationships between reflectance and the quantity of oil are discussed.
Optical correction using fourier transform heterodyne
NASA Astrophysics Data System (ADS)
Laubscher, Bryan E.; Nemzek, Robert J.; Cooke, Bradly J.; Olivas, Nicholas L.; Jorgensen, Anders M.; Smith, J. A.; Weisse-Bernstein, Nina R.
2005-08-01
In this paper we briefly present the theory of Fourier Transform Heterodyne (FTH), describe past verification experiments carried out, and discuss the experiment designed to use this new imaging technology to perform optical correction. FTH uses the scalar projection of a reference laser beam and a test laser beam onto a single element detector. The complex current in the detector yields the coefficient of the scalar projection. By projecting a complete orthonormal basis set of reference beams onto the test beam, the amplitude and phase of the test beam can be measured, allowing the reconstruction of the phasefront of the image. Experiments to determine this technique's applicability to optical correction and optical self-correction are continuing. Applications of this technique beyond optical correction include adaptive optics; interferometry; and active, high background, low signal imaging.
Fourier transform infrared spectroscopy for Mars science
NASA Astrophysics Data System (ADS)
Anderson, Mark S.; Andringa, Jason M.; Carlson, Robert W.; Conrad, Pamela; Hartford, Wayne; Shafer, Michael; Soto, Alejandro; Tsapin, Alexandre I.; Dybwad, Jens Peter; Wadsworth, Winthrop; Hand, Kevin
2005-03-01
Presented here is a Fourier transform infrared spectrometer (FTIR) for field studies that serves as a prototype for future Mars science applications. Infrared spectroscopy provides chemical information that is relevant to a number of Mars science questions. This includes mineralogical analysis, nitrogen compound recognition, truth testing of remote sensing measurements, and the ability to detect organic compounds. The challenges and scientific opportunities are given for the in situ FTIR analysis of Mars soil and rock samples. Various FTIR sampling techniques are assessed and compared to other analytical instrumentation. The prototype instrument presented is capable of providing field analysis in a Mars analog Antarctic environment. FTIR analysis of endolithic microbial communities in Antarctic rocks and a Mars meteor are given as analytical examples.
Fourier transform infrared spectroscopic study of truffles
NASA Astrophysics Data System (ADS)
Zhao, Dezhang; Liu, Gang; Song, Dingshan; Liu, Jian-hong; Zhou, Yilan; Ou, Jiaming; Sun, Shizhong
2006-01-01
Truffles are rare wild growing edible mushrooms belonging to Ascomycetes. In this paper, Fourier transform infrared (FTIR) spectroscopy was used to obtain vibrational spectra of truffles. The results show that the mushrooms exhibit characteristic spectra. The two strongest absorption bands appear at about 1077cm -1 and 1040 cm -1, which were described as C-O stretching in carbohydrate. The vibrational spectra indicate that the main compositions of the truffles are polysaccharide and protein. According to the characteristics bands and absorption ratios of spectra, different species of truffles can be discriminated. It is also found the great changes between moldy and healthy truffles, which the major differences are observed in the bands of protein. In addition, FTIR spectral differences are observed between the same species of truffles from different producing areas. It is showed that the FTIR spectroscopic method is valuable tool for rapid and nondestructive analysis of truffles prior to any extraction method used.
Uncertainty relation for the discrete Fourier transform.
Massar, Serge; Spindel, Philippe
2008-05-16
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation. PMID:18518426
Geometric interpretations of the Discrete Fourier Transform (DFT)
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
NASA Astrophysics Data System (ADS)
Laude, David A., Jr.; Johlman, Carolyn; Wilkins, Charles L.
1985-12-01
During the past few years it has been demonstrated that linkage of multiple spectrometry systems with gas chromatography (GC) offers significant advantages for structural analysis of mixture components as they are sepa-rated. In the work to be described, a Fourier transform mass spectrometer (FTMS) has been linked in parallel with a Fourier transform infrared (FTIR) spectrometer for concurrent analysis of GC eluants from a fused silica capillary column. This system provides FTIR, electron impact, and chemical ionization mass spectral analysis of each mixture component as it emerges from the GC. Furthermore, mass measurement accuracy in the low ppm range in the absence of calibrant is made possible by the FTMS. Effective use of the com-plementary information obtained is shown to produce more reliable analytical performance than for any individual measurement.
Fourier transform imaging spectropolarimeter using simultaneous polarization modulation.
Meng, Xin; Li, Jianxin; Liu, Defang; Zhu, Rihong
2013-03-01
We introduce a Fourier transform imaging spectropolarimeter composed of a simultaneous polarization modulator and a Fourier transform spectrometer without slit. The spectropolarimeter enables the generation of four sets of fringe patterns with different polarization states of light from an object point. Fourier transform of the fringe patterns provides four equations of Stokes parameters in various wavenumbers. And we can obtain the full-stokes vector from the equations. The most significant advantage of the method is that the four polarized fringe patterns are obtained simultaneously and separated without aliasing. Additionally, the advantages of the Fourier transform spectrometer are maintained, such as high radiative throughput. PMID:23455296
3D imaging of dental hard tissues with Fourier domain optical coherence tomography
NASA Astrophysics Data System (ADS)
Chen, Yueli L.; Yang, Yi; Ma, Jing; Yan, Jun; Shou, Yuanxin; Wang, Tianheng; Ramesh, Aruna; Zhao, Jing; Zhu, Quing
2011-03-01
A fiber optical coherence tomography (OCT) probe is used for three dimensional dental imaging. The probe has a lightweight miniaturized design with a size of a pen to facilitate clinic in vivo diagnostics. The probe is interfaced with a swept-source / Fourier domain optical coherence tomography at 20K axial scanning rate. The tooth samples were scanned from occlusal, buccal, lingual, mesial, and distal orientations. Three dimensional imaging covers tooth surface area up to 10 mm x 10 mm with a depth about 5 mm, where a majority of caries affection occurs. OCT image provides better resolution and contrast compared to gold standard dental radiography (X-ray). In particular, the technology is well suited for occlusal caries detection. This is complementary to X-ray as occlusal caries affection is difficult to be detected due to the X-ray projectile scan geometry. The 3D topology of occlusal surface as well as the dentin-enamel junction (DEJ) surface inside the tooth can be visualized. The lesion area appears with much stronger back scattering signal intensity.
Geostationary Fourier Transform Spectrometer (GeoFTS)
NASA Astrophysics Data System (ADS)
Sander, S. P.; Bekker, D. L.; Blavier, J. L.; Duren, R. M.; Eldering, A.; Frankenberg, C.; Key, R.; Manatt, K.; Miller, C. E.; Natraj, V.; Rider, D. M.; Wu, Y.
2012-12-01
In order to confidently project the future evolution of climate and support efforts to mitigate the climate change, quantifying the emissions of CO2 and CH4 is a national and international priority. To accomplish this goal, new observational approaches are required that operate over spatial scales ranging from regional to global, and temporal scales from diurnal to decadal. Geostationary satellite observations of CO2, CH4 and correlative quantities such as CO and chlorophyll fluorescence provide a new measurement approach to deliver the quantity and quality of data needed for improved flux estimates and an improved understanding of the partitioning between biogenic and anthropogenic sources. GeoFTS is an exciting new concept that combines the game changing technology of imaging Fourier Transform Spectroscopy with the observational advantages of a geostationary orbit. The GeoFTS observations enable well-posed surface-atmospheric carbon exchange assessments as well as quantify the atmospheric signatures of anthropogenic CO2 and CH4 emissions. GeoFTS uses a single instrument to make measurements in the near-infrared spectral region at high spectral resolution. The imaging FTS measures atmospheric CO2, CH4, and CO to deliver high-resolution maps multiple times per day. A half-meter-sized cube, the instrument is designed to be a secondary "hosted" payload on a commercial GEO satellite. The instrument leverages recent NASA technology investments, uses a flight-proven interferometer and sensor chip assemblies, and requires no new technology development. NASA and other government agencies have adopted the hosted payload implementation approach because it substantially reduces the overall mission cost. Dense continuous mapping (4 km x 4 km pixels at 40 deg. latitude) is a transformational advance beyond, and complementary to, the capabilities of the NASA missions of record in low earth orbit, providing two to three orders of magnitude improvement in the number of
Imaging Fourier transform spectrometry of chemical plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.; Gross, Kevin C.; Perram, Glen P.
2009-05-01
A midwave infrared (MWIR) imaging Fourier transform spectrometer (FTS), the Telops FIRST-MWE (Field-portable Imaging Radiometric Spectrometer Technology - Midwave Extended) has been utilized for the standoff detection and characterization of chemical plumes. Successful collection and analysis of MWIR hyperspectral imagery of jet engine exhaust has allowed us to produce spatial profiles of both temperature and chemical constituent concentrations of exhaust plumes. Successful characterization of this high temperature combustion event has led to the collection and analysis of hyperspectral imagery of lower temperature emissions from industrial smokestacks. This paper presents MWIR data from remote collection of hyperspectral imagery of methyl salicilate (MeS), a chemical warfare agent simulant, during the Chemical Biological Distributed Early Warning System (CBDEWS) test at Dugway Proving Grounds, UT in 2008. The data did not contain spectral lines associated with emission of MeS. However, a few broad spectral features were present in the background-subtracted plume spectra. Further analysis will be required to assign these features, and determine the utility of MWIR hyperspectral imagery for analysis of chemical warfare agent plumes.
VLSI Implementation Of The Fast Fourier Transform
NASA Astrophysics Data System (ADS)
Chau, Paul M.; Ku, Walter H.
1986-03-01
A VLSI implementation of a Fast Fourier Transform (FFT) processor consisting of a mesh interconnection of complex floating-point butterfly units is presented. The Cooley-Tukey radix-2 Decimation-In-Frequency (DIF) formulation of the FFT was chosen since it offered the best overall compromise between the need for fast and efficient algorithmic computation and the need for a structure amenable to VLSI layout. Thus the VLSI implementation is modular, regular, expandable to various problem sizes and has a simple systolic flow of data and control. To evaluate the FFT architecture, VLSI area-time complexity concepts are used, but are now adapted to a complex floating-point number system rather than the usual integer ring representation. We show by our construction that the Thompson area-time optimum bound for the VLSI computation of an N-point FFT, area-time2oc = ORNlogN)1+a] can be attained by an alternative number representation, and hence the theoretical bound is a tight bound regardless of number system representation.
Fourier transform spectroscopy for future planetary missions
NASA Astrophysics Data System (ADS)
Brasunas, John C.; Hewagama, Tilak; Kolasinski, John R.; Kostiuk, Theodor
2015-11-01
Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system.Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, NASA Goddard was funded via the Planetary Instrument Definition and Development Progrem (PIDDP) to develop CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. Following the initial validation of CIRS-lite operation in the laboratory, we have been acquiring atmospheric data in the 8-12 micron window at the 1.2 m telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) in Greenbelt, MD. Targets so far have included Earth's atmosphere (in emission, and in absorption against the moon), and Venus.We will present the roadmap for making CIRS-lite a viable candidate for future planetary missions.
Jing, Zhang; Sheng, Kang Bao
2016-01-01
To assist physicians to quickly find the required 3D model from the mass medical model, we propose a novel retrieval method, called DRFVT, which combines the characteristics of dimensionality reduction (DR) and feature vector transformation (FVT) method. The DR method reduces the dimensionality of feature vector; only the top M low frequency Discrete Fourier Transform coefficients are retained. The FVT method does the transformation of the original feature vector and generates a new feature vector to solve the problem of noise sensitivity. The experiment results demonstrate that the DRFVT method achieves more effective and efficient retrieval results than other proposed methods. PMID:27293478
Design of 3D isotropic metamaterial device using smart transformation optics.
Shin, Dongheok; Kim, Junhyun; Yoo, Do-Sik; Kim, Kyoungsik
2015-08-24
We report here a design method for a 3 dimensional (3D) isotropic transformation optical device using smart transformation optics. Inspired by solid mechanics, smart transformation optics regards a transformation optical medium as an elastic solid and deformations as coordinate transformations. Further developing from our previous work on 2D smart transformation optics, we introduce a method of 3D smart transformation optics to design 3D transformation optical devices by maintaining isotropic materials properties for all types of polarizations imposing free or nearly free boundary conditions. Due to the material isotropy, it is possible to fabricate such devices with structural metamaterials made purely of common dielectric materials. In conclusion, the practical importance of the method reported here lies in the fact that it enables us to fabricate, without difficulty, arbitrarily shaped 3D devices with existing 3D printing technology. PMID:26368165
Determination of Fourier Transforms on an Instructional Analog Computer
ERIC Educational Resources Information Center
Anderson, Owen T.; Greenwood, Stephen R.
1974-01-01
An analog computer program to find and display the Fourier transform of some real, even functions is described. Oscilloscope traces are shown for Fourier transforms of a rectangular pulse, a Gaussian, a cosine wave, and a delayed narrow pulse. Instructional uses of the program are discussed briefly. (DT)
Resource requirements for a fault-tolerant quantum Fourier transform
NASA Astrophysics Data System (ADS)
Goto, Hayato
2014-11-01
We investigate resource requirements for a fault-tolerant quantum Fourier transform. The quantum Fourier transform is a basic subroutine for quantum algorithms which provide an exponential speedup over known classical ones, such as Shor's algorithm for factoring. To implement single-qubit rotations required for a quantum Fourier transform in a fault-tolerant manner, we consider two types of approaches: gate synthesis and state distillation. While the gate synthesis approximates single-qubit rotations with basic quantum operations, the state distillation allows one to perform single-qubit rotations for a quantum Fourier transform exactly. It is unknown, however, which approach is better for a quantum Fourier transform. Here we develop a state-distillation method optimized for a quantum Fourier transform and compare this performance with those of state-of-the-art techniques for gate synthesis without and with ancillary states (ancillas). The performance is evaluated with the resource requirement for a quantum Fourier transform. The resource is measured by the total number of π /8 gates denoted by T , which is called the T count. Contrary to the expectation, the T count for the state distillation is considerably larger than those for the ancilla-free and ancilla-assisted gate synthesis. Thus, we conclude that the ancilla-assisted gate synthesis is a better approach to a fault-tolerant quantum Fourier transform.
Phillips, Jeffrey
2014-01-01
A physical property inversion approach based on the use of 3D (or 2D) Fourier transforms to calculate the potentialfield within a 3D (or 2D) volume from a known physical property distribution within the volume is described. Topographic surfaces and observations at arbitrary locations are easily accommodated. The limitations of the approach and applications to real data are considered.
Signal Processing Issues in Fourier Transform Spectrometers
NASA Astrophysics Data System (ADS)
Hayes, Monson H.
2002-12-01
There are a number of interesting and challenging signal processing problems related to the design of a Fourier Transform Spectrometer (FTS). In this project, we look at a few of these problems in two different types of spectrometers-the Geostationary Imaging Fourier Transform Spectrometer (GIFTS), and a Far Infrared (FIR) FTS. One of the si nal processing challenges in GIFTS is the reduction of the massive data rate (2.4 x 109 bps) to an affordable telemetry rate of less than 60 Mbps. Since the GIFTS interferograms are heavily over-sampled, the first step is to decimate (down-sample) the interferograms with minimal distortion while keeping the signal processing algorithms simple enough to be implemented in the GIFTS hardware. Therefore, the first problem we looked at was the design of the decimation filters. Specifically, we performed a detailed analysis of two competing approaches that were being considered. The first, proposed by the Space Dynamics Lab (SDL), was to use a double sideband (real) band-pass filter. The second, proposed by Lincoln Laboratories (LL), was to use a single sideband (complex) band-pass filter. What the study showed was that a complex filter (LL approach) results in a savings of about 25% in the filtering requirements for the long-wave band, while in the mid-wave band the savings are approximately 50%. As a result, the decision was made to use a complex filter. Once the decision to use a complex filter had been made, we looked at some of the consequences of this decision. The most significant of these was the discovery that, with a complex filter, it is possible to extend the long-wave IR band beyond the folding frequency of 1174/cm and recover the SO2 line at 1176.5/cm. What this requires is the design of a band-pass decimation filter with a wider passband, and consequently of higher order. Specifically, it was shown that with about 25% more filter operations, the elusive SO2 line, believed to be irretrievable, could in fact be recovered
Cryogenic Scan Mechanism for Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Brasunas, John C.; Francis, John L.
2011-01-01
A compact and lightweight mechanism has been developed to accurately move a Fourier transform spectrometer (FTS) scan mirror (a cube corner) in a near-linear fashion with near constant speed at cryogenic temperatures. This innovation includes a slide mechanism to restrict motion to one dimension, an actuator to drive the motion, and a linear velocity transducer (LVT) to measure the speed. The cube corner mirror is double-passed in one arm of the FTS; double-passing is required to compensate for optical beam shear resulting from tilting of the moving cube corner. The slide, actuator, and LVT are off-the-shelf components that are capable of cryogenic vacuum operation. The actuator drives the slide for the required travel of 2.5 cm. The LVT measures translation speed. A proportional feedback loop compares the LVT voltage with the set voltage (speed) to derive an error signal to drive the actuator and achieve near constant speed. When the end of the scan is reached, a personal computer reverses the set voltage. The actuator and LVT have no moving parts in contact, and have magnetic properties consistent with cryogenic operation. The unlubricated slide restricts motion to linear travel, using crossed roller bearings consistent with 100-million- stroke operation. The mechanism tilts several arc seconds during transport of the FTS mirror, which would compromise optical fringe efficiency when using a flat mirror. Consequently, a cube corner mirror is used, which converts a tilt into a shear. The sheared beam strikes (at normal incidence) a flat mirror at the end of the FTS arm with the moving mechanism, thereby returning upon itself and compensating for the shear
NASA Astrophysics Data System (ADS)
Kwiecien, Pavel; Richter, Ivan; Čtyroký, Jiří
2012-02-01
Frequency-domain Fourier modal methods have recently evolved into efficient tools for rigorous numerical modeling of a wide class of photonic and plasmonic structures and devices. In this contribution we describe the application of our 2D and 3D in-house tools, namely aperiodic rigorous coupled wave analysis (aRCWA) and bi-directional mode expansion propagation method using harmonic expansion (BEXX), on a recently described novel type of subwavelength grating (SWG) waveguides. They are created by means of periodically interlacing silicon segments with a superstrate material with a lower refractive index. It has been shown recently, both theoretically and experimentally, that for a suitable choice of SWG parameters such as grating period and duty cycle, the structure can support low-loss guided (Bloch) mode. Its effective index, mode profile and dispersion characteristics can thus be tailored to specific needs without the necessity of changing material composition. In our methods, either complex coordinate transformation or uniaxial anisotropic perfectly matched layers have been applied as efficient absorption boundary conditions. In order to reduce the number of expansion terms needed to reach required accuracy, the adaptive spatial resolution technique has been implemented. Structural symmetries of the devices can be fully utilized to this aim, too. Propagation constants of Bloch modes are also compared with those obtained with a full-vector film mode matching (FiMM) mode solver using the very simple effective medium theory (EMT).
NASA Astrophysics Data System (ADS)
Kwiecien, Pavel; Richter, Ivan; Čtyroký, Jiří
2011-09-01
Frequency-domain Fourier modal methods have recently evolved into efficient tools for rigorous numerical modeling of a wide class of photonic and plasmonic structures and devices. In this contribution we describe the application of our 2D and 3D in-house tools, namely aperiodic rigorous coupled wave analysis (aRCWA) and bi-directional mode expansion propagation method using harmonic expansion (BEXX), on a recently described novel type of subwavelength grating (SWG) waveguides. They are created by means of periodically interlacing silicon segments with a superstrate material with a lower refractive index. It has been shown recently, both theoretically and experimentally, that for a suitable choice of SWG parameters such as grating period and duty cycle, the structure can support low-loss guided (Bloch) mode. Its effective index, mode profile and dispersion characteristics can thus be tailored to specific needs without the necessity of changing material composition. In our methods, either complex coordinate transformation or uniaxial anisotropic perfectly matched layers have been applied as efficient absorption boundary conditions. In order to reduce the number of expansion terms needed to reach required accuracy, the adaptive spatial resolution technique has been implemented. Structural symmetries of the devices can be fully utilized to this aim, too. Propagation constants of Bloch modes are also compared with those obtained with a full-vector film mode matching (FiMM) mode solver using the very simple effective medium theory (EMT).
Color image registration based on quaternion Fourier transformation
NASA Astrophysics Data System (ADS)
Wang, Qiang; Wang, Zhengzhi
2012-05-01
The traditional Fourier Mellin transform is applied to quaternion algebra in order to investigate quaternion Fourier transformation properties useful for color image registration in frequency domain. Combining with the quaternion phase correlation, we propose a method for color image registration based on the quaternion Fourier transform. The registration method, which processes color image in a holistic manner, is convenient to realign color images differing in translation, rotation, and scaling. Experimental results on different types of color images indicate that the proposed method not only obtains high accuracy in similarity transform in the image plane but also is computationally efficient.
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses
Lim, Lucy; Yan, Fangzhi; Bach, Stephen; Pihakari, Katianna; Klein, David
2016-01-01
Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS) has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices. PMID:26784175
Fourier Transform Mass Spectrometry: The Transformation of Modern Environmental Analyses.
Lim, Lucy; Yan, Fangzhi; Bach, Stephen; Pihakari, Katianna; Klein, David
2016-01-01
Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS) has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsible for changing the face of how complex analyses are accomplished. First is the ability to quickly and with high mass accuracy determine the presence of unknown chemical residues in samples. For years, the field has been limited by mass spectrometric methods that were based on knowing what compounds of interest were. Secondly, by utilizing the high resolution capabilities coupled with the low detection limits of FTMS, analysts also could dilute the sample sufficiently to minimize the ionization changes from varied matrices. PMID:26784175
A discrete Fourier transform for virtual memory machines
NASA Technical Reports Server (NTRS)
Galant, David C.
1992-01-01
An algebraic theory of the Discrete Fourier Transform is developed in great detail. Examination of the details of the theory leads to a computationally efficient fast Fourier transform for the use on computers with virtual memory. Such an algorithm is of great use on modern desktop machines. A FORTRAN coded version of the algorithm is given for the case when the sequence of numbers to be transformed is a power of two.
Implementation of weighted summation type fractional Fourier transform on FPGA
NASA Astrophysics Data System (ADS)
Zou, Qiming; Li, Longlong; Huang, Qian; Wang, Fei
2015-07-01
Recently Fractional Fourier transform (FrFT) has got a variety of applications in digital signal and image processing. This paper presents a novel hardware architecture for real-time computation of Discrete Fractional Fourier Transform (DFrFT), which can easily be extended to other fractional transforms. The proposed architecture has been verified on Xilinx FPGA(XC6VLX240T), which can run at a frequency up to 291MHz while with high accuracy.
Bouallègue, Fayçal Ben; Crouzet, Jean-François; Comtat, Claude; Fourcade, Marjolaine; Mohammadi, Bijan; Mariano-Goulart, Denis
2007-07-01
This paper presents an extended 3-D exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation, this analytical formula also leads to an extended Fourier rebinning equation that is the basis for an approximate reprojection algorithm (extended FORE). These algorithms were evaluated on numerically simulated 3-D positron emission tomography (PET) data for the solution of the truncation problem, i.e., the estimation of the missing portions in the oblique projection data, before the application of algorithms that require complete projection data such as some rebinning methods (FOREX) or 3-D reconstruction algorithms (3DRP or direct Fourier methods). By taking advantage of all the 3-D data statistics, the iterative FOREPROJ reprojection provides a reliable alternative to the classical FOREPROJ method, which only exploits the low-statistics nonoblique data. It significantly improves the quality of the external reconstructed slices without loss of spatial resolution. As for the approximate extended FORE algorithm, it clearly exhibits limitations due to axial interpolations, but will require clinical studies with more realistic measured data in order to decide on its pertinence. PMID:17649913
Technique for the metrology calibration of a Fourier transform spectrometer
Spencer, Locke D.; Naylor, David A
2008-11-10
A method is presented for using a Fourier transform spectrometer (FTS) to calibrate the metrology of a second FTS. This technique is particularly useful when the second FTS is inside a cryostat or otherwise inaccessible.
Xgremlin: Interferograms and spectra from Fourier transform spectrometers analysis
NASA Astrophysics Data System (ADS)
Nave, G.; Griesmann, U.; Brault, J. W.; Abrams, M. C.
2015-11-01
Xgremlin is a hardware and operating system independent version of the data analysis program Gremlin used for Fourier transform spectrometry. Xgremlin runs on PCs and workstations that use the X11 window system, including cygwin in Windows. It is used to Fourier transform interferograms, plot spectra, perform phase corrections, perform intensity and wavenumber calibration, and find and fit spectral lines. It can also be used to construct synthetic spectra, subtract continua, compare several different spectra, and eliminate ringing around lines.
The quest for conformal geometric algebra Fourier transformations
NASA Astrophysics Data System (ADS)
Hitzer, Eckhard
2013-10-01
Conformal geometric algebra is preferred in many applications. Clifford Fourier transforms (CFT) allow holistic signal processing of (multi) vector fields, different from marginal (channel wise) processing: Flow fields, color fields, electro-magnetic fields, ... The Clifford algebra sets (manifolds) of √-1 lead to continuous manifolds of CFTs. A frequently asked question is: What does a Clifford Fourier transform of conformal geometric algebra look like? We try to give a first answer.
Simple optical setup implementation for digital Fourier transform holography
NASA Astrophysics Data System (ADS)
de Oliveira, G. N.; Rodrigues, D. M. C.; dos Santos, P. A. M.
2011-01-01
In the present work a simple implementation of Digital Fourier Transform Holography (DFTH) setup is discussed. This is obtained making a very simple modification in the classical setup arquiteture of the Fourier Transform holography. It is also demonstrated the easy and practical viability of the setup in an interferometric application for mechanical parameters determination. The work is also proposed as an interesting advanced introductory training for graduated students in digital holography.
NASA Technical Reports Server (NTRS)
Marko, H.
1978-01-01
A general spectral transformation is proposed and described. Its spectrum can be interpreted as a Fourier spectrum or a Laplace spectrum. The laws and functions of the method are discussed in comparison with the known transformations, and a sample application is shown.
Herz spaces and restricted summability of Fourier transforms and Fourier series
NASA Astrophysics Data System (ADS)
Weisz, Ferenc
2008-08-01
A general summability method, the so-called [theta]-summability is considered for multi-dimensional Fourier transforms and Fourier series. A new inequality for the Hardy-Littlewood maximal function is verified. It is proved that if the Fourier transform of [theta] is in a Herz space, then the restricted maximal operator of the [theta]-means of a distribution is of weak type (1,1), provided that the supremum in the maximal operator is taken over a cone-like set. From this it follows that over a cone-like set a.e. for all . Moreover, converges to f(x) over a cone-like set at each Lebesgue point of if and only if the Fourier transform of [theta] is in a suitable Herz space. These theorems are extended to Wiener amalgam spaces as well. The Riesz and Weierstrass summations are investigated as special cases of the [theta]-summation.
Blind watermark algorithm on 3D motion model based on wavelet transform
NASA Astrophysics Data System (ADS)
Qi, Hu; Zhai, Lang
2013-12-01
With the continuous development of 3D vision technology, digital watermark technology, as the best choice for copyright protection, has fused with it gradually. This paper proposed a blind watermark plan of 3D motion model based on wavelet transform, and made it loaded into the Vega real-time visual simulation system. Firstly, put 3D model into affine transform, and take the distance from the center of gravity to the vertex of 3D object in order to generate a one-dimensional discrete signal; then make this signal into wavelet transform to change its frequency coefficients and embed watermark, finally generate 3D motion model with watermarking. In fixed affine space, achieve the robustness in translation, revolving and proportion transforms. The results show that this approach has better performances not only in robustness, but also in watermark- invisibility.
Bettadapura, Radhakrishna; Rasheed, Muhibur; Vollrath, Antje; Bajaj, Chandrajit
2015-10-01
There continue to be increasing occurrences of both atomistic structure models in the PDB (possibly reconstructed from X-ray diffraction or NMR data), and 3D reconstructed cryo-electron microscopy (3D EM) maps (albeit at coarser resolution) of the same or homologous molecule or molecular assembly, deposited in the EMDB. To obtain the best possible structural model of the molecule at the best achievable resolution, and without any missing gaps, one typically aligns (match and fits) the atomistic structure model with the 3D EM map. We discuss a new algorithm and generalized framework, named PF(2) fit (Polar Fast Fourier Fitting) for the best possible structural alignment of atomistic structures with 3D EM. While PF(2) fit enables only a rigid, six dimensional (6D) alignment method, it augments prior work on 6D X-ray structure and 3D EM alignment in multiple ways: Scoring. PF(2) fit includes a new scoring scheme that, in addition to rewarding overlaps between the volumes occupied by the atomistic structure and 3D EM map, rewards overlaps between the volumes complementary to them. We quantitatively demonstrate how this new complementary scoring scheme improves upon existing approaches. PF(2) fit also includes two scoring functions, the non-uniform exterior penalty and the skeleton-secondary structure score, and implements the scattering potential score as an alternative to traditional Gaussian blurring. Search. PF(2) fit utilizes a fast polar Fourier search scheme, whose main advantage is the ability to search over uniformly and adaptively sampled subsets of the space of rigid-body motions. PF(2) fit also implements a new reranking search and scoring methodology that considerably improves alignment metrics in results obtained from the initial search. PMID:26469938
Bettadapura, Radhakrishna; Rasheed, Muhibur; Vollrath, Antje; Bajaj, Chandrajit
2015-01-01
There continue to be increasing occurrences of both atomistic structure models in the PDB (possibly reconstructed from X-ray diffraction or NMR data), and 3D reconstructed cryo-electron microscopy (3D EM) maps (albeit at coarser resolution) of the same or homologous molecule or molecular assembly, deposited in the EMDB. To obtain the best possible structural model of the molecule at the best achievable resolution, and without any missing gaps, one typically aligns (match and fits) the atomistic structure model with the 3D EM map. We discuss a new algorithm and generalized framework, named PF2 fit (Polar Fast Fourier Fitting) for the best possible structural alignment of atomistic structures with 3D EM. While PF2 fit enables only a rigid, six dimensional (6D) alignment method, it augments prior work on 6D X-ray structure and 3D EM alignment in multiple ways: Scoring. PF2 fit includes a new scoring scheme that, in addition to rewarding overlaps between the volumes occupied by the atomistic structure and 3D EM map, rewards overlaps between the volumes complementary to them. We quantitatively demonstrate how this new complementary scoring scheme improves upon existing approaches. PF2 fit also includes two scoring functions, the non-uniform exterior penalty and the skeleton-secondary structure score, and implements the scattering potential score as an alternative to traditional Gaussian blurring. Search. PF2 fit utilizes a fast polar Fourier search scheme, whose main advantage is the ability to search over uniformly and adaptively sampled subsets of the space of rigid-body motions. PF2 fit also implements a new reranking search and scoring methodology that considerably improves alignment metrics in results obtained from the initial search. PMID:26469938
3D segmentation of prostate ultrasound images using wavelet transform
NASA Astrophysics Data System (ADS)
Akbari, Hamed; Yang, Xiaofeng; Halig, Luma V.; Fei, Baowei
2011-03-01
The current definitive diagnosis of prostate cancer is transrectal ultrasound (TRUS) guided biopsy. However, the current procedure is limited by using 2D biopsy tools to target 3D biopsy locations. This paper presents a new method for automatic segmentation of the prostate in three-dimensional transrectal ultrasound images, by extracting texture features and by statistically matching geometrical shape of the prostate. A set of Wavelet-based support vector machines (WSVMs) are located and trained at different regions of the prostate surface. The WSVMs capture texture priors of ultrasound images for classification of the prostate and non-prostate tissues in different zones around the prostate boundary. In the segmentation procedure, these W-SVMs are trained in three sagittal, coronal, and transverse planes. The pre-trained W-SVMs are employed to tentatively label each voxel around the surface of the model as a prostate or non-prostate voxel by the texture matching. The labeled voxels in three planes after post-processing is overlaid on a prostate probability model. The probability prostate model is created using 10 segmented prostate data. Consequently, each voxel has four labels: sagittal, coronal, and transverse planes and one probability label. By defining a weight function for each labeling in each region, each voxel is labeled as a prostate or non-prostate voxel. Experimental results by using real patient data show the good performance of the proposed model in segmenting the prostate from ultrasound images.
SAR-based vibrometry using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Campbell, Justin B.; Wang, Qi; Ade-Bello, Jelili; Caudana, Humberto; Trujillo, Nicole B.; Bhatta, Ishwor; Dunkel, Ralf; Atwood, Thomas; Doerry, Armin; Gerstle, Walter H.; Santhanam, Balu; Hayat, Majeed M.
2015-05-01
A fundamental assumption when applying Synthetic Aperture Radar (SAR) to a ground scene is that all targets are motionless. If a target is not stationary, but instead vibrating in the scene, it will introduce a non-stationary phase modulation, termed the micro-Doppler effect, into the returned SAR signals. Previously, the authors proposed a pseudosubspace method, a modification to the Discrete Fractional Fourier Transform (DFRFT), which demonstrated success for estimating the instantaneous accelerations of vibrating objects. However, this method may not yield reliable results when clutter in the SAR image is strong. Simulations and experimental results have shown that the DFRFT method can yield reliable results when the signal-to-clutter ratio (SCR) > 8 dB. Here, we provide the capability to determine a target's frequency and amplitude in a low SCR environment by presenting two methods that can perform vibration estimations when SCR < 3 dB. The first method is a variation and continuation of the subspace approach proposed previously in conjunction with the DFRFT. In the second method, we employ the dual-beam SAR collection architecture combined with the extended Kalman filter (EKF) to extract information from the returned SAR signals about the vibrating target. We also show the potential for extending this SAR-based capability to remotely detect and classify objects housed inside buildings or other cover based on knowing the location of vibrations as well as the vibration histories of the vibrating structures that house the vibrating objects.
Fourier 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.
Transforming 2d Cadastral Data Into a Dynamic Smart 3d Model
NASA Astrophysics Data System (ADS)
Tsiliakou, E.; Labropoulos, T.; Dimopoulou, E.
2013-08-01
3D property registration has become an imperative need in order to optimally reflect all complex cases of the multilayer reality of property rights and restrictions, revealing their vertical component. This paper refers to the potentials and multiple applications of 3D cadastral systems and explores the current state-of-the art, especially the available software with which 3D visualization can be achieved. Within this context, the Hellenic Cadastre's current state is investigated, in particular its data modeling frame. Presenting the methodologies and specifications addressing the registration of 3D properties, the operating cadastral system's shortcomings and merits are pointed out. Nonetheless, current technological advances as well as the availability of sophisticated software packages (proprietary or open source) call for 3D modeling. In order to register and visualize the complex reality in 3D, Esri's CityEngine modeling software has been used, which is specialized in the generation of 3D urban environments, transforming 2D GIS Data into Smart 3D City Models. The application of the 3D model concerns the Campus of the National Technical University of Athens, in which a complex ownership status is established along with approved special zoning regulations. The 3D model was built using different parameters based on input data, derived from cadastral and urban planning datasets, as well as legal documents and architectural plans. The process resulted in a final 3D model, optimally describing the cadastral situation and built environment and proved to be a good practice example of 3D visualization.
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
3D Linear Transformations in the Form of Matrix and Vector
NASA Astrophysics Data System (ADS)
Zhang, Hua
2008-11-01
In this article, results of four 3D linear transformations (translation, rotation, scale and shear) in the form of matrix and vector are simplified into a same 3D physical coordinates system. Comparing the simplified results of those four linear transformations, the results obtained from matrix form are exactly the same as what obtained from vector algebra in final expressions, although they are different from original expressions.
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.
In Vivo 3D Meibography of the Human Eyelid Using Real Time Imaging Fourier-Domain OCT
Hwang, Ho Sik; Shin, Jun Geun; Lee, Byeong Ha; Eom, Tae Joong; Joo, Choun-Ki
2013-01-01
Recently, we reported obtaining tomograms of meibomian glands from healthy volunteers using commercial anterior segment optical coherence tomography (AS-OCT), which is widely employed in clinics for examination of the anterior segment. However, we could not create 3D images of the meibomian glands, because the commercial OCT does not have a 3D reconstruction function. In this study we report the creation of 3D images of the meibomian glands by reconstructing the tomograms of these glands using high speed Fourier-Domain OCT (FD-OCT) developed in our laboratory. This research was jointly undertaken at the Department of Ophthalmology, Seoul St. Mary's Hospital (Seoul, Korea) and the Advanced Photonics Research Institute of Gwangju Institute of Science and Technology (Gwangju, Korea) with two healthy volunteers and seven patients with meibomian gland dysfunction. A real time imaging FD-OCT system based on a high-speed wavelength swept laser was developed that had a spectral bandwidth of 100 nm at the 1310 nm center wavelength. The axial resolution was 5 µm and the lateral resolution was 13 µm in air. Using this device, the meibomian glands of nine subjects were examined. A series of tomograms from the upper eyelid measuring 5 mm (from left to right, B-scan) × 2 mm (from upper part to lower part, C-scan) were collected. Three-D images of the meibomian glands were then reconstructed using 3D “data visualization, analysis, and modeling software”. Established infrared meibography was also performed for comparison. The 3D images of healthy subjects clearly showed the meibomian glands, which looked similar to bunches of grapes. These results were consistent with previous infrared meibography results. The meibomian glands were parallel to each other, and the saccular acini were clearly visible. Here we report the successful production of 3D images of human meibomian glands by reconstructing tomograms of these glands with high speed FD-OCT. PMID:23805297
Bi-planar 2D-to-3D registration in Fourier domain for stereoscopic x-ray motion tracking
NASA Astrophysics Data System (ADS)
Zosso, Dominique; Le Callennec, Benoît; Bach Cuadra, Meritxell; Aminian, Kamiar; Jolles, Brigitte M.; Thiran, Jean-Philippe
2008-03-01
In this paper we present a new method to track bone movements in stereoscopic X-ray image series of the knee joint. The method is based on two different X-ray image sets: a rotational series of acquisitions of the still subject knee that allows the tomographic reconstruction of the three-dimensional volume (model), and a stereoscopic image series of orthogonal projections as the subject performs movements. Tracking the movements of bones throughout the stereoscopic image series means to determine, for each frame, the best pose of every moving element (bone) previously identified in the 3D reconstructed model. The quality of a pose is reflected in the similarity between its theoretical projections and the actual radiographs. We use direct Fourier reconstruction to approximate the three-dimensional volume of the knee joint. Then, to avoid the expensive computation of digitally rendered radiographs (DRR) for pose recovery, we develop a corollary to the 3-dimensional central-slice theorem and reformulate the tracking problem in the Fourier domain. Under the hypothesis of parallel X-ray beams, the heavy 2D-to-3D registration of projections in the signal domain is replaced by efficient slice-to-volume registration in the Fourier domain. Focusing on rotational movements, the translation-relevant phase information can be discarded and we only consider scalar Fourier amplitudes. The core of our motion tracking algorithm can be implemented as a classical frame-wise slice-to-volume registration task. Results on both synthetic and real images confirm the validity of our approach.
Computing the Fast Fourier Transform on a vector computer
NASA Technical Reports Server (NTRS)
Korn, D. G.; Lambiotte, J. J., Jr.
1979-01-01
Two algorithms are presented for performing a Fast Fourier Transform on a vector computer and are compared on the Control Data Corporation STAR-100. The relative merits of the two algorithms are shown to depend upon whether only a few or many independent transforms are desired. A theorem is proved which shows that a set of independent transforms can be computed by performing a partial transformation on a single vector. The results of this theorem also apply to nonvector machines and have reduced the average time per transform by a factor of two on the CDC 6600 computer.
[Spatially modulated Fourier transform imaging spectrometer data compression research].
Huang, Min; Xiangli, Bin; Yuan, Yan; Shen, Zhong; Lu, Qun-bo; Wang, Zhong-hou; Liu, Xue-bin
2010-01-01
Fourier transform imaging spectrometer is a new technic, and has been developed very fast in recent ten years. When it is used in satellite, because of the limit by the data transmission, the authors need to compress the original data obtained by the Fourier transform imaging spectrometer, then, the data can be transmitted, and can be incepted on the earth and decompressed. Then the authors can do data process to get spectrum data which can be used by user. Data compression technic used in Fourier transform imaging spectrometer is a new technic, and few papers introduce it at home and abroad. In this paper the authors will give a data compression method, which has been used in EDIS, and achieved a good result. PMID:20302132
Fixed-point error analysis of Winograd Fourier transform algorithms
NASA Technical Reports Server (NTRS)
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
Parallel fast Fourier transforms for non power of two data
Semeraro, B.D.
1994-09-01
This report deals with parallel algorithms for computing discrete Fourier transforms of real sequences of length N not equal to a power of two. The method described is an extension of existing power of two transforms to sequences with N a product of small primes. In particular, this implementation requires N = 2{sup p}3{sup q}5{sup r}. The communication required is the same as for a transform of length N = 2{sup p}. The algorithm presented is intended for use in the solution of partial differential equations, or in any situation in which a large number of forward and backward transforms must be performed and in which the Fourier Coefficients need not be ordered. This implementation is a one dimensional FFT but the techniques are applicable to multidimensional transforms as well. The algorithm has been implemented on a 128 node Intel Ipsc/860.
Real-time 3D Fourier-domain optical coherence tomography guided microvascular anastomosis
NASA Astrophysics Data System (ADS)
Huang, Yong; Ibrahim, Zuhaib; Lee, W. P. A.; Brandacher, Gerald; Kang, Jin U.
2013-03-01
Vascular and microvascular anastomosis is considered to be the foundation of plastic and reconstructive surgery, hand surgery, transplant surgery, vascular surgery and cardiac surgery. In the last two decades innovative techniques, such as vascular coupling devices, thermo-reversible poloxamers and suture-less cuff have been introduced. Intra-operative surgical guidance using a surgical imaging modality that provides in-depth view and 3D imaging can improve outcome following both conventional and innovative anastomosis techniques. Optical coherence tomography (OCT) is a noninvasive high-resolution (micron level), high-speed, 3D imaging modality that has been adopted widely in biomedical and clinical applications. In this work we performed a proof-of-concept evaluation study of OCT as an assisted intraoperative and post-operative imaging modality for microvascular anastomosis of rodent femoral vessels. The OCT imaging modality provided lateral resolution of 12 μm and 3.0 μm axial resolution in air and 0.27 volume/s imaging speed, which could provide the surgeon with clearly visualized vessel lumen wall and suture needle position relative to the vessel during intraoperative imaging. Graphics processing unit (GPU) accelerated phase-resolved Doppler OCT (PRDOCT) imaging of the surgical site was performed as a post-operative evaluation of the anastomosed vessels and to visualize the blood flow and thrombus formation. This information could help surgeons improve surgical precision in this highly challenging anastomosis of rodent vessels with diameter less than 0.5 mm. Our imaging modality could not only detect accidental suture through the back wall of lumen but also promptly diagnose and predict thrombosis immediately after reperfusion. Hence, real-time OCT can assist in decision-making process intra-operatively and avoid post-operative complications.
Geostationary Imaging Fourier Transform Spectrometer (GIFTS): science applications
NASA Astrophysics Data System (ADS)
Smith, W. L.; Revercomb, H. E.; Zhou, D. K.; Bingham, G. E.; Feltz, W. F.; Huang, H. L.; Knuteson, R. O.; Larar, A. M.; Liu, X.; Reisse, R.; Tobin, D. C.
2006-12-01
A revolutionary satellite weather forecasting instrument, called the "GIFTS" which stands for the "Geostationary Imaging Fourier Transform Spectrometer", was recently completed and successfully tested in a space chamber at the Utah State University's Space Dynamics Laboratory. The GIFTS was originally proposed by the NASA Langley Research Center, the University of Wisconsin, and the Utah State University and selected for flight demonstration as NASA's New Millennium Program (NMP) Earth Observing-3 (EO-3) mission, which was unfortunately cancelled in 2004. GIFTS is like a digital 3-d movie camera that, when mounted on a geostationary satellite, would provide from space a revolutionary four-dimensional view of the Earth's atmosphere. GIFTS will measure the distribution, change, and movement of atmospheric moisture, temperature, and certain pollutant gases, such as carbon monoxide and ozone. The observation of the convergence of invisible water vapor, and the change of atmospheric temperature, provides meteorologists with the observations needed to predict where, and when, severe thunderstorms, and possibly tornados, would occur, before they are visible on radar or in satellite cloud imagery. The ability of GIFTS to observe the motion of moisture and clouds at different altitudes enables atmospheric winds to be observed over vast, and otherwise data sparse, oceanic regions of the globe. These wind observations would provide the means to greatly improve the forecast of where tropical storms and hurricanes will move and where and when they will come ashore (i.e., their landfall position and time). GIFTS, if flown into geostationary orbit, would provide about 80,000 vertical profiles per minute, each one like a low vertical resolution (1-2km) weather balloon sounding, but with a spacing of 4 km. GIFTS is a revolutionary atmospheric sensing tool. A glimpse of the science measurement capabilities of GIFTS is provided through airborne measurements with the NPOESS Airborne
Fractional Fourier transform in temporal ghost imaging with classical light
Setaelae, Tero; Shirai, Tomohiro; Friberg, Ari T.
2010-10-15
We investigate temporal, second-order classical ghost imaging with long, incoherent, scalar plane-wave pulses. We prove that in rather general conditions, the intensity correlation function at the output of the setup is given by the fractional Fourier transform of the temporal object. In special cases, the correlation function is shown to reduce to the ordinary Fourier transform and the temporal image of the object. Effects influencing the visibility and the resolution are considered. This work extends certain known results on spatial ghost imaging into the time domain and could find applications in temporal tomography of pulses.
Modulated Fourier Transform Raman Fiber-Optic Spectroscopy
NASA Technical Reports Server (NTRS)
Jensen, Brian J. (Inventor); Cooper, John B. (Inventor); Wise, Kent L. (Inventor)
2000-01-01
A modification to a commercial Fourier Transform (FT) Raman spectrometer is presented for the elimination of thermal backgrounds in the FT Raman spectra. The modification involves the use of a mechanical optical chopper to modulate the continuous wave laser, remote collection of the signal via fiber optics, and connection of a dual-phase digital-signal-processor (DSP) lock-in amplifier between the detector and the spectrometer's collection electronics to demodulate and filter the optical signals. The resulting Modulated Fourier Transform Raman Fiber-Optic Spectrometer is capable of completely eliminating thermal backgrounds at temperatures exceeding 300 C.
Application of Fourier transform spectroscopy to air pollution problems
NASA Astrophysics Data System (ADS)
Shaw, J. H.; Calvert, J. G.
1980-11-01
The nature of information that can be retrieved from spectra obtained with Fourier transform spectroscopy is discussed. Nonlinear, least squares analysis of spectra is capable of retrieving information that is beyond the reach of conventional methods and has improved precision and accuracy. Fourier transform infrared spectroscopy was used to study quantitatively the kinetics and mechanisms of several chemical reactions that are of interest to atmospheric chemists and are important in the development of air pollution control strategies. The systems studied include the metastable, reactive, gaseous species, peroxynitric acid, hypochlorous acid, and dimethylnitrosamine.
Fourier transform profilometry for 360-deg shape using TDI camera
NASA Astrophysics Data System (ADS)
Su, Xianyu; Sajan, M. R.; Asundi, Anand K.
1997-03-01
This paper demonstrates a Fourier transform profilometry for 360 degree shape using TDI camera. Single stripe structured light can be recorded sequentially on one image when the camera is in TDI mode. An extended and deformed grating could be recorded in high speed and high resolution. The deformed fringe pattern is regarded as a fringe pattern in the Telecentric Fourier Transform Profilometry (TFTP), of which a wrapped phase is obtained directly. The unwrapped phase of TFTP gives the extended 360 degree profile without high frequency noise. Theoretical and experimental results are presented.
Extending Fourier transformations to Hamilton's quaternions and Clifford's geometric algebras
NASA Astrophysics Data System (ADS)
Hitzer, Eckhard
2013-10-01
We show how Fourier transformations can be extended to Hamilton's algebra of quaternions. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Hamilton's algebra of quaternions is only one example of the larger class of Clifford's geometric algebras, complete algebras encoding a vector space and all its subspace elements. We introduce how Fourier transformations are extended to Clifford algebras and applied in electromagnetism, and in the processing of images, color images, vector field and climate data.
Fourier-transform and global contrast interferometer alignment methods
Goldberg, Kenneth A.
2001-01-01
Interferometric methods are presented to facilitate alignment of image-plane components within an interferometer and for the magnified viewing of interferometer masks in situ. Fourier-transforms are performed on intensity patterns that are detected with the interferometer and are used to calculate pseudo-images of the electric field in the image plane of the test optic where the critical alignment of various components is being performed. Fine alignment is aided by the introduction and optimization of a global contrast parameter that is easily calculated from the Fourier-transform.
Double image encryption based on iterative fractional Fourier transform
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Liu, Shutian
2007-07-01
We present an image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders. From the encrypted image we can get two original images independently by fractional Fourier transforms with two different fractional orders. This algorithm can be independent of additional random phases as the encryption/decryption keys. Numerical results are given to analyze the capability of this proposed method. A possible extension to multi-image encryption with a fractional order multiplexing scheme has also been given.
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.
NASA Astrophysics Data System (ADS)
Lanusse, F.; Rassat, A.; Starck, J.-L.
2015-06-01
Context. Upcoming spectroscopic galaxy surveys are extremely promising to help in addressing the major challenges of cosmology, in particular in understanding the nature of the dark universe. The strength of these surveys, naturally described in spherical geometry, comes from their unprecedented depth and width, but an optimal extraction of their three-dimensional information is of utmost importance to best constrain the properties of the dark universe. Aims: Although there is theoretical motivation and novel tools to explore these surveys using the 3D spherical Fourier-Bessel (SFB) power spectrum of galaxy number counts Cℓ(k,k'), most survey optimisations and forecasts are based on the tomographic spherical harmonics power spectrum C(ij)_ℓ. The goal of this paper is to perform a new investigation of the information that can be extracted from these two analyses in the context of planned stage IV wide-field galaxy surveys. Methods: We compared tomographic and 3D SFB techniques by comparing the forecast cosmological parameter constraints obtained from a Fisher analysis. The comparison was made possible by careful and coherent treatment of non-linear scales in the two analyses, which makes this study the first to compare 3D SFB and tomographic constraints on an equal footing. Nuisance parameters related to a scale- and redshift-dependent galaxy bias were also included in the computation of the 3D SFB and tomographic power spectra for the first time. Results: Tomographic and 3D SFB methods can recover similar constraints in the absence of systematics. This requires choosing an optimal number of redshift bins for the tomographic analysis, which we computed to be N = 26 for zmed ≃ 0.4, N = 30 for zmed ≃ 1.0, and N = 42 for zmed ≃ 1.7. When marginalising over nuisance parameters related to the galaxy bias, the forecast 3D SFB constraints are less affected by this source of systematics than the tomographic constraints. In addition, the rate of increase of the
Path Integrals, Fourier Transforms, and Feynman's Operational Calculus
Ahn, Byung Moo; Johnson, G. W.
1998-03-15
The disentangling process is the key to Feynman's operational calculus for noncommuting operators. The main result of his heuristic calculations deals with disentangling an exponential factor. We use the Wiener and Feynman integrals to make this disentangling (or time-ordering) mathematically rigorous in the case where the analytic functions from earlier work are replaced by Fourier transforms of complex-valued measures.
Fourier transform spectroscopy of cotton and cotton trash
Technology Transfer Automated Retrieval System (TEKTRAN)
Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...
APPLICATION OF FOURIER TRANSFORM SPECTROSCOPY TO AIR POLLUTION PROBLEMS
The nature of information that can be retrieved from spectra obtained with Fourier transform spectroscopy is discussed. Nonlinear, least-squares analysis of spectra is capable of retrieving information that is beyond the reach of conventional methods and has improved precision an...
Theoretical study of Fourier-transform acousto-optic imaging.
Barjean, Kinia; Ramaz, François; Tualle, Jean-Michel
2016-05-01
We propose a full theoretical study of Fourier-transform acousto-optic imaging, which we recently introduced and experimentally assessed in [Opt. Lett.40, 705-708 (2015)OPLEDP0146-959210.1364/OL.40.000705] as an alternative to achieve axial resolution in acousto-optic imaging with a higher signal-to-noise ratio. PMID:27140883
Andreeva, A; Burova, M; Burov, J
2007-06-01
A metal object is computer visualized by registration of the amplitudes of the transmitted through the object short acoustic pulses. The pulses are separated by time, because of the presence of holes and internal compact components in the longitudinal section (structure along the propagation direction of acoustic wave). The acoustic field transmitted through the object is composited from a field presenting Fourier transformation of the hole shape and field, transmitted through the metal components in the longitudinal section of the object. A computer Fourier transformation of the digital data of the amplitude fields transmitted through the object components is performed instead of converging lens. The Fourier series of the object obtained as digital data after the transformation is multiplied with a term, describing the angle distribution of the field on spatial frequencies. The reconstruction of the image of the metal components is performed by reverse transformation, i.e. summing up in all spatial frequencies. 3D visualization of the transmitted through the hole acoustic field determines the hole geometry (circular, square, rectangular). It is shown that at the transmission of a short acoustic pulse through the components with different thicknesses and holes, presenting Fourier and non-Fourier transformation can be registered separately in contrast to the optics. PMID:17395232
Discrete fourier transform (DFT) analysis for applications using iterative transform methods
NASA Technical Reports Server (NTRS)
Dean, Bruce H. (Inventor)
2012-01-01
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
A prescription of Winograd's discrete Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Zohar, S.
1979-01-01
A detailed and complete description of Winograd's discrete Fourier transform algorithm (DFT) is presented omitting all proofs and derivations. The algorithm begins with the transfer of data from the input vector array to the working array where the actual transformation takes place, otherwise known as input scrambling and output unscrambling. The third array holds constraints required in the transformation stage that are evaluated in the precomputation stage. The algorithm is made up of several FORTRAN subroutines which are not to be confused with practical software algorithmic implementation since they are designed for clarity and not for speed.
Transfer Functions Via Laplace- And Fourier-Borel Transforms
NASA Technical Reports Server (NTRS)
Can, Sumer; Unal, Aynur
1991-01-01
Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.
ERIC Educational Resources Information Center
Grimm, C. A.
This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…
A Student's Guide to Fourier Transforms - 2nd Edition
NASA Astrophysics Data System (ADS)
James, J. F.
2002-09-01
Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science. Expanded to include more emphasis on applications An established successful textbook for undergraduate and graduate students Includes worked examples and copious diagrams throughout
A VLSI architecture for simplified arithmetic Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.
1992-01-01
The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.
Novel fringe scanning/Fourier transform method of synthetic imaging
Crawford, T.M.; Albano, R.K.
1993-08-01
We have developed a one-dimensional theory and a computer model for synthetically imaging scenes using a novel fringe scanning/Fourier transform technique. Our method probes a scene using two interfering beams of slightly different frequency. These beams form a moving fringe pattern which scans the scene and resonates with any spatial frequency components having the same spatial frequency as the scanning fringe pattern. A simple, non-imaging detector above the scene observes any scattered radiation from the scene falling onto it. If a resonance occurs between the scanning fringe pattern and the scene, then the scattered radiation will be modulated at the difference frequency between the two probing beams. By changing the spatial period of the fringe pattern and then measuring the amplitude and phase of the modulated radiation that is scattered from the scene, the Fourier amplitudes and phases of the different spatial frequency components making up the scene can be measured. A synthetic image of the scene being probed can be generated from this Fourier amplitude and phase data by taking the inverse Fourier transform of this information. This technique could be used to image objects using light, ultrasonic, or other electromagnetic or acoustic waves.
Fourier transform digital holographic adaptive optics imaging system
Liu, Changgeng; Yu, Xiao; Kim, Myung K.
2013-01-01
A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects. PMID:23262541
Optimal color image restoration: Wiener filter and quaternion Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, we consider the model of quaternion signal degradation when the signal is convoluted and an additive noise is added. The classical model of such a model leads to the solution of the optimal Wiener filter, where the optimality with respect to the mean square error. The characteristic of this filter can be found in the frequency domain by using the Fourier transform. For quaternion signals, the inverse problem is complicated by the fact that the quaternion arithmetic is not commutative. The quaternion Fourier transform does not map the convolution to the operation of multiplication. In this paper, we analyze the linear model of the signal and image degradation with an additive independent noise and the optimal filtration of the signal and images in the frequency domain and in the quaternion space.
Fourier transform spectrometer based on Fabry-Perot interferometer.
Al-Saeed, Tarek A; Khalil, Diaa A
2016-07-10
We analyze the Fourier transform spectrometer based on a symmetric/asymmetric Fabry-Perot interferometer. In this spectrometer, the interferogram is obtained by recording the intensity as a function of the interferometer length. Then, we recover the spectrum by applying the discrete Fourier transform (DFT) directly on the interferogram. This technique results in spectral harmonic overlap and fictitious wavenumber components outside the original spectral range. For this purpose, in this work, we propose a second method to recover the spectrum. This method is based on expanding the DFT of the interferogram and the spectrum by a Haar or box function. By this second method, we recovered the spectrum and got rid of the fictitious spectral components and spectral harmonic overlap. PMID:27409306
Development of a multi-Fourier-transform interferometer: fundamentals.
Ohta, Izumi S; Hattori, Makoto; Matsuo, Hiroshi
2006-04-20
We describe the development of an instrument that uses a Martin-Puplett-type Fourier-transform spectrometer to apply an aperture synthesis technique to millimeter and submillimeter waves. We call this instrument a multi-Fourier-transform interferometer (MuFT). The MuFT performs wideband imaging, spectroscopy, and polarimetry, at millimeter and submillimeter wavelengths. We describe the fundamentals of the MuFT and give an example of one potential implementation. A full description of the observables with a MuFT is provided. A physical explanation of the observability of complex visibility by the MuFT is given. Fundamental restrictions on observations with the MuFT, e.g., limits on spectral and spatial resolution and on fields of view, are discussed. The advantages of the MuFT are summarized. PMID:16633405
Implementing quantum Fourier transform with integrated photonic devices
NASA Astrophysics Data System (ADS)
Tabia, Gelo Noel
2014-03-01
Many quantum algorithms that exhibit exponential speedup over their classical counterparts employ the quantum Fourier transform, which is used to solve interesting problems such as prime factorization. Meanwhile, nonclassical interference of single photons achieved on integrated platforms holds the promise of achieving large-scale quantum computation with multiport devices. An optical multiport device can be built to realize any quantum circuit as a sequence of unitary operations performed by beam splitters and phase shifters on path-encoded qudits. In this talk, I will present a recursive scheme for implementing quantum Fourier transform with a multimode interference photonic integrated circuit. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Spectral measurements of exhaust gases using a Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Schruefer, Elmar; Lindermeir, Erwin; Palme, Frank; Wuelbern, K.
1993-09-01
In recent years environmental issues have become increasingly important. Especially the impact of gaseous emissions on the atmosphere is of great interest. As a consequence a group of several coworkers was established at the Institute for Electrical Measurement of the Technical University of Munich, Germany) with the task to develop and investigate spectroscopic methods and instruments for the analysis of the chemical compsition of exhaust gases. This article describes the advantages of the application of Fourier transform spectroscopy against conventional gas analysis devices. Moreover results of measurements of the exhaust of a smokestack of a coal fired power plant and of an aircraft engine are presented. The last section deals with the development of a Fourier transform spectrometer which is not equipped with any moving parts. This design was made especially for applications in harsh environments.
Fourier spectroscopy with a one-million-point transformation
NASA Technical Reports Server (NTRS)
Connes, J.; Delouis, H.; Connes, P.; Guelachvili, G.; Maillard, J.; Michel, G.
1972-01-01
A new type of interferometer for use in Fourier spectroscopy has been devised at the Aime Cotton Laboratory of the National Center for Scientific Research (CNRS), Orsay, France. With this interferometer and newly developed computational techniques, interferograms comprising as many as one million samples can now be transformed. The techniques are described, and examples of spectra of thorium and holmium, derived from one million-point interferograms, are presented.
Visible Imaging Fourier Transform Spectrometer: Design and Calibration
Wishnow, E H; Wurtz, R; Blais-Ouellette, S; Cook, K H; Carr, D; Lewis, I; Grandmont, F; Stubbs, C W
2002-09-19
We present details of the design, operation and calibration of an astronomical visible-band imaging Fourier transform spectrometer (IFTS). This type of instrument produces a spectrum for every pixel in the field of view where the spectral resolution is flexible. The instrument is a dual-input/dual-output Michelson interferometer coupled to the 3.5 meter telescope at the Apache Point Observatory. Imaging performance and interferograms and spectra from calibration sources and standard stars are discussed.
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.
Apparatus and methods for continuous beam fourier transform mass spectrometry
McLuckey, Scott A.; Goeringer, Douglas E.
2002-01-01
A continuous beam Fourier transform mass spectrometer in which a sample of ions to be analyzed is trapped in a trapping field, and the ions in the range of the mass-to-charge ratios to be analyzed are excited at their characteristic frequencies of motion by a continuous excitation signal. The excited ions in resonant motions generate real or image currents continuously which can be detected and processed to provide a mass spectrum.
Optimizing holographic data storage using a fractional Fourier transform.
Pégard, Nicolas C; Fleischer, Jason W
2011-07-01
We demonstrate a method to optimize the reconstruction of a hologram when the storage device has a limited dynamic range and a minimum grain size. The optimal solution at the recording plane occurs when the object wave has propagated an intermediate distance between the near and far fields. This distance corresponds to an optimal order and magnification of the fractional Fourier transform of the object. PMID:21725476
Fast Fourier transform analysis of rotor-bearing systems
NASA Technical Reports Server (NTRS)
Choy, K. C.; Gunter, E. J.; Allaire, P. E.
1978-01-01
Nonlinear transient analysis of rotor-bearing systems is becoming increasingly important in the analysis of modern-day rotating machinery to model such phenomena as oil film whirl. This paper develops an analysis technique incorporating modal analysis and fast Fourier transform techniques to analyze rotors with residual shaft bow and realistic nonlinear bearings. The technique is demonstrated on single-mass and three-mass rotor examples. Comparisons of the theoretical results with experimental data give excellent agreement.
Fourier transform Raman and IR spectra of snake skin
NASA Astrophysics Data System (ADS)
Barry, B. W.; Williams, A. C.; Edwards, H. G. M.
1993-06-01
The Fourier transform (FT) Raman and IR spectra of the shed dorsal skin of the snake Elaphe obsoleta (American black rat snake) are reported. Vibrational spectroscopic assignments are proposed for the first time. Although good quality Raman spectra were obtained from the hinge regions using an FT Raman microscope, the dorsal scale regions fluoresced even with 1064 nm IR excitation. This was ascribed to pigmentation markings on the scales.
Fast Fourier transformation results from gamma-ray burst profiles
NASA Technical Reports Server (NTRS)
Kouveliotou, Chryssa; Norris, Jay P.; Fishman, Gerald J.; Meegan, Charles A.; Wilson, Robert B.; Paciesas, W. S.
1992-01-01
Several gamma-ray bursts in the BATSE data have sufficiently long durations and complex temporal structures with pulses that appear to be spaced quasi-periodically. In order to test and quantify these periods we have applied fast Fourier transformations (FFT) to all these events. We have also performed cross spectral analyses of the FFT of the two extreme (high-low) energy bands in each case to determine the lead/lag of the pulses in different energies.
Construction of a Fourier-transform phase-modulation fluorometer
NASA Astrophysics Data System (ADS)
Shibata, Hironobu; Iwata, Tetsuo
2005-12-01
We have constructed a Fourier-transform phase-modulation fluorometer (FT-PMF) by which a fluorescence decay waveform can be obtained. In the FT-PMF, the modulation frequency of the excitation light source is swept continuously from a direct current (dc) to a high frequency f max with a time duration T. The resultant fluorescence signal waveform is Fourier-transformed to obtain its amplitude and phase spectra. The ratio of the amplitude spectrum and the difference of the phase spectrum over those of the reference spectra that are obtained from a non-fluorescent material are calculated, respectively, and the pair of both spectral data is inverse-Fourier-transformed again to obtain the fluorescence decay waveform. The light source used was an ultraviolet light emitting- diode (UV LED) whose typical operating condition was f max = 100 MHz and T = 10 μs. To demonstrate the performance of the FT-PMF, we carried out (1) measurement of a fluorescent decay waveform of YAG materials packed in a white LED, and (2) determination of fluorescence lifetime of 10 ppm quinine sulfate in 0.1N H IISO 4.
Construction of a Fourier-transform phase-modulation fluorometer
NASA Astrophysics Data System (ADS)
Iwata, Tetsuo; Shibata, Hironobu; Araki, Tsutomu
2005-11-01
We have constructed a Fourier-transform phase-modulation fluorometer (FT-PMF) by which a fluorescence decay waveform can be obtained. In the FT-PMF, the modulation frequency of the excitation light source is swept continuously from a direct current (dc) to a high frequency fmax with a time duration T. The resultant fluorescence signal waveform is Fourier transformed to obtain its amplitude and phase spectra. The ratio of the amplitude spectrum and the difference of the phase spectrum over those of the reference spectra from an excitation waveform are calculated, respectively, and the pair of both spectral data is inverse-Fourier-transformed again to obtain the fluorescence decay waveform. The light source used was an ultraviolet light-emitting diode (UV LED) whose operating condition was fmax = 50-120 MHz and T = 10 µs. To demonstrate the performance of the FT-PMF, we carried out (1) the measurement of a fluorescent decay waveform of YAG materials enclosed in a white LED and (2) determinations of fluorescence lifetimes of 10 ppm quinine sulfate in 0.1 N H2SO4 and 10 ppm rhodamine 6G in ethanol.
Wavelength-encoded tomography based on optical temporal Fourier transform
Zhang, Chi; Wong, Kenneth K. Y.
2014-09-01
We propose and demonstrate a technique called wavelength-encoded tomography (WET) for non-invasive optical cross-sectional imaging, particularly beneficial in biological system. The WET utilizes time-lens to perform the optical Fourier transform, and the time-to-wavelength conversion generates a wavelength-encoded image of optical scattering from internal microstructures, analogous to the interferometery-based imaging such as optical coherence tomography. Optical Fourier transform, in principle, comes with twice as good axial resolution over the electrical Fourier transform, and will greatly simplify the digital signal processing after the data acquisition. As a proof-of-principle demonstration, a 150 -μm (ideally 36 μm) resolution is achieved based on a 7.5-nm bandwidth swept-pump, using a conventional optical spectrum analyzer. This approach can potentially achieve up to 100-MHz or even higher frame rate with some proven ultrafast spectrum analyzer. We believe that this technique is innovative towards the next-generation ultrafast optical tomographic imaging application.
Wigner distribution moments in fractional Fourier transform systems
NASA Astrophysics Data System (ADS)
Bastiaans, Martin J.; Alieva, Tatiana
2002-09-01
It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. Since Wigner distribution moments are identical to derivatives of the ambiguity function at the origin, a similar relation holds for these derivatives. The general input-output relationship is then broken down into a number of rotation-type input-output relationships between certain combinations of moments. It is shown how the Wigner distribution moments (or ambiguity function derivatives) can be measured as intensity moments in the output planes of a set of appropriate fractional Fourier transform systems and thus be derived from the corresponding fractional power spectra. The minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments is derived. As an important by-product we get a number of moment combinations that are invariant under (anamorphic) fractional Fourier transformation.
Wigner distribution moments in fractional Fourier transform systems.
Bastiaans, Martin J; Alieva, Tatiana
2002-09-01
It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. Since Wigner distribution moments are identical to derivatives of the ambiguity function at the origin, a similar relation holds for these derivatives. The general input-output relationship is then broken down into a number of rotation-type input-output relationships between certain combinations of moments. It is shown how the Wigner distribution moments (or ambiguity function derivatives) can be measured as intensity moments in the output planes of a set of appropriate fractional Fourier transform systems and thus be derived from the corresponding fractional power spectra. The minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments is derived. As an important by-product we get a number of moment combinations that are invariant under (anamorphic) fractional Fourier transformation. PMID:12216870
Design of high-resolution Fourier transform lens
NASA Astrophysics Data System (ADS)
Zhang, Lei; Zhong, Xing; Jin, Guang
2007-12-01
With the development of optical information processing, high-resolution Fourier transform lens has often been used in holographic data storage system, spatial filtering and observation of particles. This paper studies the optical design method of high-resolution Fourier transform optical lenses system, which could be used in particles observation and holographic data storage system. According to Fourier transform relation between object and its frequency plane and the theory of geometrical optics, the system with working wavelength 532nm and resolution 3μm was designed based on ZEMAX. A multi-configuration method was adopted to optimize the system's lenses. In the optical system, a diaphragm was placed at the system's spectrum plane and the system demanded a low vacuum to cut down the influences of atmosphere and other particles. The result of finite element analysis indicated that the influences of vacuum pumping to optics spacing and mirror surface shape very minor, and the imaging quality not being affected. This system has many advantages, such as simple structure, good image quality and a high resolution of 3μm. So it has a wide application prospect and can be used both in holographic data storage system and particles observation.
Improved digital filters for evaluating Fourier and Hankel transform integrals
Anderson, Walter L.
1975-01-01
New algorithms are described for evaluating Fourier (cosine, sine) and Hankel (J0,J1) transform integrals by means of digital filters. The filters have been designed with extended lengths so that a variable convolution operation can be applied to a large class of integral transforms having the same system transfer function. A f' lagged-convolution method is also presented to significantly decrease the computation time when computing a series of like-transforms over a parameter set spaced the same as the filters. Accuracy of the new filters is comparable to Gaussian integration, provided moderate parameter ranges and well-behaved kernel functions are used. A collection of Fortran IV subprograms is included for both real and complex functions for each filter type. The algorithms have been successfully used in geophysical applications containing a wide variety of integral transforms
Lossy compression of hyperspectral images using shearlet transform and 3D SPECK
NASA Astrophysics Data System (ADS)
Karami, A.
2015-10-01
In this paper, a new lossy compression method for hyperspectral images (HSI) is introduced. HSI are considered as a 3D dataset with two dimensions in the spatial and one dimension in the spectral domain. In the proposed method, first 3D multidirectional anisotropic shearlet transform is applied to the HSI. Because, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and other geometrical features. Second, soft thresholding method is applied to the shearlet transform coefficients and finally the modified coefficients are encoded using Three Dimensional- Set Partitioned Embedded bloCK (3D SPECK). Our simulation results show that the proposed method, in comparison with well-known approaches such as 3D SPECK (using 3D wavelet) and combined PCA and JPEG2000 algorithms, provides a higher SNR (signal to noise ratio) for any given compression ratio (CR). It is noteworthy to mention that the superiority of proposed method is distinguishable as the value of CR grows. In addition, the effect of proposed method on the spectral unmixing analysis is also evaluated.
Reference Ultraviolet Wavelengths of Cr III Measured by Fourier Transform Spectrometry
NASA Technical Reports Server (NTRS)
Smillie, D.G.; Pickering, J.C.; Smith, P.L.
2008-01-01
We report Cr III ultraviolet (UV) transition wavelengths measured using a high-resolution Fourier transform spectrometer (FTS), for the first time, available for use as wavelength standards. The doubly ionized iron group element spectra dominate the observed opacity of hot B stars in the UV, and improved, accurate, wavelengths are required for the analysis of astronomical spectra. The spectrum was excited using a chromium-neon Penning discharge lamp and measured with the Imperial College vacuum ultraviolet FTS. 140 classified 3d(exp 3)4s- 3d(exp 3)4p Cr III transition lines, in the spectral range 38,000 to 49,000 cm(exp -1) (2632 to 2041 A), the strongest having wavelength uncertainties less than one part in 10(exp 7), are presented.
Two-Dimensional Fourier Transform Applied to Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
Santa Maria, Odilyn L.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary, but possibly harmonizable. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to show helicopter noise as harmonizable. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Two-Dimensional Fourier Transform Analysis of Helicopter Flyover Noise
NASA Technical Reports Server (NTRS)
SantaMaria, Odilyn L.; Farassat, F.; Morris, Philip J.
1999-01-01
A method to separate main rotor and tail rotor noise from a helicopter in flight is explored. Being the sum of two periodic signals of disproportionate, or incommensurate frequencies, helicopter noise is neither periodic nor stationary. The single Fourier transform divides signal energy into frequency bins of equal size. Incommensurate frequencies are therefore not adequately represented by any one chosen data block size. A two-dimensional Fourier analysis method is used to separate main rotor and tail rotor noise. The two-dimensional spectral analysis method is first applied to simulated signals. This initial analysis gives an idea of the characteristics of the two-dimensional autocorrelations and spectra. Data from a helicopter flight test is analyzed in two dimensions. The test aircraft are a Boeing MD902 Explorer (no tail rotor) and a Sikorsky S-76 (4-bladed tail rotor). The results show that the main rotor and tail rotor signals can indeed be separated in the two-dimensional Fourier transform spectrum. The separation occurs along the diagonals associated with the frequencies of interest. These diagonals are individual spectra containing only information related to one particular frequency.
Radon transform based automatic metal artefacts generation for 3D threat image projection
NASA Astrophysics Data System (ADS)
Megherbi, Najla; Breckon, Toby P.; Flitton, Greg T.; Mouton, Andre
2013-10-01
Threat Image Projection (TIP) plays an important role in aviation security. In order to evaluate human security screeners in determining threats, TIP systems project images of realistic threat items into the images of the passenger baggage being scanned. In this proof of concept paper, we propose a 3D TIP method which can be integrated within new 3D Computed Tomography (CT) screening systems. In order to make the threat items appear as if they were genuinely located in the scanned bag, appropriate CT metal artefacts are generated in the resulting TIP images according to the scan orientation, the passenger bag content and the material of the inserted threat items. This process is performed in the projection domain using a novel methodology based on the Radon Transform. The obtained results using challenging 3D CT baggage images are very promising in terms of plausibility and realism.
Animation Strategies for Smooth Transformations Between Discrete Lods of 3d Building Models
NASA Astrophysics Data System (ADS)
Kada, Martin; Wichmann, Andreas; Filippovska, Yevgeniya; Hermes, Tobias
2016-06-01
The cartographic 3D visualization of urban areas has experienced tremendous progress over the last years. An increasing number of applications operate interactively in real-time and thus require advanced techniques to improve the quality and time response of dynamic scenes. The main focus of this article concentrates on the discussion of strategies for smooth transformation between two discrete levels of detail (LOD) of 3D building models that are represented as restricted triangle meshes. Because the operation order determines the geometrical and topological properties of the transformation process as well as its visual perception by a human viewer, three different strategies are proposed and subsequently analyzed. The simplest one orders transformation operations by the length of the edges to be collapsed, while the other two strategies introduce a general transformation direction in the form of a moving plane. This plane either pushes the nodes that need to be removed, e.g. during the transformation of a detailed LOD model to a coarser one, towards the main building body, or triggers the edge collapse operations used as transformation paths for the cartographic generalization.
Partial differential equation transform — Variational formulation and Fourier analysis
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-01-01
Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The
The gridding method for image reconstruction by Fourier transformation
Schomberg, H.; Timmer, J.
1995-09-01
This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform {cflx f}. The method involves a window function {cflx w} and proceeds in three steps. First, the convolution {cflx g} = {cflx w} * {cflx f} is computed numerically on a Cartesian grid, using the available samples of {cflx f}. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating {cflx w} * {cflx f} is much less error prone than merely interpolating {cflx f}. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform.
Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.
2013-01-01
A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.
Multinozzle supersonic expansion for Fourier transform absorption spectroscopy
NASA Astrophysics Data System (ADS)
Georges, R.; Durry, G.; Bach, M.; Pétrisse, R.; Jost, R.; Herman, M.
1995-12-01
A new supersonic expansion made of several, up to 31 aligned nozzles, on top of a set of powerful Roots blowers has been built. Adequate optics allowed the recording of infrared absorption spectra in a cell with a Fourier transform interferometer, at high spectral resolution. The system was tested with N 2O, between 2000 and 4800 cm -1. The ν1 + 2 ν2 + ν3 combination band, estimated to be some 10000 times weaker than the ν2 fundamental, could be observed among all the other expected bands, thus setting a limit for the sensitivity of the system. The formation of large N 2O clusters was observed.
Birefringent Fourier transform imaging spectrometer with a rotating retroreflector.
Bai, Caixun; Li, Jianxin; Shen, Yan; Zhou, Jianqiang
2016-08-01
A birefringent Fourier transform imaging spectrometer with a new lateral shearing interferometer is presented. The interferometer includes a Wollaston prism and a retroreflector. It splits an incident light beam into two shearing parallel parts to obtain interference fringe patterns of an imaging target, which is well established as an aid in reducing problems associated with optical alignment and manufacturing precision. Continuously rotating the retroreflector enables the spectrometer to acquire two-dimensional spectral images without spatial scanning. This technology, with a high work efficiency and low complexity, is inherently compact and robust. The effectiveness of the proposed method is demonstrated by the experimental results. PMID:27472640
Fiber-optic thermometer using Fourier transform spectroscopy
NASA Technical Reports Server (NTRS)
Beheim, Glenn; Sotomayor, Jorge L.; Flatico, Joseph M.; Azar, Massood T.
1991-01-01
An integrated-optic Mach-Zender interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This configuration provides a high degree of immunity to the effects of changes in the source spectrum, and it readily permits the interrogation of a number of different sensors using a single spectrometer. In addition, this system has a potentially low cost because it uses optical communications hardware that may in the future be manufactured in large quantities.
Fourier transform spectrometry for fiber-optic sensor systems
NASA Technical Reports Server (NTRS)
Beheim, Glenn; Tuma, Margaret L.; Sotomayor, Jorge L.; Flatico, Joseph M.
1993-01-01
An integrated-optic Mach-Zehnder interferometer is used as a Fourier transform spectrometer to analyze the input and output spectra of a temperature-sensing thin-film etalon. This type of spectrometer has an advantage over conventional grating spectrometers because it is better suited for use with time-division-multiplexed sensor networks. In addition, this spectrometer has the potential for low cost due to its use of a component that could be manufactured in large quantities for the optical communications industry.
Double passing the Kitt Peak 1-m Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Jennings, D. E.; Hubbard, R.; Brault, J. W.
1985-01-01
Attention is given to a simple technique for performing the conversion of the Kitt Peak 1-m Fourier transform spectrometer's dual input/output optical configuration to a double pass configuration that improves spectral resolution by a factor of 2. The modification is made by placing a flat mirror in the output beam from each cat's eye, retroreflecting the beams back through the cat's eyes to the first beam splitter. A single detector is placed at the second input port, which then becomes the instrument's output.
A high-resolution Fourier-transform infrared spectrometer.
NASA Technical Reports Server (NTRS)
Johnson, H. L.; Forbes, F. F.; Thompson, R. I.; Steinmetz , D. L.; Harris, O.
1973-01-01
We have developed a Fourier-transform infrared spectrometer having a resolution of 0.5/cm over the range of wavelength from 1 to 5.5 microns. It has been used to observe the sun over this wavelength range from a Lear Jet flying at an altitude of 14 km, and to observe a number of stars from the ground, using the 229-cm telescope of the Steward Observatory and the 152-cm aluminum-mirror telescope at the Observatorio Astronomico Nacional in the Sierra de San Pedro Martir, Baja California, Mexico. The solar spectrum is given here, while the ground-based spectra are being published separately.
Beam profile for the Herschel-SPIRE Fourier transform spectrometer.
Makiwa, Gibion; Naylor, David A; Ferlet, Marc; Salji, Carl; Swinyard, Bruce; Polehampton, Edward; van der Wiel, Matthijs H D
2013-06-01
One of the instruments on board the Herschel Space Observatory is the Spectral and Photometric Imaging Receiver (SPIRE). SPIRE employs a Fourier transform spectrometer with feed-horn-coupled bolometers to provide imaging spectroscopy. To interpret the resultant spectral images requires knowledge of the wavelength-dependent beam, which in the case of SPIRE is complicated by the use of multimoded feed horns. In this paper we describe a series of observations and the analysis conducted to determine the wavelength dependence of the SPIRE spectrometer beam profile. PMID:23736346
SCUBA-2 Fourier transform spectrometer (FTS-2) commissioning results
NASA Astrophysics Data System (ADS)
Gom, Brad G.; Naylor, David A.; Friberg, Per; Bell, Graham S.; Bintley, Daniel; Abdelazim, Sherif; Sherwood, Matt
2014-07-01
We present the latest commissioning results and instrument performance for the SCUBA-2 imaging Fourier Transform Spectrometer (FTS-2) installed at the James Clerk Maxwell Telescope (JCMT). This ancillary instrument provides intermediate spectral resolution (R ~10 to 5000) across both the 450 and 850 μm atmospheric transmission windows with a FOV of ~5 arcmin2. The superconducting TES sensors and SQUID readout of SCUBA-2 present unique challenges for operation of an FTS; the sensitivity requirements demand high detector linearity and stability in addition to control of systematic atmospheric and optical spillover effects. We discuss the challenges encountered during commissioning and ongoing efforts to mitigate their effects.
Comparison of Fourier transform methods for calculating MTF
NASA Astrophysics Data System (ADS)
LaVeigne, Joseph D.; Burks, Stephen D.; Nehring, Brian
2008-04-01
Fourier transform methods common in infrared spectroscopy were applied to the problem of calculating the modulation transfer function (MTF) from a system's measured line spread function (LSF). Algorithms, including apodization and phase correction, are discussed in their application to remove unwanted noise from the higher frequency portion of the MTF curve. In general, these methods were found to significantly improve the calculated MTF. Apodization reduces the proportion of noise by discarding areas of the LSF where there is no appreciable signal. Phase correction significantly reduces the rectification of noise that occurs when the MTF is calculated by taking the power spectrum of the complex optical transfer function (OTF).
Wavelength-controlled variable-order optical fractional Fourier transform.
Hennelly, Bryan; Kelly, Damian; Sheridan, John T
2004-03-01
The relationship between optical fractional Fourier transforms (OFRTs) obtained at different wavelengths is derived by use of the ABCD matrix formalism. It is shown that varying the wavelength while retaining the same optical system can be used to control the order of the OFRT. The advantage of this method of varying OFRT order is that no variation in the characteristics of the bulk optics is required. A general experimental verification of the theory is provided by showing the exact equivalence of two OFRT systems of different order when they are replayed using the same input function at different wavelengths. PMID:15005181
Fourier-transform Raman spectroscopic study of human hair
NASA Astrophysics Data System (ADS)
Akhtar, W.; Edwards, H. G. M.; Farwell, D. W.; Nutbrown, M.
1997-07-01
Fourier-transform Raman microscopic spectra of normal, untreated and bleached hair fibres are presented. Vibrational assignments are made and differences are ascribed to the production of cysteic acid from cysteine. Changes in conformation associated with the disulphide bond in the keratotic component are noted from the ν(CSSC) vibrational modes at wave numbers near 500 cm -1. Raman spectra of hair root ends have also been investigated with a diminution in cysteine content being observed. Application of the technique to the biomedical investigation of healthy and diseased hair is proposed.
Dispersive Fourier transform spectroscopy with gases in the visible region
NASA Astrophysics Data System (ADS)
Kerl, K.; Häusler, H.
1984-05-01
The method of dispersive Fourier transform spectroscopy (DFTS) with gases in the visible wavenumber range is described in detail and compared with the method of scanning-wavelength interferometry (SWI). Measurements of the dispersion of the complex refractive index of gases can be performed successively in several minutes using the same apparatus and gas sample conditions for both methods. In the reported experiments with CH 4 a very simple mirror drive was used. Nevertheless, reasonable results are obtained for the dispersion of the real refractive index of CH 4 in the wavenumber range 16,000 ⩽ σ ⩽ 23,000 cm -1.
Particle field holography data reduction by Fourier transform analysis
NASA Technical Reports Server (NTRS)
Hess, Cecil F.; Trolinger, James D.
1987-01-01
The size distribution of a particle field hologram is obtained with a Fourier transformation of the Fraunhofer diffraction pattern of the reconstructed hologram. Off-axis absorption holograms of particle fields with known characteristics were obtained and analyzed with a commercially available instrument. The mean particle size of the reconstructed hologram was measured with an error of + or - 5 percent, while the distribution broadening was estimated within + or - 15 percent. Small sections of a pulsed laser hologram of a synthetic fuel spray were analyzed with this method thus yielding a spatially resolved size distribution. The method yields fast and accurate automated analysis of particle field holograms.
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
NASA Astrophysics Data System (ADS)
Klimyk, A.; Patera, J.
2007-09-01
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms involving the symmetric and antisymmetric multivariate sine and cosine functions.
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.
Triple image encryption scheme in fractional Fourier transform domains
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Dai, Jingmin; Sun, Xiaogang; Liu, Shutian
2009-02-01
We proposed a triple image encryption scheme by use of fractional Fourier transform. In this algorithm, an original image is encoded in amplitude part and other two images are encoded into phase information. The key of encryption algorithm is obtained from the difference between the third image and the output phase of transform. In general case, random phase encoding technology is not required in the proposed algorithm. Moreover, all information of images is preserved in theory when image are decrypted with correct key. The optical implementation of the algorithm is presented with an electro-optical hybrid structure. Numerical simulations have demonstrated the efficiency and the security of this algorithm. Based on this scheme a multiple image algorithm is expanded and designed.
A high-resolution Fourier Transform Spectrometer for planetary spectroscopy
NASA Technical Reports Server (NTRS)
Cruikshank, D. P.; Sinton, W. M.
1973-01-01
The employment of a high-resolution Fourier Transform Spectrometer (FTS) is described for planetary and other astronomical spectroscopy in conjunction with the 88-inch telescope at Mauna Kea Observatory. The FTS system is designed for a broad range of uses, including double-beam laboratory spectroscopy, infrared gas chromatography, and nuclear magnetic resonance spectroscopy. The data system is well-suited to astronomical applications because of its great speed in acquiring and transforming data, and because of the enormous storage capability of the magnetic tape unit supplied with the system. The basic instrument is outlined 2nd some of the initial results from the first attempted use on the Mauna Kea 88-inch telescope are reported.
Fast Fourier Transform Co-processor (FFTC), towards embedded GFLOPs
NASA Astrophysics Data System (ADS)
Kuehl, Christopher; Liebstueckel, Uwe; Tejerina, Isaac; Uemminghaus, Michael; Witte, Felix; Kolb, Michael; Suess, Martin; Weigand, Roland; Kopp, Nicholas
2012-10-01
Many signal processing applications and algorithms perform their operations on the data in the transform domain to gain efficiency. The Fourier Transform Co-Processor has been developed with the aim to offload General Purpose Processors from performing these transformations and therefore to boast the overall performance of a processing module. The IP of the commercial PowerFFT processor has been selected and adapted to meet the constraints of the space environment. In frame of the ESA activity "Fast Fourier Transform DSP Co-processor (FFTC)" (ESTEC/Contract No. 15314/07/NL/LvH/ma) the objectives were the following: • Production of prototypes of a space qualified version of the commercial PowerFFT chip called FFTC based on the PowerFFT IP. • The development of a stand-alone FFTC Accelerator Board (FTAB) based on the FFTC including the Controller FPGA and SpaceWire Interfaces to verify the FFTC function and performance. The FFTC chip performs its calculations with floating point precision. Stand alone it is capable computing FFTs of up to 1K complex samples in length in only 10μsec. This corresponds to an equivalent processing performance of 4.7 GFlops. In this mode the maximum sustained data throughput reaches 6.4Gbit/s. When connected to up to 4 EDAC protected SDRAM memory banks the FFTC can perform long FFTs with up to 1M complex samples in length or multidimensional FFT-based processing tasks. A Controller FPGA on the FTAB takes care of the SDRAM addressing. The instructions commanded via the Controller FPGA are used to set up the data flow and generate the memory addresses. The paper will give an overview on the project, including the results of the validation of the FFTC ASIC prototypes.
Ultrafast and versatile spectroscopy by temporal Fourier transform
Zhang, Chi; Wei, Xiaoming; Marhic, Michel E.; Wong, Kenneth K. Y.
2014-01-01
One of the most remarkable and useful properties of a spatially converging lens system is its inherent ability to perform the Fourier transform; the same applies for the time-lens system. At the back focal plane of the time-lens, the spectral information can be instantaneously obtained in the time axis. By implementing temporal Fourier transform for spectroscopy applications, this time-lens-based architecture can provide orders of magnitude improvement over the state-of-art spatial-dispersion-based spectroscopy in terms of the frame rate. On the other hand, in addition to the single-lens structure, the multi-lens structures (e.g. telescope or wide-angle scope) will provide very versatile operating conditions. Leveraging the merit of instantaneous response, as well as the flexible lens structure, here we present a 100-MHz frame rate spectroscopy system – the parametric spectro-temporal analyzer (PASTA), which achieves 17 times zoom in/out ratio for different observation ranges. PMID:24939667
Integrated optics in an electrically scanned imaging Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Breckinridge, James B. (Inventor); Ocallaghan, Fred G. (Inventor)
1982-01-01
An efficient, lightweight and stable, Fourier transform spectrometer was developed. The mechanical slide mechanism needed to create a path difference was eliminated by the use of retro-reflecting mirrors in a monolithic interferometer assembly in which the mirrors are not at 90 degrees to the propagation vector of the radiation, but rather at a small angle. The resulting plane wave fronts create a double-sided inteferogram of the source irradiance distribution which is detected by a charge-coupled device image sensor array. The position of each CCD pixel in the array is an indication of the path difference between the two retro-reflecting mirrors in the monolithic optical structure. The Fourier transform of the signals generated by the image sensor provide the spectral irradiance distribution of the source. For imaging, the interferometer assembly scans the source of irradiation by moving the entire instrument, such as would occur if it was fixedly mounted to a moving platform, i.e., a spacecraft. During scanning, the entrace slot to the monolithic optical structure sends different pixels to corresponding interferograms detected by adjacent columns of pixels of the image sensor.
Relationship between fractional calculus and fractional Fourier transform
NASA Astrophysics Data System (ADS)
Zhang, Yanshan; Zhang, Feng; Lu, Mingfeng
2015-09-01
The fractional calculus (FC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. The fractional Fourier transform (FRFT), which has been found having many applications in optics and other areas, is a generalization of the usual Fourier transform. The FC and the FRFT are two of the most interesting and useful fractional areas. In recent years, it appears many papers on the FC and FRFT, however, few of them discuss the connection of the two fractional areas. We study their relationship. The relational expression between them is deduced. The expectation of interdisciplinary cross fertilization is our motivation. For example, we can use the properties of the FC (non-locality, etc.) to solve the problem which is difficult to be solved by the FRFT in optical engineering; we can also through the physical meaning of the FRFT optical implementation to explain the physical meaning of the FC. The FC and FRFT approaches can be transposed each other in the two fractional areas. It makes that the success of the fractional methodology is unquestionable with a lot of applications, namely in nonlinear and complex system dynamics and image processing.
Imaging Fourier transform spectrometer (IFTS): parametric sensitivity analysis
NASA Astrophysics Data System (ADS)
Keller, Robert A.; Lomheim, Terrence S.
2005-06-01
Imaging Fourier transform spectrometers (IFTS) allow for very high spectral resolution hyperspectral imaging while using moderate size 2D focal plane arrays in a staring mode. This is not the case for slit scanning dispersive imaging spectrometers where spectral sampling is related to the focal plane pixel count along the spectral dimension of the 2D focal plane used in such an instrument. This can become a major issue in the longwave infrared (LWIR) where the operability and yield of highly sensitivity arrays (i.e.HgCdTe) of large dimension are generally poor. However using an IFTS introduces its own unique set of issues and tradeoffs. In this paper we develop simplified equations for describing the sensitivity of an IFTS, including the effects of data windowing. These equations provide useful insights into the optical, focal plane and operational design trade space that must be considered when examining IFTS concepts aimed at a specific sensitivity and spectral resolution application. The approach is illustrated by computing the LWIR noise-equivalent spectral radiance (NESR) corresponding to the NASA Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) concept assuming a proven and reasonable noise-equivalent irradiance (NEI) capability for the focal plane.
Versatile and Sensitive Dual Comb Fourier Transform Spectroscopy
NASA Astrophysics Data System (ADS)
Jacquey, M.; Jacquet, P.; Mandon, J.; Thon, R.; Guelachvili, G.; Hänsch, T. W.; Picqué, N.
2010-06-01
Fourier transform spectroscopy based on time-domain interferences between two slightly detuned frequency comb sources holds much promise for the real-time diagnostic of gaseous, liquid or solid-state samples. In one very recent example, cavity-enhanced absorption spectroscopy with two infrared frequency combs has demonstrated a dramatically enhanced sensitivity, compared to conventional Fourier spectroscopy, with intriguing implications for instantaneous trace gas analysis. It however remains challenging to match continuously the comb and cavity modes across a broad spectral bandwidth during the time of a measurement. An obvious alternative for reaching a long interaction path is a conventional multipass cell. Additionally, differential detection schemes may be devised to increase the dynamic range of the interferometric measurements, thus providing enhanced signal to noise ratio. Experimental demonstrations will be given in the 1.5 μm region with a dual comb set-up based on two Er-doped fiber femtosecond lasers. The versatility and performances of these solutions will be compared to the cavity-enhanced dual comb technique and other state-of-the-art alternatives. P. Jacquet, J. Mandon, B. Bernhardt, R. Holzwarth, G. Guelachvili, T. W. Hänsch, N. Picqué, Frequency Comb Fourier Transform Spectroscopy with kHz Optical Resolution, The Optical Society of America, Washington, DC 2009, paper FMB2 (2009). B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T.W. Hänsch, N. Picqué, Cavity-enhanced dual-comb spectroscopy, Nature Photonics 4, 55-57 (2010),
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.
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
Multiresolution graph Fourier transform for compression of piecewise smooth images.
Hu, Wei; Cheung, Gene; Ortega, Antonio; Au, Oscar C
2015-01-01
Piecewise smooth (PWS) images (e.g., depth maps or animation images) contain unique signal characteristics such as sharp object boundaries and slowly varying interior surfaces. Leveraging on recent advances in graph signal processing, in this paper, we propose to compress the PWS images using suitable graph Fourier transforms (GFTs) to minimize the total signal representation cost of each pixel block, considering both the sparsity of the signal's transform coefficients and the compactness of transform description. Unlike fixed transforms, such as the discrete cosine transform, we can adapt GFT to a particular class of pixel blocks. In particular, we select one among a defined search space of GFTs to minimize total representation cost via our proposed algorithms, leveraging on graph optimization techniques, such as spectral clustering and minimum graph cuts. Furthermore, for practical implementation of GFT, we introduce two techniques to reduce computation complexity. First, at the encoder, we low-pass filter and downsample a high-resolution (HR) pixel block to obtain a low-resolution (LR) one, so that a LR-GFT can be employed. At the decoder, upsampling and interpolation are performed adaptively along HR boundaries coded using arithmetic edge coding, so that sharp object boundaries can be well preserved. Second, instead of computing GFT from a graph in real-time via eigen-decomposition, the most popular LR-GFTs are pre-computed and stored in a table for lookup during encoding and decoding. Using depth maps and computer-graphics images as examples of the PWS images, experimental results show that our proposed multiresolution-GFT scheme outperforms H.264 intra by 6.8 dB on average in peak signal-to-noise ratio at the same bit rate. PMID:25494508
A rheumatoid arthritis study by Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Carvalho, Carolina S.; Silva, Ana Carla A.; Santos, Tatiano J. P. S.; Martin, Airton A.; dos Santos Fernandes, Ana Célia; Andrade, Luís E.; Raniero, Leandro
2012-01-01
Rheumatoid arthritis is a systemic inflammatory disease of unknown causes and a new methods to identify it in early stages are needed. The main purpose of this work is the biochemical differentiation of sera between normal and RA patients, through the establishment of a statistical method that can be appropriately used for serological analysis. The human sera from 39 healthy donors and 39 rheumatics donors were collected and analyzed by Fourier Transform Infrared Spectroscopy. The results show significant spectral variations with p<0.05 in regions corresponding to protein, lipids and immunoglobulins. The technique of latex particles, coated with human IgG and monoclonal anti-CRP by indirect agglutination known as FR and CRP, was performed to confirm possible false-negative results within the groups, facilitating the statistical interpretation and validation of the technique.
Extreme-ultraviolet lensless Fourier-transform holography.
Lee, S H; Naulleau, P; Goldberg, K A; Cho, C H; Jeong, S; Bokor, J
2001-06-01
We demonstrate 100-nm-resolution holographic aerial image monitoring based on lensless Fourier-transform holography at extreme-UV (EUV) wavelengths, using synchrotron-based illumination. This method can be used to monitor the coherent imaging performance of EUV lithographic optical systems. The system has been implemented in the EUV phase-shifting point-diffraction interferometer recently developed at Lawrence Berkeley National Laboratory. Here we introduce the idea of the holographic aerial image-recording technique and present imaging performance characterization results for a 10x Schwarzschild objective, a prototype EUV lithographic optic. The results are compared with simulations, and good agreement is obtained. Various object patterns, including phase-shift-enhanced patterns, have been studied. Finally, the application of the holographic aerial image-recording technique to EUV multilayer mask-blank defect characterization is discussed. PMID:18357280
Discrimination of different Chrysanthemums with Fourier transform infrared spectroscopy
NASA Astrophysics Data System (ADS)
Liu, Hong-xia; Zhou, Qun; Sun, Su-qin; Bao, Hong-juan
2008-07-01
Use Fourier transform infrared spectroscopy (FT-IR) to analyze simultaneously the main chemical constituents in different solvent extracts of seven kinds of Chrysanthemum samples of different regions. The findings indicate that different Chrysanthemum samples have dissimilar fingerprint characters in FT-IR spectra. Such spectral technique can provide substance structural information of the complicated test samples. According to these spectral fingerprint features, we cannot only identify the main components of different extracts, but also distinguish the origins of the Chrysanthemum samples from different regions easily, which is a troublesome work by existing analytical methods. FT-IR, with the characters of speediness, good repeatability and easy operation, can be used as an effective analytical means to study the complicated system, in our research, the tradition Chinese medicines.
A Fourier transform spectrometer for site testing at Dome A
NASA Astrophysics Data System (ADS)
Li, Xin-Xing; Paine, Scott; Yao, Qi-Jun; Shi, Sheng-Cai; Matsuo, Hiroshi; Yang, Ji; Zhang, Qi-Zhou
2009-07-01
Observations in tera-hertz astronomy can only be done at a site with good atmospheric transmission at millimeter and submillimeter wavelengths. With extremely dry weather and calm atmosphere resulted by high altitude and cold temperature, Dome A (or Dome Argus), Antarctica, is possibly the best site on this earth for THz astronomy. To evaluate the site condition there, we are constructing a Fourier Transform Spectrometer (FTS) based on Martin-Puplett interferometer to measure the atmospheric transmission in the frequency range of 0.75~15THz. The whole FTS system is designed for unattended and outdoor (temperatures even below -70 degrees Celsius) operation. Its total power consumption is estimated to be approximately 200W. This contribution will give a brief overview of this FTS development.
Control Of Cryogenic Fourier Transform Spectrometer Scanning Mirrors
NASA Astrophysics Data System (ADS)
Tripathi, S. S.; Gowrinathan, S.
1981-12-01
The Perkin-Elmer Corporation has designed and built a cryogenically cooled Fourier transform spectrometer for spaceborne applications. In operation, the spectrometer requires mirrors moving at constant velocity in both forward and reverse directions. To maintain efficiency and accuracy, the time taken to reverse direction and the vibration induced due to this reversal must be kept within low limits. This paper deals with the control system design for maintaining a constant velocity during forward and reverse scans and for smooth direction reversals. The systems aspects of the problem are described, and time-domain techniques of modern control theory are applied for optimization of turn-around profile. The analysis leads to a suboptimal design easily implemented by using analog-type components. Test results of satisfactory performance are also included.
Calibration of the Geostationary Imaging Fourier Transform Spectrometer (GIFTS)
NASA Technical Reports Server (NTRS)
Best, F. A.; Revercomb, H. E.; Bingham, G. E.; Knuteson, R. O.; Tobin, D. C.; LaPorte, D. D.; Smith, W. L.
2001-01-01
The NASA New Millennium Program's Geostationary Imaging Fourier Transform Spectrometer (GIFTS) requires highly accurate radiometric and spectral calibration in order to carry out its mission to provide water vapor, wind, temperature, and trace gas profiling from geostationary orbit. A calibration concept has been developed for the GIFTS Phase A instrument design. The in-flight calibration is performed using views of two on-board blackbody sources along with cold space. A radiometric calibration uncertainty analysis has been developed and used to show that the expected performance for GIFTS exceeds its top level requirement to measure brightness temperature to better than 1 K. For the Phase A GIFTS design, the spectral calibration is established by the highly stable diode laser used as the reference for interferogram sampling, and verified with comparisons to atmospheric calculations.
Analysis of far-infrared emission Fourier transform spectra
NASA Technical Reports Server (NTRS)
Park, J. H.; Carli, B.
1986-01-01
An analysis method that uses the nonlinear least-squares fit technique has been developed for emission spectra obtained with a Fourier transform spectrometer. This method is used for the analysis of submillimeter-region atmospheric emission spectra obtained with a balloon-borne FT spectrometer that was carried out as a correlative measurement for the Limb IR Monitor of the Stratosphere (LIMS) satellite experiment. The retrieved mixing ratios of H2O and O3 in the stratosphere from four spectral intervals have standard deviations of about 10 percent, and the average values agree to within 10 percent of corresponding results from the LIMS satellite experiment which used a broadband emission radiometer in the IR region.
Optical design of the ATMOS Fourier transform spectrometer
NASA Technical Reports Server (NTRS)
Abel, I. R.; Reynolds, B. R.; Breckinridge, J. B.; Pritchard, J.
1979-01-01
The optical system design of the ATMOS Fourier transform spectrometer to be operated from Spacelab for the measurement of stratospheric trace molecules is described. The design contains features which can achieve the required fringe contrast of 80% and spectral resolution of 0.02/cm over a spectral range of 2-16 microns. In particular, the design is based on the following features which alleviate the usual requirements for alignment precision: (1) 'cat's eye' mirror configuration in the two arms of the interferometer for retroreflection stability, (2) tilt-compensated system of beamsplitter, compensator, and fold mirrors for wavefront directional stability, (3) paraboloidal 'cat's eye' primary mirror for wavefront stability against shear, (4) rotatable compensator for matching chromatic dispersion, and (5) wedged refractive components to avoid channel spectra due to the Fabry-Perot effect.
Experimental results from an airborne static Fourier transform imaging spectrometer.
Ferrec, Yann; Taboury, Jean; Sauer, Hervé; Chavel, Pierre; Fournet, Pierre; Coudrain, Christophe; Deschamps, Joël; Primot, Jérôme
2011-10-20
A high étendue static Fourier transform spectral imager has been developed for airborne use. This imaging spectrometer, based on a Michelson interferometer with rooftop mirrors, is compact and robust and benefits from a high collection efficiency. Experimental airborne images were acquired in the visible domain. The processing chain to convert raw images to hyperspectral data is described, and airborne spectral images are presented. These experimental results show that the spectral resolution is close to the one expected, but also that the signal to noise ratio is limited by various phenomena (jitter, elevation fluctuations, and one parasitic image). We discuss the origin of those limitations and suggest solutions to circumvent them. PMID:22015418
High throughput full Stokes Fourier transform imaging spectropolarimetry.
Meng, Xin; Li, Jianxin; Xu, Tingting; Liu, Defang; Zhu, Rihong
2013-12-30
A complete full Stokes imaging spectropolarimeter is proposed. Four separate polarized spectra are fed into the Sagnac Fourier transform spectrometer without slit using different angle combinations of the polarized elements. The four polarized spectra are separated without spatial aliasing. And the system has a good performance to resist the instrument noise due to its high light throughput. The mathematical model for the approach is derived and an optimization of the retardance is discussed. For acquiring the four spectra simultaneously, an improved robust polarization modulator using aperture division is outlined. Then the system is discussed in detail including the imaging principle and spectral resolution. Lastly, two proven experiments are carried out and the experimental results in visible light are outlined. PMID:24514802
Multifunctional metasurface lens for imaging and Fourier transform
NASA Astrophysics Data System (ADS)
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-06-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping.
Instrument concept of the imaging Fourier transform spectrometer GLORIA
NASA Astrophysics Data System (ADS)
Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.
2014-03-01
The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the Upper Troposphere/Lower Stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated in a gimbal. The assembly can be mounted in the belly pod of the German high altitude and long range research aircraft HALO and in instrument bays of the Russian M55 Geophysica. Measurements are made predominantly in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
Instrument concept of the imaging Fourier transform spectrometer GLORIA
NASA Astrophysics Data System (ADS)
Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.
2014-10-01
The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the upper troposphere/lower stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated into a gimbal. The assembly can be mounted in the belly pod of the German High Altitude and Long Range research aircraft (HALO) and in instrument bays of the Russian M55 Geophysica. Measurements are made in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, and the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition, the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
Fourier transform infrared phase shift cavity ring down spectrometer
NASA Astrophysics Data System (ADS)
Schundler, Elizabeth; Mansur, David J.; Vaillancourt, Robert; Benedict-Gill, Ryan; Newbry, Scott P.; Engel, James R.; Rentz Dupuis, Julia
2013-05-01
We report on our current status towards the development of a prototype Fourier transform infrared phase shift cavity ring down spectrometer (FTIR-PS-CRDS) system under a U.S. EPA SBIR contract. Our system uses the inherent wavelength-dependent modulation imposed by the FTIR on a broadband thermal source for the phase shift measurement. This spectrally-dependent phase shift is proportional to the spectrally-dependent ring down time, which is proportional to the losses of the cavity including those due to molecular absorption. Our approach is a broadband and spectral range enhancement to conventional CRDS which is typically done in the near IR at a single wavelength; at the same time our approach is a sensitivity enhancement to traditional FTIR owing to the long effective path of the resonant cavity. In this paper we present a summary of the theory including performance projections and the design details of the prototype FTIR-PS-CRDS system.
On the abstracted dataflow complexity of Fast Fourier Transforms
Boehm, A.P.W.; Hiromoto, R.E.; Kelly, K.A.; Ashley, J.M.
1992-05-01
In this paper we develop and analyze the simulated performance of codes for the Fast Fourier Transform written in If and targeted for execution on Motorola`s dataflow machine Monsoon. The FFT application is of interest because of its computational parallelism, its requirement for global communications, and its array element data dependences. We use the parallel profiling simulator Id World to study the dataflow performance of various implementations. Our approach is comparative. We study two approaches, a recursive and an iterative one, and in each version we examine the effect of a variety of implementations. We contend that only through such comparative evaluations can significant insight be gained in understanding the computational and structural details of functional algorithms.
Highly sensitive Fourier transform spectroscopy with LED sources
NASA Astrophysics Data System (ADS)
Serdyukov, V. I.; Sinitsa, L. N.; Vasil'chenko, S. S.
2013-08-01
It is shown that the use of high luminance LED emitters as a light source for Fourier transform spectrometers permits to enhance their threshold sensitivity in the visible range by orders of magnitude. Using a 2.5 W Edixeon EDEI-1LS3 emitter in the range of 11,350-11,700 cm-1 as a light source for the spectrometer with a 60-cm multipass cell during a 24-h measurement time, we have achieved a signal-to-noise ratio of 4.5 × 104 which corresponds to the minimal detectable absorption coefficient of 1.2 × 10-8 cm-1. Such enhanced sensitivity spectrometer has been used to measure the transition frequencies of CO2 vibrational bands 00051-00001 and 01151-01101 in the range of 11,400-11,500 cm-1.
Indirect Fourier transform in the context of statistical inference.
Muthig, Michael; Prévost, Sylvain; Orglmeister, Reinhold; Gradzielski, Michael
2016-09-01
Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments. PMID:27580204
Motion saliency detection using a temporal fourier transform
NASA Astrophysics Data System (ADS)
Chen, Zhe; Wang, Xin; Sun, Zhen; Wang, Zhijian
2016-06-01
Motion saliency detection aims at detecting the dynamic semantic regions in a video sequence. It is very important for many vision tasks. This paper proposes a new type of motion saliency detection method, Temporal Fourier Transform, for fast motion saliency detection. Different from conventional motion saliency detection methods that use complex mathematical models or features, variations in the phase spectrum of consecutive frames are identified and extracted as the key to obtaining the location of salient motion. As all the calculation is made on the temporal frequency spectrum, our model is independent of features, background models, or other forms of prior knowledge about scenes. The benefits of the proposed approach are evaluated for various videos where the number of moving objects, illumination, and background are all different. Compared with some the state of the art methods, our method achieves both good accuracy and fast computation.
Solar radiometry at millimeter wavelengths. [Fast Fourier Transformation solutions
NASA Technical Reports Server (NTRS)
Henze, W.
1974-01-01
In the area of resolution enhancement, the use of Fast Fourier Transform programs was investigated for possible application to millimeter wavelength maps of the sun. A difficulty arises with the La Posta maps in that they are limited to 35 arc-minutes square while the smeared out solar image is larger than that. A list of possible cometary emission lines near 13 millimeters is presented. Although preparation of the list was inspired by the appearance of Comet Kohoutek, the results are applicable to any future comet. The brightness temperature of the sun at 8.6 millimeters was measured using the moon as a calibration source. The result does not confirm a deep absorption feature as apparently observed by earlier workers.
On the abstracted dataflow complexity of Fast Fourier Transforms
Boehm, A.P.W. . Dept. of Computer Science); Hiromoto, R.E.; Kelly, K.A. ); Ashley, J.M. . Dept. of Computer Science)
1992-01-01
In this paper we develop and analyze the simulated performance of codes for the Fast Fourier Transform written in If and targeted for execution on Motorola's dataflow machine Monsoon. The FFT application is of interest because of its computational parallelism, its requirement for global communications, and its array element data dependences. We use the parallel profiling simulator Id World to study the dataflow performance of various implementations. Our approach is comparative. We study two approaches, a recursive and an iterative one, and in each version we examine the effect of a variety of implementations. We contend that only through such comparative evaluations can significant insight be gained in understanding the computational and structural details of functional algorithms.
Multifunctional metasurface lens for imaging and Fourier transform
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-01-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping. PMID:27272601
Generation of Fourier-transform-limited heralded single photons
U'Ren, Alfred B.; Jeronimo-Moreno, Yasser; Garcia-Gracia, Hipolito
2007-02-15
In this paper we study the spectral (temporal) properties of heralded single photon wave packets, triggered by the detection of an idler photon in the process of parametric down conversion. The generated single photons are studied within the framework of the chronocyclic Wigner function, from which the single photon spectral width and temporal duration can be computed. We derive specific conditions on the two-photon joint spectral amplitude which result in both pure and Fourier-transform-limited heralded single photons. Likewise, we present specific source geometries which lead to the fulfillment of these conditions and show that one of these geometries leads, for a given pump bandwidth, to the temporally shortest possible heralded single photon wave packets.
Universal calculation formula and calibration method in Fourier transform profilometry
Wen Yongfu; Li Sikun; Cheng Haobo; Su Xianyu; Zhang Qican
2010-12-01
We propose a universal calculation formula of Fourier transform profilometry and give a strict theoretical analysis about the phase-height mapping relation. As the request on the experimental setup of the universal calculation formula is unconfined, the projector and the camera can be located arbitrarily to get better fringe information, which makes the operation flexible. The phase-height calibration method under the universal condition is proposed, which can avoid measuring the system parameters directly. It makes the system easy to manipulate and improves the measurement velocity. A computer simulation and experiment are conducted to verify its validity. The calculation formula and calibration method have been applied to measure an object of 22.00 mm maximal height. The relative error of the measurement result is only 0.59%. The experimental results prove that the three-dimensional shape of tested objects can be reconstructed exactly by using the calculation formula and calibration method, and the system has better universality.
A study of geometric phase topology using Fourier transform method
NASA Astrophysics Data System (ADS)
Samlan, C. T.; Naik, Dinesh N.; Viswanathan, Nirmal K.
2016-07-01
Topological aspect of the geometric phase (GP) due to pure polarization projection is studied using the 2D Fourier transform (2D-FT) method. Projection of orthogonal polarization state results in a phase singularity in the 2D parameter space of ellipticity and orientation of polarization ellipse. Projection of its surrounding states results in an accumulation of GP in different amount that form a spiral structure. A half wave plate–quarter wave plate combination is used to generate different polarization states which are projected using a polarizer. The accumulated phase for each orientation of the wave plate is extracted from 2D-FT of the interferogram, obtained by interfering it with a reference beam in a Mach–Zehnder like interferometer.
Multifunctional metasurface lens for imaging and Fourier transform.
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-01-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping. PMID:27272601
Gas emission analysis based on Fourier transformed infrared spectroscopy
NASA Astrophysics Data System (ADS)
Shu, Xiaowen; Zhang, Xiaofu; Lian, Xu; Jin, Hui
2014-12-01
Solar occultation flux (SOF), a new optical technology to detect the gas based on the traditional Fourier transformed infrared spectroscopy (FTIR) developed quickly recently. In this paper, the system and the data analysis is investigated. First a multilayer transmission model of solar radiation is simulated. Then the retrieval process is illustrated. In the proceeding of the data analysis, the Levenberg-Marquardt non-linear square fitting is used to obtain the gas column concentration and the related emission ratio. After the theory certification, the built up system is conducted in a fertilizer plant in Hefei city .The results show SOF is available in the practice and the retrieved gas column concentration can give important information about the pollution emission and dispersion
Denoising and deblurring of Fourier transform infrared spectroscopic imaging data
NASA Astrophysics Data System (ADS)
Nguyen, Tan H.; Reddy, Rohith K.; Walsh, Michael J.; Schulmerich, Matthew; Popescu, Gabriel; Do, Minh N.; Bhargava, Rohit
2012-03-01
Fourier transform infrared (FT-IR) spectroscopic imaging is a powerful tool to obtain chemical information from images of heterogeneous, chemically diverse samples. Significant advances in instrumentation and data processing in the recent past have led to improved instrument design and relatively widespread use of FT-IR imaging, in a variety of systems ranging from biomedical tissue to polymer composites. Various techniques for improving signal to noise ratio (SNR), data collection time and spatial resolution have been proposed previously. In this paper we present an integrated framework that addresses all these factors comprehensively. We utilize the low-rank nature of the data and model the instrument point spread function to denoise data, and then simultaneously deblurr and estimate unknown information from images, using a Bayesian variational approach. We show that more spatial detail and improved image quality can be obtained using the proposed framework. The proposed technique is validated through experiments on a standard USAF target and on prostate tissue specimens.
Color image encryption based on joint fractional Fourier transform correlator
NASA Astrophysics Data System (ADS)
Lu, Ding; Jin, Weimin
2011-06-01
In this paper, an optical color image encryption/decryption technology based on joint fractional Fourier transform correlator and double random phase encoding (DRPE) is developed. In this method, the joint fractional power spectrum of the image to be encrypted and the key codes is recorded as the encrypted data. Different from the case with classical DRPE, the same key code was used both in the encryption and decryption. The security of the system is enhanced because of the fractional order as a new added key. This method takes full advantage of the parallel processing features of the optical system, and could optically realize single-channel color image encryption. The experimental results indicate that the new method is feasible.
Application of Fourier transform infrared spectroscopy to examination of documents
NASA Astrophysics Data System (ADS)
Zieba-Palus, Janina; Trzcinska, Beata
1992-03-01
Some 30 samples of writing and wrapping paper were examined using two techniques: transmission (as a KBr disc) and diffuse reflectance. About 15 blue ball pen ink samples were extracted directly from the document by means of a C2H5OH - CHCl3 mixture using an extraction apparatus which enables the separation of impurities (coming from a paper) from the extracted ball pen inks. Infrared spectra were measured on a Digilab Fourier transform spectrometer FTS-15 within the range 400 - 3800 cm-1. Statistical inference based on T2 Hotelling's test to assess the significance of differences observed in IR spectra of samples without examining the origin and essence of those differences was applied. The analysis of the spectral data was performed on a IBM-AT computer.
Sound resonance in pipes with discrete Fourier transform
NASA Astrophysics Data System (ADS)
Aljalal, Abdulaziz M.
2015-09-01
Sound resonance in pipes is investigated using a readily available setup consisting of a pipe, loudspeaker, microphone, and laptop. Discrete Fourier transform is used to extract the amplitude and phase spectra from the recorded sound enabling determination of locations and shapes of resonance peaks accurately. Either white noise signal or sharp pulse signal is used as an excited input sound signal. Both have broad frequency spectra and the difference between them is explored. The shapes of the amplitude and phase spectra are found to be well fitted to the predicted shapes. The pipe is either closed at both ends, closed at only one end, or open at both ends. The speed of sound and the effective location of reflection at the open end are in excellent agreement with theory.
Adaptive Controller for Compact Fourier Transform Spectrometer with Space Applications
NASA Astrophysics Data System (ADS)
Keymeulen, D.; Yiu, P.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.; Conroy, M.
2014-12-01
Here we present noise mitigation techniques developed as part of an adaptive controller for a very compact Compositional InfraRed Interferometric Spectrometer (CIRIS) implemented on a stand-alone field programmable gate array (FPGA) architecture with emphasis on space applications in high radiation environments such as Europa. CIRIS is a novel take on traditional Fourier Transform Spectrometers (FTS) and replaces linearly moving mirrors (characteristic of Michelson interferometers) with a constant-velocity rotating refractor to variably phase shift and alter the path length of incoming light. The design eschews a monochromatic reference laser typically used for sampling clock generation and instead utilizes constant time-sampling via internally generated clocks. This allows for a compact and robust device, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 µm) on planetary exploration missions. The instrument's embedded microcontroller is implemented on a VIRTEX-5 FPGA and a PowerPC with the aim of sampling the instrument's detector and optical rotary encoder in order to construct interferograms. Subsequent onboard signal processing provides spectral immunity from the noise effects introduced by the compact design's removal of a reference laser and by the radiation encountered during space flight to destinations such as Europa. A variety of signal processing techniques including resampling, radiation peak removal, Fast Fourier Transform (FFT), spectral feature alignment, dispersion correction and calibration processes are applied to compose the sample spectrum in real-time with signal-to-noise-ratio (SNR) performance comparable to laser-based FTS designs in radiation-free environments. The instrument's FPGA controller is demonstrated with the FTS to characterize its noise mitigation techniques and highlight its suitability for implementation in space systems.
Parameterized Spectral Bathymetric Roughness Using the Nonequispaced Fast Fourier Transform
NASA Astrophysics Data System (ADS)
Fabre, David Hanks
The ocean and acoustic modeling community has specifically asked for roughness from bathymetry. An effort has been undertaken to provide what can be thought of as the high frequency content of bathymetry. By contrast, the low frequency content of bathymetry is the set of contours. The two-dimensional amplitude spectrum calculated with the nonequispaced fast Fourier transform (Kunis, 2006) is exploited as the statistic to provide several parameters of roughness following the method of Fox (1996). When an area is uniformly rough, it is termed isotropically rough. When an area exhibits lineation effects (like in a trough or a ridge line in the bathymetry), the term anisotropically rough is used. A predominant spatial azimuth of lineation summarizes anisotropic roughness. The power law model fit produces a roll-off parameter that also provides insight into the roughness of the area. These four parameters give rise to several derived parameters. Algorithmic accomplishments include reviving Fox's method (1985, 1996) and improving the method with the possibly geophysically more appropriate nonequispaced fast Fourier transform. A new composite parameter, simply the overall integral length of the nonlinear parameterizing function, is used to make within-dataset comparisons. A synthetic dataset and six multibeam datasets covering practically all depth regimes have been analyzed with the tools that have been developed. Data specific contributions include possibly discovering an aspect ratio isotropic cutoff level (less than 1.2), showing a range of spectral fall-off values between about -0.5 for a sandybottomed Gulf of Mexico area, to about -1.8 for a coral reef area just outside of the Saipan harbor. We also rank the targeted type of dataset, the best resolution gridded datasets, from smoothest to roughest using a factor based on the kernel dimensions, a percentage from the windowing operation, all multiplied by the overall integration length.
High-resolution lensless Fourier transform holography for microstructure imaging
NASA Astrophysics Data System (ADS)
Zhao, Jie; Wang, Dayong; Wang, Huaying; Xie, Jianjun
2007-12-01
Digital holography combines the advantages of the optical holography and the computers. It can implement an all-digital processing and has the quasi real-time property. With lensless Fourier transform recording architecture, the limited bandwidth of CCD camera can be utilized sufficiently, and the sampling theorem is satisfied easily. Therefore, high-resolution can be achieved. So it is preferred in the microstructure imaging. In the paper, based on the Fresnel diffraction theory and the off-axis lensless Fourier transform recording architecture, the experimental optimization and correspondingly the digital reconstruction was investigated. Also, the lateral resolution of the reconstructed image was analyzed and improved by the proposed techniques. When the USAF test target was imaged without any pre-magnification, the lateral resolution of 3.1μm was achieved, which matched the theoretical prediction very well. The key points to achieve high resolution image are to use the smaller object and to arrange the distance between the object and the CCD plane as short as possible. Meanwhile, properly overlapping the reconstructed image with the DC term was helpful to improve the resolution. The noise in the reconstructed image could be reduced greatly by choosing the optical elements precisely and adjusting the beam path finely. The experimental results demonstrated that it is possible for the digital holographic microscopy to produce the high resolution image without the objective pre-magnification. The results also showed that, with a high quality hologram, the special image processing during the reconstruction may be unnecessary to obtain a high quality image.
Fourier Transform Spectroscopy Using Surface Electromagnetic Waves With Aperture Excitation
NASA Astrophysics Data System (ADS)
Gushanskaya, N. Y.; Yakovlev, V. A.; Zhizhin, G. N.; Chesters, M. A.; Parker, S. F.
1989-12-01
The surface electromagnetic wave (SEW) spectroscopy 1 with laser sources of the IR radiat on has demonstrated high sensitivity to the state of the surface. The measurements of SEW attenuation on the sample give the information about the sample conductivity, surface roughness and about the presence of oxide or adsorbate on the metal surface, especially If their absorption bands are in the spectral region where laser lines are available. High sensitivity of modern Fourier transform spectrometers allows to detect SEW excited by broadband source. We have used Fourier transform spectrometers FTS-20V (Digilab) and IFS-113 (Bruker) with liquid nitrogen cooled detectors (Hg-CD-Te). On the metal (Ag, Al, Au, Cu, V, Be) surface SEW were excited using aperture coupling. The experiment is schematically shown on the fig.1. IR radiation from interferometer was focused on the gap between the sample 3 surface and the screen 1 placed at the distance of the order of 100 μm. In such a way on the gap propagating along a metal SEW and bulk radiation above the metal are excited. SEW runs from the aperture coupler to the edge of the sample (this distance could be varied from 2 to 30 mm) and decouples into the bulk radiation on the edge. The second screen 2 above the edge cut the bulk radiation from the aperture coupler. If we change the distance between the screens it is possible to obtain SEW absorption coefficient at different frequences from the output intensity variation. Fig.2 shows SEW propagation length spectra for Au and Cu. For these metals and also for Ag 2 propagation length is proportional to the square of the wavelength as it is predicted by Drude model. For Al such dependence is valid in the oxide transperancy region, in the region 800-1000 cm -1 natural oxide film give absorption band shown on Oxide films are well recognizible also on Be and V. Thermal growth or oxide film was studied (rig.4).
Pattern Transformation of Heat-Shrinkable Polymer by Three-Dimensional (3D) Printing Technique
Zhang, Quan; Yan, Dong; Zhang, Kai; Hu, Gengkai
2015-01-01
A significant challenge in conventional heat-shrinkable polymers is to produce controllable microstructures. Here we report that the polymer material fabricated by three-dimensional (3D) printing technique has a heat-shrinkable property, whose initial microstructure can undergo a spontaneous pattern transformation under heating. The underlying mechanism is revealed by evaluating internal strain of the printed polymer from its fabricating process. It is shown that a uniform internal strain is stored in the polymer during the printing process and can be released when heated above its glass transition temperature. Furthermore, the internal strain can be used to trigger the pattern transformation of the heat-shrinkable polymer in a controllable way. Our work provides insightful ideas to understand a novel mechanism on the heat-shrinkable effect of printed material, but also to present a simple approach to fabricate heat-shrinkable polymer with a controllable thermo-structural response. PMID:25757881
Kalnins, E.G.; Kress, J.M.; Miller, W. Jr.
2006-04-15
This article is one of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat spaces. In the first part of the article we study the Staeckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Staeckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems.
A 3-D constitutive model for pressure-dependent phase transformation of porous shape memory alloys.
Ashrafi, M J; Arghavani, J; Naghdabadi, R; Sohrabpour, S
2015-02-01
Porous shape memory alloys (SMAs) exhibit the interesting characteristics of porous metals together with shape memory effect and pseudo-elasticity of SMAs that make them appropriate for biomedical applications. In this paper, a 3-D phenomenological constitutive model for the pseudo-elastic behavior and shape memory effect of porous SMAs is developed within the framework of irreversible thermodynamics. Comparing to micromechanical and computational models, the proposed model is computationally cost effective and predicts the behavior of porous SMAs under proportional and non-proportional multiaxial loadings. Considering the pressure dependency of phase transformation in porous SMAs, proper internal variables, free energy and limit functions are introduced. With the aim of numerical implementation, time discretization and solution algorithm for the proposed model are also presented. Due to lack of enough experimental data on multiaxial loadings of porous SMAs, we employ a computational simulation method (CSM) together with available experimental data to validate the proposed constitutive model. The method is based on a 3-D finite element model of a representative volume element (RVE) with random pores pattern. Good agreement between the numerical predictions of the model and CSM results is observed for elastic and phase transformation behaviors in various thermomechanical loadings. PMID:25528691
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.