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.
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.
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.
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
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
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.
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
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
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.
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.
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 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
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.
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.
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.
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 Astrophysics Data System (ADS)
Zhao, Chengliang; Huang, Kaikai; Lu, Xuanhui
2010-03-01
The properties of Bessel-Gaussian beams (BGBs) and Bessel beams (BBs) propagating through a fractional Fourier transform (FRT) optical system have been investigated. The analytical transformation formulae for BBs and BGBs propagation through a FRT optical system are derived based on definition of the FRT in the cylindrical coordinate system. By using the derived formula, numerical examples are illustrated.
Wigner distribution and fractional Fourier transform for two-dimensional symmetric optical beams.
Alieva, T; Bastiaans, M J
2000-12-01
A useful relationship between the fractional Fourier transform power spectra of a two-dimensional symmetric optical beam, on the one hand, and its Wigner distribution, on the other, is established. This relationship allows a significant simplification of the standard procedure for the reconstruction of the Wigner distribution from the field intensity distributions in the fractional Fourier domains. The Wigner distribution of a symmetric optical beam is analyzed, both in the coherent and in the partially coherent case. PMID:11140492
Optical alignment of high resolution Fourier transform spectrometers
NASA Technical Reports Server (NTRS)
Breckinridge, J. B.; Ocallaghan, F. G.; Cassie, A. G.
1980-01-01
Remote sensing, high resolution FTS instruments often contain three primary optical subsystems: Fore-Optics, Interferometer Optics, and Post, or Detector Optics. We discuss the alignment of a double-pass FTS containing a cat's-eye retro-reflector. Also, the alignment of fore-optics containing confocal paraboloids with a reflecting field stop which relays a field image onto a camera is discussed.
Fast Fourier and Wavelet Transforms for Wavefront Reconstruction in Adaptive Optics
Dowla, F U; Brase, J M; Olivier, S S
2000-07-28
Wavefront reconstruction techniques using the least-squares estimators are computationally quite expensive. We compare wavelet and Fourier transforms techniques in addressing the computation issues of wavefront reconstruction in adaptive optics. It is shown that because the Fourier approach is not simply a numerical approximation technique unlike the wavelet method, the Fourier approach might have advantages in terms of numerical accuracy. However, strictly from a numerical computations viewpoint, the wavelet approximation method might have advantage in terms of speed. To optimize the wavelet method, a statistical study might be necessary to use the best basis functions or ''approximation tree.''
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler. PMID:21686007
NASA Astrophysics Data System (ADS)
Sun, Zhiwei; Zhi, Ya'nan; Liu, Liren; Sun, Jianfeng; Zhou, Yu; Hou, Peipei
2013-09-01
The synthetic aperture imaging ladar (SAIL) systems typically generate large amounts of data difficult to compress with digital method. This paper presents an optical SAIL processor based on compensation of quadratic phase of echo in azimuth direction and two dimensional Fourier transform. The optical processor mainly consists of one phase-only liquid crystal spatial modulator(LCSLM) to load the phase data of target echo and one cylindrical lens to compensate the quadratic phase and one spherical lens to fulfill the task of two dimensional Fourier transform. We show the imaging processing result of practical target echo obtained by a synthetic aperture imaging ladar demonstrator. The optical processor is compact and lightweight and could provide inherent parallel and the speed-of-light computing capability, it has a promising application future especially in onboard and satellite borne SAIL systems.
A new iterative Fourier transform algorithm for optimal design in holographic optical tweezers
NASA Astrophysics Data System (ADS)
Memmolo, P.; Miccio, L.; Merola, F.; Ferraro, P.; Netti, P. A.
2012-06-01
We propose a new Iterative Fourier Transform Algorithm (IFTA) capable to suppress ghost traps and noise in Holographic Optical Tweezers (HOT), maintaining a high diffraction efficiency in a computational time comparable with the others iterative algorithms. The process consists in the planning of the suitable ideal target of optical tweezers as input of classical IFTA and we show we are able to design up to 4 real traps, in the field of view imaged by the microscope objective, using an IFTA built on fictitious phasors, located in strategic positions in the Fourier plane. The effectiveness of the proposed algorithm is evaluated both for numerical and optical reconstructions and compared with the other techniques known in literature.
Jing, Juan-Juan; Zhou, Jin-Song; Xiangli, Bin; Lü, Qun-Bo; Wei, Ru-Yi
2010-06-01
The principle of reflecting rotating Fourier transform spectrometer was introduced in the present paper. The nonlinear problem of optical path difference (OPD) of rotating Fourier transform spectrometer universally exists, produced by the rotation of rotating mirror. The nonlinear OPD will lead to fictitious recovery spectrum, so it is necessary to compensate the nonlinear OPD. Three methods of correction for the nonlinear OPD were described and compared in this paper, namely NUFFT method, OPD replace method and interferograms fitting method. The result indicates that NUFFT was the best method for the compensation of nonlinear OPD, OPD replace method was better, its precision was almost the same as NUFFT method, and their relative error are superior to 0.13%, but the computation efficiency of OPD replace method is slower than NUFFT method, while the precision and computation efficiency of interferograms fitting method are not so satisfied, because the interferograms are rapid fluctuant especially around the zero optical path difference, so it is unsuitable for polynomial fitting, and because this method needs piecewise fitting, its computation efficiency is the slowest, thus the NUFFT method is the most suited method for the nonlinear OPD compensation of reflecting rotating Fourier transform spectrometer. PMID:20707175
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
Remote Fourier transform-infrared spectral imaging system with hollow-optical fiber bundle.
Huang, Chenhui; Kino, Saiko; Katagiri, Takashi; Matsuura, Yuji
2012-10-10
A spectral imaging system consisting of a Fourier transform-infrared spectrometer, a high-speed infrared camera, and a bundle of hollow-optical fibers transmitting infrared radiation images was constructed. Infrared transmission spectra were obtained by carefully processing multiple interferograms taken by high-speed photography. Infrared spectral images of a variety of samples captured by the system were measured. We successfully detected existence maps of the oil and fat of biological samples by mapping the transmission of specific wavelengths in the spectrum. PMID:23052066
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.
Real-time Fourier transformation of lightwave spectra and application in optical reflectometry.
Malacarne, Antonio; Park, Yongwoo; Li, Ming; LaRochelle, Sophie; Azaña, José
2015-12-14
We propose and experimentally demonstrate a fiber-optics scheme for real-time analog Fourier transform (FT) of a lightwave energy spectrum, such that the output signal maps the FT of the spectrum of interest along the time axis. This scheme avoids the need for analog-to-digital conversion and subsequent digital signal post-processing of the photo-detected spectrum, thus being capable of providing the desired FT processing directly in the optical domain at megahertz update rates. The proposed concept is particularly attractive for applications requiring FT analysis of optical spectra, such as in many optical Fourier-domain reflectrometry (OFDR), interferometry, spectroscopy and sensing systems. Examples are reported to illustrate the use of the method for real-time OFDR, where the target axial-line profile is directly observed in a single-shot oscilloscope trace, similarly to a time-of-flight measurement, but with a resolution and depth of range dictated by the underlying interferometry scheme. PMID:26699041
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
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-01
In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption. PMID:27505799
Howard, John
2002-01-01
A new electro-optically modulated optical solid-state (MOSS) interferometer has been constructed for measurement of quantities related to the low-order spectral moments of line emission from optically thin radiant media such as plasmas. When Doppler broadening is dominant, the spectral moments give the Radon transform of corresponding moments of the velocity distribution function of the radiating species. The instrument, which is based on the principle of the Fourier-transform spectrometer, has high etendue and is rugged and compact. When electro-optical path-length modulation techniques are employed, the spectral information is encoded in the temporal frequency domain at harmonics of the modulation frequency and can be obtained by use of a single photodetector. Specifically, for a plasma in drifting local thermodynamic equilibrium the zeroth moment (brightness) is given by the average signal level, the first moment (shift) by the interferometric phase, and the second moment (linewidth) by the fringe visibility. To illustrate the MOSS performance, I present spectroscopic measurements of the time evolution of the plasma ion temperature and flow velocity for rf-heated discharges in the H-1 heliac, a toroidal plasma magnetic confinement at the Australian National University. PMID:11900436
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 Astrophysics Data System (ADS)
Georges, James A., III
2007-09-01
This article reports on the novel patent pending Optical Spatial Heterodyne Interferometric Fourier Transform Technique (the OSHIFT technique), the resulting interferometer also referred to as OSHIFT, and its preliminary results. OSHIFT was borne out of the following requirements: wavefront sensitivity on the order of 1/100 waves, high-frequency wavefront spatial sampling, snapshot 100Hz operation, and the ability to deal with discontinuous wavefronts. The first two capabilities lend themselves to the use of traditional interferometric techniques; however, the last two prove difficult for standard techniques, e.g., phase shifting interferometry tends to take a time sequence of images and most interferometers require estimation of a center fringe across wavefront discontinuities. OSHIFT overcomes these challenges by employing a spatial heterodyning concept in the Fourier (image) plane of the optic-under-test. This concept, the mathematical theory, an autocorrelation view of operation, and the design with results of OSHIFT will be discussed. Also discussed will be future concepts such as a sensor that could interrogate an entire imaging system as well as a methodology to create innovative imaging systems that encode wavefront information onto the image. Certain techniques and systems described in this paper are the subject of a patent application currently pending in the United States Patent Office.
NASA Technical Reports Server (NTRS)
Verber, C. M.; Vahey, D. W.; Wood, V. E.; Kenan, R. P.; Hartman, N. F.
1977-01-01
The possibility of producing an integrated optics data processing device based upon Fourier transformations or other parallel processing techniques, and the ways in which such techniques may be used to upgrade the performance of present and projected NASA systems were investigated. Activities toward this goal include; (1) production of near-diffraction-limited geodesic lenses in glass waveguides; (2) development of grinding and polishing techniques for the production of geodesic lenses in LiNbO3 waveguides; (3) development of a characterization technique for waveguide lenses; and (4) development of a theory for corrected aspheric geodesic lenses. A holographic subtraction system was devised which should be capable of rapid on-board preprocessing of a large number of parallel data channels. The principle involved is validated in three demonstrations.
Yi, Jiawang; Tan, Guanzheng
2015-12-20
Optical cryptosystems combined with compressed sensing can achieve compression and encryption simultaneously. But they usually use the same measurement matrix to sample all blocks of an image, which makes it easy to estimate the measurement matrix in the chosen plaintext attack. In this paper, we propose a robust scheme adopting multiple measurement matrices to overcome this shortcoming. The matrices can be efficiently derived by applying random row exchanging to a basic one, which is also encoded into the fractional Fourier transform (FrFT) domain to improve the visual effect of wrongly decrypted images. Chaos-based pixel scrambling is added into our double FrFT cryptosystem to guarantee its nonlinearity. Simulation results have shown the security and effectiveness of our scheme. PMID:26837032
Nanowire humidity optical sensor system based on fast Fourier transform technique
NASA Astrophysics Data System (ADS)
Rota-Rodrigo, S.; Pérez-Herrera, R.; Lopez-Aldaba, A.; López Bautista, M. C.; Esteban, O.; López-Amo, M.
2015-09-01
In this paper, a new sensor system for relative humidity measurements based on its interaction with the evanescent field of a nanowire is presented. The interrogation of the sensing head is carried out by monitoring the fast Fourier transform phase variations of one of the nanowire interference frequencies. This method is independent of the signal amplitude and also avoids the necessity of tracking the wavelength evolution in the spectrum, which can be a handicap when there are multiple interference frequency components with different sensitivities. The sensor is operated within a wide humidity range (20%-70% relative humidity) with a maximum sensitivity achieved of 0.14rad/% relative humidity. Finally, due to the system uses an optical interrogator as unique active element, the system presents a cost-effective feature.
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-01
In this paper we propose the design of communication systems based on using periodic nonlinear Fourier transform (PNFT), following the introduction of the method in the Part I. We show that the famous "eigenvalue communication" idea [A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993)] can also be generalized for the PNFT application: In this case, the main spectrum attributed to the PNFT signal decomposition remains constant with the propagation down the optical fiber link. Therefore, the main PNFT spectrum can be encoded with data in the same way as soliton eigenvalues in the original proposal. The results are presented in terms of the bit-error rate (BER) values for different modulation techniques and different constellation sizes vs. the propagation distance, showing a good potential of the technique. PMID:27505800
Kelly, Damien P.; Hennelly, Bryan M.; Sheridan, John T
2005-05-01
The optical fractional Fourier transform (OFRT) in combination with speckle photography has previously been used to measure the magnitude of surface tilting and translation. Previous OFRT techniques used to determine motion have not been able to discern the direction of the tilt and translation. A simple new approach involving use of correlation is presented to overcome this limitation. Controlled variation of the minimum resolution and dynamical range of measurement is demonstrated. It is then experimentally confirmed that if a rigid body's motion is captured by two OFRT systems of different orders, the direction and magnitude of both the tilting and the in-plane translation motion of the body can be independently determined without a priori knowledge. The experimental results confirm the validity of previous theoretical predictions.
Study on optical design of all-reflective Fourier transform imaging spectrometer
NASA Astrophysics Data System (ADS)
Liang, Min-yong; Liao, Ning-fang
2008-03-01
The Fourier Transform Imaging Spectrometer (FTIS) used for remote sensing has been developed rapidly in the past two decades. Most of the Temporarily Modulated FTIS and the Spatially Modulated FTIS include a beam splitter structure, such as Sagnac prism or double refraction crystal beam splitter. The material of the beam splitter which is optical glass, crystalline materials or plastic optical materials all have the transmission limitation, so the spectrum range would be limited; the transparent material also would cause the chromatic aberration. We presented an all-reflective optical structure based on the Fresnel double mirror interference structure that could overcome these two shortcomings. The three-mirror anastigmat (TMA) telescope is employed to realize all-reflective fore-optics, it has a compact structure, wide field of view (FOV) and competent modulation transfer function (MTF). An abaxial parabolic-cylindrical mirror has been designed to focus the interference fringes onto the plane focal array (FPA) which would increase the signal to noise ratio (SNR).
Rugged optical mirrors for Fourier-Transform Spectrometers operated in harsh environments
NASA Astrophysics Data System (ADS)
Feist, D. G.; Arnold, S. G.; Hase, F.; Ponge, D.
2015-10-01
The Total Carbon Column Observing Network (TCCON) and the Network for the Detection of Atmospheric Composition Change (NDACC) operate a number of Fourier-Transform Spectrometers (FTSs) that measure trace gases in the atmosphere by observing solar spectra. To guide the sunlight into the FTS, a solar tracker has to be placed outside. This device needs high-quality optical mirrors with good reflectivity in the near and mid infrared. More and more FTS stations are operated in remote locations with harsh environments. Optical mirrors are usually made for laboratory conditions and might not last very long there. At the MPI-BGC's TCCON site on Ascension Island, several mirrors from different optical manufacturers were destroyed within weeks. To continue operation, the MPI-BGC had to develop rugged mirrors that could sustain the harsh conditions for months or even years. While commercially available mirrors are typically made from a substrate coverered with a thin reflective coating, these rugged mirrors were made from stainless steel with no additional coating. Except for their lower reflectivity (which can easily be compensated for), their optical properties are comparable to existing mirrors. However, their rugged design makes them mostly immune to corrosion and scratching. Unlike most coated mirrors, they can also be cleaned easily.
Rugged optical mirrors for Fourier transform spectrometers operated in harsh environments
NASA Astrophysics Data System (ADS)
Feist, Dietrich G.; Arnold, Sabrina G.; Hase, Frank; Ponge, Dirk
2016-05-01
The Total Carbon Column Observing Network (TCCON) and the Network for the Detection of Atmospheric Composition Change (NDACC) operate a number of Fourier transform spectrometers (FTSs) that measure trace gases in the atmosphere by observing solar spectra. To guide the sunlight into the FTS, a solar tracker has to be placed outside. This device needs high-quality optical mirrors with good reflectance in the near and mid-infrared.More and more FTS stations are operated in remote locations with harsh environments. Optical mirrors are usually made for laboratory conditions and might not last very long there. At the TCCON site on Ascension Island which is operated by the Max Planck Institute for Biogeochemistry (MPI-BGC), several mirrors from different optical manufacturers were destroyed within weeks.To continue operation, the MPI-BGC had to develop rugged mirrors that could sustain the harsh conditions for months or even years. While commercially available mirrors are typically made from a substrate covered with a thin reflective coating, these rugged mirrors were made from stainless steel with no additional coating. Except for their lower reflectance (which can easily be compensated for), their optical properties are comparable to existing mirrors. However, their rugged design makes them mostly immune to corrosion and scratching. Unlike most coated mirrors, they can also be cleaned easily.
Capacity estimates for optical transmission based on the nonlinear Fourier transform.
Derevyanko, Stanislav A; Prilepsky, Jaroslaw E; Turitsyn, Sergei K
2016-01-01
What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km. PMID:27611059
Using nonequispaced fast Fourier transformation to process optical coherence tomography signals
NASA Astrophysics Data System (ADS)
Hillmann, Dierck; Hüttmann, Gereon; Koch, Peter
2009-07-01
In OCT imaging the spectra that are used for Fourier transformation are in general not acquired linearly in k-space. Therefore one needs to apply an algorithm to re-sample the data and finally do the Fourier Transformation to gain depth information. We compare three algorithms (Non-Equispaced DFT, interpolated FFT and Non-Equispaced FFT) for this purpose in terms of speed and accuracy. The optimal algorithm depends on the OCT device (speed, SNR) and the object.
Optical design of a static LWIR Fourier-transform imaging spectrometer with high throughput
NASA Astrophysics Data System (ADS)
Wang, Hai-yang; Fu, Yan-peng; Zheng, Wei-jian; Liao, Ning-fang; Jin, Wei-qi
2013-08-01
A LWIR Fourier-transform imaging spectrometer based on the static Michelson interferometer with high throughput is presented. Advantages and disadvantages of some common structures of imaging spectrometer are analyzed. Some selection of optimum configurations for imaging spectrometer is proceeded. The interferogram is acquired over the whole field of the camera while the scene of interest scans the path difference range, and vignetting should be strongly limited while keeping the size of the interferometer as small as possible for manufacturability and practicability reasons. The key point is to put the entrance pupil of the imaging lens inside the interferometer. The design of optical system is proposed. The field of view(FOV) is 10°.The operating wavelength range is from 8 to 12μm, F number is 2 and the working temperature range is -20°C～40°C. Optical system with 100% cold shield efficiency is good adaptability to wide environment temperature change. The spectrometer system has low utilization of solar energy in the infrared band, so to ensure its transmittance, and it is necessary to use a small amount of lenses as possible, so here the method of the active electromechanical athermalisation just uses four lenses in the system. Modulation transfer function (MTF), aberrant and distortion etc of optical system are analyzed. The results show that an excellent performance and image performance are obtained despite the simple structure.
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).
Rugged optical mirrors for the operation of Fourier-Transform Spectrometers in rough environments
NASA Astrophysics Data System (ADS)
Feist, Dietrich G.
2014-05-01
The Total Carbon Column Observing Network (TCCON) and the Network for the Detection of Atmospheric Composition Change (NDACC) operate a growing number of Fourier-Transform Spectrometers (FTS) that measure the total column of several atmospheric trace gases. For these measurements, the sun is used as a light source. This is typically achieved by a solar tracker that uses a pair of optical mirrors to guide the sunlight into the instrument. There is a growing demand to operate these instruments in remote locations that fill the gaps in the global observation network. Besides the logistical challenges of running a remote site, the environment at these locations can be very harsh compared to the sheltered environment of the instruments' home institutions. While the FTS itself is usually well protected inside a building or container, the solar tracker and especially its mirrors are exposed to the environment. There they may suffer from - temperature fluctuations - high humidity - sea salt corrosion at coastal sites - dirt and dust - air pollution from anthropogenic sources - deposition from plants or animals The Max Planck Institute for Biogeochemistry (MPI-BGC) operates a TCCON station on Ascension Island, about 200 m from the sea. Under the rough conditions at this site, typical optical mirrors that are made for laboratory conditions are destroyed by sea salt spray within a few weeks. Besides, typical gold-coated mirrors cannot be cleaned as their soft surface is easily scratched or damaged. To overcome these problems, the MPI-BGC has developed optical mirrors that - offer good reflectivity in the near and mid infrared - are highly resistant to salt and chlorine - have a hard surface so that they can be cleaned often and easily - are not affected by organic solvents - last for months in very harsh environments - can be reused after polishing These mirrors could be applied to most TCCON and NDACC sites. This way, the network could be expanded to regions where operation
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.
NASA Astrophysics Data System (ADS)
Afanasyeva, Natalia I.; Kolyakov, Sergei F.; Letokhov, Vladilen S.; Golovkina, Viktoriya N.
1997-08-01
Fiber optic evanescent wave Fourier transform infrared (FEW- FTIR) spectroscopy using fiberoptic sensors operated in the attenuated total reflection (ATR) regime in the middle infrared (IR) region of the spectrum (850 - 1850 cm-1) has recently found application in the diagnostics of tissues. The method is suitable for noninvasive and rapid (seconds) direct measurements of the spectra of normal and pathological tissues in vitro, ex vivo and in vivo. The aim of our studies is the express testing of various tumor tissues at the early stages of their development. The method is expected to be further developed for endoscopic and biopsy applications. We measured in vivo the skin normal and malignant tissues on surface (directly on patients) in various cases of basaloma, melanoma and nevus. The experiments were performed in operating room for measurements of skin in the depth (under/in the layers of epidermis), human breast, stomach, lung, kidney tissues. The breast and skin tissues at different stages of tumor or cancer were distinguished very clearly in spectra of amide, side cyclic and noncyclic hydrogen bonded fragments of aminoacid residuals, phosphate groups and sugars. Computer monitoring is being developed for diagnostics.
Various new applications of fiber optic infrared Fourier transform spectroscopy for dermatology
NASA Astrophysics Data System (ADS)
Bruch, Reinhard F.; Afanasyeva, Natalia I.; Sukuta, Sydney; Brooks, Angelique L.; Makhine, Volodymyr; Kolyakov, Sergei F.
1999-02-01
Fiberoptical evanescent wave Fourier transform infrared (FEW- FTIR) spectroscopy has been applied in the middle infrared (MIR) wavelength range (3 to 20 micrometer) to the in vivo diagnostics of normal skin tissue, acupuncture points as well as precancerous and cancerous conditions. The FTIR-FEW technique, using nontoxic unclad fibers, is suitable for noninvasive, sensitive investigations of skin tissue for various dermatological studies of skin caner, aging, laser treatment, cosmetics, skin allergies, etc. This method is direct, nondestructive, and fast (seconds). Our optical fibers are nonhygroscopic, flexible, and characterized by extremely low losses. In this study, we have noninvasively investigated more than 300 cases of normal skin, acupuncture points, precancerous and cancerous tissue in the range of 1400 to 1800 cm-1. The results of our analysis of skin and other tissue are discussed in terms of structural and mathematical similarities and differences on a molecular level. In addition, we have also performed cluster analysis, using principal component scores, to confirm pathological classifications and to discriminate between genders. We have found good agreement with prior pathological classifications for normal skin tissue and melanoma tumors and normal females were distinctly separate from males.
Imaging Fourier Transform Spectrometer
Bennett, C.L.; Carter, M.R.; Fields, D.J.; Hernandez, J.
1993-04-14
The operating principles of an Imaging Fourier Transform Spectrometer (IFTS) are discussed. The advantages and disadvantages of such instruments with respect to alternative imaging spectrometers are discussed. The primary advantages of the IFTS are the capacity to acquire more than an order of magnitude more spectral channels than alternative systems with more than an order of magnitude greater etendue than for alternative systems. The primary disadvantage of IFTS, or FTS in general, is the sensitivity to temporal fluctuations, either random or periodic. Data from the IRIFTS (ir IFTS) prototype instrument, sensitive in the infrared, are presented having a spectral sensitivity of 0.01 absorbance units, a spectral resolution of 6 cm{sup {minus}1} over the range 0 to 7899 cm{sup {minus}1}, and a spatial resolution of 2.5 mr.
Fourier Transform Spectrometer System
NASA Technical Reports Server (NTRS)
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
NASA Astrophysics Data System (ADS)
Lü, X.; Schrottke, L.; Grahn, H. T.
2016-06-01
We present scattering rates for electrons at longitudinal optical phonons within a model completely formulated in the Fourier domain. The total intersubband scattering rates are obtained by averaging over the intrasubband electron distributions. The rates consist of the Fourier components of the electron wave functions and a contribution depending only on the intersubband energies and the intrasubband carrier distributions. The energy-dependent part can be reproduced by a rational function, which allows for the separation of the scattering rates into a dipole-like contribution, an overlap-like contribution, and a contribution which can be neglected for low and intermediate carrier densities of the initial subband. For a balance between accuracy and computation time, the number of Fourier components can be adjusted. This approach facilitates an efficient design of complex heterostructures with realistic, temperature- and carrier density-dependent rates.
NASA Astrophysics Data System (ADS)
Gao, Ch. Y.; Yu, H. T.; Wen, J.; Zhao, M.; Shang, J. J.; Li, X. L.
2016-02-01
A method for probing quadratic electro-optic(QEO) coefficient of tantalum potassium niobate crystal based on Fourier transform was proposed. We acquired all the independent component of QEO coefficient tensor of crystal, they are h11 = 1.56 ×10-14m2 /V2 , h12 = 1.24 ×10-14m2 /V2 and h44 = 0.160 ×10-14m2 /V2 respectively. With the help of the computer digital image processing technology, this method should have further application prospect in the areas of optical properties parameters measuring to the optical functional materials.
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.
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.
NASA Astrophysics Data System (ADS)
Han, Yanong; Sonnenberg, Wendi; Short, Kurt W.; Spangler, Lee H.
1999-10-01
We have developed methods of measuring absorption of transient species utilizing stepped-scan Fourier transform interferometry that allows a combination of broad spectral coverage (10,000 - 15,000 cm-1 per spectrum), good spectral resolution, and up to ns temporal resolution with possibilities of extension to the ps domain. Nanosecond, psec or fsec laser systems, tunable from UV to IR can be used as the pump source to prepare the transient species. The absorption of that species is measured with broadband, incoherent light and can be simultaneously time and frequency resolved.
NASA Astrophysics Data System (ADS)
Foltynowicz, Aleksandra; Rutkowski, Lucile; Johanssson, Alexandra C.; Khodabakhsh, Amir; Maslowski, Piotr; Kowzan, Grzegorz; Lee, Kevin; Fermann, Martin
2015-06-01
Fourier transform spectrometers (FTS) based on optical frequency combs (OFC) allow detection of broadband molecular spectra with high signal-to-noise ratios within acquisition times orders of magnitude shorter than traditional FTIRs based on thermal sources. Due to the pulsed nature of OFCs the interferogram consists of a series of bursts rather than a single burst at zero optical path difference (OPD). The comb mode structure can be resolved by acquiring multiple bursts, in both mechanical FTS systems and dual-comb spectroscopy. However, in all existing demonstrations the resolution was ultimately limited either by the maximum available OPD between the interferometer arms or by the total acquisition time enabled by the storage memory. We present a method that provides spectral resolution exceeding the limit set by the maximum OPD using an interferogram containing only a single burst. The method allows measurements of absorption lines narrower than the OPD-limited resolution without any influence of the instrumental lineshape function. We demonstrate this by measuring undistorted CO2 and CO absorption lines with linewidth narrower than the OPD-limited resolution using OFC-based mechanical FTS in the near- and mid-infrared wavelength ranges. The near-infrared system is based on an Er:fiber femtosecond laser locked to a high finesse cavity, while the mid-infrared system is based on a Tm:fiber-laser-pumped optical parametric oscillator coupled to a multi-pass cell. We show that the method allows acquisition of high-resolution molecular spectra with interferometer length orders of magnitude shorter than traditional FTIR. Mandon, J., G. Guelachvili, and N. Picque, Nat. Phot., 2009. 3(2): p. 99-102. Zeitouny, M., et al., Ann. Phys., 2013. 525(6): p. 437-442. Zolot, A.M., et al., Opt. Lett., 2012. 37(4): p. 638-640.
Xu, Daguang; Huang, Yong; Kang, Jin U
2014-06-16
We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral). PMID:24977582
Xu, Daguang; Huang, Yong; Kang, Jin U.
2014-01-01
We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial)×1000(lateral). PMID:24977582
NASA Astrophysics Data System (ADS)
Montejo, Ludguier D.; Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.
2013-03-01
We apply the Fourier Transform to absorption and scattering coefficient images of proximal interphalangeal (PIP) joints and evaluate the performance of these coefficients as classifiers using receiver operator characteristic (ROC) curve analysis. We find 25 features that yield a Youden index over 0.7, 3 features that yield a Youden index over 0.8, and 1 feature that yields a Youden index over 0.9 (90.0% sensitivity and 100% specificity). In general, scattering coefficient images yield better one-dimensional classifiers compared to absorption coefficient images. Using features derived from scattering coefficient images we obtain an average Youden index of 0.58 +/- 0.16, and an average Youden index of 0.45 +/- 0.15 when using features from absorption coefficient images.
Feng, Ming-Chun; Xu, Liang; Gao, Min-Guang; Jiao, Yang; Wei, Xiu-Li; Jin, Ling; Cheng, Si-Yang; Li, Xiang-Xian; Feng, Shu-Xiang
2012-12-01
The authors measured IR transmission spectra of two different concentrations of Bacillus subtilis spores by using Fourier transform infrared spectroscopy (FTIR) technology. The mass extinction cross section k of Bacillus subtilis spores was calculated according to Lambert-Beer law and the imaginary part n(i) of the complex refractive index was also calculated through k. The real part n(r) of the complex refractive index was derived from the KK (Kramers-Kronig) relationship and the experimental results were also analyzed and discussed with the study of measurement and analysis method of the complex refractive index on Bacillus subtilis spores, it is of great significance to further research the absorption and scattering characteristics, and to broaden the measurement and remote sensing technology method of the biological aerosols. PMID:23427533
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.
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.
Chen, Yu; Leach, Franklin E; Kaiser, Nathan K; Dang, Xibei; Ibrahim, Yehia M; Norheim, Randolph V; Anderson, Gordon A; Smith, Richard D; Marshall, Alan G
2015-01-01
Enhancements to the ion source and transfer optics of our 9.4 T Fourier transform ion cyclotron resonance (ICR) mass spectrometer have resulted in improved ion transmission efficiency for more sensitive mass measurement of complex mixtures at the MS and MS/MS levels. The tube lens/skimmer has been replaced by a dual ion funnel and the following octopole by a quadrupole for reduced ion cloud radial expansion before transmission into a mass-selective quadrupole. The number of ions that reach the ICR cell is increased by an order of magnitude for the funnel/quadrupole relative to the tube lens/skimmer/octopole. PMID:25601704
NASA Astrophysics Data System (ADS)
Galizzi, Gustavo E.; Cuadrado-Laborde, Christian
2015-10-01
In this work we study the joint transform correlator setup, finding two analytical expressions for the extensions of the joint power spectrum and its inverse Fourier transform. We found that an optimum efficiency is reached, when the bandwidth of the key code is equal to the sum of the bandwidths of the image plus the random phase mask (RPM). The quality of the decryption is also affected by the ratio between the bandwidths of the RPM and the input image, being better as this ratio increases. In addition, the effect on the decrypted image when the detection area is lower than the encrypted signal extension was analyzed. We illustrate these results through several numerical examples.
Cheng, Mengfan; Deng, Lei; Li, Hao; Liu, Deming
2014-03-10
We propose a scheme whereby a time domain fractional Fourier transform (FRFT) is used to post process the optical chaotic carrier generated by an electro-optic oscillator. The time delay signature of the delay dynamics is successfully masked by the FRFT when some conditions are satisfied. Meanwhile the dimension space of the physical parameters is increased. Pseudo random binary sequence (PRBS) with low bit rate (hundreds of Mbps) is introduced to control the parameters of the FRFT. The chaotic optical carrier, FRFT parameters and the PRBS are covered by each other so that the eavesdropper has to search the whole key space to crack the system. The scheme allows enhancing the security of communication systems based on delay dynamics without modifying the chaotic source. In this way, the design of chaos based communication systems can be implemented in a modular manner. PMID:24663864
Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
1998-01-01
In the new generation interferometer, incident photons pass through the entrance aperture of the insturment and are divided by a beam splitter into two paths. In each path, the photons experience multiple reflections from optical components. Eventually, the photons are recombined at the beamsplitter and are focused on an array of detectors. The energy from the photons is then converted into electrical analog signals.
NASA Astrophysics Data System (ADS)
Krause, Katie M.; Genest, Jerome
2006-07-01
The impact of the interferometer optical path difference (OPD) speed profile on the spectrum, derived through the use of Fourier-transform spectrometry (FTS), of a synchronous optical network (SONET) signal is found. The SONET signal carries high-speed data traffic. It also may be modulated by low-frequency intensity or frequency modulation. It is found that the SONET header, high-speed data traffic and low-frequency modulation all manifest themselves as artifacts in the FTS-derived spectrum of the SONET signal. It is shown that a nonconstant OPD speed profile can smooth out these artifacts, making it unlikely that they will be mistaken for carrier signal peaks. However, it is found that smoothing out these artifacts lessens the achievable dynamic range of the FTS instrument in the frequency range of interest, the International Telecommunications Union common (C) and long (L) bands.
SnO2-MOF-Fabry-Perot humidity optical sensor system based on fast Fourier transform technique
NASA Astrophysics Data System (ADS)
Lopez-Aldaba, A.; Lopez-Torres, D.; Ascorbe, J.; Rota-Rodrigo, S.; Elosua, C.; Lopez-Amo, M.; Arregui, F. J.; Corres, J. M.; Auguste, J.-L.; Jamier, R.; Roy, P.
2016-05-01
In this paper, a new sensor system for relative humidity measurements based on a SnO2 sputtering deposition on a microstructured optical fiber (MOF) low-finesse Fabry-Perot (FP) sensing head is presented and characterized. The interrogation of the sensing head is carried out by monitoring the Fast Fourier Transform phase variations of the FP interference frequency. This method is low-sensitive to signal amplitude variations and also avoids the necessity of tracking the evolution of peaks and valleys in the spectrum. The sensor is operated within a wide humidity range (20%-90% relative humidity) with a maximum sensitivity achieved of 0.14rad/%. The measurement method uses a commercial optical interrogator as the only active element, this compact solution allows real time analysis of the data.
Fieldable Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Hatchell, Brian K.; Harper, Warren W.; Schultz, John F.
2004-10-01
The infrared sensors group at the Pacific Northwest National Laboratory (PNNL) is focused on the science and technology of remote and in-situ chemical sensors for detecting proliferation and countering terrorism. To support these vital missions, PNNL is developing frequency-modulation techniques for remote probing over long optical paths by means of differential-absorption light detecting and ranging (LIDAR). This technique can easily monitor large areas, or volumes, that could only be accomplished with a large network of point sensors. Recently, PNNL began development of a rugged frequency-modulation differential-abosrption LIDAR (FM-DIAL) system to conduct field experiments. To provide environmentla protection for the system and facilitate field deployments and operations, a large, well insulated, temperature controlled trailer was specified and acquired. The trailer was outfitted with a shock-mounted optical bench, an electronics rack, a liquid nitrogen Dewar, and a power generator. A computer-controlled gimbal-mounted mirror was added to allow the telescope beam to be accurately pointed in both the vertical and horizontal plane. This turned out to be the most complicated addition, and is described in detail. This paper provides an overview of the FM-DIAL system and illustrates innovative solutions developed to overcome several alignment and stability issues encountered in the field.
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
Wang, Kai; Ding, Zhihua; Wu, Tong; Wang, Chuan; Meng, Jie; Chen, Minghui; Xu, Lei
2009-07-01
We develop a high speed spectral domain optical coherence tomography (SD-OCT) system based on a custom-built spectrometer and non-uniform discrete Fourier transform (NDFT) to realize minimized depth dependent sensitivity fall-off. After precise spectral calibration of the spectrometer, NDFT of the acquired spectral data is adopted for image reconstruction. The spectrometer is able to measure a wavelength range of about 138 nm with a spectral resolution of 0.0674 nm at central wavelength of 835 nm, corresponding to an axial imaging range of 2.56 mm in air. Zemax simulations and sensitivity fall-off measurements under two alignment states of the spectrometer are given. Both theoretical simulations and experiments are done to study the depth dependent sensitivity of the developed system based on NDFT in contrast to those based on conventional discrete Fourier transform (DFT) with and without interpolation. In vivo imaging on human finger from volunteer is conducted at A-scan rate of 29 kHz and reconstruction is done based on different methods. The comparing results confirm that reconstruction method based on NDFT indeed improves sensitivity especially at large depth while maintaining the coherence-function-limited depth resolution. PMID:19582127
NASA Astrophysics Data System (ADS)
Peterseim, Tobias; Dressel, Martin
2016-06-01
The time-dependent optical properties of molecular systems are investigated by step-scan Fourier-transform spectroscopy in order to explore the dynamics at phase transitions and molecular orientation in the milli- and microsecond range. The electrical switching of liquid crystals traced by vibrational spectroscopy reveals a rotation of the molecules with a relaxation time of 2 ms. The photo-induced neutral-ionic transition in TTF-CA takes place by a suppression of the dimerization in the ionic phase and creation of neutral domains. The time-dependent infrared spectra, employed to investigate the domain-wall dynamics, depend on temperature and laser pulse intensity; the relaxation of the spectra follows a stretched-exponential decay with relaxation times in the microsecond range strongly dependent on temperature and laser intensity. We present all details of the experimental setups and thoroughly discuss the technical challenges.
Xie, Weilin; Zhou, Qian; Bretenaker, Fabien; Xia, Zongyang; Shi, Hongxiao; Qin, Jie; Dong, Yi; Hu, Weisheng
2016-07-01
We report on a versatile optical frequency-modulated continuous-wave interferometry technique that exploits wideband phase locking for generating highly coherent linear laser frequency chirps. This technique is based on an ultra-short delay-unbalanced interferometer, which leads to a large bandwidth, short lock time, and robust operation even in the absence of any isolation from environmental perturbations. In combination with a digital delay-matched phase error compensation, this permits the achievement of a range window about 60 times larger than the intrinsic laser coherence length with a 1.25 mm Fourier transform-limited spatial resolution. The demonstrated configuration can be easily applied to virtually any semiconductor laser. PMID:27367076
NASA Astrophysics Data System (ADS)
Sukuta, Sydney; Bruch, Reinhard F.
2002-05-01
The goal of this study is to test the feasibility of using noise factor/eigenvector bands as general clinical analytical tools for diagnoses. We developed a new technique, Noise Band Factor Cluster Analysis (NBFCA), to diagnose benign tumors via their Fourier transform IR fiber optic evanescent wave spectral data for the first time. The middle IR region of human normal skin tissue and benign and melanoma tumors, were analyzed using this new diagnostic technique. Our results are not in full-agreement with pathological classifications hence there is a possibility that our approaches could complement or improve these traditional classification schemes. Moreover, the use of NBFCA make it much easier to delineate class boundaries hence this method provides results with much higher certainty.
NASA Astrophysics Data System (ADS)
Salim, S.; Wang, C. A.; Driver, R. D.; Jensen, K. F.
1996-12-01
We describe fiber-optics-based Fourier transform infrared (FOB-FTIR) spectroscopy for in situ monitoring of input partial pressures of organometallic precursors in a vertical rotating-disk organometallic vapor phase epitaxy reactor. Detection limits as low as 0.05 Torr for trimethylgallium and 0.006 Torr for tritertiarybutylaluminum (TTBAl) are achieved using a 1 s scan time, which are comparable to established ultrasonic measurements. In addition, the FOB-FTIR approach has the ability to detect parasitic Lewis acid-base interactions between organometallic precursors, as demonstrated for in situ measurements of TTBAl mixed with arsine, trimethylantimony or triethylantimony. Such observations are shown to provide insight into unexpected results in epitaxial growth.
NASA Astrophysics Data System (ADS)
Hillerkuss, D.; Schmogrow, R.; Schellinger, T.; Jordan, M.; Winter, M.; Huber, G.; Vallaitis, T.; Bonk, R.; Kleinow, P.; Frey, F.; Roeger, M.; Koenig, S.; Ludwig, A.; Marculescu, A.; Li, J.; Hoh, M.; Dreschmann, M.; Meyer, J.; Ben Ezra, S.; Narkiss, N.; Nebendahl, B.; Parmigiani, F.; Petropoulos, P.; Resan, B.; Oehler, A.; Weingarten, K.; Ellermeyer, T.; Lutz, J.; Moeller, M.; Huebner, M.; Becker, J.; Koos, C.; Freude, W.; Leuthold, J.
2011-06-01
Optical transmission systems with terabit per second (Tbit s-1) single-channel line rates no longer seem to be too far-fetched. New services such as cloud computing, three-dimensional high-definition television and virtual-reality applications require unprecedented optical channel bandwidths. These high-capacity optical channels, however, are fed from lower-bitrate signals. The question then is whether the lower-bitrate tributary information can viably, energy-efficiently and effortlessly be encoded to and extracted from terabit per second data streams. We demonstrate an optical fast Fourier transform scheme that provides the necessary computing power to encode lower-bitrate tributaries into 10.8 and 26.0 Tbit s-1 line-rate orthogonal frequency-division multiplexing (OFDM) data streams and to decode them from fibre-transmitted OFDM data streams. Experiments show the feasibility and ease of handling terabit per second data with low energy consumption. To the best of our knowledge, this is the largest line rate ever encoded onto a single light source.
NASA Astrophysics Data System (ADS)
Kester, Michael; Trygstad, Marc; Chabot, Paul
2003-09-01
A unique analytical methodology has recently been developed to perform real-time, on-line chemical analysis of bath solutions in semiconductor fabrication tools. A novel, patented fiber optic sensor is used to transmit infrared light directly through the tube walls of the circulating bath solutions within the fabrication tool in a completely non-invasive, non-extractive way. The sensor simply "clips" onto the tubing, thus permitting immediate analysis of the bath composition by Fourier Transform infrared (FTIR) spectroscopy. The infrared spectrometer is capable of multiplexing up to eight "Clippir™" sensor heads to a single interferometer using fiber optic cables. The instrument can analyze almost any bath solution utilized today. The analysis is performed using the near-infrared (NIR) portion of the electromagnetic spectrum, where absorption bands related to molecular vibrations can be found. The Fourier Transform infrared spectrometer gives access to absorption bands over a wide range of frequencies (or wavelengths), and the absorptions are correlated to concentrations using a chemometric approach employing a partial least-squares algorithm. Models are generated from this approach for each chemistry to be analyzed. This paper will review the analytical technology necessary to make such measurements, and discuss the instrument performance criteria required to achieve accurate and precise measurements of bath chemistries. The ability to measure non-infrared absorbing compounds will be discussed, as will the nature of the influence of sample temperature on measurement. Issues critical to the development of robust models and their direct implementation on multiple channels and even different instruments will be considered.
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 New Physical Optics Notebook: Tutorials in Fourier Optics.
ERIC Educational Resources Information Center
Reynolds, George O.; And Others
This is a textbook of Fourier optics for the classroom or self-study. Major topics included in the 38 chapters are: Huygens' principle and Fourier transforms; image formation; optical coherence theory; coherent imaging; image analysis; coherent noise; interferometry; holography; communication theory techniques; analog optical computing; phase…
Analyzing Fourier Transforms for NASA DFRC's Fiber Optic Strain Sensing System
NASA Technical Reports Server (NTRS)
Fiechtner, Kaitlyn Leann
2010-01-01
This document provides a basic overview of the fiber optic technology used for sensing stress, strain, and temperature. Also, the document summarizes the research concerning speed and accuracy of the possible mathematical algorithms that can be used for NASA DFRC's Fiber Optic Strain Sensing (FOSS) system.
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…
NASA Astrophysics Data System (ADS)
Afanasyeva, Natalia I.; Kolyakov, Sergei F.; Butvina, Leonid N.
1998-04-01
The new method of fiber-optical evanescent wave Fourier transform IR (FEW-FTIR) spectroscopy has been applied to the diagnostics of normal tissue, as well as precancerous and cancerous conditions. The FEW-FTIR technique is nondestructive and sensitive to changes of vibrational spectra in the IR region, without heating and damaging human and animal skin tissue. Therefore this method and technique is an ideal diagnostic tool for tumor and cancer characterization at an early stage of development on a molecular level. The application of fiber optic technology in the middle IR region is relatively inexpensive and can be adapted easily to any commercially available tabletop FTIR spectrometers. This method of diagnostics is fast, remote, and can be applied to many fields Noninvasive medical diagnostics of skin cancer and other skin diseases in vivo, ex vivo, and in vitro allow for the development convenient, remote clinical applications in dermatology and related fields. The spectral variations from normal to pathological skin tissue and environmental influence on skin have been measured and assigned in the regions of 850-4000 cm-1. The lipid structure changes are discussed. We are able to develop the spectral histopathology as a fast and informative tool of analysis.
NASA Astrophysics Data System (ADS)
Afanasyeva, Natalia I.; Welser, Leslie; Bruch, Reinhard F.; Kano, Angelique; Makhine, Volodymyr
1999-10-01
A new infrared (IR) interferometric method has been developed in conjunction with low-loss, flexible optical fibers, sensors, and probes. This combination of fiber optical sensors and Fourier Transform (FT) spectrometers can be applied to many fields, including (1) noninvasive medical diagnostics of cancer and other different diseases in vivo, (2) minimally invasive bulk diagnostics of tissue, (3) remote monitoring of tissue, chemical processes, and environment, (4) surface analysis of polymers and other materials, (5) characterization of the quality of food, pharmacological products, cosmetics, paper, and other wood-related products, as well as (6) agricultural, forensic, geological, mining, and archeological field measurements. In particular, our nondestructive, fast, compact, portable, remote and highly sensitive diagnostics tools are very promising for subsurface analysis at the molecular level without sample preparation. For example, this technique is ideal for different types of soft porous foams, rough polymers, and rock surfaces. Such surfaces, as well as living tissue, are very difficult to investigate by traditional FTIR methods. We present here FEW-FTIR spectra of polymers, banana and grapefruit peels, and living tissues detected directly at surfaces. In addition, results on the vibrational spectral analysis of normal and pathological skin tissue in the region of 850 - 4000 cm-1 are discussed.
NASA Astrophysics Data System (ADS)
Kolyakov, Sergei; Afanasyeva, Natalia; Bruch, Reinhard; Afanasyeva, Natalia
1998-05-01
The new method of fiber optical evanescent wave Fourier transform infrared (FEW-FTIR) spectroscopy has been applied to the diagnostics of normal skin tissue, as well as precancerous and cancerous conditions. The FEW-FTIR technique is nondestructive and sensitive to changes of vibrational spectra in the IR region, without heating and damaging human and animal skin tissue. Therefore this method and technique is an ideal diagnostic tool for tumor and cancer characterization at an early stage of development on a molecular level. The application of fiber optic technology in the middle infrared (MIR) region is relatively inexpensive and can be adapted easily to any commercially available tabletop FTIR spectrometers. This method of diagnostics is fast (several seconds), and can be applied to many fields. Noninvasive medical diagnostics of skin cancer and other skin diseases in vivo, ex vivo, and in vitro allow for the development of convenient, remote clinical applications in dermatology and related fields. The spectral variations from normal to pathological skin tissue and environmental influence on skin have been measured.
Optical-Path-Difference Linear Mechanism for the Panchromatic Fourier Transform Spectrometer
NASA Technical Reports Server (NTRS)
Blavier, Jean-Francois L.; Heverly, Matthew C.; Key, Richard W.; Sander, Stanley P.
2011-01-01
A document discusses a mechanism that uses flex-pivots in a parallelogram arrangement to provide frictionless motion with an unlimited lifetime. A voicecoil actuator drives the parallelogram over the required 5-cm travel. An optical position sensor provides feedback for a servo loop that keeps the velocity within 1 percent of expected value. Residual tip/tilt error is compensated for by a piezo actuator that drives the interferometer mirror. This mechanism builds on previous work that targeted ground-based measurements. The main novelty aspects include cryogenic and vacuum operation, high reliability for spaceflight, compactness of the design, optical layout compatible with the needs of an imaging FTS (i.e. wide overall field-of-view), and mirror optical coatings to cover very broad wavelength range (i.e., 0.26 to 15 m).
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.
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 infrared (FTIR) fiber optic monitoring of composites during cure in an autoclave
NASA Technical Reports Server (NTRS)
Druy, Mark A.; Elandjian, Lucy; Stevenson, William A.; Driver, Richard D.; Leskowitz, Garett M.
1990-01-01
Real-time in situ monitoring of the chemical states of epoxy resins was investigated during cure in an autoclave using infrared evanescent spectroscopy. Fiber evanescent sensors were developed which may be sandwiched between the plies of the prepreg sample. A short length of sapphire fiber was used as the sensor cell portion of the fiber probe. Heavy metal fluoride glass optical fiber cables were designed for connecting the FTIR spectrometer to the sensor fiber within the autoclave. The sapphire fibers have outstanding mechanical thermal properties which should permit their use as an embedded link in all thermoset composites. The system is capable of operation at a temperature of 250 C for periods up to 8 hours without major changes to the fiber transmission. A discussion of the selection of suitable sensor fibers, the construction of a fiber-optic interface, and the interpretation of in situ infrared spectra of the curing process is presented.
NASA Technical Reports Server (NTRS)
Shackelford, R. G.; Walsh, J. R., Jr.
1975-01-01
An automatic Fourier transform diffraction pattern sampling system, used to investigate techniques for forestry classification of six band multispectral aerial photography is presented. Photographs and diagrams of the design, development and fabrication of a hybrid optical-digital Fourier transform detector are shown. The detector was designed around a concentric ring fiber optic array. This array was formed from many optical fibers which were sorted into concentric rings about a single fiber. All the fibers in each ring were collected into a bundle and terminated into a single photodetector. An optical/digital interface unit consisting of a high level multiplexer, and an analog-to-digital amplifier was also constructed and is described.
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.
Kamali, Tschackad; Považay, Boris; Kumar, Sunil; Silberberg, Yaron; Hermann, Boris; Werkmeister, René; Drexler, Wolfgang; Unterhuber, Angelika
2014-10-01
We demonstrate a multimodal optical coherence tomography (OCT) and online Fourier transform coherent anti-Stokes Raman scattering (FTCARS) platform using a single sub-12 femtosecond (fs) Ti:sapphire laser enabling simultaneous extraction of structural and chemical ("morphomolecular") information of biological samples. Spectral domain OCT prescreens the specimen providing a fast ultrahigh (4×12 μm axial and transverse) resolution wide field morphologic overview. Additional complementary intrinsic molecular information is obtained by zooming into regions of interest for fast label-free chemical mapping with online FTCARS spectroscopy. Background-free CARS is based on a Michelson interferometer in combination with a highly linear piezo stage, which allows for quick point-to-point extraction of CARS spectra in the fingerprint region in less than 125 ms with a resolution better than 4 cm(-1) without the need for averaging. OCT morphology and CARS spectral maps indicating phosphate and carbonate bond vibrations from human bone samples are extracted to demonstrate the performance of this hybrid imaging platform. PMID:25360965
Fourier transform and Vernier spectroscopy using an optical frequency comb at 3-5.4 μm.
Khodabakhsh, Amir; Ramaiah-Badarla, Venkata; Rutkowski, Lucile; Johansson, Alexandra C; Lee, Kevin F; Jiang, Jie; Mohr, Christian; Fermann, Martin E; Foltynowicz, Aleksandra
2016-06-01
We present a versatile mid-infrared frequency comb spectroscopy system based on a doubly resonant optical parametric oscillator tunable in the 3-5.4 μm range and two detection methods: a Fourier transform spectrometer (FTS) and a continuous-filtering Vernier spectrometer (CF-VS). Using the FTS with a multipass cell, we measure high precision broadband absorption spectra of CH_{4} at 3.3 μm and NO at 5.25 μm, the latter for the first time with comb spectroscopy, and we detect atmospheric species (CH_{4}, CO, CO_{2}, and H_{2}O) in air in the signal and idler ranges. Multiline fitting yields minimum detectable concentrations of 10-20 ppb Hz^{-1/2} for CH_{4}, NO, and CO. For the first time in the mid-infrared, we perform CF-VS using an enhancement cavity, a grating, and a single detector, and we measure the absorption spectrum of CH_{4} and H_{2}O in ambient air at ∼3.3 μm, reaching a 40 ppb concentration detection limit for CH_{4} in 2 ms. PMID:27244409
Mulvad, Hans Christian Hansen; Palushani, Evarist; Hu, Hao; Ji, Hua; Lillieholm, Mads; Galili, Michael; Clausen, Anders T; Pu, Minhao; Yvind, Kresten; Hvam, Jørn M; Jeppesen, Palle; Oxenløwe, Leif K
2011-12-12
We demonstrate conversion from 64 × 10 Gbit/s optical time-division multiplexed (OTDM) data to dense wavelength division multiplexed (DWDM) data with 25 GHz spacing. The conversion is achieved by time-domain optical Fourier transformation (OFT) based on four-wave mixing (FWM) in a 3.6 mm long silicon nanowire. A total of 40 out of 64 tributaries of a 64 × 10 Gbit/s OTDM-DPSK data signal are simultaneously converted with a bit-error rate (BER) performance below the 2 × 10(-3) FEC limit. Using a 50 m long highly nonlinear fiber (HNLF) for higher FWM conversion efficiency, 43 tributaries of a 64 × 10 Gbit/s OTDM-OOK data signal are converted with error-free performance (BER<10(-9)). PMID:22274110
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
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.
Introduction to Fourier Optics
ERIC Educational Resources Information Center
Huggins, Elisha
2007-01-01
Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…
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 (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
Chen, Yu; Leach, Franklin E.; Kaiser, Nathan K.; Dang, Xibei; Ibrahim, Yehia M.; Norheim, Randolph V.; Anderson, Gordon A.; Smith, Richard D.; Marshall, Alan G.
2015-01-19
Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry provides unparalleled mass accuracy and resolving power.[1],[2] With electrospray ionization (ESI), ions are typically transferred into the mass spectrometer through a skimmer, which serves as a conductance-limiting orifice. However, the skimmer allows only a small fraction of incoming ions to enter the mass spectrometer. An ion funnel, originally developed by Smith and coworkers at Pacific Northwest National Laboratory (PNNL)[3-5] provides much more efficient ion focusing and transfer. The large entrance aperture of the ion funnel allows almost all ions emanating from a heated capillary to be efficiently captured and transferred, resulting in nearly lossless transmission.
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; 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.
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.
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.
Chen, Yu; Leach, Franklin E.; Kaiser, Nathan K.; Dang, Xibei; Ibrahim, Yehia M.; Norheim, Randolph V.; Anderson, Gordon A.; Smith, Richard D.; Marshall, Alan G.
2015-01-19
Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry provides unparalleled mass accuracy and resolving power.[1],[2] With electrospray ionization (ESI), ions are typically transferred into the mass spectrometer through a skimmer, which serves as a conductance-limiting orifice. However, the skimmer allows only a small fraction of incoming ions to enter the mass spectrometer. An ion funnel, originally developed by Smith and coworkers at Pacific Northwest National Laboratory (PNNL)[3-5] provides much more efficient ion focusing and transfer. The large entrance aperture of the ion funnel allows almost all ions emanating from a heated capillary to be efficiently captured and transferred, resulting inmore » nearly lossless transmission.« less
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...
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.
NASA Astrophysics Data System (ADS)
Afanasyeva, Natalia I.; Makhine, Volodymyr; Bruch, Reinhard F.
1999-06-01
Fourier transform IR fiberoptic evanescent wave (FTIR-FEW) spectroscopy has been suggested as a powerful tool for clinical diagnostics of normal, pre-cancerous, and cancerous breast tissue ex vivo and in vitro in the middle IR region of the spectrum(850-1850 cm-1). This method is suitable for noninvasive and direct measurements of the spectra of normal and pathological tissues in vitro, ex vivo and in vivo. For the first time this method has been use nondestructively, rapidly, fast (15-20 sec) and remotely in the operating rooms of clinics. The aim of our studies has been the on-line testing of various tumor tissues during surgery to optimize and localize an area to remove tissue. We measured very small samples of normal and malignant breast tissue ex vivo with a fiber bent to a special angle, forming a special tip probe configuration. We also suggest here the minimally invasive FTIR-FEW diagnosis tool using 'needle' changeable tip probe for biopsy applications. The corresponding spectral histopathology scheme could be developed with help of this technique in vitro. The breast tissue at different stages of tumor or cancer has been distinguished very clearly in spectra of amide, cyclic and non-cyclic hydrogen bonded fragments, phosphate groups and sugars.
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)
α-bandlimited diffuser in fractional Fourier optics
NASA Astrophysics Data System (ADS)
Patiño-Vanegas, Alberto; Durand, Pierre-Emmanuel; Torres, Rafael; Pellat-Finet, Pierre
2016-04-01
We propose a method for calculating appropriate α-band limited diffusers using the fractional Fourier transform. In order to do this, we implement a method for performing a numerical interpolation in the fractional Fourier domain. Such diffusers with compact support in the Fresnel regime may be used in fractional Fourier optical systems where the use of diffusers produce speckles, e.g. digital holography or optical encryption. Numerical simulations are presented.
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.
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
NASA Astrophysics Data System (ADS)
Sokolov, Victor; Frank, George; Kolyakov, Sergei; Afanasyeva, Natalia; Bruch, Reinhard; Artujschenko, Slava
1998-05-01
Fiber Optic Evanescent Wave Fourier Transform Infrared (FEW-FTIR) spectroscopy using ultra sensitive fiber probes with low losses in the attenuated total reflection (ATR) regime in the middle infrared (MIR) region of the spectrum (850-1800 cm-1) was used for noninvasive and rapid (seconds) direct measurements of the spectra of normal and pathological breast tissue in vitro, ex vivo and in vivo. The aim of our studies is to perform accurate testing of tumor tissue at the early stages of their development. We have tested very small human samples (about 1mm) of normal and malignant tissue with fiber tip probes. As the first step we have performed a few experiments to optimize the fiber bending angle. In addition we are constructing and testing changeable tip probes for biopsy applications. Furthermore we are designing and creating needle probes for minimally invasive biopsy and fluid examinations.
Niedziela, R.F.; Norman, M.L.; DeForest, C.L.; Miller, R.E.; Worsnop, D.R.
1999-10-07
Frequency-dependent optical constants have been determined from the Fourier transform infrared spectra of laboratory-generated liquid sulfuric acid/water aerosols over a range of temperatures and compositions that are relevant to the upper troposphere and lower stratosphere of Earth. The compositions of the particles were determined in situ using a tunable diode laser to monitor equilibrium water vapor pressures. The infrared complex refractive indices of sulfuric acid are shown to be strongly dependent on temperature and composition, because of changes in the equilibrium between sulfate and bisulfate ions. Results from this study also have implications in understanding the temperature dependence of intermolecular interactions within ionic solutions. The database presented here is the most extensive yet available for the liquid solutions of sulfuric acid.
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.
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.
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
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.
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.
Arnott, W P; Schmitt, C; Liu, Y; Hallett, J
1997-07-20
Infrared extinction optical depth (500-5000 cm(-1)) has been measured with a Fourier transform infrared spectrometer for clouds produced with an ultrasonic nebulizer. Direct measurement of the cloud droplet size spectra agree with size spectra retrieved from inversion of the extinction measurements. Both indicate that the range of droplet sizes is 1-14 mum. The retrieval was accomplished with an iterative algorithm that simultaneously obtains water-vapor concentration. The basis set of droplet extinction functions are computed once by using numerical integration of the Lorenz-Mie theory over narrow size bins, and a measured water-vapor extinction curve was used. Extinction and size spectra are measured and computed for both steady-state and dissipating clouds. It is demonstrated that anomalous diffraction theory produces relatively poor droplet size and synthetic extinction spectra and that extinction measurements are helpful in assessing the validity of various theories. Calculations of cloud liquid-water content from retrieved size distributions agree with a parameterization based on optical-depth measurements at a wave number of 906 cm(-1) for clouds that satisfy the size spectral range assumptions of the parameterization. Significance of droplet and vapor contribution to the total optical depth is used to evaluate the reliability of spectral inversions. PMID:18259335
Fourier phase in Fourier-domain optical coherence tomography
Uttam, Shikhar; Liu, Yang
2015-01-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided. PMID:26831383
NASA Astrophysics Data System (ADS)
Hassan, Moinuddin; Ilev, Ilko
2016-03-01
Ophthalmic Viscosurgical Devices (OVDs) in clinical setting are a major health risk factor for potential endotoxin contamination in the eye, due to their extensive applications in cataract surgery for space creation, stabilization and protection of intraocular tissue and intraocular lens (IOL) during implantation. Endotoxin contamination of OVDs is implicated in toxic anterior syndrome (TASS), a severe complication of cataract surgery that leads to intraocular damage and even blindness. Current standard methods for endotoxin contamination detection utilize rabbit assay or Limulus amoebocyte lysate (LAL) assays. These endotoxin detection strategies are extremely difficult for gel-like type devices such as OVDs. To overcome the endotoxin detection limitations in OVDs, we have developed an alternative optical detection methodology for label-free and real-time sensing of bacterial endotoxin in OVDs, based on fiber-optic Fourier transform infrared (FO-FTIR) transmission spectrometry in the mid-IR spectral range from 2.5 micron to 12 micron. Endotoxin contaminated OVD test samples were prepared by serial dilutions of endotoxins on OVDs. The major results of this study revealed two salient spectral peak shifts (in the regions 2925 to 2890 cm^-1 and 1125 to 1100 cm^-1), which are associated with endotoxin in OVDs. In addition, FO-FTIR experimental results processed using a multivariate analysis confirmed the observed specific peak shifts associated with endotoxin contamination in OVDs. Thus, employing the FO-FTIR sensing methodology integrated with a multivariate analysis could potentially be used as an alternative endotoxin detection technique in OVD.
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.
NASA Technical Reports Server (NTRS)
Wise, Stephanie A.; Hardy, Robin C.; Dausch, David E.
1997-01-01
A new piezoelectric drive mechanism has been developed for optical translation in space-based spectrometer systems. The mechanism utilizes a stack of RAINBOW high displacement piezoelectric actuators to move optical components weighing less than 250 grams through a one centimeter travel. The mechanism uses the direct motion of the piezoelectric devices, stacked such that the displacement of the individual RAINBOW actuators is additive. A prototype device has been built which utilizes 21 RAINBOWs to accomplish the necessary travel. The mechanism weighs approximately 0.6 kilograms and uses less than 2 Watts of power at a scanning frequency of 0.5 Hertz, significantly less power than that required by state-of-the-art motor systems.
Chen, Yu; Leach, Franklin E.; Kaiser, Nathan K.; Dang, Xibei; Ibrahim, Yehia M.; Norheim, Randolph V.; Anderson, Gordon A.; Smith, Richard D.; Marshall, Alan G.
2014-01-01
Enhancements to the ion source and transfer optics of our 9.4 T FT-ICR mass spectrometer have resulted in improved ion transmission efficiency for more sensitive mass measurement of complex mixtures at the MS and MS/MS levels. The tube lens/skimmer has been replaced by a dual ion funnel and the following octopole by a quadrupole for reduced ion cloud radial expansion before transmission into a mass-selective quadrupole. The number of ions that reach the ICR cell is increased by an order of magnitude for the funnel/quadrupole relative to the tube lens/skimmer/octopole. PMID:25601704
NASA Astrophysics Data System (ADS)
Debnath, Lokenath
2012-07-01
Yu, Yifei; Luo, Linqing; Li, Bo; Guo, Linfeng; Yan, Jize; Soga, Kenichi
2015-10-01
The measured distance error caused by double peaks in the BOTDRs (Brillouin optical time domain reflectometers) system is a kind of Brillouin scattering spectrum (BSS) deformation, discussed and simulated for the first time in the paper, to the best of the authors' knowledge. Double peak, as a kind of Brillouin spectrum deformation, is important in the enhancement of spatial resolution, measurement accuracy, and crack detection. Due to the variances of the peak powers of the BSS along the fiber, the measured starting point of a step-shape frequency transition region is shifted and results in distance errors. Zero-padded short-time-Fourier-transform (STFT) can restore the transition-induced double peaks in the asymmetric and deformed BSS, thus offering more accurate and quicker measurements than the conventional Lorentz-fitting method. The recovering method based on the double-peak detection and corresponding BSS deformation can be applied to calculate the real starting point, which can improve the distance accuracy of the STFT-based BOTDR system. PMID:26479653
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.
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.
Uemura, T; Nishida, K; Sakakida, M; Ichinose, K; Shimoda, S; Shichiri, M
1999-01-01
Non-invasive blood glucose measurement through the mucous membrane of the lip was investigated using Fourier transform infrared (FT-IR) spectroscopy with an attenuated total reflection (ATR) prism. To achieve easy attachment and easy control of attachment pressure of the ATR prism to the mucous membrane of the lip, a chalcogenide optical fiber with an ATR prism built in the tip was used. The same glucose-specific peaks at wave numbers of 1080 and 1033 cm-1 as glucose solutions were found in a spectrum through the mucous membrane of the lip. With a constant pressure of the ATR prism to the mucous membrane of the lip of 6.7 x 10(3) dyn/cm2, coefficients of variation of measurements within the day and of day-to-day measurements were 3.8 and 5.4% respectively. To eliminate baseline drifts and interference of body constituents other than glucose, the difference absorbances at 1080 cm-1 between spectra measured at the postprandial state and background spectrum obtained at the fasting state as an individual characteristic were evaluated. Following i.v. pulsatile injection of glucose, the difference absorbances at 1080 cm-1 nicely followed the changes in blood glucose concentrations with a time delay of 4 min. In daily blood glucose monitoring, a highly significant correlation between the difference absorbances and increases in blood glucose concentrations above the fasting level was obtained (r = 0.920, P < 0.01). From these experiments, it was suggested that FT-IR spectroscopy with a chalcogenide optical fiber could be useful clinically for non-invasive monitoring of glucose through the mucous membrane of the lip. PMID:10450500
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.
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
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.
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.
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",…
Analysis of eccentric photorefraction by Fourier optics
NASA Astrophysics Data System (ADS)
Liu, Yong; Chen, Jiabi
2007-03-01
Eccentric photorefraction usually is used as early eyesight diagnostic test of infants and small children. Unlike currently approved geometrical optical model of eccentric photorefractometer, the crescent formation and the light-intensity distribution in the pupil image of a myopic eye are analyzed by Fourier optics with the assumption of an isotropic scattering retina. In the case of little circular light source and rectangular slit, the simulation results of different myopic diopters are obtained by geometrical optical theory and Fourier optics respectively. It is found that the simulation results by Fourier optics are similar as those obtained by geometrical optics, and all simulations are almost corresponding to the experimental result. The result demonstrates that the new method presented here is feasible.
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.
Surface Inspection using fourier transform infrared spectroscopy
Powell, G.L.; Smyrl, N.R.; Williams, D.M.; Meyers, H.M. III; Barber, T.E.; Marrero-Rivera, M.
1994-08-08
The use of reflectance Fourier transform infrared (FTIR) spectroscopy as a tool for surface inspection is described. Laboratory instruments and portable instruments can support remote sensing probes that can map chemical contaminants on surfaces. Detection limits under the best of conditions are in the subnanometer range (i.e., near absolute cleanliness), excellent performance is obtained in the submicrometer range, and useful performance may exist for films tens of microns thick. Identifying and quantifying contamination such as mineral oils and greases, vegetable oils, and silicone oils on aluminum foil, galvanized sheet steel, smooth aluminum tubing, and gritblasted 7075 aluminum alloy and D6AC steel are described. The ability to map in time and space the distribution of oil stains on metals is demonstrated. Techniques for quantitatively applying oils to metals, subsequently verifying the application, and nonlinear relationships between reflectance and the quantity of oil are discussed.
Fourier transform infrared spectroscopy for Mars science
NASA Astrophysics Data System (ADS)
Anderson, Mark S.; Andringa, Jason M.; Carlson, Robert W.; Conrad, Pamela; Hartford, Wayne; Shafer, Michael; Soto, Alejandro; Tsapin, Alexandre I.; Dybwad, Jens Peter; Wadsworth, Winthrop; Hand, Kevin
2005-03-01
Presented here is a Fourier transform infrared spectrometer (FTIR) for field studies that serves as a prototype for future Mars science applications. Infrared spectroscopy provides chemical information that is relevant to a number of Mars science questions. This includes mineralogical analysis, nitrogen compound recognition, truth testing of remote sensing measurements, and the ability to detect organic compounds. The challenges and scientific opportunities are given for the in situ FTIR analysis of Mars soil and rock samples. Various FTIR sampling techniques are assessed and compared to other analytical instrumentation. The prototype instrument presented is capable of providing field analysis in a Mars analog Antarctic environment. FTIR analysis of endolithic microbial communities in Antarctic rocks and a Mars meteor are given as analytical examples.
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.
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.
Time-domain surface profile imaging via a hyperspectral Fourier transform spectrometer.
Dupuis, Julia Rentz; Unlü, M Selim
2008-06-15
We describe a method for time-domain surface profile measurements via white-light reflection spectroscopy using a hyperspectral Fourier transform spectrometer (HS-FTS). This technique measures the frequency of the spectral modulation of reflected light from a multilayer optical surface and reports the spatially resolved optical thickness. Owing to the Fourier relationship, the Fourier transform spectrometer manifests this spectral modulation as temporal satellites in interferogram space. We show that measurement of the positions of these satellites can be used to reconstruct the optical thickness profile over a surface using the HS-FTS. PMID:18552962
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
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
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.
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).
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.
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.
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.
Oliveira, N. de; Polack, F.; Vervloet, M.; Nahon, L.; Joyeux, D.; Phalippou, D.; Rodier, J. C.
2009-04-15
We describe a Fourier transform (FT) spectrometer designed to operate down to 60 nm (20 eV) on a synchrotron radiation beamline for high resolution absorption spectrometry. As far as we know, such an instrument is not available below 140 nm mainly because manufacturing accurate and efficient beam splitters remains a major problem at these wavelengths, especially if a wide bandwidth operation is desired. In order to overcome this difficulty, we developed an interferometer based on wave front division instead of amplitude division. It relies on a modified Fresnel bimirror configuration that requires only flat mirrors. The instrument provides path difference scanning through the translation of one reflector. During the scanning, the moving reflector is controlled by an optical system that keeps its direction constant within a tolerable value and provides an accurate interferometric measurement of the path difference variation. Therefore, a regular interferogram sampling is obtained, producing a nominal spectral impulse response and an accurate spectral calibration. The first results presented in this paper show a measured spectral resolution of {delta}{sigma}=0.33 cm{sup -1} (interval between spectral samples). This was obtained with a sampling interval of 29 nm (path difference) and 512 K samples from a one-sided interferogram using a cosine FT. Such a sampling interval should allow the recording of large bandwidth spectra down to {lambda}=58 nm with an ultimate resolving power of 500 000 at this wavelength. In order to check the instrument performances, we first recorded an interferogram from a He-Ne stabilized laser. This provided the actual spectral impulse function, which was found to be fully satisfactory. The determination of the impulse response distortion and of the noise on the vacuum ultraviolet (VUV) spectral range provided accurate information in the sampling error profile over a typical scan. Finally, the instrument has been moved to the SU5 undulator
NASA Astrophysics Data System (ADS)
de Oliveira, N.; Joyeux, D.; Phalippou, D.; Rodier, J. C.; Polack, F.; Vervloet, M.; Nahon, L.
2009-04-01
We describe a Fourier transform (FT) spectrometer designed to operate down to 60 nm (20 eV) on a synchrotron radiation beamline for high resolution absorption spectrometry. As far as we know, such an instrument is not available below 140 nm mainly because manufacturing accurate and efficient beam splitters remains a major problem at these wavelengths, especially if a wide bandwidth operation is desired. In order to overcome this difficulty, we developed an interferometer based on wave front division instead of amplitude division. It relies on a modified Fresnel bimirror configuration that requires only flat mirrors. The instrument provides path difference scanning through the translation of one reflector. During the scanning, the moving reflector is controlled by an optical system that keeps its direction constant within a tolerable value and provides an accurate interferometric measurement of the path difference variation. Therefore, a regular interferogram sampling is obtained, producing a nominal spectral impulse response and an accurate spectral calibration. The first results presented in this paper show a measured spectral resolution of δσ =0.33 cm-1 (interval between spectral samples). This was obtained with a sampling interval of 29 nm (path difference) and 512 K samples from a one-sided interferogram using a cosine FT. Such a sampling interval should allow the recording of large bandwidth spectra down to λ&dotbelow;>=58 nm with an ultimate resolving power of 500 000 at this wavelength. In order to check the instrument performances, we first recorded an interferogram from a He-Ne stabilized laser. This provided the actual spectral impulse function, which was found to be fully satisfactory. The determination of the impulse response distortion and of the noise on the vacuum ultraviolet (VUV) spectral range provided accurate information in the sampling error profile over a typical scan. Finally, the instrument has been moved to the SU5 undulator
Spectral/Fourier Domain Optical Coherence Tomography
NASA Astrophysics Data System (ADS)
de Boer, Johannes F.
Optical coherence tomography is a low-coherence interferometric method for imaging of biological tissue [1, 2]. For more than a decade after its inception between 1988 and 1991, the dominant implementation has been time domain OCT (TD-OCT), in which the length of a reference arm is rapidly scanned. The first spectral or Fourier domain OCT (SD/FD-OCT) implementation was reported in 1995 [3]. In SD-OCT the reference arm is kept stationary, and the depth information is obtained by a Fourier transform of the spectrally resolved interference fringes in the detection arm of a Michelson interferometer. This approach has provided a significant advantage in signal-to-noise ratio (SNR), which despite reports as early as 1997 [4, 5] has taken about half a decade to be recognized fully by the OCT community in 2003 [6-8]. The first demonstration of SD-OCT for in vivo retinal imaging in 2002 [9] was followed by a full realization of the sensitivity advantage by video rate in vivo retinal imaging [10], including high-speed 3-D volumetric imaging [11], ultrahigh-resolution video rate imaging [12, 13], and Doppler blood flow determination in the human retina [14, 15]. The superior sensitivity of SD-OCT, combined with the lack of need for a fast mechanical scanning mechanism, has opened up the possibility of much faster scanning without loss of image quality and provided a paradigm shift from point sampling to volumetric mapping of biological tissue in vivo. The technology has been particularly promising for ophthalmology [16, 17]. In this chapter, the principles and system design considerations of SD-OCT will be discussed in more detail.
Geostationary Fourier Transform Spectrometer (GeoFTS)
NASA Astrophysics Data System (ADS)
Sander, S. P.; Bekker, D. L.; Blavier, J. L.; Duren, R. M.; Eldering, A.; Frankenberg, C.; Key, R.; Manatt, K.; Miller, C. E.; Natraj, V.; Rider, D. M.; Wu, Y.
2012-12-01
In order to confidently project the future evolution of climate and support efforts to mitigate the climate change, quantifying the emissions of CO2 and CH4 is a national and international priority. To accomplish this goal, new observational approaches are required that operate over spatial scales ranging from regional to global, and temporal scales from diurnal to decadal. Geostationary satellite observations of CO2, CH4 and correlative quantities such as CO and chlorophyll fluorescence provide a new measurement approach to deliver the quantity and quality of data needed for improved flux estimates and an improved understanding of the partitioning between biogenic and anthropogenic sources. GeoFTS is an exciting new concept that combines the game changing technology of imaging Fourier Transform Spectroscopy with the observational advantages of a geostationary orbit. The GeoFTS observations enable well-posed surface-atmospheric carbon exchange assessments as well as quantify the atmospheric signatures of anthropogenic CO2 and CH4 emissions. GeoFTS uses a single instrument to make measurements in the near-infrared spectral region at high spectral resolution. The imaging FTS measures atmospheric CO2, CH4, and CO to deliver high-resolution maps multiple times per day. A half-meter-sized cube, the instrument is designed to be a secondary "hosted" payload on a commercial GEO satellite. The instrument leverages recent NASA technology investments, uses a flight-proven interferometer and sensor chip assemblies, and requires no new technology development. NASA and other government agencies have adopted the hosted payload implementation approach because it substantially reduces the overall mission cost. Dense continuous mapping (4 km x 4 km pixels at 40 deg. latitude) is a transformational advance beyond, and complementary to, the capabilities of the NASA missions of record in low earth orbit, providing two to three orders of magnitude improvement in the number of
Imaging Fourier transform spectrometry of chemical plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.; Gross, Kevin C.; Perram, Glen P.
2009-05-01
A midwave infrared (MWIR) imaging Fourier transform spectrometer (FTS), the Telops FIRST-MWE (Field-portable Imaging Radiometric Spectrometer Technology - Midwave Extended) has been utilized for the standoff detection and characterization of chemical plumes. Successful collection and analysis of MWIR hyperspectral imagery of jet engine exhaust has allowed us to produce spatial profiles of both temperature and chemical constituent concentrations of exhaust plumes. Successful characterization of this high temperature combustion event has led to the collection and analysis of hyperspectral imagery of lower temperature emissions from industrial smokestacks. This paper presents MWIR data from remote collection of hyperspectral imagery of methyl salicilate (MeS), a chemical warfare agent simulant, during the Chemical Biological Distributed Early Warning System (CBDEWS) test at Dugway Proving Grounds, UT in 2008. The data did not contain spectral lines associated with emission of MeS. However, a few broad spectral features were present in the background-subtracted plume spectra. Further analysis will be required to assign these features, and determine the utility of MWIR hyperspectral imagery for analysis of chemical warfare agent plumes.
VLSI Implementation Of The Fast Fourier Transform
NASA Astrophysics Data System (ADS)
Chau, Paul M.; Ku, Walter H.
1986-03-01
A VLSI implementation of a Fast Fourier Transform (FFT) processor consisting of a mesh interconnection of complex floating-point butterfly units is presented. The Cooley-Tukey radix-2 Decimation-In-Frequency (DIF) formulation of the FFT was chosen since it offered the best overall compromise between the need for fast and efficient algorithmic computation and the need for a structure amenable to VLSI layout. Thus the VLSI implementation is modular, regular, expandable to various problem sizes and has a simple systolic flow of data and control. To evaluate the FFT architecture, VLSI area-time complexity concepts are used, but are now adapted to a complex floating-point number system rather than the usual integer ring representation. We show by our construction that the Thompson area-time optimum bound for the VLSI computation of an N-point FFT, area-time2oc = ORNlogN)1+a] can be attained by an alternative number representation, and hence the theoretical bound is a tight bound regardless of number system representation.
Fourier transform spectroscopy for future planetary missions
NASA Astrophysics Data System (ADS)
Brasunas, John C.; Hewagama, Tilak; Kolasinski, John R.; Kostiuk, Theodor
2015-11-01
Thermal-emission infrared spectroscopy is a powerful tool for exploring the composition, temperature structure, and dynamics of planetary atmospheres; and the temperature of solid surfaces. A host of Fourier transform spectrometers (FTS) such as Mariner IRIS, Voyager IRIS, and Cassini CIRS from NASA Goddard have made and continue to make important new discoveries throughout the solar system.Future FTS instruments will have to be more sensitive (when we concentrate on the colder, outer reaches of the solar system), and less massive and less power-hungry as we cope with decreasing resource allotments for future planetary science instruments. With this in mind, NASA Goddard was funded via the Planetary Instrument Definition and Development Progrem (PIDDP) to develop CIRS-lite, a smaller version of the CIRS FTS for future planetary missions. Following the initial validation of CIRS-lite operation in the laboratory, we have been acquiring atmospheric data in the 8-12 micron window at the 1.2 m telescope at the Goddard Geophysical and Astronomical Observatory (GGAO) in Greenbelt, MD. Targets so far have included Earth's atmosphere (in emission, and in absorption against the moon), and Venus.We will present the roadmap for making CIRS-lite a viable candidate for future planetary missions.
Determination of Fourier Transforms on an Instructional Analog Computer
ERIC Educational Resources Information Center
Anderson, Owen T.; Greenwood, Stephen R.
1974-01-01
An analog computer program to find and display the Fourier transform of some real, even functions is described. Oscilloscope traces are shown for Fourier transforms of a rectangular pulse, a Gaussian, a cosine wave, and a delayed narrow pulse. Instructional uses of the program are discussed briefly. (DT)
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.
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
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.
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
Multifunctional metasurface lens for imaging and Fourier transform
NASA Astrophysics Data System (ADS)
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-06-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping.
Multifunctional metasurface lens for imaging and Fourier transform
Wen, Dandan; Yue, Fuyong; Ardron, Marcus; Chen, Xianzhong
2016-01-01
A metasurface can manipulate light in a desirable manner by imparting local and space-variant abrupt phase change. Benefiting from such an unprecedented capability, the conventional concept of what constitutes an optical lens continues to evolve. Ultrathin optical metasurface lenses have been demonstrated based on various nanoantennas such as V-shape structures, nanorods and nanoslits. A single device that can integrate two different types of lenses and polarities is desirable for system integration and device miniaturization. We experimentally demonstrate such an ultrathin metasurface lens that can function either as a spherical lens or a cylindrical lens, depending on the helicity of the incident light. Helicity-controllable focal line and focal point in the real focal plane, as well as imaging and 1D/2D Fourier transforms, are observed on the same lens. Our work provides a unique tool for polarization imaging, image processing and particle trapping. PMID:27272601
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
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),
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
Recording of incoherent reflective volume Fourier holograms for optical correlators
NASA Astrophysics Data System (ADS)
Rodin, Vladislav G.; Starikov, Sergey N.
2007-01-01
The scheme of recording of reflective volume Fourier holograms in monochromatic light with partial spatial coherence is presented. The scheme contains posed on one optical axis an illuminated or self-luminous object, Fourier-objective, photosensitive medium and concave mirror. The light is proposed to be monochromatic with partial spatial coherence. The object is located in a front focal plane of the Fourier-objective. Photosensitive medium is placed in a back focal plane of the Fourier-objective, and the mirror is posed on a double focal length of the mirror from photosensitive medium. The light from input object is focused by the Fourier-objective in a volume of photosensitive medium, shaping a far field diffraction pattern of input object. This pattern is partial coherent analog of Fourier transform of input object. The light transmitted through the medium falls on the concave mirror and is reflected back, thus the mirror shapes the second copy of far field diffraction pattern of input object in the volume of photosensitive medium. Thus, these two light waves, propagating in the opposite directions, form the interference pattern in photosensitive medium, and a reflective volume Fourier hologram is recorded by monochromatic light with partial spatial coherence. The experiments on recording of these holograms and image reconstruction were realized. Patent by Russian Federation No2176099 on the device of recording of reflective volume holographic Fourier-filter in light with partial spatial coherence was taken out. Described reflective volume Fourier-holograms can be used in optical correlators as the spatial filters and spectral selectors at image recognition both in monochromatic and polychromatic light.
NASA Technical Reports Server (NTRS)
Boriakoff, Valentin
1994-01-01
The goal of this project was the feasibility study of a particular architecture of a digital signal processing machine operating in real time which could do in a pipeline fashion the computation of the fast Fourier transform (FFT) of a time-domain sampled complex digital data stream. The particular architecture makes use of simple identical processors (called inner product processors) in a linear organization called a systolic array. Through computer simulation the new architecture to compute the FFT with systolic arrays was proved to be viable, and computed the FFT correctly and with the predicted particulars of operation. Integrated circuits to compute the operations expected of the vital node of the systolic architecture were proven feasible, and even with a 2 micron VLSI technology can execute the required operations in the required time. Actual construction of the integrated circuits was successful in one variant (fixed point) and unsuccessful in the other (floating point).
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.
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.
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.
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
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.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Boriakoff, Valentin; Chen, Wei
1990-01-01
The NASA-Cornell Univ.-Worcester Polytechnic Institute Fast Fourier Transform (FFT) chip based on the architecture of the systolic FFT computation as presented by Boriakoff is implemented into an operating device design. The kernel of the system, a systolic inner product floating point processor, was designed to be assembled into a systolic network that would take incoming data streams in pipeline fashion and provide an FFT output at the same rate, word by word. It was thoroughly simulated for proper operation, and it has passed a comprehensive set of tests showing no operational errors. The black box specifications of the chip, which conform to the initial requirements of the design as specified by NASA, are given. The five subcells are described and their high level function description, logic diagrams, and simulation results are presented. Some modification of the Read Only Memory (ROM) design were made, since some errors were found in it. Because a four stage pipeline structure was used, simulating such a structure is more difficult than an ordinary structure. Simulation methods are discussed. Chip signal protocols and chip pinout are explained.
NASA Astrophysics Data System (ADS)
Afanasyeva, Natalia I.; Kolyakov, Sergei F.; Artioushenko, Vjacheslav G.; Sokolov, Victor V.; Frank, George A.
1998-04-01
Fourier transform IR fiberoptic evanescent wave spectroscopy has been suggested as a powerful tool for clinical diagnostics of normal, precancerous, and cancerous breast tissue ex vivo and in vitro in the middle IR region of the spectrum. This method is suitable for noninvasive and direct measurements of the spectra of normal and pathological tissues in vitro, ex vivo and in vivo. For the first time this method has been used nondestructively, rapidly, fast and remotely in the operating rooms of clinics. The aim of our studies has been the express testing of various tumor tissues during surgery to optimize and localize an area of removing tissue. We measured very small samples of normal and malignant breast tissue ex vivo with a fiber bent to a special angle, forming a special tip probe configuration. We also suggest her the minimally invasive FTIR-FEW diagnosis tool using 'needle' changeable tip probe for biopsy applications. The spectral histopathology branching could be developed with help of this technique in vitro. The breast tissue at different stages of tumor or cancer has been distinguished very clearly in spectra of amide, cyclic and noncyclic hydrogen bonded fragments, phosphate groups and sugars.
Mode analysis in optics through fractional transforms.
Alieva, T; Bastiaans, M J
1999-09-01
The relationship between the mode content and the fractional Fourier and fractional Hankel transforms of a function is established. It is shown that the Laguerre-Gauss spectrum of a rotationally symmetric wave front can be determined from the wave front's fractional Hankel transforms taken at the optical axis. PMID:18073985
Spectroscopic Stokes polarimetry based on Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Liu, Yeng-Cheng; Lo, Yu-Lung; Li, Chang-Ye; Liao, Chia-Chi
2015-02-01
Two methods are proposed for measuring the spectroscopic Stokes parameters using a Fourier transform spectrometer. In the first method, it is designed for single point measurement. The parameters are extracted using an optical setup comprising a white light source, a polarizer set to 0°, a quarter-wave plate and a scanning Michelson interferometer. In the proposed approach, the parameters are extracted from the intensity distributions of the interferograms produced with the quarter-wave plate rotated to 0°, 22.5°, 45° and -45°, respectively. For the second approach, the full-field and dynamic measurement can be designed based upon the first method with special angle design in a polarizer and a quarter-wave plate. Hence, the interferograms of two-dimensional detection also can be simultaneously extracted via a pixelated phase-retarder and polarizer array on a high-speed CCD camera and a parallel read-out circuit with a multi-channel analog to digital converter. Thus, a full-field and dynamic spectroscopic Stokes polarimetry without any rotating components could be developed. The validity of the proposed methods is demonstrated both numerically and experimentally. To the authors' knowledge, this could be the simplest optical arrangement in extracting the spectral Stokes parameters. Importantly, the latter one method avoids the need for rotating components within the optical system and therefore provides an experimentally straightforward means of extracting the dynamic spectral Stokes parameters.
Yang, G; Zhang, J; Gong, J; Chen, J; Ho, Y
1987-10-15
The phase mask distribution of optical sine transformation (OST) has been calculated according to the optical general transformation theory. To avoid the diffraction loss of the phase mask, the optical waveguide method is used. Computation shows that the optical sine transformation is possible with only one phase mask, i.e., one-half of a cylindrical lens in the 1-D case and one-quarter of a spherical lens in the 2-D case. Experimental results agree with the theoretical prediction. Image compression by OST is also given. PMID:20523380
Overlapped Fourier coding for optical aberration removal
Horstmeyer, Roarke; Ou, Xiaoze; Chung, Jaebum; Zheng, Guoan; Yang, Changhuei
2014-01-01
We present an imaging procedure that simultaneously optimizes a camera’s resolution and retrieves a sample’s phase over a sequence of snapshots. The technique, termed overlapped Fourier coding (OFC), first digitally pans a small aperture across a camera’s pupil plane with a spatial light modulator. At each aperture location, a unique image is acquired. The OFC algorithm then fuses these low-resolution images into a full-resolution estimate of the complex optical field incident upon the detector. Simultaneously, the algorithm utilizes redundancies within the acquired dataset to computationally estimate and remove unknown optical aberrations and system misalignments via simulated annealing. The result is an imaging system that can computationally overcome its optical imperfections to offer enhanced resolution, at the expense of taking multiple snapshots over time. PMID:25321982
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.
Nontensorial Transformation Optics
NASA Astrophysics Data System (ADS)
García-Meca, C.; Barceló, C.
2016-06-01
We present an alternative version of transformation optics that allows us to mold the flow of light without rotating or scaling the electromagnetic fields. The resulting media experience unusual force densities, are nonreciprocal, and exhibit loss or gain. Because of these singular features, a variety of effects and devices unreachable by standard transformation optics can be achieved, including reflectionless light compression, optical modes with arbitrary in-plane polarization, and special isolators.
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
Orthonormal mode sets for the two-dimensional fractional Fourier transformation.
Alieva, Tatiana; Bastiaans, Martin J
2007-05-15
A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied. PMID:17440542
Adaptive 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.
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.
Speckle size in optical Fourier domain imaging
NASA Astrophysics Data System (ADS)
Lamouche, G.; Vergnole, S.; Bisaillon, C.-E.; Dufour, M.; Maciejko, R.; Monchalin, J.-P.
2007-06-01
As in conventional time-domain optical coherence tomography (OCT), speckle is inherent to any Optical Fourier Domain Imaging (OFDI) of biological tissue. OFDI is also known as swept-source OCT (SS-OCT). The axial speckle size is mainly determined by the OCT resolution length and the transverse speckle size by the focusing optics illuminating the sample. There is also a contribution from the sample related to the number of scatterers contained within the probed volume. In the OFDI data processing, there is some liberty in selecting the range of wavelengths used and this allows variation in the OCT resolution length. Consequently the probed volume can be varied. By performing measurements on an optical phantom with a controlled density of discrete scatterers and by changing the probed volume with different range of wavelengths in the OFDI data processing, there is an obvious change in the axial speckle size, but we show that there is also a less obvious variation in the transverse speckle size. This work contributes to a better understanding of speckle in OCT.
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.
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.
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.
Transformational plasmon optics.
Liu, Yongmin; Zentgraf, Thomas; Bartal, Guy; Zhang, Xiang
2010-06-01
We propose and demonstrate efficiently molding surface plasmon polaritons (SPPs) based on transformation optics. SPPs are surface modes of electromagnetic waves tightly bound at metal-dielectric interfaces, which allow us to scale optics beyond the diffraction limit. Taking advantage of transformation optics, here we show that the propagation of SPPs can be manipulated in a prescribed manner by careful control of the dielectric material properties adjacent to a metal. Since the metal properties are completely unaltered, this methodology provides a practical way for routing light at very small scales. For instance, our approach enables SPPs to travel at uneven and curved surfaces over a broad wavelength range, where SPPs would normally suffer significant scattering losses. In addition, a plasmonic 180 degrees waveguide bend and a plasmonic Luneburg lens with simple designs are presented. The unique design flexibility of the transformational plasmon optics introduced here may open a new door to nano optics and downscaling of photonic circuits. PMID:20465268
A commercial Fourier transform interferometer system with telescopic optics has been installed in a van and used to make long-path absorption and single-ended emission measurements of gaseous pollutant concentrations at a number of geographical locations. The system covers the in...
Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM.
Sorokina, Mariia; Sygletos, Stylianos; Ellis, Andrew; Turitsyn, Sergei
2015-07-01
We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats). PMID:26125381
Hermann, Peter; Hoehl, Arne; Patoka, Piotr; Huth, Florian; Rühl, Eckart; Ulm, Gerhard
2013-02-11
We demonstrate scanning near-field optical microscopy with a spatial resolution below 100 nm by using low intensity broadband synchrotron radiation in the IR regime. The use of such a broadband radiation source opens up the possibility to perform nano-Fourier-transform infrared spectroscopy over a wide spectral range. PMID:23481749
Technology Transfer Automated Retrieval System (TEKTRAN)
Over 32,000 interferograms measured during open-path Fourier transform infrared (OP/FT-IR) measurements at dairy and hog farms were evaluated for anomalies. Five types of anomalies could be distinguished: a reduction in the interferogram intensity because of weather-related optical misalignment; an ...
[Using Fourier transform to calculate gas concentration in DOAS].
Liu, Qian-lin; Wang, Li-shi; Huang, Xin-jian; Wu, Yan-dan; Xiao, Ming-wei
2008-12-01
Being an analysis tool of high sensitivity, high resolution, multicomponents, real-time and fast monitoring, the differential optical absorption spectrometry (DOAS) is becoming a new method in atmosphere pollution monitoring. In the DOAS technique, many gases spectra have periodicity evidently, such as those from SO2, NO, NH3 and NO2. Aiming at three kinds of main air-polluted gases, i.e., SO2, NO and NO2 in atmosphere, the DOAS technique is used to monitor them, and Fourier transform is used to analyse the above-mentioned absorption spectra. Under the condition of Hanning Windows, Fourier transforma is used to process various gases spectra which have periodicity. In the process, the value of the characteristic frequency has a linearity relation to the gas concentration. So a new analysis method of DOAS is proposed, which is utilizing the relation between the value of the characteristic frequency and the gas concentration to deduce a linearity formula to calculate the gas concentration. So the value of the characteristic frequency can be used to get the gas concentration. For the gases with evident spectrum periodicity, such as SO2 and NO, this method is good. But for some gases with periodicity not evident, the error in the calculated concentration is beyond the allowable value. So in this method, the important process is frequency separation. It is also the main part in the future study. In a word, this method frees itself from the basic theory in the DOAS technique, cuts down on the process of the concentration calculation and the spectral analysis, and deserves further study. PMID:19248493
Signal processing with unequally spaced data in Fourier-domain optical coherence tomography
NASA Astrophysics Data System (ADS)
Vergnole, Sébastien; Lévesque, Daniel; Sherif, Sherif S.; Lamouche, Guy
2010-02-01
Different algorithms for performing Fourier transforms with unequally sampled data in wavenumber space for Fourier-domain optical coherence tomography are considered. The efficiency of these algorithms is evaluated from point-spread functions obtained with a swept-source optical coherence tomography system and from computational time. Images of a 4-layer phantom processed with these different algorithms are compared. We show that convolving the data with an optimized Kaiser-Bessel window allowing a small oversampling factor before computing the fast Fourier transform provides the optimal trade-off between image quality and computational time.
SPICA/SAFARI Fourier transform spectrometer mechanism evolutionary design
NASA Astrophysics Data System (ADS)
van den Dool, Teun C.; Kruizinga, Bob; Braam, Ben C.; Hamelinck, Roger F. M. M.; Loix, Nicolas; Van Loon, Dennis; Dams, Johan
2012-09-01
TNO, together with its partners, have designed a cryogenic scanning mechanism for use in the SAFARI1 Fourier Transform Spectrometer (FTS) on board of the SPICA mission. SPICA is one of the M-class missions competing to be launched in ESA's Cosmic Vision Programme2 in 2022. JAXA3 leads the development of the SPICA satellite and SRON is the prime investigator of the Safari instrument. The FTS scanning mechanism (FTSM) has to meet a 35 mm stroke requirement with an Optical Path Difference resolution of less then 15 nm and must fit in a small volume. It consists of two back-to-back roof-top mirrors mounted on a small carriage, which is moved using a magnetic bearing linear guiding system in combination with a magnetic linear motor serving as the OPD actuator. The FTSM will be used at cryogenic temperatures of 4 Kelvin inducing challenging requirements on the thermal power dissipation and heat leak. The magnetic bearing enables movements over a scanning stroke of 35.5 mm in a small volume. It supports the optics in a free-floating way with no friction, or other non-linearities, with sub-nanometer accuracy. This solution is based on the design of the breadboard ODL (Optical Delay Line) developed for the ESA Darwin mission4 and the MABE mechanism developed by Micromega Dynamics. During the last couple of years the initial design of the SAFARI instrument, as described in an earlier SPIE 2010 paper5, was adapted by the SAFARI team in an evolutionary way to meet the changing requirements of the SPICA payload module. This presentation will focus on the evolution of the FTSM to meet these changing requirements. This work is supported by the Netherlands Space Office (NSO).
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.
NASA Astrophysics Data System (ADS)
Goda, Keisuke; Tsia, Kevin K.; Jalali, Bahram
2008-09-01
Dispersive Fourier transformation is a powerful technique in which the spectrum of an optical pulse is mapped into a time-domain waveform using chromatic dispersion. It replaces a diffraction grating and detector array with a dispersive fiber and single photodetector. This simplifies the system and, more importantly, enables fast real-time measurements. Here we describe a novel ultrafast barcode reader and displacement sensor that employs internally amplified dispersive Fourier transformation. This technique amplifies and simultaneously maps the spectrally encoded barcode into a temporal waveform. It achieves a record acquisition speed of 25MHz—four orders of magnitude faster than the current state of the art.
Fourier and Hadamard transform spectrometers - A limited comparison
NASA Technical Reports Server (NTRS)
Tai, M. H.; Harwit, M.
1976-01-01
An encoding figure of merit is established for a detector-noise limited Fourier transform spectrometer (FTS) and compared to the comparable figure for a Hadamard transform spectrometer (HTS). The limitation of the Fourier system is partly that it does not truly Fourier analyze the radiation. Instead a cosine squared modulation is imposed on the different spectral frequencies. An additional difficulty is that neither the cosine nor the cosine squared functions form an orthonormal set. This makes the Fellgett's advantage (root-mean-squared figure of merit) for a single detector Michelson interferometer a factor of the square root of (N/8) greater than for a conventional grating instrument - rather than the square root of (N/2). The theoretical limit would be the square root of N.
Path Integrals, Fourier Transforms, and Feynman's Operational Calculus
Ahn, Byung Moo; Johnson, G. W.
1998-03-15
The disentangling process is the key to Feynman's operational calculus for noncommuting operators. The main result of his heuristic calculations deals with disentangling an exponential factor. We use the Wiener and Feynman integrals to make this disentangling (or time-ordering) mathematically rigorous in the case where the analytic functions from earlier work are replaced by Fourier transforms of complex-valued measures.
Fourier transform spectroscopy of cotton and cotton trash
Technology Transfer Automated Retrieval System (TEKTRAN)
Fourier Transform techniques have been shown to have higher signal-to-noise capabilities, higher throughput, negligible stray light, continuous spectra, and higher resolution. In addition, FT spectroscopy affords for frequencies in spectra to be measured all at once and more precise wavelength calib...
APPLICATION OF FOURIER TRANSFORM SPECTROSCOPY TO AIR POLLUTION PROBLEMS
The nature of information that can be retrieved from spectra obtained with Fourier transform spectroscopy is discussed. Nonlinear, least-squares analysis of spectra is capable of retrieving information that is beyond the reach of conventional methods and has improved precision an...
Remote detection of organics using Fourier transform infrared spectroscopy
Demirgian, J.C.; Spurgash, S.M.
1990-01-01
Fourier transform infrared (FTIR) spectroscopy is an ideal technique for remote detection of organic emissions. There is an atmospheric window in the 1200 to 800 cm{sup {minus}1} region, which corresponds to the fingerprint'' region for organic molecules. Virtually all organic molecules have a unique absorption/emission pattern in the fingerprint region. A remote-passive FTIR relies on ambient emission of infrared energy from organics to obtain spectra. The instrumentation consists of inlet optics, and interferometer, a mercury cadmium telluride (MCT) detector, and an on-board computer. The transportable unit measures 40 cm by 50 cm and has been used to collect data while mounted on a helicopter or ground vehicle. Through the use of this FTIR combined with least squares software, it is possible to analyze qualitatively and quantitatively for organic vapors from either the air or ground. The data presented will include quantitative releases of common organics present in incinerator stacks, hazardous wastes, and illegal laboratories. Data will be presented for pure compounds, mixtures, and target analytes in the presence of interfering compounds. The sensitivity, reproducibility, and the potential of the technique will be discussed. 1 ref., 8 figs., 6 tabs.
High-sensitive full-range optical vibrometry based on Fourier-domain optical coherence tomography
NASA Astrophysics Data System (ADS)
Subhash, Hrebesh M.; Leahy, Martin
2014-03-01
Optical vibrometery based on low coherence Fourier-domain optical coherence tomography (FD-OCT) technique are well capable for providing depth resolved vibration information in comparison with conventional laser based vibrometery. Recently, there has been growing interest in developing coherence-domain vibrometry for various clinical and pre-clinical applications. However, a major drawback of the conventional vibrometer based on Fourier-domain low coherence interferometry is the complex-conjugate ambiguity. This is because in FD-OCT, the detected real valued spectral interferogram is Fourier transformed to localize the scatter within the sample. The Fourier transform of a real valued function is Hermitian, so the reconstructed image is symmetric with respect to the zero-phase delay of the interferometer, leading to ambiguity in interpretation of the resulted OCT images. In this paper, we introduce a full range optical coherence vibrometry to utilize the whole imaging range of the spectrometer. The mirror image elimination is based on the linear phase modulation of the interferometer's reference arm mirror and with an algorithm that exploits Hilbert transform to obtain full range complex imaging.
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 VLSI architecture for simplified arithmetic Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Reed, Irving S.; Shih, Ming-Tang; Truong, T. K.; Hendon, E.; Tufts, D. W.
1992-01-01
The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.
Microholography by Numerical Wavefront Reconstruction in the Fourier Transform Geometry.
NASA Astrophysics Data System (ADS)
Haddad, Waleed Sami
New techniques for pulsed holographic microimaging with x-rays and visible light based on the Fourier transform geometry are presented. A charge-coupled device (CCD) is used to record the holographic information. Images are reconstructed numerically by fast Fourier transform (FFT) and by a novel "stigmatic" aberration-free technique. It is shown by numerical simulation that reconstruction by FFT inherently suffers from coma. An innovative design for a Fourier transform x -ray holographic microscope incorporating a metallic microsphere as the reference wave producing element is presented. The design is optimized for use with an x-ray laser source operating in the range lambda~eq43 A; nickel is found to be the best material for the reference sphere in this range. A visible light analog of the x-ray microscope was built and tested yielding an image of Ascaris larva. Two unique visible light Fourier transform holographic microscopes are also presented. The first incorporates a glycerol microdrop reference lens. This microscope was operated at N.A. ~ 0.25 with an argon ion laser at lambda = 514.5 nm. The transverse point spread function of the system was measured to be 1.40 mum, near the theoretical diffraction limit of 1.29 mu m. The second is a design based on a Mach-Zehnder interferometer. This Fourier Mach Zehnder holographic microscope (FMZHM) offers great flexibility and many advantages. The FMZHM was operated at N.A. _sp{~ }{>} 0.25 with lambda = 514.5 nm and yielded many 2-D and 3-D images of biological samples. A study of potential biological applications of visible and x-ray holographic microscopy is also presented.
Ding, Zhenyang; Liu, Tiegen; Meng, Zhuo; Liu, Kun; Chen, Qinnan; Du, Yang; Li, Dingjie; Yao, X Steve
2012-06-01
We propose using non-uniform FFT to minimize the degrading effect of frequency tuning nonlinearity of a tunable laser source (TLS) in an optical frequency-domain reflectometry (OFDR) system. We use an auxiliary interferometer to obtain the required instantaneous optical frequency of the TLS and successfully demonstrate 100 times enhancement in spatial resolution of OFDR with only a 20% increase in computation time. The corresponding measurement reflectivity sensitivity is better than -80 dB, sufficient to detect bending induced index changes in an optical fiber. PMID:22755676
NASA Astrophysics Data System (ADS)
Ding, Zhenyang; Liu, Tiegen; Meng, Zhuo; Liu, Kun; Chen, Qinnan; Du, Yang; Li, Dingjie; Yao, X. Steve
2012-06-01
We propose using non-uniform FFT to minimize the degrading effect of frequency tuning nonlinearity of a tunable laser source (TLS) in an optical frequency-domain reflectometry (OFDR) system. We use an auxiliary interferometer to obtain the required instantaneous optical frequency of the TLS and successfully demonstrate 100 times enhancement in spatial resolution of OFDR with only a 20% increase in computation time. The corresponding measurement reflectivity sensitivity is better than -80 dB, sufficient to detect bending induced index changes in an optical fiber.
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
Optimal Padding for the Two-Dimensional Fast Fourier Transform
NASA Technical Reports Server (NTRS)
Dean, Bruce H.; Aronstein, David L.; Smith, Jeffrey S.
2011-01-01
One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that
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.
Optical Security System with Fourier Plane encoding
NASA Astrophysics Data System (ADS)
Javidi, Bahram; Ahouzi, Esmail
1998-09-01
We propose a new technique for security verification of personal documents and other forms of personal identifications such as ID cards, passports, or credit cards. In this technique a primary pattern that might be a phase-encoded image is convolved by a random code. The information is phase encoded on the personal document. Therefore the information cannot be reproduced by an intensity detector such as a CCD camera. An optical processor based on the nonlinear joint transform correlator is used to perform the verification and the validation of documents with this technique. By verification of the biometrics information and the random code simultaneously, the proposed optical system determines whether a card is authentic or is being used by an authorized person. We tested the performance of the optical system for security and validation in the presence of input noise and in the presence of distortion of the information on the card. The performance of the proposed method is evaluated by use of a number of metrics. Statistical analysis of the system is performed to investigate the noise tolerance and the discrimination against false inputs for security verification.
Optical Security System with Fourier Plane encoding.
Javidi, B; Ahouzi, E
1998-09-10
We propose a new technique for security verification of personal documents and other forms of personal identifications such as ID cards, passports, or credit cards. In this technique a primary pattern that might be a phase-encoded image is convolved by a random code. The information is phase encoded on the personal document. Therefore the information cannot be reproduced by an intensity detector such as a CCD camera. An optical processor based on the nonlinear joint transform correlator is used to perform the verification and the validation of documents with this technique. By verification of the biometrics information and the random code simultaneously, the proposed optical system determines whether a card is authentic or is being used by an authorized person. We tested the performance of the optical system for security and validation in the presence of input noise and in the presence of distortion of the information on the card. The performance of the proposed method is evaluated by use of a number of metrics. Statistical analysis of the system is performed to investigate the noise tolerance and the discrimination against false inputs for security verification. PMID:18286124
Optimal color image restoration: Wiener filter and quaternion Fourier transform
NASA Astrophysics Data System (ADS)
Grigoryan, Artyom M.; Agaian, Sos S.
2015-03-01
In this paper, we consider the model of quaternion signal degradation when the signal is convoluted and an additive noise is added. The classical model of such a model leads to the solution of the optimal Wiener filter, where the optimality with respect to the mean square error. The characteristic of this filter can be found in the frequency domain by using the Fourier transform. For quaternion signals, the inverse problem is complicated by the fact that the quaternion arithmetic is not commutative. The quaternion Fourier transform does not map the convolution to the operation of multiplication. In this paper, we analyze the linear model of the signal and image degradation with an additive independent noise and the optimal filtration of the signal and images in the frequency domain and in the quaternion space.
Fourier transform spectrometer based on Fabry-Perot interferometer.
Al-Saeed, Tarek A; Khalil, Diaa A
2016-07-10
We analyze the Fourier transform spectrometer based on a symmetric/asymmetric Fabry-Perot interferometer. In this spectrometer, the interferogram is obtained by recording the intensity as a function of the interferometer length. Then, we recover the spectrum by applying the discrete Fourier transform (DFT) directly on the interferogram. This technique results in spectral harmonic overlap and fictitious wavenumber components outside the original spectral range. For this purpose, in this work, we propose a second method to recover the spectrum. This method is based on expanding the DFT of the interferogram and the spectrum by a Haar or box function. By this second method, we recovered the spectrum and got rid of the fictitious spectral components and spectral harmonic overlap. PMID:27409306
Development of a multi-Fourier-transform interferometer: fundamentals.
Ohta, Izumi S; Hattori, Makoto; Matsuo, Hiroshi
2006-04-20
We describe the development of an instrument that uses a Martin-Puplett-type Fourier-transform spectrometer to apply an aperture synthesis technique to millimeter and submillimeter waves. We call this instrument a multi-Fourier-transform interferometer (MuFT). The MuFT performs wideband imaging, spectroscopy, and polarimetry, at millimeter and submillimeter wavelengths. We describe the fundamentals of the MuFT and give an example of one potential implementation. A full description of the observables with a MuFT is provided. A physical explanation of the observability of complex visibility by the MuFT is given. Fundamental restrictions on observations with the MuFT, e.g., limits on spectral and spatial resolution and on fields of view, are discussed. The advantages of the MuFT are summarized. PMID:16633405
Spectral measurements of exhaust gases using a Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Schruefer, Elmar; Lindermeir, Erwin; Palme, Frank; Wuelbern, K.
1993-09-01
In recent years environmental issues have become increasingly important. Especially the impact of gaseous emissions on the atmosphere is of great interest. As a consequence a group of several coworkers was established at the Institute for Electrical Measurement of the Technical University of Munich, Germany) with the task to develop and investigate spectroscopic methods and instruments for the analysis of the chemical compsition of exhaust gases. This article describes the advantages of the application of Fourier transform spectroscopy against conventional gas analysis devices. Moreover results of measurements of the exhaust of a smokestack of a coal fired power plant and of an aircraft engine are presented. The last section deals with the development of a Fourier transform spectrometer which is not equipped with any moving parts. This design was made especially for applications in harsh environments.
Transforming the optical landscape.
Pendry, J B; Luo, Yu; Zhao, Rongkuo
2015-05-01
Electromagnetism provides us with some of the most powerful tools in science, encompassing lasers, optical microscopes, magnetic resonance imaging scanners, radar, and a host of other techniques. To understand and develop the technology requires more than a set of formal equations. Scientists and engineers have to form a vivid picture that fires their imaginations and enables intuition to play a full role in the process of invention. It is to this end that transformation optics has been developed, exploiting Faraday's picture of electric and magnetic fields as lines of force, which can be manipulated by the electrical permittivity and magnetic permeability of surrounding materials. Transformation optics says what has to be done to place the lines of force where we want them to be. PMID:25931549
Transforming the optical landscape
NASA Astrophysics Data System (ADS)
Pendry, J. B.; Luo, Yu; Zhao, Rongkuo
2015-05-01
Electromagnetism provides us with some of the most powerful tools in science, encompassing lasers, optical microscopes, magnetic resonance imaging scanners, radar, and a host of other techniques. To understand and develop the technology requires more than a set of formal equations. Scientists and engineers have to form a vivid picture that fires their imaginations and enables intuition to play a full role in the process of invention. It is to this end that transformation optics has been developed, exploiting Faraday’s picture of electric and magnetic fields as lines of force, which can be manipulated by the electrical permittivity and magnetic permeability of surrounding materials. Transformation optics says what has to be done to place the lines of force where we want them to be.
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.
Dual Comb Fourier Transform Spectroscopy in the Green Region
NASA Astrophysics Data System (ADS)
Knize, R. J.; Bernhardt, B.; Picqué, N.; Hänsch, T. W.
2010-06-01
Laser combs in combination with other advancing tools of laser science, nonlinear optics, photonics, and electronic signal processing have the potential to vastly enhance the range and capabilities of molecular laser spectroscopy. The high versatility of frequency comb sources can indeed harness new techniques for ultra-rapid and ultra-sensitive recording of complex molecular spectra. The recent proof-of-principle demonstrations of dual comb Fourier transform spectroscopy have mostly been carried out in the near-infrared region, around 1.0 and 1.5 μm. The mode-locked ytterbium- or erbium-doped fiber femtosecond laser systems emitting in this range indeed require few adjustment thanks to their guided light and permit reliable unattended operation. With expanded wavelength coverage and continued improvements in speed and sensitivity, dual comb spectroscopy should find use as a novel, time-domain spectroscopic analytical tool. As far as molecular spectroscopy is concerned, the mid-infrared and visible-ultraviolet wavelength regions show both the potential for specificity and sensitivity for tracing molecules. In particular, the visible-ultraviolet region complements the mid-infrared molecular fingerprint range, as it provides access to many electronic transitions, in particular belonging to reactive species. In this contribution, we report on our progress in the implementation of dual comb spectroscopy in the 520 nm green region. We present preliminary results on a powerful new sensitive ultra-rapid tool for linear rovibronic absorption spectroscopy, based on frequency-doubled ytterbium-doped fiber lasers and we discuss its intriguing prospects for spectroscopy of short lived transient species.
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.
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
Universal discrete Fourier optics RF photonic integrated circuit architecture.
Hall, Trevor J; Hasan, Mehedi
2016-04-01
This paper describes a coherent electro-optic circuit architecture that generates a frequency comb consisting of N spatially separated orders using a generalised Mach-Zenhder interferometer (MZI) with its N × 1 combiner replaced by an optical N × N Discrete Fourier Transform (DFT). Advantage may be taken of the tight optical path-length control, component and circuit symmetries and emerging trimming algorithms offered by photonic integration in any platform that offers linear electro-optic phase modulation such as LiNbO_{3,} silicon, III-V or hybrid technology. The circuit architecture subsumes all MZI-based RF photonic circuit architectures in the prior art given an appropriate choice of output port(s) and dimension N although the principal application envisaged is phase correlated subcarrier generation for all optical orthogonal frequency division multiplexing. A transfer matrix approach is used to model the operation of the architecture. The predictions of the model are validated by simulations performed using an industry standard software tool. Implementation is found to be practical. PMID:27137048
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
Fourier information optics for the ultrafast time domain.
Weiner, Andrew M
2008-02-01
Ultrafast photonic signal processing based on Fourier optics principles offers exciting possibilities to go beyond the processing speeds of electronics technologies for applications in high-speed fiber communications and ultrawideband wireless. I review our recent work on processing of ultrafast optical signals via conversion between time, space, and optical frequency (Fourier) domains. Specific topics include optical arbitrary waveform generation, application of optical pulse shaping technologies for wavelength-parallel compensation of fiber transmission impairments and for experimental studies of optical code-division multiple-access communications, and application of photonic methods for precompensation of dispersion effects in wireless transmission of radio-frequency signals over ultrawideband antenna links. PMID:18239704
Unsal, E; Nugay, I I; Offenbach, I; Gross, M; Manning, C; Cakmak, M
2013-07-01
The design and performance of a multisensory instrument to track physical and chemical changes of thin polymer films (typically 5 μm < thickness < 100 μm) subjected to thermal and mechanical treatments are described in this paper. For the first time, real-time measurements of spectral birefringence, true stress, true strain, and temperature are integrated together with ultra-rapid-scan polarized FT-IR spectrometer (URS-FT-IR) to investigate the relationships between true mechanical measures and structural features at different length scales. The rheo-optical properties (birefringence-true stress-true strain) are collected at a rate of 10 data points∕s and URS-FT-IR data are collected at a rate of 300 complete spectra∕s. The IR dichroism measurement is performed by exposing the sample to non-polarized IR beam in transmission mode with two mutually perpendicular polarizations, parallel and perpendicular to the stretching direction, received by detector unit. This design allows to analyze both polarizations simultaneously wavenumbers in the range of 500 cm(-1)-4000 cm(-1). Controlled processing parameters include air speed, air temperature, stretching rate, stretching ratio, stretch cycling, and holding times; while simultaneously measuring optical retardation, sample width, temperature, load cell, and both parallel and perpendicular IR spectra. Calibration and performance of this instrument is demonstrated with several film samples. These are: A polystyrene standard, an atactic polystyrene (homo-polymer), a polyurethane (consists of hard and soft segments) for physical changes during uniaxial deformation, and a polyamic acid during imidization reaction. This measurement system is particularly useful in unraveling molecular level details of complex physical and chemical events that take place during very fast deformation schemes (uniaxial stretching, retraction, relaxation, annealing, etc.) relevant to industrial processes. These include specific orientation
NASA Astrophysics Data System (ADS)
Unsal, E.; Nugay, I. I.; Offenbach, I.; Gross, M.; Manning, C.; Cakmak, M.
2013-07-01
The design and performance of a multisensory instrument to track physical and chemical changes of thin polymer films (typically 5 μm < thickness < 100 μm) subjected to thermal and mechanical treatments are described in this paper. For the first time, real-time measurements of spectral birefringence, true stress, true strain, and temperature are integrated together with ultra-rapid-scan polarized FT-IR spectrometer (URS-FT-IR) to investigate the relationships between true mechanical measures and structural features at different length scales. The rheo-optical properties (birefringence-true stress-true strain) are collected at a rate of 10 data points/s and URS-FT-IR data are collected at a rate of 300 complete spectra/s. The IR dichroism measurement is performed by exposing the sample to non-polarized IR beam in transmission mode with two mutually perpendicular polarizations, parallel and perpendicular to the stretching direction, received by detector unit. This design allows to analyze both polarizations simultaneously wavenumbers in the range of 500 cm-1-4000 cm-1. Controlled processing parameters include air speed, air temperature, stretching rate, stretching ratio, stretch cycling, and holding times; while simultaneously measuring optical retardation, sample width, temperature, load cell, and both parallel and perpendicular IR spectra. Calibration and performance of this instrument is demonstrated with several film samples. These are: A polystyrene standard, an atactic polystyrene (homo-polymer), a polyurethane (consists of hard and soft segments) for physical changes during uniaxial deformation, and a polyamic acid during imidization reaction. This measurement system is particularly useful in unraveling molecular level details of complex physical and chemical events that take place during very fast deformation schemes (uniaxial stretching, retraction, relaxation, annealing, etc.) relevant to industrial processes. These include specific orientation behavior of
A compact, high numerical aperture imaging Fourier transform spectrometer and its application
NASA Astrophysics Data System (ADS)
Alcock, R. D.; Coupland, J. M.
2006-11-01
This paper describes a compact imaging Fourier transform spectrometer with high numerical aperture. In comparison with other optical arrangements in which extended interferometer paths are required for the inclusion of dispersion compensation optics, this technique utilizes a rudimentary cubic beam splitter based Michelson interferometer with minimal optical path so that the numerical aperture of the system is maximized. Mathematical modelling is presented showing that the fringe distortions caused by the dispersion in the cubic beam splitter can be entirely removed without any loss of the spectral information. An illustration of the power of the technique is given classifying between different plant foliage performed using a Fisher discriminant function based optimal linear filtering.
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.
Hassan, Moinuddin Ilev, Ilko
2014-10-15
Contamination of medical devices has become a critical and prevalent public health safety concern since medical devices are being increasingly used in clinical practices for diagnostics, therapeutics and medical implants. The development of effective sensing methods for real-time detection of pathogenic contamination is needed to prevent and reduce the spread of infections to patients and the healthcare community. In this study, a hollow-core fiber-optic Fourier transform infrared spectroscopy methodology employing a grazing incidence angle based sensing approach (FO-FTIR-GIA) was developed for detection of various biochemical contaminants on medical device surfaces. We demonstrated the sensitivity of FO-FTIR-GIA sensing approach for non-contact and label-free detection of contaminants such as lipopolysaccharide from various surface materials relevant to medical device. The proposed sensing system can detect at a minimum loading concentration of approximately 0.7 μg/cm{sup 2}. The FO-FTIR-GIA has the potential for the detection of unwanted pathogen in real time.
NASA Astrophysics Data System (ADS)
Huo, Yanfeng; Duan, Minzheng; Tian, Wenshou; Min, Qilong
2015-08-01
A differential optical absorption spectroscopy (DOAS)-like algorithm is developed to retrieve the column-averaged dryair mole fraction of carbon dioxide from ground-based hyper-spectral measurements of the direct solar beam. Different to the spectral fitting method, which minimizes the difference between the observed and simulated spectra, the ratios of multiple channel-pairs—one weak and one strong absorption channel—are used to retrieve from measurements of the shortwave infrared (SWIR) band. Based on sensitivity tests, a super channel-pair is carefully selected to reduce the effects of solar lines, water vapor, air temperature, pressure, instrument noise, and frequency shift on retrieval errors. The new algorithm reduces computational cost and the retrievals are less sensitive to temperature and H2O uncertainty than the spectral fitting method. Multi-day Total Carbon Column Observing Network (TCCON) measurements under clear-sky conditions at two sites (Tsukuba and Bremen) are used to derive xxxx for the algorithm evaluation and validation. The DOAS-like results agree very well with those of the TCCON algorithm after correction of an airmass-dependent bias.
Field-of-view analysis of a polarization interference Fourier transform imaging spectrometer.
DeHoog, Edward; Xia, Xiaowei; Parfenov, Alexander; Shih, Min-Yi
2011-09-20
The Fourier transform imaging spectrometer (FTIS) is an important tool for the measurement of spectral information in a scene. Advances in electro-optic crystal systems have led to the advent of the FTIS based on polarization interference filters. The operation of these devices as spectrometers has been well characterized, but the imaging capabilities have yet to be thoroughly explored. We explore the field-of-view limitations that occur when using this particular type of FTIS. PMID:21947057
Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform.
Alieva, T; Bastiaans, M J
2000-12-01
The ambiguity function and Cohen's class of bilinear phase-space distributions are represented in a quasipolar coordinate system instead of in a Cartesian system. Relationships between these distributions and the fractional Fourier transform are derived; in particular, derivatives of the ambiguity function are related to moments of the fractional power spectra. A simplification is achieved for the description of underspread signals, for optical beam characterization, and for the generation of signal-adaptive phase-space distributions. PMID:11140493
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
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
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.
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
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.
Broadband Mid-Infrared Comb-Resolved Fourier Transform Spectroscopy
NASA Astrophysics Data System (ADS)
Lee, Kevin; Mills, Andrew; Mohr, Christian; Jiang, Jie; Fermann, Martin; Maslowski, Piotr
2014-06-01
We report on a comb-resolved, broadband, direct-comb spectroscopy system in the mid-IR and its application to the detection of trace gases and molecular line shape analysis. By coupling an optical parametric oscillator (OPO), a 100 m multipass cell, and a high-resolution Fourier transform spectrometer (FTS), sensitive, comb-resolved broadband spectroscopy of dilute gases is possible. The OPO has radiation output at 3.1-3.7 and 4.5-5.5 μm. The laser repetition rate is scanned to arbitrary values with 1 Hz accuracy around 417 MHz. The comb-resolved spectrum is produced with an absolute frequency axis depending only on the RF reference (in this case a GPS disciplined oscillator), stable to 1 part in 10^9. The minimum detectable absorption is 1.6x10-6 wn Hz-1/2. The operating range of the experimental setup enables access to strong fundamental transitions of numerous molecular species for applications based on trace gas detection such as environmental monitoring, industrial gas calibration or medical application of human breath analysis. In addition to these capabilities, we show the application for careful line shape analysis of argon-broadened CO band spectra around 4.7 μm. Fits of the obtained spectra clearly illustrate the discrepancy between the measured spectra and the Voigt profile (VP), indicating the need to include effects such as Dicke narrowing and the speed-dependence of the collisional width and shift in the line shape model, as was shown in previous cw-laser studies. In contrast to cw-laser based experiments, in this case the entire spectrum (˜ 250 wn) covering the whole P and R branches can be measured in 16 s with 417 MHz resolution, decreasing the acquisition time by orders of magnitude. The parallel acquisition allows collection of multiple lines simultaneously, removing the correlation of possible temperature and pressure drifts. While cw-systems are capable of measuring spectra with higher precision, this demonstration opens the door for fast
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
Truncated sampling for the Fourier-Mellin transform with applications to wideband WVD computation
NASA Astrophysics Data System (ADS)
Allen, Jeffrey
1990-11-01
The Fourier-Mellin transform (FMT) of an input function is defined as and is the magnitude squared of the Mellin transform of the magnitude squared of the Fourier transform of the input function [1]. As such the FMT is unchanged by translations and dilations of the input function. While the FMT has found applications in optical pattern recognition [3] [5] ship classification by sonar and radar [15] and image processing [10] only cursory attention has been paid to the truncation error incurred by using a finite number of samples of the input function. This paper establishes truncation bounds for computing the FMT for band-limited functions from a finite number of samples of the input function. These bounds naturally suggest an implementation of the FMT by the method of direct expansions [4] [14]. This approach readily generalizes to a direct expansion for the Wigner-Ville distribution [13] and the Q distribution [2]. 1 Principal Notation u(x) fff00 e_2tu(t)dt Fourier transform of u M(u s) fD X_i2r8() Mellin transform of u . FM(u s) M(lI(x)I2 s)________ Fourier-Mellin transform of u Q(U V f002rt U(wft)_V(w/fr) Q distribution of U and V W(U V t w) fe_i2ntY U(w + y/2) V(w y/2) dy Wigner-Ville distribution of U and V
Gaseous effluent monitoring and identification using an imaging Fourier transform spectrometer
Carter, M.R.; Bennett, C.L.; Fields, D.J.; Hernandez, J.
1993-10-01
We are developing an imaging Fourier transform spectrometer for chemical effluent monitoring. The system consists of a 2-D infrared imaging array in the focal plane of a Michelson interferometer. Individual images are coordinated with the positioning of a moving mirror in the Michelson interferometer. A three dimensional data cube with two spatial dimensions and one interferogram dimension is then Fourier transformed to produce a hyperspectral data cube with one spectral dimension and two spatial dimensions. The spectral range of the instrument is determined by the choice of optical components and the spectral range of the focal plane array. Measurements in the near UV, visible, near IR, and mid-IR ranges are possible with the existing instrument. Gaseous effluent monitoring and identification measurements will be primarily in the ``fingerprint`` region of the spectrum, ({lambda} = 8 to 12 {mu}m). Initial measurements of effluent using this imaging interferometer in the mid-IR will be presented.
de Oliveira, M E; de Oliveira, G N; de Souza, J C; dos Santos, P A M
2016-02-10
In the present paper, the method of simultaneous moiré-like fringe pattern projection for Fourier transform profilometry is described. The photorefractive holographic interferometric process produces controlled moiré-like patterns with two or more different variation directions. Each low spatial frequency fringe pattern is experimentally obtained as a result of the superposition of two high spatial frequency sinusoidal gratings, with slightly different pitches, for each fringe variation direction. These dynamic moiré-like patterns are induced due to an optical holographic beating of the sinusoidal induced gratings in the volume of the photorefractive Bi₁₂TiO₂₀ (BTO) crystal sample used as dynamic holographic medium. Two or more moiré-like fringe patterns, with at least two different variation directions, simultaneously (or not), are projected onto the object surface. Thus, this is the 2D fringe projection stage of our proposed Fourier transform procedure to determine the profile of a simple object. PMID:26906374
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.
Extending Single-Molecule Microscopy Using Optical Fourier Processing
2015-01-01
This article surveys the recent application of optical Fourier processing to the long-established but still expanding field of single-molecule imaging and microscopy. A variety of single-molecule studies can benefit from the additional image information that can be obtained by modulating the Fourier, or pupil, plane of a widefield microscope. After briefly reviewing several current applications, we present a comprehensive and computationally efficient theoretical model for simulating single-molecule fluorescence as it propagates through an imaging system. Furthermore, we describe how phase/amplitude-modulating optics inserted in the imaging pathway may be modeled, especially at the Fourier plane. Finally, we discuss selected recent applications of Fourier processing methods to measure the orientation, depth, and rotational mobility of single fluorescent molecules. PMID:24745862
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.
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.
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
Instrument concept of the imaging Fourier transform spectrometer GLORIA
NASA Astrophysics Data System (ADS)
Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.
2014-03-01
The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the Upper Troposphere/Lower Stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated in a gimbal. The assembly can be mounted in the belly pod of the German high altitude and long range research aircraft HALO and in instrument bays of the Russian M55 Geophysica. Measurements are made predominantly in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
Instrument concept of the imaging Fourier transform spectrometer GLORIA
NASA Astrophysics Data System (ADS)
Friedl-Vallon, F.; Gulde, T.; Hase, F.; Kleinert, A.; Kulessa, T.; Maucher, G.; Neubert, T.; Olschewski, F.; Piesch, C.; Preusse, P.; Rongen, H.; Sartorius, C.; Schneider, H.; Schönfeld, A.; Tan, V.; Bayer, N.; Blank, J.; Dapp, R.; Ebersoldt, A.; Fischer, H.; Graf, F.; Guggenmoser, T.; Höpfner, M.; Kaufmann, M.; Kretschmer, E.; Latzko, T.; Nordmeyer, H.; Oelhaf, H.; Orphal, J.; Riese, M.; Schardt, G.; Schillings, J.; Sha, M. K.; Suminska-Ebersoldt, O.; Ungermann, J.
2014-10-01
The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is an imaging limb emission sounder operating in the thermal infrared region. It is designed to provide measurements of the upper troposphere/lower stratosphere with high spatial and high spectral resolution. The instrument consists of an imaging Fourier transform spectrometer integrated into a gimbal. The assembly can be mounted in the belly pod of the German High Altitude and Long Range research aircraft (HALO) and in instrument bays of the Russian M55 Geophysica. Measurements are made in two distinct modes: the chemistry mode emphasises chemical analysis with high spectral resolution, and the dynamics mode focuses on dynamical processes of the atmosphere with very high spatial resolution. In addition, the instrument allows tomographic analyses of air volumes. The first measurement campaigns have shown compliance with key performance and operational requirements.
3-D Printed Slit Nozzles for Fourier Transform Microwave Spectroscopy
NASA Astrophysics Data System (ADS)
Dewberry, Chris; Mackenzie, Becca; Green, Susan; Leopold, Ken
2015-06-01
3-D printing is a new technology whose applications are only beginning to be explored. In this report, we describe the application of 3-D printing to the facile design and construction of supersonic nozzles. The efficacy of a variety of designs is assessed by examining rotational spectra OCS and Ar-OCS using a Fourier transform microwave spectrometer with tandem cavity and chirped-pulse capabilities. This work focuses primarily on the use of slit nozzles but other designs have been tested as well. New nozzles can be created for 0.50 or less each, and the ease and low cost should facilitate the optimization of nozzle performance (e.g., jet temperature or cluster size distribution) for the needs of any particular experiment.
Fourier transform infrared phase shift cavity ring down spectrometer
NASA Astrophysics Data System (ADS)
Schundler, Elizabeth; Mansur, David J.; Vaillancourt, Robert; Benedict-Gill, Ryan; Newbry, Scott P.; Engel, James R.; Rentz Dupuis, Julia
2013-05-01
We report on our current status towards the development of a prototype Fourier transform infrared phase shift cavity ring down spectrometer (FTIR-PS-CRDS) system under a U.S. EPA SBIR contract. Our system uses the inherent wavelength-dependent modulation imposed by the FTIR on a broadband thermal source for the phase shift measurement. This spectrally-dependent phase shift is proportional to the spectrally-dependent ring down time, which is proportional to the losses of the cavity including those due to molecular absorption. Our approach is a broadband and spectral range enhancement to conventional CRDS which is typically done in the near IR at a single wavelength; at the same time our approach is a sensitivity enhancement to traditional FTIR owing to the long effective path of the resonant cavity. In this paper we present a summary of the theory including performance projections and the design details of the prototype FTIR-PS-CRDS system.
On the abstracted dataflow complexity of Fast Fourier Transforms
Boehm, A.P.W.; Hiromoto, R.E.; Kelly, K.A.; Ashley, J.M.
1992-05-01
In this paper we develop and analyze the simulated performance of codes for the Fast Fourier Transform written in If and targeted for execution on Motorola`s dataflow machine Monsoon. The FFT application is of interest because of its computational parallelism, its requirement for global communications, and its array element data dependences. We use the parallel profiling simulator Id World to study the dataflow performance of various implementations. Our approach is comparative. We study two approaches, a recursive and an iterative one, and in each version we examine the effect of a variety of implementations. We contend that only through such comparative evaluations can significant insight be gained in understanding the computational and structural details of functional algorithms.
Highly sensitive Fourier transform spectroscopy with LED sources
NASA Astrophysics Data System (ADS)
Serdyukov, V. I.; Sinitsa, L. N.; Vasil'chenko, S. S.
2013-08-01
It is shown that the use of high luminance LED emitters as a light source for Fourier transform spectrometers permits to enhance their threshold sensitivity in the visible range by orders of magnitude. Using a 2.5 W Edixeon EDEI-1LS3 emitter in the range of 11,350-11,700 cm-1 as a light source for the spectrometer with a 60-cm multipass cell during a 24-h measurement time, we have achieved a signal-to-noise ratio of 4.5 × 104 which corresponds to the minimal detectable absorption coefficient of 1.2 × 10-8 cm-1. Such enhanced sensitivity spectrometer has been used to measure the transition frequencies of CO2 vibrational bands 00051-00001 and 01151-01101 in the range of 11,400-11,500 cm-1.
Indirect Fourier transform in the context of statistical inference.
Muthig, Michael; Prévost, Sylvain; Orglmeister, Reinhold; Gradzielski, Michael
2016-09-01
Inferring structural information from the intensity of a small-angle scattering (SAS) experiment is an ill-posed inverse problem. Thus, the determination of a solution is in general non-trivial. In this work, the indirect Fourier transform (IFT), which determines the pair distance distribution function from the intensity and hence yields structural information, is discussed within two different statistical inference approaches, namely a frequentist one and a Bayesian one, in order to determine a solution objectively From the frequentist approach the cross-validation method is obtained as a good practical objective function for selecting an IFT solution. Moreover, modern machine learning methods are employed to suppress oscillatory behaviour of the solution, hence extracting only meaningful features of the solution. By comparing the results yielded by the different methods presented here, the reliability of the outcome can be improved and thus the approach should enable more reliable information to be deduced from SAS experiments. PMID:27580204
Motion saliency detection using a temporal fourier transform
NASA Astrophysics Data System (ADS)
Chen, Zhe; Wang, Xin; Sun, Zhen; Wang, Zhijian
2016-06-01
Motion saliency detection aims at detecting the dynamic semantic regions in a video sequence. It is very important for many vision tasks. This paper proposes a new type of motion saliency detection method, Temporal Fourier Transform, for fast motion saliency detection. Different from conventional motion saliency detection methods that use complex mathematical models or features, variations in the phase spectrum of consecutive frames are identified and extracted as the key to obtaining the location of salient motion. As all the calculation is made on the temporal frequency spectrum, our model is independent of features, background models, or other forms of prior knowledge about scenes. The benefits of the proposed approach are evaluated for various videos where the number of moving objects, illumination, and background are all different. Compared with some the state of the art methods, our method achieves both good accuracy and fast computation.
Solar radiometry at millimeter wavelengths. [Fast Fourier Transformation solutions
NASA Technical Reports Server (NTRS)
Henze, W.
1974-01-01
In the area of resolution enhancement, the use of Fast Fourier Transform programs was investigated for possible application to millimeter wavelength maps of the sun. A difficulty arises with the La Posta maps in that they are limited to 35 arc-minutes square while the smeared out solar image is larger than that. A list of possible cometary emission lines near 13 millimeters is presented. Although preparation of the list was inspired by the appearance of Comet Kohoutek, the results are applicable to any future comet. The brightness temperature of the sun at 8.6 millimeters was measured using the moon as a calibration source. The result does not confirm a deep absorption feature as apparently observed by earlier workers.
On the abstracted dataflow complexity of Fast Fourier Transforms
Boehm, A.P.W. . Dept. of Computer Science); Hiromoto, R.E.; Kelly, K.A. ); Ashley, J.M. . Dept. of Computer Science)
1992-01-01
In this paper we develop and analyze the simulated performance of codes for the Fast Fourier Transform written in If and targeted for execution on Motorola's dataflow machine Monsoon. The FFT application is of interest because of its computational parallelism, its requirement for global communications, and its array element data dependences. We use the parallel profiling simulator Id World to study the dataflow performance of various implementations. Our approach is comparative. We study two approaches, a recursive and an iterative one, and in each version we examine the effect of a variety of implementations. We contend that only through such comparative evaluations can significant insight be gained in understanding the computational and structural details of functional algorithms.
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.
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.
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.
Infrared Fourier transform spectroscopy of C-13 methanol
NASA Astrophysics Data System (ADS)
Predoi-Cross, Adriana
This work is a high-resolution Fourier transform infrared study of three vibrational states of C-13 methanol. We have investigated the regions from 1000-1400 cm-1 at 0.002 cm-1 resolution and from 1850-1950 cm-1 at 0.0028 cm-1 resolution. The vibrational modes covered by this study are: the CH3-Rocking band, the OH-Bending band and the first CO-Stretch overtone band. This study has led to (i) determination of excited-state molecular constants, (ii) characterization of a variety of interactions coupling the different vibrational modes, and (iii) identification of a number of reported far-infrared (FIR) lasing transitions and the prediction of new FIR laser emissions. The weak CH3-Rocking band is found to have principally a parallel character and has a double-peaked Q-branch and widely spread sub-bands due to a 28% increase in the torsional barrier height as compared to the ground state. We have assigned thirty ground torsional sub-bands and about ten sub-bands for the first excited torsional state. These sub-bands have been fitted to J(J+1) power-series expansions to obtain the sub- band origins and state-specific expansion parameters. The asymmetry splitting coefficients have also been determined. In our spectrum we have observed the effects of Coriolis coupling between rocking (K - 1) and CO- Stretching K levels for K values from 6 to 10. Other interesting interactions encountered are J-localized perturbations due to level crossing resonances with the CO-Stretch state. Two far-infrared laser emissions reported for the 10R(26) CO2 pump system are the result of a ΔK = 3 interaction. The OH-Bending band is widely spread with Q-subbranches grouped in two peaks at about 1312 cm-1 and 1338 cm-1. The OH-Bending state strongly interacts with the first excited torsional CH3-Rocking state and we have observed several 'extra' forbidden sub-bands arising from intensity borrowing from the allowed interacting sub-bands. The asymmetry splitting of the K = 2 doublet was found to
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.
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).
Bi-centenary of successes of Fourier theorem: its power and limitations in optical system designs
NASA Astrophysics Data System (ADS)
Roychoudhuri, Chandrasekhar
2007-09-01
We celebrate the two hundred years of successful use of the Fourier theorem in optics. However, there is a great enigma associated with the Fourier transform integral. It is one of the most pervasively productive and useful tool of physics and optics because its foundation is based on the superposition of harmonic functions and yet we have never declared it as a principle of physics for valid reasons. And, yet there are a good number of situations where we pretend it to be equivalent to the superposition principle of physics, creating epistemological problems of enormous magnitude. The purpose of the paper is to elucidate the problems while underscoring the successes and the elegance of the Fourier theorem, which are not explicitly discussed in the literature. We will make our point by taking six major engineering fields of optics and show in each case why it works and under what restricted conditions by bringing in the relevant physics principles. The fields are (i) optical signal processing, (ii) Fourier transform spectrometry, (iii) classical spectrometry of pulsed light, (iv) coherence theory, (v) laser mode locking and (vi) pulse broadening. We underscore that mathematical Fourier frequencies, not being physical frequencies, cannot generate real physical effects on our detectors. Appreciation of this fundamental issue will open up ways to be innovative in many new optical instrument designs. We underscore the importance of always validating our design platforms based on valid physics principles (actual processes undergoing in nature) captured by an appropriate hypothesis based on diverse observations. This paper is a comprehensive view of the power and limitations of Fourier Transform by summarizing a series of SPIE conference papers presented during 2003-2007.
Matter wave propagation using the Fourier optics approach
NASA Astrophysics Data System (ADS)
Shayganmanesh, M.; Hematizadeh, A.
2016-09-01
In this paper propagation of matter wave of particles is modeled using the Fourier optics approach. In first step the Schrödinger equation of quantum mechanics is used to find the wave function of the particle. In the second step Fourier optics is employed to model the diffraction of the wave function of the particle through single and double slits. The results of the calculations are presented as graphs of diffraction patterns. The results of the presented method are compared to the existing results in the literature (with different methods) to check the validity of the introduced model. It is shown that the Fourier optics approach is applicable to matter wave of particles in diffraction through slits.
High-SNR static Fourier-transform imaging spectrometer based on differential structure
NASA Astrophysics Data System (ADS)
Jin, Peng; Zhu, Shuaishuai; Zhang, Yu; Lin, Jie
2015-03-01
Fourier-transform imaging spectrometers are rapidly developed due to their extensive use in industrial monitoring, target detection, and chemical identification. Static Fourier-transform imaging spectrometer (SFIS) containing a birefringent interferometer is one of the most popular directions due to its inherent robustness. However, the SFIS suffers from its low achievable signal-to-noise ratio (SNR) because of the restriction of incident angle. Meanwhile, in applications, the SNR is perhaps the most important factor to determine the usefulness of an instrument. In this paper, we report here a Static Fourier-transform imaging spectrometer based on differential structure (SFIS-DS) in the 400-800nm wavelength range with a high SNR. As in electronic system, the differential structure can double optical efficiency and strongly restrain common mode error in the SFIS-DS. And the differential structure described here is also available for any instruments containing a birefringent interferometer. However, the drawback of the SFIS-DS is that the two images obtained by the two differential channels need precise registration which can be overcome by a sub-pixel spatial registration algorithm. The experimental results indicate the SFIS-DS can increase the SNR by no less than 40%.
A compact Fourier transform imaging spectrometer employing a variable gap Fabry-Perot interferometer
NASA Astrophysics Data System (ADS)
Lucey, Paul G.; Akagi, Jason; Bingham, Adam L.; Hinrichs, John L.; Knobbe, Edward T.
2014-05-01
Fourier transform spectroscopy is a widely employed method for obtaining visible and infrared spectral imagery, with applications ranging from the desktop to remote sensing. Most fielded Fourier transform spectrometers (FTS) employ the Michelson interferometer and measure the spectrum encoded in a time-varying signal imposed by the source spectrum interaction with the interferometer. A second, less widely used form of FTS is the spatial FTS, where the spectrum is encoded in a pattern sampled by a detector array. Recently we described using a Fabry-Perot interferometer, with a deliberately wedged gap geometry and engineered surface reflectivities, to produce an imaging spatial FTS. The Fabry-Perot interferometer can be much lighter and more compact than a conventional interferometer configuration, thereby making them suitable for portable and handheld applications. This approach is suitable for use over many spectral regimes of interest, including visible and infrared regions. Primary efforts to date have focused on development and demonstration of long wave infrared (LWIR) spectral imagers. The LWIR version of the miniaturized Fabry-Perot has been shown to be effective for various applications including spectral imaging-based chemical detection. The compact LWIR spectral imager employs uncooled optics and a microbolometer camera; a handheld version is envisioned for future development. Recent advancements associated with the spatial Fourier Transform imaging spectrometer system are described.
Effect of the fringe visibility on spectrum SNR of Fourier transform imaging spectrometer
NASA Astrophysics Data System (ADS)
Wang, Shuang; Bin, Xiangli; Jing, Juanjuan; Pi, Haifeng
2013-08-01
The principle of Fourier transform spectrometer is based on the relationship of Fourier-Transform between interferogram and spectrum. The spectral information of Fourier transform imaging spectrometer (FTIS) reconstructed from raw interferogram by data processing. So there are two kinds of signal-to-noise ratio (SNR) to evaluate instrument performance, one regarding interferogram and the other regarding reconstructed spectrum. Because the raw interferogram is intuitive, the interferogram SNR is studied usually. On the contrary, the spectrum SNR is studied less because of the complexity of the data processing from interferogram to spectrum. The research about the effect of the interference fringe visibility on the spectrum SNR is especially few. This paper present a research work on the relations between the interference fringe visibility and the spectrum SNR. Firstly, the reduction of fringe visibility caused by imaging lens defocus was analyzed. Secondly, the changes of the average spectrum signal and noise caused by the reduction of fringe visibility were calculated. For average spectrum signal, the math deductions are done base on Fourier transform theory. The average noise with different input signal optic-electrons number are simulated. the results show that the average spectrum signal is directly proportional to the fringe visibility, and the effect of fringe visibility on the noise related to signal can be ignorable. Finally, In order to demonstrate above results, the imaging experiment was done with white-light source, using LASIS (Large aperture static imaging spectrometer) based on Sagnac Interferometer. The average spectrum SNRs under different fringe visibility are calculated and analyzed. The experimental results show that: the average spectrum SNRs increase from 42.7 to 62.4.along with the fringe visibility increasing from 0.5051 to 0.687. the reconstructed spectrum SNR is directly proportional to the fringe visibility. As a result, the interferogram
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.
A Fourier-transform infrared system, operable at pathlengths up to 2 km, has been constructed for the detection and measurement of trace contaminants in the ambient atmosphere and in controlled smog formation studies. The long optical path is achieved by the use of an eight-mirro...
High-resolution Fourier-transform spectrometer chip with microphotonic silicon spiral waveguides.
Velasco, Aitor V; Cheben, Pavel; Bock, Przemek J; Delâge, André; Schmid, Jens H; Lapointe, Jean; Janz, Siegfried; Calvo, María L; Xu, Dan-Xia; Florjańczyk, Mirosław; Vachon, Martin
2013-03-01
We report a stationary Fourier-transform spectrometer chip implemented in silicon microphotonic waveguides. The device comprises an array of 32 Mach-Zehnder interferometers (MZIs) with linearly increasing optical path delays between the MZI arms across the array. The optical delays are achieved by using Si-wire waveguides arranged in tightly coiled spirals with a compact device footprint of 12 mm2. Spectral retrieval is demonstrated in a single measurement of the stationary spatial interferogram formed at the output waveguides of the array, with a wavelength resolution of 40 pm within a free spectral range of 0.75 nm. The phase and amplitude errors arising from fabrication imperfections are compensated using a transformation matrix spectral retrieval algorithm. PMID:23455272
The use of Fourier reverse transforms in crystallographic phase refinement
Ringrose, S.
1997-10-08
Often a crystallographer obtains an electron density map which shows only part of the structure. In such cases, the phasing of the trial model is poor enough that the electron density map may show peaks in some of the atomic positions, but other atomic positions are not visible. There may also be extraneous peaks present which are not due to atomic positions. A method for determination of crystal structures that have resisted solution through normal crystallographic methods has been developed. PHASER is a series of FORTRAN programs which aids in the structure solution of poorly phased electron density maps by refining the crystallographic phases. It facilitates the refinement of such poorly phased electron density maps for difficult structures which might otherwise not be solvable. The trial model, which serves as the starting point for the phase refinement, may be acquired by several routes such as direct methods or Patterson methods. Modifications are made to the reverse transform process based on several assumptions. First, the starting electron density map is modified based on the fact that physically the electron density map must be non-negative at all points. In practice a small positive cutoff is used. A reverse Fourier transform is computed based on the modified electron density map. Secondly, the authors assume that a better electron density map will result by using the observed magnitudes of the structure factors combined with the phases calculated in the reverse transform. After convergence has been reached, more atomic positions and less extraneous peaks are observed in the refined electron density map. The starting model need not be very large to achieve success with PHASER; successful phase refinement has been achieved with a starting model that consists of only 5% of the total scattering power of the full molecule. The second part of the thesis discusses three crystal structure determinations.
[Biological Process Oriented Online Fourier Transform Infrared Spectrometer].
Xie, Fei; Wu, Qiong-shui; Zeng, Li-bo
2015-08-01
An online Fourier Transform Infrared Spectrometer and an ATR (Attenuated Total Reflection) probe, specifically at the application of real time measurement of the reaction substrate concentration in biological processes, were designed. (1) The spectrometer combined the theories of double cube-corner reflectors and flat mirror, which created a kind of high performance interferometer system. The light path folding way was utilized to makes the interferometer compact structure. Adopting double cube-corner reflectors, greatly reduces the influence of factors in the process of moving mirror movement such as rotation, tilt, etc. The parallelogram oscillation flexible support device was utilized to support the moving mirror moves. It cancelled the friction and vibration during mirror moving, and ensures the smooth operation. The ZnSe splitter significantly improved the hardware reliability in high moisture environment. The method of 60° entrance to light splitter improves the luminous flux. (2) An ATR in situ measuring probe with simple structure, large-flux, economical and practical character was designed in this article. The transmission of incident light and the light output utilized the infrared pipe with large diameter and innerplanted-high plating membrane, which conducted for the infrared transmission media of ATR probe. It greatly reduced the energy loss of infrared light after multiple reflection on the inner wall of the light pipe. Therefore, the ATR probe obtained high flux, improved the signal strength, which make the signal detected easily. Finally, the high sensitivity of MCT (Mercury Cadmium Telluride) detector was utilized to realize infrared interference signal collection, and improved the data quality of detection. The test results showed that the system yields the advantages of perfect moisture-proof performance, luminous flux, online measurement, etc. The designed online Fourier infrared spectrometer can real-time measured common reactant substrates
Application of a nonuniform spectral resampling transform in Fourier-transform spectrometry.
Sarkissian, Edwin; Bowman, Kevin W
2003-02-20
We describe a nonuniform spectral resampling transform (NUSRT) that resamples a frequency-scaled spectrum that has been measured by a Fourier-transform spectrometer (FTS). Frequency scaling of a spectrum can arise from measurements made with off-axis detectors and Doppler shift induced by motion of a spaceborne FTS relative to an input radiation source. In addition, a spectrum may need to be rescaled in frequency to match spectral lines for applications such as the retrieval of atmospheric state parameters. The NUSRT is cast as a linear algebraic expression that relates a nonuniformly sampled interferogram to an input spectrum. A polynomial approximation is applied to this expression that reduces the inverse of the NUSRT to a series of Fourier transforms that can be implemented as fast Fourier transforms (FFTs). We show that this NUSRT algorithm requires on the order of 6N log N flops, which reduces the computational cost of rescaling by more than 1 order of magnitude compared with conventional FFT-based Shannon interpolation techniques while comparable accuracy is maintained. PMID:12617230
Diffractive optical elements for transformation of modes in lasers
Sridharan, Arun K.; Pax, Paul H.; Heebner, John E.; Drachenberg, Derrek R.; Armstrong, James P.; Dawson, Jay W.
2015-09-01
Spatial mode conversion modules are described, with the capability of efficiently transforming a given optical beam profile, at one plane in space into another well-defined optical beam profile at a different plane in space, whose detailed spatial features and symmetry properties can, in general, differ significantly. The modules are comprised of passive, high-efficiency, low-loss diffractive optical elements, combined with Fourier transform optics. Design rules are described that employ phase retrieval techniques and associated algorithms to determine the necessary profiles of the diffractive optical components. System augmentations are described that utilize real-time adaptive optical techniques for enhanced performance as well as power scaling.
Diffractive optical elements for transformation of modes in lasers
Sridharan, Arun K; Pax, Paul H; Heebner, John E; Drachenberg, Derrek R.; Armstrong, James P.; Dawson, Jay W.
2016-06-21
Spatial mode conversion modules are described, with the capability of efficiently transforming a given optical beam profile, at one plane in space into another well-defined optical beam profile at a different plane in space, whose detailed spatial features and symmetry properties can, in general, differ significantly. The modules are comprised of passive, high-efficiency, low-loss diffractive optical elements, combined with Fourier transform optics. Design rules are described that employ phase retrieval techniques and associated algorithms to determine the necessary profiles of the diffractive optical components. System augmentations are described that utilize real-time adaptive optical techniques for enhanced performance as well as power scaling.
Fourier transform spectroscopy of the nu3 band of the N3 radical
NASA Technical Reports Server (NTRS)
Brazier, C. R.; Bernath, P. F.; Burkholder, James B.; Howard, Carleton J.
1988-01-01
The nu3 transitions of N3 radicals produced by HN3-Cl reactions in a multipass cell (effective path length 100 m) are investigated experimentally using a Fourier-transform spectrometer with maximum resolution 0.004/cm. A total of 176 rotation-vibration lines are listed in a table and used, in combination with published data on 240 optical lines (Douglas and Jones, 1965), to determine the nu3 molecular constants. The lower-than-expected value of the nu3 fundamental frequency (1644.6784/cm) is attributed to the vibronic interaction discussed by Kawaguchi et al. (1981).
NASA Astrophysics Data System (ADS)
Osowiecki, Gaël. D.; Madi, Mohammad; Shorubalko, Ivan; Philipoussis, Irène; Alberti, Edoardo; Scharf, Toralf; Herzig, Hans P.
2015-09-01
We show the miniaturization and parallelization of a scanning standing wave spectrometer with a long term goal of creating a compact imaging spectrometer. In our standing wave integrated Fourier transform spectrometer, light is injected with micro-lenses into several optical polymer waveguides. A piezo actuated mirror located at the waveguide end-facet can shift the interferogram to increase its sampling frequency. The spatial distribution of the standing wave intensity inside the waveguide is partially scattered out of the plane by a periodic metallic grating and recorded by a CCD camera. We present spectra acquisition for six adjacent waveguides simultaneously at a wavelength of 632.8 nm.
Application of micro-Fourier transform infrared spectroscopy to the examination of paint samples
NASA Astrophysics Data System (ADS)
Zięba-Palus, J.
1999-11-01
The examination and identification of automobile paints is an important problem in road accidents investigations. Since the real sample available is very small, only sensitive microtechniques can be applied. The methods of optical microscopy and micro-Fourier transform infrared spectroscopy (MK-FTIR) supported by scanning electron microscopy together with X-ray microanalysis (SEM-EDX) allow one to carry out the examination of each paint layer without any separation procedure. In this paper an attempt is made to discriminate between different automobile paints of the same colour by the use of these methods for criminalistic investigations.
Strehl ratio as the Fourier transform of a probability density of error differences.
Alonso, Miguel A; Forbes, G W
2016-08-15
To give useful insight into the impact of mid-spatial frequency structure on optical performance, the Strehl ratio is shown to correspond to the Fourier transform of a simple statistical characterization of the aberration in the exit pupil. This statistical description is found simply by autocorrelating a histogram of the aberration values. In practice, the histogram itself can often be approximated by a convolution of underlying histograms associated with fabrication steps and, together with the final autocorrelation, it follows from the central limit theorem that the Strehl ratio as a function of the scale of the phase error is generally approximated well by a Gaussian. PMID:27519076
Three-dimensional profiling using the Fourier transform method with a hexagonal grating projection
Iwata, Koichi; Kusunoki, Fuminori; Moriwaki, Kousuke; Fukuda, Hiroki; Tomii, Takaharu
2008-04-20
We present three-dimensional profilometry based on triangulation in which a hexagonal pattern is projected on the object. To obtain an accurate result with a one-shot photographic image, the Fourier transform method and method of excess fraction are adopted. The three grating components of the hexagonal pattern are used. For compactness a new pattern projection scheme is introduced. The experimental results show that the constructed optical system works well for measuring the profile of a mannequin with a height resolution of {approx} {+-} 1 mm.
Universal and special keys based on phase-truncated Fourier transform
NASA Astrophysics Data System (ADS)
Qin, Wan; Peng, Xiang; Meng, Xiangfeng; Gao, Bruce
2011-08-01
We propose a novel optical asymmetric cryptosystem based on a phase-truncated Fourier transform. Two decryption keys independent of each other are generated. They are referred to as universal key and special key, respectively. Each of them can be used for decryption independently in absence of the other. The universal key is applicable to decrypt any ciphertext encoded by the same encryption key, but with poor legibility. On the contrary, the special key is adequate for legible decryption, but only valid for one ciphertext corresponding to the specified plaintext. A set of simulation results show the interesting performance of two types of decryption keys.
Fourier holographic display for augmented reality using holographic optical element
NASA Astrophysics Data System (ADS)
Li, Gang; Lee, Dukho; Jeong, Youngmo; Lee, Byoungho
2016-03-01
A method for realizing a three-dimensional see-through augmented reality in Fourier holographic display is proposed. A holographic optical element (HOE) with the function of Fourier lens is adopted in the system. The Fourier hologram configuration causes the real scene located behind the lens to be distorted. In the proposed method, since the HOE is transparent and it functions as the lens just for Bragg matched condition, there is not any distortion when people observe the real scene through the lens HOE (LHOE). Furthermore, two optical characteristics of the recording material are measured for confirming the feasibility of using LHOE in the proposed see-through augmented reality holographic display. The results are verified experimentally.
Gas Analysis by Fourier Transform Mm-Wave Spectroscopy
NASA Astrophysics Data System (ADS)
Harris, Brent J.; Steber, Amanda L.; Lehmann, Kevin K.; Pate, Brooks H.
2013-06-01
Molecular rotational spectroscopy of low pressure, room temperature gases offers high chemical selectivity and sensitivity with the potential for a wide range of applications in gas analysis. A strength of the technique is the potential to identify molecules that have not been previously studied by rotational spectroscopy by comparing experimental results to predictions of the spectroscopic parameters from quantum chemistry -6 so called library-free detection. The development of Fourier transform mm-wave spectrometers using high peak power (30 mW) active multiplier chain mm-wave sources brings new measurement capabilities to the analysis of complex gas mixtures. Strategies for gas analysis based on high-throughput mm-wave spectroscopy and arbitrary waveform generator driven mm-wave sources are described. Several new measurement capabilities come from the intrinsic time-domain measurement technique. High-sensitivity double-resonance measurements can be performed to speed the analysis of a complex gas sample containing several species. This technique uses a "pi-pulse" to selectively invert the population of two selected rotational energy levels and the effect of this excitation pulse on all other transitions in the spectrometer operating range is monitored using segmented chirped-pulse Fourier transform spectroscopy. This method can lead to automated determination of the molecular rotational constants. Rapid pulse duration scan experiments can be used to estimate the magnitude and direction of the dipole moment of the molecule from an unknown spectrum. Coherent pulse echo experiments, using the traditional Hahn sequence or two-color population recovery methods, can be used to determine the collisional relaxation rate of the unknown molecule. This rate determination improves the ability to estimate the mass of the unknown molecule from the determination of the Doppler dephasing rate. By performing a suite of automated, high-throughput measurements, there is the
Single beam Fourier transform digital holographic quantitative phase microscopy
Anand, A. Chhaniwal, V. K.; Mahajan, S.; Trivedi, V.; Faridian, A.; Pedrini, G.; Osten, W.; Dubey, S. K.; Javidi, B.
2014-03-10
Quantitative phase contrast microscopy reveals thickness or height information of a biological or technical micro-object under investigation. The information obtained from this process provides a means to study their dynamics. Digital holographic (DH) microscopy is one of the most used, state of the art single-shot quantitative techniques for three dimensional imaging of living cells. Conventional off axis DH microscopy directly provides phase contrast images of the objects. However, this process requires two separate beams and their ratio adjustment for high contrast interference fringes. Also the use of two separate beams may make the system more vulnerable to vibrations. Single beam techniques can overcome these hurdles while remaining compact as well. Here, we describe the development of a single beam DH microscope providing whole field imaging of micro-objects. A hologram of the magnified object projected on to a diffuser co-located with a pinhole is recorded with the use of a commercially available diode laser and an arrayed sensor. A Fourier transform of the recorded hologram directly yields the complex amplitude at the image plane. The method proposed was investigated using various phase objects. It was also used to image the dynamics of human red blood cells in which sub-micrometer level thickness variation were measurable.
Fourier Transform Microwave and Infrared Spectroscopic Investigation of Propiolactone
NASA Astrophysics Data System (ADS)
Chen, Ziqiu; van Wijngaarden, Jennifer
2009-06-01
The pure rotational spectrum of the four-membered ester ring propiolactone (C{_3}H{_4}O{_2}) has been measured in a supersonic jet between 7 and 22 GHz using Fourier transform microwave (FTMW) spectroscopy. For the normal isotopologue, a total of 19 a- and b-type transitions have been recorded. Fifteen transitions due to three different ^{13}C isotopologues have also been observed. The microwave spectrum was analyzed to obtain an improved set of ground state rotational constants in comparison to earlier microwave experiments. The new set of rotational parameters was used to predict the rovibrational band structure of the lowest frequency modes of propiolactone. A total of 12 vibrational band origins have been observed between 400 and 1500 cm^{-1} using the far infrared beamline of the Canadian Light Source coupled to a Bruker IFS125HR spectrometer. The spectra were recorded with a resolution of 0.000969 cm^{-1} and although the intensities of the bands vary, 9 bands are of sufficient quality for complete rovibrational assignment. The progress of the assignment of this rich spectrum will be discussed. D. W. Boone, C O. Britt and J. E. Boggs J. Chem. Phys. 43 (1190), 1965.
Applications of the VUV Fourier Transform Spectrometer at Synchrotron Soleil
NASA Astrophysics Data System (ADS)
de Oliveira, Nelson; Joyeux, Denis; Ito, Kenji; Gans, Berenger; Nahon, Laurent
2015-06-01
Fourier transform spectrometers (FTS) are usually based upon amplitude division interferometers through beamsplitters (BS) as in the Michelson interferometer geometry. However, the manufacture of broadband BS is difficult and even impossible in the far VUV (below λ = 140 nm). We therefore conceived an instrument based upon an original design involving only reflective plane surfaces, giving access to the whole VUV range without the restrictions associated with BS. The VUV- FTS is a permanent endstation connected to one of the three experimental branches of the DESIRS beamline and devoted to high resolution photoabsorption in the UV-VUV spectral range, typically between λ = 300 and 40 nm Since 2008, a large international community of users interested in laboratory measurements with applications in astrophysics, molecular physics or planetary atmospheres has been attracted by the VUV - FTS capabilities including its efficiency in terms of signal to noise ratio, even when high spectral resolution was not an issue. A large number of dedicated gas phase sample environments have been developed including a windowless cell that can be cooled down, a heated windowless cell, a free molecular jet set-up and various windowed cells. Besides, a new discharge gas cell for production and study of transient species gave recently its first results. As an illustration, the VUV absorption spectrum of the CH_3 radical down to 140 nm will be shown in this presentation. Nahon et al., J. Synchrotron Radiat., 19, 508(2012) De Oliveira et al., Nat. Photonics, 5, 149(2011)
Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS): Imaging and Tracking Capability
NASA Technical Reports Server (NTRS)
Zhou, D. K.; Larar, A. M.; Liu, Xu; Reisse, R. A.; Smith, W. L.; Revercomb, H. E.; Bingham, G. E.; Zollinger, L. J.; Tansock, J. J.; Huppi, Ronald J.
2007-01-01
The geosynchronous-imaging Fourier transform spectrometer (GIFTS) engineering demonstration unit (EDU) is an imaging infrared spectrometer designed for atmospheric soundings. It measures the infrared spectrum in two spectral bands (14.6 to 8.8 microns, 6.0 to 4.4 microns) using two 128 128 detector arrays with a spectral resolution of 0.57/cm with a scan duration of approx. 11 seconds. From a geosynchronous orbit, the instrument will have the capability of taking successive measurements of such data to scan desired regions of the globe, from which atmospheric status, cloud parameters, wind field profiles, and other derived products can be retrieved. The GIFTS EDU provides a flexible and accurate testbed for the new challenges of the emerging hyperspectral era. The EDU ground-based measurement experiment, held in Logan, Utah during September 2006, demonstrated its extensive capabilities and potential for geosynchronous and other applications (e.g., Earth observing environmental measurements). This paper addresses the experiment objectives and overall performance of the sensor system with a focus on the GIFTS EDU imaging capability and proof of the GIFTS measurement concept.
Californium-252 plasma desorption with Fourier transform mass spectroscopy
Loo, J.A; Williams, E.R.; Amster, I.J.; Furlong, J.J.P.; Wang, B.H.; McLafferty, F.W.; Chait, B.T.; Field, F.H.
1987-01-01
Plasma desorption (PD) such, as that induced by the 100-MeV fission products of /sup 252/Cf, is a particularly promising ionization method for large molecules, yielding molecular ion species even from trypsin, molecular weight 23,463. Further, with trypsin using nitrocellulose as the substrate, (M + 3H)/sup 3 +/ is the most abundant molecular ion species and (M + 6H)/sup 6 +/ is measurable, which greatly extends the mass values (m) observable for instruments with an upper m/z limit (z = number of charges). However, a 50-..mu..Ci /sup 252/Cf source only produces 55,000 fissions s/sup -1/, yielding ion currents that are generally much too low for scanning instruments. An instrument with unusual capabilities for these, as well as for simultaneous ion detection over a wide mass range, is the Fourier transform (FT) mass spectrometer. With FTMS, Hunt has measured (M + H)/sup +/ ions of cytochrome c, molecular weight 12,384, ionized in an exterior fast-atom-bombardment source. Here the authors describe techniques for obtaining PD/FT mass spectra for a variety of compounds with abundant molecular ion species of masses as high as 2016 (alamethicin).
Fourier transform infrared phase shift cavity ring down spectrometer
NASA Astrophysics Data System (ADS)
Schundler, Elizabeth; Mansur, David J.; Vaillancourt, Robert; Benedict-Gill, Ryan; Newbry, Scott P.; Engel, James R.; Dupuis, Julia Rentz
2014-05-01
OPTRA has developed a Fourier transform infrared phase shift cavity ring down spectrometer (FTIR-PS-CRDS) system under a U.S. EPA SBIR contract. This system uses the inherent wavelength-dependent modulation imposed by the FTIR on a broadband thermal source for the phase shift measurement. This spectrally-dependent phase shift is proportional to the spectrally-dependent ring down time. The spectral dependence of both of these values is introduced by the losses of the cavity including those due to the molecular absorption of the sample. OPTRA's approach allows broadband detection of chemicals across the feature-rich fingerprint region of the long-wave infrared. This represents a broadband and spectral range enhancement to conventional CRDS which is typically done at a single wavelength in the near IR; at the same time the approach is a sensitivity enhancement to traditional FTIR, owing to the long effective path of the resonant cavity. In previous papers1,2, OPTRA has presented a breadboard system aimed at demonstrating the feasibility of the approach and a prototype design implementing performance enhancements based on the results of breadboard testing. In this final paper in the series, we will present test results illustrating the realized performance of the fully assembled and integrated breadboard, thereby demonstrating the utility of the approach.
Liquid chromatography/Fourier transform IR spectrometry interface flow cell
Johnson, Charles C.; Taylor, Larry T.
1986-01-01
A zero dead volume (ZDV) microbore high performance liquid chromatography (.mu.HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a .mu.HPLC column end fitting to minimize the transfer volume of the effluents exiting the .mu.HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF.sub.2), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.
Toward a soft x-ray Fourier-transform spectrometer
Howells, M.R.; Frank, K.; Hussain, Z.; Moler, E.J.; Reich, T. |; Moeller, D.; Shirley, D.A.
1993-10-29
The use of Fourier transform spectroscopy (FTS) in the soft x-ray region is advocated as a possible route to spectral resolution superior to that attainable with a grating system. A technical plan is described for applying FTS to the study of the absorption spectrum of helium in the region of double ionization around 60--80 eV. The proposed scheme includes a Mach-Zehnder interferometer deformed into a rhombus shape to provide grazing incidence reflections. The path difference between the interfering beams is to be tuned by translation of a table carrying four mirrors over a range {+-}1 cm which, in the absence of errors generating relative tilts of the wave fronts, would provide a resolving power equal to the number of waves of path difference: half a million at 65 eV, for example. The signal-to-noise ratio of the spectrum is analyzed and for operation on an Advanced Light Source bending magnet beam line should be about 330.
Realization of a scalable coherent quantum Fourier transform
NASA Astrophysics Data System (ADS)
Debnath, Shantanu; Linke, Norbert; Figgatt, Caroline; Landsman, Kevin; Wright, Ken; Monroe, Chris
2016-05-01
The exponential speed-up in some quantum algorithms is a direct result of parallel function-evaluation paths that interfere through a quantum Fourier transform (QFT). We report the implementation of a fully coherent QFT on five trapped Yb+ atomic qubits using sequences of fundamental quantum logic gates. These modular gates can be used to program arbitrary sequences nearly independent of system size and distance between qubits. We use this capability to first perform a Deutsch-Jozsa algorithm where several instances of three-qubit balanced and constant functions are implemented and then examined using single qubit QFTs. Secondly, we apply a fully coherent five-qubit QFT as a part of a quantum phase estimation protocol. Here, the QFT operates on a five-qubit superposition state with a particular phase modulation of its coefficients and directly produces the corresponding phase to five-bit precision. Finally, we examine the performance of the QFT in the period finding problem in the context of Shor's factorization algorithm. This work is supported by the ARO with funding from the IARPA MQCO program and the AFOSR MURI on Quantum Measurement and Verification.
Liquid chromatography/Fourier transform IR spectrometry interface flow cell
Johnson, C.C.; Taylor, L.T.
1985-01-04
A zero dead volume (ZDV) microbore high performance liquid chromatography (..mu.. HPLC)/Fourier transform infrared (FTIR) interface flow cell includes an IR transparent crystal having a small diameter bore therein through which a sample liquid is passed. The interface flow cell further includes a metal holder in combination with a pair of inner, compressible seals for directly coupling the thus configured spectrometric flow cell to the outlet of a ..mu.. HPLC column end fitting to minimize the transfer volume of the effluents exiting the ..mu.. HPLC column which exhibit excellent flow characteristics due to the essentially unencumbered, open-flow design. The IR beam passes transverse to the sample flow through the circular bore within the IR transparent crystal, which is preferably comprised of potassium bromide (KBr) or calcium fluoride (CaF/sub 2/), so as to minimize interference patterns and vignetting encountered in conventional parallel-plate IR cells. The long IR beam pathlength and lensing effect of the circular cross-section of the sample volume in combination with the refractive index differences between the solvent and the transparent crystal serve to focus the IR beam in enhancing sample detection sensitivity by an order of magnitude.
External Second Gate-Fourier Transform Ion Mobility Spectrometry.
Tarver, Edward E., III
2005-01-01
Ion mobility spectrometry (IMS) is recognized as one of the most sensitive and versatile techniques for the detection of trace levels of organic vapors. IMS is widely used for detecting contraband narcotics, explosives, toxic industrial compounds and chemical warfare agents. Increasing threat of terrorist attacks, the proliferation of narcotics, Chemical Weapons Convention treaty verification as well as humanitarian de-mining efforts has mandated that equal importance be placed on the analysis time as well as the quality of the analytical data. (1) IMS is unrivaled when both speed of response and sensitivity has to be considered. (2) With conventional (signal averaging) IMS systems the number of available ions contributing to the measured signal to less than 1%. Furthermore, the signal averaging process incorporates scan-to-scan variations decreasing resolution. With external second gate Fourier Transform ion mobility spectrometry (FT-IMS), the entrance gate frequency is variable and can be altered in conjunction with other data acquisition parameters to increase the spectral resolution. The FT-IMS entrance gate operates with a 50% duty cycle and so affords a 7 to 10-fold increase in sensitivity. Recent data on high explosives are presented to demonstrate the parametric optimization in sensitivity and resolution of our system.
Fourier transform molecular rotational resonance spectroscopy for reprogrammable chemical sensing
NASA Astrophysics Data System (ADS)
Harris, Brent J.; Pulliam, Robin L.; Neill, Justin L.; Muckle, Matt T.; Reynolds, Roger; Pate, Brooks H.
2015-03-01
Molecular rotational resonance (MRR) spectroscopy gives spectral signatures with high chemical selectivity. At room temperature, the peak intensity of the MRR spectrum occurs in the 100 GHz - 1 THz frequency range for volatile species with mass <= 100 amu. Advances in high-power sub-mm-wave light sources has made it possible to implement time-domain Fourier transform (FT) spectroscopy techniques that are similar to FT nuclear magnetic resonance (FT-NMR) measurements. In these measurements, the gas sample is excited by a short (200 ns) excitation pulse that creates a macroscopic sample polarization. The electric field of the subsequent transient molecular emission is detected using a heterodyne receiver and a high-speed digitizer. FT-MRR spectroscopy offers speed and sensitivity improvements over absorption spectroscopy. For chemical analysis, FT-MRR spectrometers combine the benefits of broad chemical coverage typical of gas chromatography - mass spectrometry (GC-MS) instruments and the direct measurement capabilities of infrared gas sensors all in a reprogrammable platform. Pulse sequence measurements can be implemented for advanced spectroscopic analysis. Trace level quantitation of volatile species at ppbv concentration can be performed on the time scale of a minute. In cases where the sample is a complex mixture, a double-resonance pulse sequence can be used to achieve chemical selectivity even in cases where spectral overlap occurs. These measurement capabilities are illustrated using the application of FT-MRR spectroscopy to residual solvent analysis of pharmaceutical products.
Imaging Fourier Transform Spectro-polarimetry in the Infrared
NASA Astrophysics Data System (ADS)
Jurgenson, C. A.; Stencel, R. E.; Stout, J.
2004-12-01
Imaging spectro-polarimetry has the capability to trace polarization changes in dust grains throughout an extended region of interest. An instrument that has the capability to achieve moderately high resolution (R = 2000 at 10 microns) via a stepping Fourier transform spectrometer, while preserving imaging polarimetry capabilities (TNTCAM2, Jurgenson et al. 2003), is set to achieve first light during early 2005. Motion control of the interferometer, as well as array control/readout is accomplished via an FPGA card programmed in LabVIEW(c). Mid-IR polarization studies are useful in approximating grain shapes and sizes in dusty environments. Correlation studies between mid and near-IR features can be used to test the core-mantle arrangement of grain growth. Polarization analysis is currently only possible between 8-13 microns, but the interferometer, as well as TNTCAM2, can operate at selected bandpasses in the near-IR region. A wire grid and waveplate would need to be purchased for work in the near-IR. Laboratory calibration results, both spectral and polarization, are reported. We are seeking collaborators in shared-risk science with this instrument, so please contact the authors if interested. Sigma Xi Grants In Aid of Research as well as the estate of William Herschel Womble provided funding for this endeavor.
Fourier transform infrared spectroscopy (FTIR) of laser-irradiated cementum
NASA Astrophysics Data System (ADS)
Rechmann, Peter; White, Joel M.; Cecchini, Silvia C. M.; Hennig, Thomas
2003-06-01
Utilizing Fourier Transform Infrared Spectroscopy (FTIR) in specular reflectance mode chemical changes of root cement surfaces due to laser radiation were investigated. A total of 18 samples of root cement were analyzed, six served as controls. In this study laser energies were set to those known for removal of calculus or for disinfection of periodontal pockets. Major changes in organic as well as inorganic components of the cementum were observed following Nd:YAG laser irradiation (wavelength 1064 nm, pulse duration 250 μs, free running, pulse repetition rate 20 Hz, fiber diameter 320 μm, contact mode; Iskra Twinlight, Fontona, Slovenia). Er:YAG laser irradiation (wavelength 2.94 μm, pulse duration 250 μs, free running, pulse repetition rate 6 Hz, focus diameter 620 μm, air water cooling 30 ml/min; Iskra Twinlight, Fontona, Slovenia) significantly reduced the Amid bands due to changes in the organic components. After irradiation with a frequency doubled Alexandrite laser (wavelength 377 nm, pulse duration 200 ns, q-switched, pulse repetition rate 20 Hz, beam diameter 800 μm, contact mode, water cooling 30 ml/min; laboratory prototype) only minimal reductions in the peak intensity of the Amide-II band were detected.
SAR-based vibrometry using the fractional Fourier transform
NASA Astrophysics Data System (ADS)
Campbell, Justin B.; Wang, Qi; Ade-Bello, Jelili; Caudana, Humberto; Trujillo, Nicole B.; Bhatta, Ishwor; Dunkel, Ralf; Atwood, Thomas; Doerry, Armin; Gerstle, Walter H.; Santhanam, Balu; Hayat, Majeed M.
2015-05-01
A fundamental assumption when applying Synthetic Aperture Radar (SAR) to a ground scene is that all targets are motionless. If a target is not stationary, but instead vibrating in the scene, it will introduce a non-stationary phase modulation, termed the micro-Doppler effect, into the returned SAR signals. Previously, the authors proposed a pseudosubspace method, a modification to the Discrete Fractional Fourier Transform (DFRFT), which demonstrated success for estimating the instantaneous accelerations of vibrating objects. However, this method may not yield reliable results when clutter in the SAR image is strong. Simulations and experimental results have shown that the DFRFT method can yield reliable results when the signal-to-clutter ratio (SCR) > 8 dB. Here, we provide the capability to determine a target's frequency and amplitude in a low SCR environment by presenting two methods that can perform vibration estimations when SCR < 3 dB. The first method is a variation and continuation of the subspace approach proposed previously in conjunction with the DFRFT. In the second method, we employ the dual-beam SAR collection architecture combined with the extended Kalman filter (EKF) to extract information from the returned SAR signals about the vibrating target. We also show the potential for extending this SAR-based capability to remotely detect and classify objects housed inside buildings or other cover based on knowing the location of vibrations as well as the vibration histories of the vibrating structures that house the vibrating objects.
Fourier transform infrared spectroscopic analysis of cell differentiation
NASA Astrophysics Data System (ADS)
Ishii, Katsunori; Kimura, Akinori; Kushibiki, Toshihiro; Awazu, Kunio
2007-02-01
Stem cells and its differentiations have got a lot of attentions in regenerative medicine. The process of differentiations, the formation of tissues, has become better understood by the study using a lot of cell types progressively. These studies of cells and tissue dynamics at molecular levels are carried out through various approaches like histochemical methods, application of molecular biology and immunology. However, in case of using regenerative sources (cells, tissues and biomaterials etc.) clinically, they are measured and quality-controlled by non-invasive methods from the view point of safety. Recently, the use of Fourier Transform Infrared spectroscopy (FT-IR) has been used to monitor biochemical changes in cells, and has gained considerable importance. The objective of this study is to establish the infrared spectroscopy of cell differentiation as a quality control of cell sources for regenerative medicine. In the present study, as a basic study, we examined the adipose differentiation kinetics of preadipocyte (3T3-L1) and the osteoblast differentiation kinetics of bone marrow mesenchymal stem cells (Kusa-A1) to analyze the infrared absorption spectra. As a result, we achieved to analyze the adipose differentiation kinetics using the infrared absorption peak at 1739 cm-1 derived from ester bonds of triglyceride and osteoblast differentiation kinetics using the infrared absorption peak at 1030 cm-1 derived from phosphate groups of calcium phosphate.
Fourier transform infrared spectroscopy in physics laboratory courses
NASA Astrophysics Data System (ADS)
Möllmann, K.-P.; Vollmer, M.
2013-11-01
Infrared spectrometry is one of the most important tools in the field of spectroscopic analysis. This is due to the high information content of spectra in the so-called spectroscopic fingerprint region, which enables measurement not only of gases, but also of liquids and solids. Today, infrared spectroscopy is almost completely dominated by Fourier transform infrared (FTIR) spectroscopy. FTIR spectroscopy is able to detect minute quantities in the ppm and ppb ranges, and the respective analyses are now standard tools in science as well as industry. Therefore FTIR spectroscopy should be taught within the standard curriculum at university to physicists and engineers. Here we present respective undergraduate laboratory experiments designed for students at the end of their third year. Experiments deal first with understanding the spectrometer and second with recording and analysing spectra. On the one hand, transmission spectra of gases are treated which relate to environmental analytics (being probably the most prominent and well-known examples), and on the other hand, the focus is on the transmission and reflection spectra of solids. In particular, silicon wafers are studied—as is regularly done in the microelectronics industry—in order to characterize their thickness, oxygen content and phonon modes.
Continued Development of a Planetary Imaging Fourier Transform Spectrometer (PIFTS)
NASA Technical Reports Server (NTRS)
Sromovsky, L. A.
2002-01-01
This report describes continued efforts to evaluate a breadboard of a Planetary Imaging Fourier Transform Spectrometer (PIFTS). The PIFTS breadboard was developed under prior PIDDP funding. That effort is described in the final report for NASA Grant NAG5-6248 and in two conference papers (Sromovsky et al. 2000; Revercomb et al. 2000). The PIFTS breadboard was designed for near-IR (1-5.2 micrometer imaging of planetary targets with spectral resolving powers of several hundred to several thousand, using an InSb detector array providing at least 64x64 pixels imaging detail. The major focus of the development effort was to combine existing technologies to produce a small and low power design compatible with a very low mass flyable instrument. The objective of this grant (NAG5-10729) was further characterization of the breadboard performance, including intercomparisons with the highly accurate non-imaging Advanced Emitted Radiance Interferometer (AERI) (Revercomb et al. 1994; Best et al. 1997).
Reconstruction of piecewise homogeneous images from partial knowledge of their Fourier Transform
NASA Astrophysics Data System (ADS)
Féron, Olivier; Chama, Zouaoui; Mohammad-Djafari, Ali
2004-11-01
Fourier synthesis (FS) inverse problem consists in reconstructing a multi-variable function from the measured data which correspond to partial and uncertain knowledge of its Fourier Transform (FT). By partial knowledge we mean either partial support and/or the knowledge of only the module and by uncertain we mean both uncertainty of the model and noisy data. This inverse problem arises in many applications such as : optical imaging, radio astronomy, magnetic resonance imaging (MRI) and diffraction scattering (ultrasounds or microwave imaging). Most classical methods of inversion are based on interpolation of the data and fast inverse FT. But when the data do not fill uniformly the Fourier domain or when the phase of the signal is lacking as in optical interferometry, the results obtained by such methods are not satisfactory, because these inverse problems are ill-posed. The Bayesian estimation approach, via an appropriate modeling of the unknown functions gives the possibility of compensating the lack of information in the data, thus giving satisfactory results. In this paper we study the case where the observations are a part of the FT modulus of objects which are composed of a few number of homogeneous materials. To model such objects we use a Hierarchical Hidden Markov Modeling (HMM) and propose a Bayesian inversion method using appropriate Markov Chain Monte Carlo (MCMC) algorithms.
Eliminating zero spectra in Fourier transform profilometry by application of Hilbert transform
NASA Astrophysics Data System (ADS)
Luo, Feng; Chen, Wenjing; Su, Xianyu
2016-04-01
Hilbert transform has the features of inducing a phase shifting of 90 degree and removing the DC component. We propose a novel method based on the piecewise Hilbert transform to suppress the background intensity of the deformed fringe pattern using only one fringe pattern in Fourier transform profilometry according to the approximation that the background of the fringe is a slowly varying function and its distribution in each half period of the fringe can be regarded as a constant. In the method, Hilbert transform deals with each segmented fringe section to remove the DC component and then forms a result fringe whose background intensity is suppressed well by putting the fringe pieces together. The proposed method can enlarge the measurement range and reduce the measurement error of FTP. The theoretical analysis is given. Computer simulations and experimental results demonstrate the effectiveness of the proposed method.
A new hybrid algorithm for computing a fast discrete Fourier transform
NASA Technical Reports Server (NTRS)
Reed, I. S.; Truong, T. K.
1979-01-01
In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplished by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.
Adaptive optics assisted Fourier domain OCT with balanced detection
NASA Astrophysics Data System (ADS)
Meadway, A.; Bradu, A.; Hathaway, M.; Van der Jeught, S.; Rosen, R. B.; Podoleanu, A. Gh.
2011-03-01
Two factors are of importance to optical coherence tomography (OCT), resolution and sensitivity. Adaptive optics improves the resolution of a system by correcting for aberrations causing distortions in the wave-front. Balanced detection has been used in time domain OCT systems by removing excess photon noise, however it has not been used in Fourier domain systems, as the cameras used in the spectrometers saturated before excess photon noise becomes a problem. Advances in camera technology mean that this is no longer the case and balanced detection can now be used to improve the signal to noise ratio in a Fourier domain (FD) OCT system. An FD-OCT system, enhanced with adaptive optics, is presented and is used to show the improvement that balanced detection can provide. The signal to noise ratios of single camera detection and balanced detection are assessed and in-vivo retinal images are acquired to demonstrate better image quality when using balance detection.
The Green's function for the three-dimensional linear Boltzmann equation via Fourier transform
NASA Astrophysics Data System (ADS)
Machida, Manabu
2016-04-01
The linear Boltzmann equation with constant coefficients in the three-dimensional infinite space is revisited. It is known that the Green's function can be calculated via the Fourier transform in the case of isotropic scattering. In this paper, we show that the three-dimensional Green's function can be computed with the Fourier transform even in the case of arbitrary anisotropic scattering.
NASA Astrophysics Data System (ADS)
Xia, Xiang-Gen; Wang, Genyuan; Chen, Victor C.
2001-03-01
This paper first reviews some basic properties of the discrete chirp-Fourier transform and then present an adaptive chirp- Fourier transform, a generalization of the amplitude and phase estimation of sinusoids (APES) algorithm proposed by Li and Stoica for sinusoidal signals. We finally applied it to the ISAR imaging of maneuvering targets.
A prototype stationary Fourier transform spectrometer for near-infrared absorption spectroscopy.
Li, Jinyang; Lu, Dan-feng; Qi, Zhi-mei
2015-09-01
A prototype stationary Fourier transform spectrometer (FTS) was constructed with a fiber-coupled lithium niobate (LiNbO3) waveguide Mach-Zehnder interferometer (MZI) for the purpose of rapid on-site spectroscopy of biological and chemical measurands. The MZI contains push-pull electrodes for electro-optic modulation, and its interferogram as a plot of intensity against voltage was obtained by scanning the modulating voltage from -60 to +60 V in 50 ms. The power spectrum of input signal was retrieved by Fourier transform processing of the interferogram combined with the wavelength dispersion of half-wave voltage determined for the MZI used. The prototype FTS operates in the single-mode wavelength range from 1200 to 1700 nm and allows for reproducible spectroscopy. A linear concentration dependence of the absorbance at λmax = 1451 nm for water in ethanolic solution was obtained using the prototype FTS. The near-infrared spectroscopy of solid samples was also implemented, and the different spectra obtained with different materials evidenced the chemical recognition capability of the prototype FTS. To make this prototype FTS practically applicable, work on improving its spectral resolution by increasing the maximum optical path length difference is in progress. PMID:26414526
Practical aspects of Fourier transform and correlation based processing of spectrochemical data
NASA Astrophysics Data System (ADS)
Ng, R. C. L.; Horlick, Gary
Fourier transform based signal processing methods are beginning to be widely used for the treatment of spectrochemical data. The most common approach to Fourier transformation is through the utilization of the so called Fast Fourier Transform algorithm or FFT as it is usually designated. However, several versions of the FFT abound in the literature and in program libraries and many subtleties exist with respect to data pre-treatment, data post-treatment, inverse Fourier transformation and manipulation of real and imaginary arrays that can cause considerable grief to the uninitiated. In this presentation numerous examples will be presented illustrating several practical aspects of implementing FFT's and cross-correlations (Fourier transform route) on spectrochemical data sets. Particular attention is paid to the manipulation to the input and output real and imaginary arrays.
Fourier Transform Spectrometer measurements of Atmospheric Carbon Dioxide and Methane
NASA Astrophysics Data System (ADS)
Kivi, Rigel; Heikkinen, Pauli; Chen, Huilin; Hatakka, Juha; Laurila, Tuomas
2016-04-01
Ground based remote sensing measurements of column CO2 and CH4 using Fourier Transform Spectrometers (FTS) within the Total Carbon Column Observing Network (TCCON) are known for high precision and accuracy. These measurements are performed at various locations globally and they have been widely used in carbon cycle studies and validation of space born measurements. The relevant satellite missions include the Orbiting Carbon Observatory-2 (OCO-2) by the National Aeronautics and Space Administration (NASA); the SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY (SCIAMACHY) by the European Space Agency (ESA); the Greenhouse gases Observing SATellite (GOSAT) by the Japan Aerospace Exploration Agency (JAXA) and the upcoming Sentinel-5 Precursor mission, which is an ESA mission and scheduled for launch in 2016. Results of the column CO2 and CH4 measurements at Sodankylä in northern Finland (at 67.4° N, 26.6° E) are reported in this study. The measurements have been performed on regular basis since the beginning of the program in early 2009. We also present evaluation of the data quality of the ground based measurements and comparisons with the available satellite based retrievals. In case of comparisons between the GOSAT and ground based retrievals of CO2 and CH4 no significant biases were found. Sodankylä is one of the northernmost stations in the TCCON network. However, the data coverage has been relatively good thanks to the progress towards automation of the FTS measurement system. At Sodankylä the retrievals have been also compared with the balloon borne AirCore measurements at the site. AirCore sampling system is directly related to the World Meteorological Organization in situ trace gas measurement scales. The balloon platform allows sampling in both stratosphere and troposphere, which is a benefit, compared to the aircraft in situ measurements.
Geostationary Imaging Fourier Transform Spectrometer (GIFTS): science applications
NASA Astrophysics Data System (ADS)
Smith, W. L.; Revercomb, H. E.; Zhou, D. K.; Bingham, G. E.; Feltz, W. F.; Huang, H. L.; Knuteson, R. O.; Larar, A. M.; Liu, X.; Reisse, R.; Tobin, D. C.
2006-12-01
A revolutionary satellite weather forecasting instrument, called the "GIFTS" which stands for the "Geostationary Imaging Fourier Transform Spectrometer", was recently completed and successfully tested in a space chamber at the Utah State University's Space Dynamics Laboratory. The GIFTS was originally proposed by the NASA Langley Research Center, the University of Wisconsin, and the Utah State University and selected for flight demonstration as NASA's New Millennium Program (NMP) Earth Observing-3 (EO-3) mission, which was unfortunately cancelled in 2004. GIFTS is like a digital 3-d movie camera that, when mounted on a geostationary satellite, would provide from space a revolutionary four-dimensional view of the Earth's atmosphere. GIFTS will measure the distribution, change, and movement of atmospheric moisture, temperature, and certain pollutant gases, such as carbon monoxide and ozone. The observation of the convergence of invisible water vapor, and the change of atmospheric temperature, provides meteorologists with the observations needed to predict where, and when, severe thunderstorms, and possibly tornados, would occur, before they are visible on radar or in satellite cloud imagery. The ability of GIFTS to observe the motion of moisture and clouds at different altitudes enables atmospheric winds to be observed over vast, and otherwise data sparse, oceanic regions of the globe. These wind observations would provide the means to greatly improve the forecast of where tropical storms and hurricanes will move and where and when they will come ashore (i.e., their landfall position and time). GIFTS, if flown into geostationary orbit, would provide about 80,000 vertical profiles per minute, each one like a low vertical resolution (1-2km) weather balloon sounding, but with a spacing of 4 km. GIFTS is a revolutionary atmospheric sensing tool. A glimpse of the science measurement capabilities of GIFTS is provided through airborne measurements with the NPOESS Airborne
Libyan Desert Glass: New field and Fourier transform infrared data
NASA Astrophysics Data System (ADS)
Fröhlich, F.; Poupeau, G.; Badou, A.; Le Bourdonnec, F. X.; Sacquin, Y.; Dubernet, S.; Bardintzeff, J. M.; Véran, M.; Smith, D. C.; Diemer, E.
2013-12-01
Results are presented of new geological observations and laboratory analyses on Libyan Desert Glass (LDG), a unique kind of impact glass found in Egypt, probably 28.5-29.4 million years in age. A new LDG occurrence has been discovered some 50 km southward of the main LDG occurrences in the Great Sand Sea. From Fourier transform infrared (FTIR) analysis, the molecular structure of LDG is refined and significant differences are shown between LDG specimens and other pure silica glasses (fulgurite, industrial fused quartz, and amorphous biogenic silica) that are related to differences in their structures. The slight variations observed here for the mean Si-O-Si angle between the different glasses are attributed to their thermal histories. With regard to the other glasses analyzed, the LDG infrared spectral parameters point to a higher ratio of discontinuities and defects in the tetrahedral (SiO4) network. The quantitative mineralogical constitutions of sandstones and quartzites from the LDG geological setting were analyzed by FTIR. Cretaceous sandstones have a specific composition (about 90 wt% quartz, 10% dickite), clearly different from the Paleozoic ones (about 90 wt% quartz, but ≥7% kaolinite). It is shown that the reddish silts bearing the LDG are constituted mainly of microquartz enriched with dickite, whose particle size distribution is characteristic of fluvio-lacustrine deposits, probably Oligocene to Miocene in age. The target rocks, most probably quartz sand, resulted from the weathering (loss of the cementing microquartz) of the Cretaceous sandstones from the Gilf Khebir Plateau with deposition in a high-energy environment.
Systematic characterization of the Herschel SPIRE Fourier Transform Spectrometer
NASA Astrophysics Data System (ADS)
Hopwood, R.; Polehampton, E. T.; Valtchanov, I.; Swinyard, B. M.; Fulton, T.; Lu, N.; Marchili, N.; van der Wiel, M. H. D.; Benielli, D.; Imhof, P.; Baluteau, J.-P.; Pearson, C.; Clements, D. L.; Griffin, M. J.; Lim, T. L.; Makiwa, G.; Naylor, D. A.; Noble, G.; Puga, E.; Spencer, L. D.
2015-05-01
A systematic programme of calibration observations was carried out to monitor the performance of the Spectral and Photometric Imaging REceiver (SPIRE) Fourier Transform Spectrometer (FTS) instrument on board the Herschel Space Observatory. Observations of planets (including the prime point-source calibrator, Uranus), asteroids, line sources, dark sky and cross-calibration sources were made in order to monitor repeatability and sensitivity, and to improve FTS calibration. We present a complete analysis of the full set of calibration observations and use them to assess the performance of the FTS. Particular care is taken to understand and separate out the effect of pointing uncertainties, including the position of the internal beam steering mirror for sparse observations in the early part of the mission. The repeatability of spectral-line centre positions is <5 km s-1, for lines with signal-to-noise ratios >40, corresponding to <0.5-2.0 per cent of a resolution element. For spectral-line flux, the repeatability is better than 6 per cent, which improves to 1-2 per cent for spectra corrected for pointing offsets. The continuum repeatability is 4.4 per cent for the SPIRE Long Wavelength spectrometer (SLW) band and 13.6 per cent for the SPIRE Short Wavelength spectrometer (SSW) band, which reduces to ˜1 per cent once the data have been corrected for pointing offsets. Observations of dark sky were used to assess the sensitivity and the systematic offset in the continuum, both of which were found to be consistent across the FTS-detector arrays. The average point-source calibrated sensitivity for the centre detectors is 0.20 and 0.21 Jy [1σ; 1 h], for SLW and SSW. The average continuum offset is 0.40 Jy for the SLW band and 0.28 Jy for the SSW band.
Fractal surface synthesis based on two dimensional discrete Fourier transform
NASA Astrophysics Data System (ADS)
Zhou, Chao; Gao, Chenghui; Huang, Jianmeng
2013-11-01
The discrete Fourier transform(DFT) is used for fractional Brownian motion(FBM) surface synthesis in tribology(i.e., contact, sliding, and sealing, etc). However, the relationship between fractal parameters(fractal dimension and scale factor) and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface ( Sq) is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height( Sz), the skewness( Ssk) and the kurtosis( Sku) are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.
Kyatkin, A.B.; Chirikjian, G.S.
1999-06-01
The authors apply the Fourier transform on the discrete-motion group to the problem of computing the configuration-space obstacles of mobile robots which move among static obstacles, the problem of finding the workspace density of binary manipulators with many actuators, and the problem of determining workspace boundaries of manipulators with continuous-motion actuators. They develop and implement Fourier transforms for the discrete-motion group of the plane. These transforms allow them to apply fast Fourier transform methods to the computation of convolution-like integrals that arise in robot kinematics and motion planning. The results of the implementation are discussed for particular examples.
NASA Technical Reports Server (NTRS)
Miller, J. M.
1980-01-01
ATMOS is a Fourier transform spectrometer to measure atmospheric trace molecules over a spectral range of 2-16 microns. Assessment of the system performance of ATMOS includes evaluations of optical system errors induced by thermal and structural effects. In order to assess the optical system errors induced from thermal and structural effects, error budgets are assembled during system engineering tasks and line of sight and wavefront deformations predictions (using operational thermal and vibration environments and computer models) are subsequently compared to the error budgets. This paper discusses the thermal/structural error budgets, modelling and analysis methods used to predict thermal/structural induced errors and the comparisons that show that predictions are within the error budgets.
NASA Astrophysics Data System (ADS)
Nagler, Peter C.; Fixsen, Dale J.; Kogut, Alan; Tucker, Gregory S.
2015-11-01
The detection of the primordial B-mode polarization signal of the cosmic microwave background (CMB) would provide evidence for inflation. Yet as has become increasingly clear, the detection of a such a faint signal requires an instrument with both wide frequency coverage to reject foregrounds and excellent control over instrumental systematic effects. Using a polarizing Fourier transform spectrometer (FTS) for CMB observations meets both of these requirements. In this work, we present an analysis of instrumental systematic effects in polarizing FTSs, using the Primordial Inflation Explorer (PIXIE) as a worked example. We analytically solve for the most important systematic effects inherent to the FTS—emissive optical components, misaligned optical components, sampling and phase errors, and spin synchronous effects—and demonstrate that residual systematic error terms after corrections will all be at the sub-nK level, well below the predicted 100 nK B-mode signal.
NASA Astrophysics Data System (ADS)
Rivet, Sylvain; Marques, Manuel J.; Bradu, Adrian; Podoleanu, Adrian
2016-06-01
This article presents a theoretical study on an optical module (OM) that can be inserted between an object under investigation and a Fourier-domain optical coherence tomography system, transforming the latter into a polarisation-sensitive optical coherence tomography optical coherence tomography (OCT) system. The module consists of two electro-optic modulators, a Faraday rotator, a linear polariser and a quarter-wave plate. A detailed description on how the module can be used to extract both the net retardance and the fast axis orientation of a linear birefringent sample is presented. This is achieved by taking two sequential measurements for different values of retardance produced by the electro-optic modulator. The module keeps measurements free from undesired polarimetric effects due to birefringence in the single-mode optical fibre and diattenuation in fibre-based couplers within OCT systems. Simulations have been carried out in order to evaluate the effects of chromatic behaviour of the components within the OM.
Far-field radiation patterns of aperture antennas by the Winograd Fourier transform algorithm
NASA Technical Reports Server (NTRS)
Heisler, R.
1978-01-01
A more time-efficient algorithm for computing the discrete Fourier transform, the Winograd Fourier transform (WFT), is described. The WFT algorithm is compared with other transform algorithms. Results indicate that the WFT algorithm in antenna analysis appears to be a very successful application. Significant savings in cpu time will improve the computer turn around time and circumvent the need to resort to weekend runs.
Pisani, Marco; Zucco, Massimo
2009-05-11
An imaging spectrometer based on a Fabry-Perot interferometer is presented. The Fabry-Perot interferometer scans the mirror distance up to contact and the intensity modulated light signal is transformed using a Fourier Transform based algorithm, as the Michelson based Fourier Transform Spectrometers does. The resulting instrument has the advantage of a compact, high numerical aperture, high luminosity hyperspectral imaging device. Theory of operation is described along with one experimental realization and preliminary results. PMID:19434165
A Synthetic Quadrature Phase Detector/Demodulator for Fourier Transform Transform Spectrometers
NASA Technical Reports Server (NTRS)
Campbell, Joel
2008-01-01
A method is developed to demodulate (velocity correct) Fourier transform spectrometer (FTS) data that is taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low cost, high resolution audio digitizers to record high quality data without the need for an event timer or quadrature laser hardware, and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simplicity implementation makes it an attractive alternative in space based applications when compared to previous methods such as the Brault algorithm.
NASA Technical Reports Server (NTRS)
Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.
2012-01-01
By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.
Midwave infrared imaging Fourier transform spectrometry of combustion plumes
NASA Astrophysics Data System (ADS)
Bradley, Kenneth C.
A midwave infrared (MWIR) imaging Fourier transform spectrometer (IFTS) was used to successfully capture and analyze hyperspectral imagery of combustion plumes. Jet engine exhaust data from a small turbojet engine burning diesel fuel at a low rate of 300 cm3/min was collected at 1 cm -1 resolution from a side-plume vantage point on a 200x64 pixel window at a range of 11.2 meters. Spectral features of H2O, CO, and CO2 were present, and showed spatial variability within the plume structure. An array of thermocouple probes was positioned within the plume to aid in temperature analysis. A single-temperature plume model was implemented to obtain spatially-varying temperatures and plume concentrations. Model-fitted temperatures of 811 +/- 1.5 K and 543 +/- 1.6 K were obtained from plume regions in close proximity to thermocouple probes measuring temperatures of 719 K and 522 K, respectively. Industrial smokestack plume data from a coal-burning stack collected at 0.25 cm-1 resolution at a range of 600 meters featured strong emission from NO, CO, CO2, SO 2, and HCl in the spectral region 1800-3000 cm-1. A simplified radiative transfer model was employed to derive temperature and concentrations for clustered regions of the 128x64 pixel scene, with corresponding statistical error bounds. The hottest region (closest to stack centerline) was 401 +/- 0.36 K, compared to an in-stack measurement of 406 K, and model-derived concentration values of NO, CO2, and SO2 were 140 +/- 1 ppmV, 110,400 +/- 950 ppmV, and 382 +/- 4 ppmV compared to in-stack measurements of 120 ppmV (NOx), 94,000 ppmV, and 382 ppmV, respectively. In-stack measurements of CO and HCl were not provided by the stack operator, but model-derived values of 19 +/- 0.2 ppmV and 111 +/- 1 ppmV are reported near stack centerline. A deployment to Dugway Proving Grounds, UT to collect hyperspectral imagery of chemical and biological threat agent simulants resulted in weak spectral signatures from several species. Plume
Rapid Bacterial Identification Using Fourier Transform Infrared Spectroscopy
Valentine, Nancy B.; Johnson, Timothy J.; Su, Yin-Fong; Forrester, Joel B.
2007-02-01
Recent studies at Pacific Northwest National Laboratory (PNNL) using infrared spectroscopy combined with statistical analysis have shown the ability to identify and discriminate vegetative bacteria, bacterial spores and background interferents from one another. Since the anthrax releases in 2001, rapid identification of unknown powders has become a necessity. Bacterial endospores are formed by some Bacillus species as a result of the vegetative bacteria undergoing environmental stress, e.g. a lack of nutrients. Endospores are formed as a survival mechanism and are extremely resistant to heat, cold, sunlight and some chemicals. They become airborne easily and are thus readily dispersed which was demonstrated in the Hart building. Fourier Transform Infrared (FTIR) spectroscopy is one of several rapid analytical methods used for bacterial endospore identification. The most common means of bacterial identification is culturing, but this is a time-consuming process, taking hours to days. It is difficult to rapidly identify potentially harmful bacterial agents in a highly reproducible way. Various analytical methods, including FTIR, Raman, photoacoustic FTIR and Matrix Assisted Laser Desorption/Ionization (MALDI) have been used to identify vegetative bacteria and bacterial endospores. Each has shown certain areas of promise, but each has shortcomings in terms of sensitivity, measurement time or portability. IR spectroscopy has been successfully used to distinguish between the sporulated and vegetative state. [1,2] It has also shown its utility at distinguishing between the spores of different species. [2-4] There are several Bacillus species that occur commonly in nature, so it is important to be able to distinguish between the many different species versus those that present an imminent health threat. The spectra of the different sporulated species are all quite similar, though there are some subtle yet reproducible spectroscopic differences. Thus, a more robust and
Transformation optics with windows
NASA Astrophysics Data System (ADS)
Oxburgh, Stephen; White, Chris D.; Antoniou, Georgios; Orife, Ejovbokoghene; Courtial, Johannes
2014-09-01
Identity certification in the cyberworld has always been troublesome if critical information and financial transaction must be processed. Biometric identification is the most effective measure to circumvent the identity issues in mobile devices. Due to bulky and pricy optical design, conventional optical fingerprint readers have been discarded for mobile applications. In this paper, a digital variable-focus liquid lens was adopted for capture of a floating finger via fast focusplane scanning. Only putting a finger in front of a camera could fulfill the fingerprint ID process. This prototyped fingerprint reader scans multiple focal planes from 30 mm to 15 mm in 0.2 second. Through multiple images at various focuses, one of the images is chosen for extraction of fingerprint minutiae used for identity certification. In the optical design, a digital liquid lens atop a webcam with a fixed-focus lens module is to fast-scan a floating finger at preset focus planes. The distance, rolling angle and pitching angle of the finger are stored for crucial parameters during the match process of fingerprint minutiae. This innovative compact touchless fingerprint reader could be packed into a minute size of 9.8*9.8*5 (mm) after the optical design and multiple focus-plane scan function are optimized.
Medical Image Processing Using Real-Time Optical Fourier Technique
NASA Astrophysics Data System (ADS)
Rao, D. V. G. L. N.; Panchangam, Appaji; Sastry, K. V. L. N.; Material Science Team
2001-03-01
Optical Image Processing Techniques are inherently fast in view of parallel processing. A self-adaptive Optical Fourier Processing system using photo induced dichroism in a Bacteriorhodopsin film was experimentally demonstrated for medical image processing. Application of this powerful analog all-optical interactive technique for cancer diagnostics is illustrated with mammograms and Pap smears. Micro calcification clusters buried in surrounding tissue showed up clearly in the processed image. By playing with one knob, which rotates the analyzer in the optical system, either the micro calcification clusters or the surrounding dense tissue can be selectively displayed. Bacteriorhodopsin films are stable up to 140^oC and environmental friendly. As no interference is involved in the experiments, vibration isolation and even a coherent light source are not required. It may be possible to develop a low-cost rugged battery operated portable signal-enhancing magnifier.
NASA Astrophysics Data System (ADS)
Graf, Robert N.; Chen, Xiaoxin; Brown, William; Wax, Adam
2008-02-01
Fourier Domain Low Coherence Interferometry (fLCI) is a promising technique which combines the depth resolution of low coherence interferometry with the sensitivity of light scattering spectroscopy for probing the health of epithelial tissue layers. Our new fLCI system configuration utilizes a white light Xe arc lamp source and a 4-f interferometer which re-images light scattered from the sample onto the detection plane. The system employs an imaging spectrometer at the detection plane to acquire depth resolved profiles from 252 adjacent spatial points without the need for any scanning. The limited spatial coherence of the light source requires the resolution of adjacent spatial points for the generation of depth information. Depth-resolved spectral information is recovered by performing a short-time Fourier transform on the detected spectra, similar to spectroscopic optical coherence tomography. Wavelength dependent variations in scattering intensity are analyzed as a function of depth to obtain information about the neoplastic transformation of the probed cells. Previous studies have demonstrated fLCI as an excellent technique for probing the scatterer morphology of simple phantoms and of in vitro cancer cell monolayers. We now seek to assess the ability of the new fLCI system to measure the health of subsurface tissue layers using the hamster cheek pouch model. Seven hamsters will have one cheek pouch treated with the known carcinogen DMBA. At the conclusion of the 24 week treatment period the animals will be anesthetized and the cheek pouches will be extracted. We will use the fLCI optical system to measure the neoplastic transformation of the in situ subsurface tissue layers in both the normal and DMBA-treated cheek pouches. Traditional histological analysis will be used to verify the fLCI measurements. We expect our results to establish the feasibility of fLCI to distinguish between healthy and dysplastic epithelial tissues in the hamster cheek pouch.
NASA Astrophysics Data System (ADS)
Otten, Leonard John, III; Butler, Eugene W.; Rafert, Bruce; Sellar, R. Glenn
1995-06-01
Kestrel Corporation and the Florida Institute of Technology have designed, and are now manufacturing, a Fourier transform visible hyperspectral imager system for use in a single engine light aircraft. The system is composed of a Sagnac-based interferometer optical subsystem, a data management system, and an aircraft attitude and current position sybsystem. The system is designed to have better than 5 nm spectral resolution at 450 nm, operates over the 440 nm to 1150 nm spectral band and has a 2D spatial resolution of 0.8 mrad. An internal calibration source is recorded with every frame of data to retain radiometric accuracy. The entire system fits into a Cessna 206 and uses a conventional downward looking view port located in the baggage compartment. During operation, data are collected at a rate of 15 Mbytes per second and stored direct to a disk array. Data storage has been sized to accommodate 56 minutes of observations. Designed for environmental mapping, this Fourier transform imager has uses in emergency response and military operations.
NASA Astrophysics Data System (ADS)
Naylor, David A.; Gom, Bradley G.; Schofield, Ian; Tompkins, Gregory; Davis, Gary R.
2003-02-01
Astronomical spectroscopy at submillimeter wavelengths holds much promise for fields as diverse as the study of planetary atmospheres, molecular clouds and extragalactic sources. Fourier transform spectrometers (FTS) represent an important class of spectrometers well suited to observations that require broad spectral coverage at intermediate spectral resolution. In this paper we present the design and performance of a novel FTS, which has been developed for use at the James Clerk Maxwell Telescope (JCMT). The design uses two broadband intensity beamsplitters in a Mach-Zehnder configuration, which provide access to all four interferometer ports while maintaining a high and uniform efficiency over a broad spectral range. Since the interferometer processes both polarizations it is twice as efficient as the Martin-Puplett interferometer (MPI). As with the MPI, the spatial separation of the two input ports allows a reference blackbody to be viewed at all times in one port, while continually viewing the astronomical source in the other. Furthermore, by minimizing the size of the optical beam at the beamsplitter, the design is well suited to imaging Fourier transform spectroscopy (IFTS) as evidenced by its selection for the SPIRE instrument on Herschel.
NASA Astrophysics Data System (ADS)
Zhang, B.; Sang, Jun; Alam, Mohammad S.
2013-03-01
An image hiding method based on cascaded iterative Fourier transform and public-key encryption algorithm was proposed. Firstly, the original secret image was encrypted into two phase-only masks M1 and M2 via cascaded iterative Fourier transform (CIFT) algorithm. Then, the public-key encryption algorithm RSA was adopted to encrypt M2 into M2' . Finally, a host image was enlarged by extending one pixel into 2×2 pixels and each element in M1 and M2' was multiplied with a superimposition coefficient and added to or subtracted from two different elements in the 2×2 pixels of the enlarged host image. To recover the secret image from the stego-image, the two masks were extracted from the stego-image without the original host image. By applying public-key encryption algorithm, the key distribution was facilitated, and also compared with the image hiding method based on optical interference, the proposed method may reach higher robustness by employing the characteristics of the CIFT algorithm. Computer simulations show that this method has good robustness against image processing.
Measurement of absolute optical thickness of mask glass by wavelength-tuning Fourier analysis.
Kim, Yangjin; Hbino, Kenichi; Sugita, Naohiko; Mitsuishi, Mamoru
2015-07-01
Optical thickness is a fundamental characteristic of an optical component. A measurement method combining discrete Fourier-transform (DFT) analysis and a phase-shifting technique gives an appropriate value for the absolute optical thickness of a transparent plate. However, there is a systematic error caused by the nonlinearity of the phase-shifting technique. In this research the absolute optical-thickness distribution of mask blank glass was measured using DFT and wavelength-tuning Fizeau interferometry without using sensitive phase-shifting techniques. The error occurring during the DFT analysis was compensated for by using the unwrapping correlation. The experimental results indicated that the absolute optical thickness of mask glass was measured with an accuracy of 5 nm. PMID:26125394
Real-time 2D floating-point fast Fourier transforms for seeker simulation
NASA Astrophysics Data System (ADS)
Chamberlain, Richard; Lord, Eric; Shand, David J.
2002-07-01
The floating point Fast Fourier Transform (FFT) is one of the most useful basic functions available to the image and signal processing engineer allowing many complex and detailed special functions to be implemented more simply in the frequency domain. In the Hardware-in-the-Loop field an image transformed using FFT would allow the designer to think about accurate frequency based simulation of seeker lens effects, motion blur, detector transfer functions and much more. Unfortunately, the transform requires many hundreds of thousands or millions of floating point operations on a single modest sized image making it impractical for realtime Hardware-in-the-Loop systems. .until now. This paper outlines the development, by Nallatech, of an FPGA based IEEE floating point core. It traces the subsequent use of this core to develop a full 256 X 256 FFT and filter process implemented on COTS hardware at frame rates up to 150Hz. This transform can be demonstrated to model optical transfer functions at a far greater accuracy than the current spatial models. Other applications and extensions of this technique will be discussed such as filtering for image tracking algorithms and in the simulation of radar processing in the frequency domain.
Ota, T. A.
2013-10-15
Photonic Doppler velocimetry, also known as heterodyne velocimetry, is a widely used optical technique that requires the analysis of frequency modulated signals. This paper describes an investigation into the errors of short time Fourier transform analysis. The number of variables requiring investigation was reduced by means of an equivalence principle. Error predictions, as the number of cycles, samples per cycle, noise level, and window type were varied, are presented. The results were found to be in good agreement with analytical models.
NASA Astrophysics Data System (ADS)
Ota, T. A.
2013-10-01
Photonic Doppler velocimetry, also known as heterodyne velocimetry, is a widely used optical technique that requires the analysis of frequency modulated signals. This paper describes an investigation into the errors of short time Fourier transform analysis. The number of variables requiring investigation was reduced by means of an equivalence principle. Error predictions, as the number of cycles, samples per cycle, noise level, and window type were varied, are presented. The results were found to be in good agreement with analytical models.
Entanglement of periodic states, the quantum Fourier transform, and Shor's factoring algorithm
Most, Yonatan; Biham, Ofer; Shimoni, Yishai
2010-05-15
The preprocessing stage of Shor's algorithm generates a class of quantum states referred to as periodic states, on which the quantum Fourier transform is applied. Such states also play an important role in other quantum algorithms that rely on the quantum Fourier transform. Since entanglement is believed to be a necessary resource for quantum computational speedup, we analyze the entanglement of periodic states and the way it is affected by the quantum Fourier transform. To this end, we derive a formula that evaluates the Groverian entanglement measure for periodic states. Using this formula, we explain the surprising result that the Groverian entanglement of the periodic states built up during the preprocessing stage is only slightly affected by the quantum Fourier transform.
The Fourier Transform in Chemistry. Part 1. Nuclear Magnetic Resonance: Introduction.
ERIC Educational Resources Information Center
King, Roy W.; Williams, Kathryn R.
1989-01-01
Using fourier transformation methods in nuclear magnetic resonance has made possible increased sensitivity in chemical analysis. This article describes these methods as they relate to magnetization, the RF magnetic field, nuclear relaxation, the RF pulse, and free induction decay. (CW)
A commercial Fourier transform infrared (FTIR) spectrometer, modified for automated analysis of particulate-associated sulfate, was used to obtain transmission spectra samples of particulate matter collected from the ambient air onto Teflon filters. n evaluation of this instrumen...
NASA Technical Reports Server (NTRS)
Cageao, R.; Sander, S.; Blavier, J.; Jiang, Y.; Nemtchinov, V.
2000-01-01
A compact, high resolution Fourier-transform spectrometer for atmospheric near ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4N, 117.7 W, elevation 2290m).
This project explored the feasibility of developing new techniques for evaluation of the effects of environmental toxic materials on complex biopolymer systems using high sensitivity Fourier transform nuclear magnetic resonance (nmr) spectroscopy. Commercial instrumentation avail...
Computational chemistry, in conjunction with gas chromatography/mass spectrometry/Fourier transform infrared spectrometry (GC/MS/FT-IR), was used to tentatively identify seven tetrachlorobutadiene (TCBD) isomers detected in an environmental sample. Computation of the TCBD infrare...
Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR.
ERIC Educational Resources Information Center
Perkins, W. D.
1987-01-01
This is Part II in a series on Fourier transform infrared spectroscopy (FT-IR). Described are various advantages of FT-IR spectroscopy including energy advantages, wavenumber accuracy, constant resolution, polarization effects, and stepping at grating changes. (RH)
NASA Technical Reports Server (NTRS)
Bowman, K.; Worden, H.; Beer, R.
1999-01-01
Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.
Infrared (IR) spectroscopy has been widely used for the structural investigation of humic substances. Although Fourier Transform Infrared (FTIR) instrumentation has been available for sometime, relatively little work with these instruments has been reported for humic substances,...
Forecasting performance of denoising signal by Wavelet and Fourier Transforms using SARIMA model
NASA Astrophysics Data System (ADS)
Ismail, Mohd Tahir; Mamat, Siti Salwana; Hamzah, Firdaus Mohamad; Karim, Samsul Ariffin Abdul
2014-07-01
The goal of this research is to determine the forecasting performance of denoising signal. Monthly rainfall and monthly number of raindays with duration of 20 years (1990-2009) from Bayan Lepas station are utilized as the case study. The Fast Fourier Transform (FFT) and Wavelet Transform (WT) are used in this research to find the denoise signal. The denoise data obtained by Fast Fourier Transform and Wavelet Transform are being analyze by seasonal ARIMA model. The best fitted model is determined by the minimum value of MSE. The result indicates that Wavelet Transform is an effective method in denoising the monthly rainfall and number of rain days signals compared to Fast Fourier Transform.
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time. PMID:26150988
NASA Astrophysics Data System (ADS)
Landry, Jean-Thomas; Grandmont, Frédéric
2006-06-01
This paper presents an overview of a step scanning mechanism employing a flexure stage coupled with a dynamically aligned mirror used in the SpIOMM (Spectrometre Imageur de l'Observatoire du Mont Megantic) instrument, an Imaging Fourier Transform Spectrometer (IFTS) concept for ground based telescopes produced in collaboration with ABB and Universite Laval. This instrument can acquire spectra of variable resolutions up to R = λ/Δλ = 10 000 from the near UV to the near IR (350 nm to 900 nm). It is designed to fit the f/8 focus of the Mont Megantic (Quebec, Canada) 1.6m optical telescope. The innovative aspect of this instrument compared to other imaging spectrometers is the spatial coverage. The FOV covers spans of 12 arc minutes in diameter with a pixel sampling of 0.55 arc seconds. Hence spectra of more than a million scene elements are acquired at each measurement.
Prepreg cure monitoring using diffuse reflectance-FTIR. [Fourier Transform Infrared Technique
NASA Technical Reports Server (NTRS)
Young, P. R.; Chang, A. C.
1984-01-01
An in situ diffuse reflectance-Fourier transform infrared technique was developed to determine infrared spectra of graphite fiber prepregs as they were being cured. A bismaleimide, an epoxy, and addition polyimide matrix resin prepregs were studied. An experimental polyimide adhesive was also examined. Samples were positioned on a small heater at the focal point of diffuse reflectance optics and programmed at 15 F/min while FTIR spectra were being scanned, averaged, and stored. An analysis of the resulting spectra provided basic insights into changes in matrix resin molecular structure which accompanied reactions such as imidization and crosslinking. An endo-exothermal isomerization involving reactive end-caps was confirmed for the addition polyimide prepregs. The results of this study contribute to a fundamental understanding of the processing of composites and adhesives. Such understanding will promote the development of more efficient cure cycles.
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.
Meindl, Peter; Wähmer, Martin; Monte, Christian
2014-10-20
The suitability of a commercially available Fourier transform spectrometer equipped with a fiber-coupled global entrance optic as a reference spectroradiometer for the measurement of spectral solar ultraviolet irradiance at ground level has been investigated. The instrument has been characterized with respect to the wavelength uncertainty, and a calibration of the spectral irradiance responsivity has been performed by using the calculable irradiance of a high temperature black-body radiator and by using a secondary irradiance standard lamp. The relative standard uncertainty of solar irradiance measurements in the wavelength range from 310 nm to 400 nm with this spectroradiometer, based on the described methodology, is 1.6% for solar zenith angles of less than 60°. PMID:25401540
Photoacoustic detection of blood in dental pulp by using short-time Fourier transform
NASA Astrophysics Data System (ADS)
Yamada, Azusa; Kakino, Satoko; Matsuura, Yuji
2016-03-01
A method based on photoacoustic analysis is proposed to diagnose dental pulp vitality. Photoacoustic analysis enables to get signal from deeper tissues than other optical analyses and therefore, signal detection from root canal of thick dental tissues such as molar teeth is expected. As a light source for excitation of photoacoustic waves, a microchip Q-switched YAG laser with a wavelength of 1064 nm was used and owing to large penetration depth of the near infrared laser, photoacoustic signals from dental root were successfully obtained. It was found that the photoacoustic signals from the teeth containing hemoglobin solution in the pulp cavity provide vibration in high frequency region. It was also shown that the intensities of the high frequency component have correlation with the hemoglobin concentration of solution. We applied short-time Fourier transform for evaluation of photoacoustic signals and this analysis clearly showed photoacoustic signals from dental root.
Shaw, Jared B; Robinson, Errol W; Paša-Tolić, Ljiljana
2016-03-15
We revisited the implementation of 193 nm ultraviolet photodissociation (UVPD) within the ion cyclotron resonance (ICR) cell of a Fourier transform-ion cyclotron resonance (FT-ICR) mass spectrometer. UVPD performance characteristics were examined in the context of recent developments in the understanding of UVPD and in-cell tandem mass spectrometry. Efficient UVPD and photo-ECD of a model peptide and proteins within the ICR cell of a FT-ICR mass spectrometer are accomplished through appropriate modulation of laser pulse timing, relative to ion magnetron motion and the potential applied to an ion optical element upon which photons impinge. It is shown that UVPD yields efficient and extensive fragmentation, resulting in excellent sequence coverage for model peptide and protein cations. PMID:26882021
Dynamic interferometer alignment and its utility in UV Fourier transform spectrometer systems
NASA Technical Reports Server (NTRS)
Dorval, Rick K.; Engel, James R.; Wyntjes, Geert J.
1993-01-01
Dynamic alignment has been demonstrated as a practical approach to alignment maintenance for systems in the infrared region of the spectrum. On the basis of work done by OPTRA, this technique was introduced in commercial Fourier transform spectrometer systems in 1982 and in various forms is now available from a number of manufacturers. This paper reports on work by OPTRA to extend the basic technique to systems operating in the ultraviolet. In addition, this paper reports the preliminary results of the development of an alignment system using a laser diode in place of a gas laser normally found in dynamic alignment systems. A unique optical system and spatial heterodyne technique allows for achievement of a metrology system with characteristics that fully satisfy the requirements of an ultraviolet spectrometer system.
Harig, Roland; Braun, René; Dyer, Chris; Howle, Chris; Truscott, Benjamin
2008-04-14
An imaging Fourier transform spectrometer developed at TUHH was used for short-range remote detection and identification of liquids on surfaces. The method is based on the measurement of infrared radiation emitted and reflected by the surface and the liquid. A radiative transfer model that takes both the real and imaginary parts of the refractive index of the materials into account has been developed. The model is applied for the detection and identification of potentially hazardous liquids. Measurements of various liquids on diverse surfaces were performed. The measured spectra depend on the optical properties of the background surface. However, using the radiative transfer model, automatic remote detection and identification of the liquids is possible. The agreement between measured spectra and spectra calculated using the radiative transfer model is excellent. PMID:18542678
Astigmatism error modification for absolute shape reconstruction using Fourier transform method
NASA Astrophysics Data System (ADS)
He, Yuhang; Li, Qiang; Gao, Bo; Liu, Ang; Xu, Kaiyuan; Wei, Xiaohong; Chai, Liqun
2014-12-01
A method is proposed to modify astigmatism errors in absolute shape reconstruction of optical plane using Fourier transform method. If a transmission and reflection flat are used in an absolute test, two translation measurements lead to obtain the absolute shapes by making use of the characteristic relationship between the differential and original shapes in spatial frequency domain. However, because the translation device cannot guarantee the test and reference flats rigidly parallel to each other after the translations, a tilt error exists in the obtained differential data, which caused power and astigmatism errors in the reconstructed shapes. In order to modify the astigmatism errors, a rotation measurement is added. Based on the rotation invariability of the form of Zernike polynomial in circular domain, the astigmatism terms are calculated by solving polynomial coefficient equations related to the rotation differential data, and subsequently the astigmatism terms including error are modified. Computer simulation proves the validity of the proposed method.
NASA Astrophysics Data System (ADS)
Yi, Wei-song; Cui, Dian-sheng; Li, Zhi; Wu, Lan-lan; Shen, Ai-guo; Hu, Ji-ming
2013-01-01
The manuscript has investigated the application of near-infrared (NIR) spectroscopy for differentiation gastric cancer. The 90 spectra from cancerous and normal tissues were collected from a total of 30 surgical specimens using Fourier transform near-infrared spectroscopy (FT-NIR) equipped with a fiber-optic probe. Major spectral differences were observed in the CH-stretching second overtone (9000-7000 cm-1), CH-stretching first overtone (6000-5200 cm-1), and CH-stretching combination (4500-4000 cm-1) regions. By use of unsupervised pattern recognition, such as principal component analysis (PCA) and cluster analysis (CA), all spectra were classified into cancerous and normal tissue groups with accuracy up to 81.1%. The sensitivity and specificity was 100% and 68.2%, respectively. These present results indicate that CH-stretching first, combination band and second overtone regions can serve as diagnostic markers for gastric cancer.
NASA Astrophysics Data System (ADS)
Ogilvie, Jennifer
2010-03-01
Two-dimensional (2D) Fourier transform electronic spectroscopy has recently emerged as a powerful tool for the study of energy transfer in complex condensed-phase systems. Its experimental implementation is challenging but can be greatly simplified by implementing a pump-probe geometry, where the two phase-stable collinear pump pulses are created with an acousto-optic pulse-shaper. This approach also allows the use of a continuum probe pulse, expanding the available frequency range of the detection axis and allowing studies of energy transfer and electronic coupling over a broad range of frequencies. We discuss several benefits of 2D electronic spectroscopy and present 2D data on the D1-D2 reaction center complex of Photosystem II from spinach. We discuss the ability of 2D spectroscopy to distinguish between current models of energy and charge transfer in this system.
The Fourier Transform Microwave/millimeter Spectrum of ScO (X^2Σ^+)
NASA Astrophysics Data System (ADS)
Halfen, D. T.; Min, J.; Ziurys, L. M.
2013-06-01
The pure rotational spectra of ScO (X^2Σ^+) have been recorded in the 4 - 90 GHz range using Fourier transform microwave/millimeter (FTM/mmW) techniques. This species was created in a supersonic jet expansion of laser-ablated scandium vapor and N_2O gas, diluted in argon. The N = 1 → 0 and 2 → 1 rotational transitions in both v = 0 and 1 have been measured near 30 and 61 GHz, respectively. The data over 60 GHz were obtained using a new E-band (60 - 90 GHz) FTmmW spectrometer system. The data have been analyzed, and rotational, fine, and hyperfine constants have been determined, which are in good agreement with those from past optical studies. ScO is a potential circumstellar molecule in giant/supergiant stars, where it is produced in oxygen-burning nucleosynthesis.
Spectral line position calibration for the SPIRIT III Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Hansen, Scott M.
1997-11-01
The spatial infrared imaging telescope (SPIRIT III) Fourier transform spectrometer, a Michelson interferometer, contains six IR detectors having independent fields of view and spectral responsivities. The Space Dynamics Laboratory at Utah State University (SDL/USU) designed, built, and calibrated the instrument for the Midcourse Space Experiment (MSX) sponsored by the Ballistic Missile Defense Organization (BMDO). The spectrometer uses a HeNe laser to record the optical path difference introduced by moving one mirror in the spectrometer. Spectral line position errors in the spectrometer were expected as a result of slight deviations in the optical axes of each detector and the reference laser detector relative to the optical axis of the instrument. These spectral line position errors were measured for the spectrometer by comparing measurements of earthlimb radiance to published line position values from the HITRAN database. These errors were fit to a model of the expected optical axis deviations to generate correction factors of the SPIRIT III spectrometer and to infer the approximate effective focal plane location of the reference laser detector relative to the focal plane location of each detector.
NASA Astrophysics Data System (ADS)
Scholefield, Paul; Hussain, Ali; Mortimer, Hugh; Tipping, Ed; Monteith, Don; Adams, Jess; Dos Santos Pereira, Gloria
2016-04-01
We have developed a novel, highly portable and physically robust Fourier Transform Spectrometer working in the UV-VIS spectral region (250nm to 700nm) and configured to measure DOC concentrations in water in real time. We present details of the instrument's components, optical configuration, and signal output. Our new method eliminates the use of a fibre and the problems associated with it such as the higher absorption in the UV spectral region and optical coupling loss from the dip probe mirror. We use a free space approach by moving the flash lamp source away from the spectrometer and allowing for a cuvette or a flow cell be placed in the beam optical path. The optical absorption interaction occurs over a path length of 10mm but shorter path lengths can be used by changing the cell, so that more turbid samples can be analysed. This improved the instrument's performance and accounted for the higher absorption in the deep UV from water containing higher concentrations of DOC. We also present some initial test results based on water samples collected from a range of natural waters
Performance of the Fourier transform reconstructor for the European Extremely Large Telescope
NASA Astrophysics Data System (ADS)
Montilla, I.; Reyes, M.; Le Louarn, M.; Marichal-Hernández, J. G.; Rodríguez-Ramos, J. M.; Rodríguez-Ramos, L. F.
2008-07-01
The forthcoming Extremely Large Telescopes, and the new generation of Extreme Adaptive Optics systems, carry on a boost in the number of actuators that makes the real-time correction of the atmospheric aberration computationally challenging. It is necessary to study new algorithms for performing Adaptive Optics at the required speed. Among the last generation algorithms that are being studied, the Fourier Transform Reconstructor (FTR) appears as a promising candidate. Its feasibility to be used for Single-Conjugate Adaptive Optics has been extensively proved by Poyneer et al.[1] As part of the activities supported by the ELT Design Study (European Community's Framework Programme 6) we have studied the performance of this algorithm applied to the case of the European ELT, in two different cases: single-conjugate and ground-layer adaptive optics and we are studying different approaches to apply it to the more complex multi-conjugate case. The algorithm has been tested on ESO's OCTOPUS software, which simulates the atmosphere, the deformable mirror, the sensor and the closed-loop control. The performance has been compared with other algorithms as well as their response in the presence of noise and with various atmospheric conditions. The good results on performance and robustness, and the possibility of parallelizing the algorithm (shown by Rodríguez-Ramos and Marichal-Hernández) make it an excellent alternative to the typically used Matrix-Vector Multiply algorithm.
NASA Astrophysics Data System (ADS)
van den Dool, Teun C.; Hamelinck, Roger F. M. M.; Kruizinga, Bob; Gielesen, Wim L. M.; Braam, Ben C.; Nijenhuis, Jan R.; Loix, Nicolas; Luyckx, Stanislas; van Loon, Dennis; Kooijman, Peter Paul; Swinyard, Bruce M.
2010-07-01
TNO, together with its partners Micromega and SRON, have designed a cryogenic scanning mechanism for use in the SAFARI Fourier Transform Spectrometer (FTS) on board of the SPICA mission. The optics of the FTS scanning mechanism (FTSM) consists of two back-to-back cat's-eyes. The optics are mounted on a central "back-bone" tube which houses all the important mechatronic parts: the magnetic bearing linear guiding system, a magnetic linear motor serving as the OPD actuator, internal metrology with nanometer resolution, and a launch lock. A magnetic bearing is employed to enable a large scanning stroke in a small volume. It supports the optics in a free-floating way with no friction, or other non-linearities, enabling sub-nanometer accuracy within a single stage with a stroke of -4 mm to +31.5 mm. Because the FTSM will be used at cryogenic temperatures of 4 Kelvin, the main structure and optics are all constructed from 6061 Aluminum. The overall outside dimensions of the FTSM are: 393 x 130 x 125 mm, and the mass is 2.2 kg.
Gasoline analysis and brand identification using a static Fourier-transform ultraviolet spectrometer
NASA Astrophysics Data System (ADS)
Steers, Darren; Gerrard, Carl; Hirst, Bill; Sibbett, Wilson; Padgett, Miles J.
1999-11-01
The ultraviolet (UV) absorption spectra of several gasoline samples are measured using a compact static Fourier-transform (FT) spectrometer. The FT-UV spectrometer is constructed from crystalline quartz Wollaston prisms and polarizers fabricated from beta barium borate to form an interferogram in the spatial domain. The interferogram is recorded with a UV-sensitive detector array and Fourier transformed to yield spectra. Investigation using principal component analysis enables the identification of important gasoline properties such as origin.
Gain-assisted transformation optics.
Han, Tiancheng; Qiu, Cheng-Wei; Hao, Jiaming; Tang, Xiaohong; Zouhdi, Said
2011-04-25
Loss severely degrades the cloaking effect of the device designed by traditional transformation. In this letter, we propose gain-assisted transformation optics to overcome the loss problem by introducing gain media into a spherical cloak. The gain media, which can amplify the electromagnetic fields, is controlled precisely to compensate the inherent loss in experimental realization of cloaks. We discuss the significance of controlling embedded gain materials in the context of the inverse design mechanism, which allows us to wisely select realizable materials with constant gain and loss along the radius. For practical realizations, isotropic spherical gain-assisted cloak is designed. Full-wave simulations validate the proposed design concept, which can be utilized to alleviate the inevitable loss problem in transformational optical devices. PMID:21643112
Zheng, Y. |; Shirley, D.A.
1995-02-01
The authors show by Fourier analyses of experimental data, with no further treatment, that the positions of all the strong peaks in Fourier transforms of angle-resolved photoemission extended fine structure (ARPEFS) from adsorbed surfaces can be explicitly predicted from a trial structure with an accuracy of about {+-} 0.3 {angstrom} based on a single-scattering cluster model together with the concept of a strong backscattering cone, and without any additional analysis. This characteristic of ARPEFS Fourier transforms can be developed as a simple method for determining the structures of adsorbed surfaces to an accuracy of about {+-} 0.1 {angstrom}.
Luo, David; Kudenov, Michael W
2016-05-16
Systematic phase errors in Fourier transform spectroscopy can severely degrade the calculated spectra. Compensation of these errors is typically accomplished using post-processing techniques, such as Fourier deconvolution, linear unmixing, or iterative solvers. This results in increased computational complexity when reconstructing and calibrating many parallel interference patterns. In this paper, we describe a new method of calibrating a Fourier transform spectrometer based on the use of artificial neural networks (ANNs). In this way, it is demonstrated that a simpler and more straightforward reconstruction process can be achieved at the cost of additional calibration equipment. To this end, we provide a theoretical model for general systematic phase errors in a polarization birefringent interferometer. This is followed by a discussion of our experimental setup and a demonstration of our technique, as applied to data with and without phase error. The technique's utility is then supported by comparison to alternative reconstruction techniques using fast Fourier transforms (FFTs) and linear unmixing. PMID:27409947
Fourier Transform Methods Applied To The Analysis Of Microphotometric Images Of Histologic Sections
NASA Astrophysics Data System (ADS)
Dytch, Harvey E.; Wied, George L.
1989-06-01
Implementation of one-dimensional Fourier transform techniques for the analysis of histologic sections is discussed, as is the motivation for their use. Features of the frequency domain representation derived by such a transform are shown to be related to several important diagnostic clues. The interpretation of the Fourier magnitude spectrum in histologically relevant terms is examined by means of Fourier transforms of idealized tissue simulations. Some of the perturbations of these ideal spectra produced by biologic reality are discussed. Three classic types of cervical epithelial tissue are modeled, and their representation as Fourier magnitude spectra interpreted in the light of the previous results: characteristic frequency domain signatures are obtained for each. It is concluded that these techniques may provide diagnostically important objective measures, and may be applied to otherwise intractable histologic specimens with crowded and overlapping nuclei.
Laroche, G.; Vallade, J.; Bazinette, R.; Hernandez, E.; Hernandez, G.; Massines, F.; Nijnatten, P. van
2012-10-15
This paper describes an optical setup built to record Fourier transform infrared (FTIR) absorption spectra in an atmospheric pressure plasma with a spatial resolution of 2 mm. The overall system consisted of three basic parts: (1) optical components located within the FTIR sample compartment, making it possible to define the size of the infrared beam (2 mm Multiplication-Sign 2 mm over a path length of 50 mm) imaged at the site of the plasma by (2) an optical interface positioned between the spectrometer and the plasma reactor. Once through the plasma region, (3) a retro-reflector module, located behind the plasma reactor, redirected the infrared beam coincident to the incident path up to a 45 Degree-Sign beamsplitter to reflect the beam toward a narrow-band mercury-cadmium-telluride detector. The antireflective plasma-coating experiments performed with ammonia and silane demonstrated that it was possible to quantify 42 and 2 ppm of these species in argon, respectively. In the case of ammonia, this was approximately three times less than this gas concentration typically used in plasma coating experiments while the silane limit of quantification was 35 times lower. Moreover, 70% of the incoming infrared radiation was focused within a 2 mm width at the site of the plasma, in reasonable agreement with the expected spatial resolution. The possibility of reaching this spatial resolution thus enabled us to measure the gaseous precursor consumption as a function of their residence time in the plasma.
NASA Astrophysics Data System (ADS)
Rodríguez-Lorenzo, F.; Dorrío, B. V.; Blanco, J.
2012-09-01
The knowledge of the flow structure of fluids is essential in many industrial sectors as it determines the quality and success of processes like welding, cutting or material treatment. The employed fluid flow plays a fundamental role and in all cases to understand the complex pressure and shock waves patterns becomes necessary. The only way to absolutely ensure that the theoretical behavior predicted by numerical simulations fits with the real gas flow behavior is the experimental check. For such application, the optical techniques are very well suited resources due to their non invasive features. Schlieren, shadowgraph and interferometry are the typical techniques used for the study of the mass flow in fluids. In this work, we present the qualitative results obtained from a conventional interferometric technique combined with a new numerical approach used for analyzing the inner structure of supersonic flows provided by nozzles with Laval profile used in industrial oxy-fuel cutting processes. The extraction of the optical phase from the fringe patterns is performed through a Differential Fourier Transform Evaluation. We show that with further numerical processing we can obtain a complete qualitative description of the flow field including the first and second optical phase derivatives (Gradient and Lapacian phase maps).
Detection of urban O3, NO2, H2CO, and SO2 using Fourier transform spectroscopy
NASA Astrophysics Data System (ADS)
Vandaele, Ann Carine; Carleer, M.; Colin, R.; Simon, Paul C.
1993-02-01
Concentrations of SO2, NO2, H2CO, and O3 have been measured regularly since October 1990 at the urban site of the Campus of the Universite Libre de Bruxelles, using the differential optical absorption spectroscopy (DOAS) technique associated with a Fourier Transform Spectrometer. The experimental set up has already been described elsewhere (Vandaele et al., 1992). It consists of a source (either a high pressure xenon lamp or a tungsten filament) and an 800 m long path system. The spectra are recorded in the 26,000 - 38,000 cm-1 and 14,000 - 30,000 cm-1 spectral regions, at the dispersion of 7.7 cm-1. The analytical method of the DOAS technique is based on the fact that in atmospheric measurements, it is impossible to obtain an experimental blank spectrum. Therefore, the Beer-Lambert law has to be rewritten as: I equals I'oen(Delta (sigma) d) where I is the measured intensity, Io the measured intensity from which all absorption structures have been removed, n the concentration, d the optical path length, and (Delta) (sigma) the differential absorption cross section of the molecule. Numerous methods for determining I'o exist. Fourier transform filtering has been used in this work. This method defines I'o as the inverse Fourier transform of the lower frequencies portion of the power spectrum of the experimental data. A least squares procedure is then applied in order to determine the concentration of the desired molecules.
NASA Astrophysics Data System (ADS)
Kirsten, Lars; Walther, Julia; Cimalla, Peter; Gaertner, Maria; Meissner, Sven; Koch, Edmund
2011-06-01
Optical coherence tomography (OCT) is a noninvasive imaging modality generating cross sectional and volumetric images of translucent samples. In Fourier domain OCT (FD OCT), the depth profile is calculated by a fast Fourier transformation of the interference spectrum, providing speed and SNR advantage and thus making FD OCT well suitable in biomedical applications. The interference spectrum can be acquired spectrally resolved in spectral domain OCT or time-resolved in optical frequency domain imaging (OFDI). Since OCT images still suffer from motion artifacts, especially under in vivo conditions, increased depth scan rates are required. Therefor, the principle of Fourier domain mode locking has been presented by R. Huber et al. circumventing the speed limitations of conventional FD OCT systems. In FDML lasers, a long single mode fiber is inserted in the ring resonator of the laser resulting in an optical round trip time of a few microseconds. Sweeping the wavelength synchronously by a tunable Fabry-Perot filter can provide wavelength sweeps with repetition rates up to a few MHz used for OFDI. Imaging of subpleural lung tissue for investigation of lung dynamics and its elastic properties is a further biomedical application demanding high-speed OCT imaging techniques. For the first time, the visualization of subpleural alveolar structures of a rabbit lung is presented by the use of an FDML-based OCT system enabling repetition rates of 49.5 kHz and 122.6 kHz, respectively.
Fourier optics analysis of grating sensors with tilt errors.
Ferhanoglu, Onur; Toy, M Fatih; Urey, Hakan
2011-06-15
Dynamic diffraction gratings can be microfabricated with precision and offer extremely sensitive displacement measurements and light intensity modulation. The effect of pure translation of the moving part of the grating on diffracted order intensities is well known. This study focuses on the parameters that limit the intensity and the contrast of the interference. The effects of grating duty cycle, mirror reflectivities, sensor tilt and detector size are investigated using Fourier optics theory and Gaussian beam optics. Analytical findings reveal that fringe visibility becomes <0.3 when the optical path variation exceeds half the wavelength within the grating interferometer. The fringe visibility can be compensated by monitoring the interfering portion of the diffracted order light only through detector size reduction in the expense of optical power. Experiments were conducted with a grating interferometer that resulted in an eightfold increase in fringe visibility with reduced detector size, which is in agreement with theory. Findings show that diffraction grating readout principle is not limited to translating sensors but also can be used for sensors with tilt or other deflection modes. PMID:21685984
A Graphical Presentation to Teach the Concept of the Fourier Transform
ERIC Educational Resources Information Center
Besalu, E.
2006-01-01
A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.
NASA Astrophysics Data System (ADS)
Onishi, Hiroyuki; Suzuki, Hisashi
1997-03-01
Let a reference image and an input image that is magnified, rotated, and parallel-translated from the reference image be given. This paper discusses a method of computing the scale of magnification, the angle of rotation, and the quantity of parallel translation with a Hough transform of O'Gorman- Clowes version and a Fourier-Mellin transform. Differently from known methods using Fourier or Hough transforms, the discussed method can compute uniquely the angle of rotation. Moreover, the discussed method can process even low quality images since it does not require extracting feature points differently from known methods. Experiments were applied to actual images of bills.
Adaptive motion mapping in pancreatic SBRT patients using Fourier transforms
Jones, Bernard L.; Schefter, Tracey; Miften, Moyed
2015-01-01
Background and Purpose Recent studies suggest that 4DCT is unable to accurately measure respiratory-induced pancreatic tumor motion. In this work, we assessed the daily motion of pancreatic tumors treated with SBRT, and developed adaptive strategies to predict and account for this motion. Materials and Methods The daily motion trajectory of pancreatic tumors during CBCT acquisition was calculated using a model which reconstructs the instantaneous 3D position in each 2D CBCT projection image. We developed a metric (termed “Spectral Coherence,” SC) based on the Fourier frequency spectrum of motion in the SI direction, and analyzed the ability of SC to predict motion-based errors and classify patients according to motion characteristics. Results The amplitude of daily motion exceeded the predictions of pre-treatment 4DCT imaging by an average of 3.0 mm, 2.3 mm, and 3.5 mm in the AP/LR/SI directions. SC was correlated with daily motion differences and tumor dose coverage. In a simulated adaptive protocol, target margins were adjusted based on SC, resulting in significant increases in mean target D95, D99, and minimum dose. Conclusions Our Fourier-based approach differentiates between consistent and inconsistent motion characteristics of respiration and correlates with daily motion deviations from pre-treatment 4DCT. The feasibility of an SC-based adaptive protocol was demonstrated, and this patient-specific respiratory information was used to improve target dosimetry by expanding coverage in inconsistent breathers while shrinking treatment volumes in consistent breathers. PMID:25890573
Does the entorhinal cortex use the Fourier transform?
Orchard, Jeff; Yang, Hao; Ji, Xiang
2013-01-01
Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4-12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed "theta precession." Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415
Does the entorhinal cortex use the Fourier transform?
Orchard, Jeff; Yang, Hao; Ji, Xiang
2013-01-01
Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4–12 Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed “theta precession.” Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011) exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labor for implementing spatial maps: position vs. map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF) neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all. PMID:24376415
Study of Fourier transform infrared spectra of cockroach nervous tissue and chitin
NASA Astrophysics Data System (ADS)
Ghadage, Vijay H.; Kulkarni, Gauri R.; Bhoraskar, Sudha V.
2012-03-01
Fourier Transform Infrared Spectroscopy (FTIR) is a very sensitive tool which is capable of providing strong insight on structural and functional changes in lipids and proteins induced by laser radiation. In the present work cockroach nervous tissue and chitin from tibia region are irradiated with Nd: YAG laser (λ= 1064 nm, Power =150mW) via fiber optics (Numerical aperture=0.22, diameter = 8 μ). Nd: YAG laser exposure time is varied from 10 sec to 50 sec for nervous tissue and chitin. FTIR (Fourier Transform Infra Red spectra) of cockroach nervous tissue and chitin are compared before and after laser irradiation. The FTIR spectrum of non irradiated cockroach nervous tissue shows clearly the peaks due to O-H (Carboxylic acid), C=O (Amide I), C=C (Aromatic), N=0 (Nitro), C-H (Alkenes), CH (Aromatics). FTIR Spectra of non irradiated cockroach chitin clearly shows O-H (Carboxylic acid), C=O (Carbonyl stretch), C=C (Aromatic), N=O (Nitro), C-O, (anhydrides), C-H (Alkenes stretch) group. FTIR spectra of laser radiated nervous tissue from cockroach tibia and chitin shows significant changes in transmittance for O-H, C=O, C=C, C-H, N=O, C-O and C-H groups. The percentage transmittance increases for O-H, C=C group for exposure time 10sec, 40sec and 50 sec for nervous tissue. The percentage transmittance increases for O-H, C=C group for exposure time 10sec, 20sec, 30sec and 40 sec for chitin. The study shows clearly that FTIR spectroscopy of nervous tissue can reveal the interactions between infrared laser light and nervous tissue.
Large-scale analytical Fourier transform of photomask layouts using graphics processing units
NASA Astrophysics Data System (ADS)
Sakamoto, Julia A.
2015-10-01
Compensation of lens-heating effects during the exposure scan in an optical lithographic system requires knowledge of the heating profile in the pupil of the projection lens. A necessary component in the accurate estimation of this profile is the total integrated distribution of light, relying on the squared modulus of the Fourier transform (FT) of the photomask layout for individual process layers. Requiring a layout representation in pixelated image format, the most common approach is to compute the FT numerically via the fast Fourier transform (FFT). However, the file size for a standard 26- mm×33-mm mask with 5-nm pixels is an overwhelming 137 TB in single precision; the data importing process alone, prior to FFT computation, can render this method highly impractical. A more feasible solution is to handle layout data in a highly compact format with vertex locations of mask features (polygons), which correspond to elements in an integrated circuit, as well as pattern symmetries and repetitions (e.g., GDSII format). Provided the polygons can decompose into shapes for which analytical FT expressions are possible, the analytical approach dramatically reduces computation time and alleviates the burden of importing extensive mask data. Algorithms have been developed for importing and interpreting hierarchical layout data and computing the analytical FT on a graphics processing unit (GPU) for rapid parallel processing, not assuming incoherent imaging. Testing was performed on the active layer of a 392- μm×297-μm virtual chip test structure with 43 substructures distributed over six hierarchical levels. The factor of improvement in the analytical versus numerical approach for importing layout data, performing CPU-GPU memory transfers, and executing the FT on a single NVIDIA Tesla K20X GPU was 1.6×104, 4.9×103, and 3.8×103, respectively. Various ideas for algorithm enhancements will be discussed.
NASA Astrophysics Data System (ADS)
Rafert, J. B.; Holbert, E. T.; Rusk, E. T.; Durham, S. E.; Caudill, E.; Keating, D.; Newby, H.
1992-12-01
We have constructed several visible, Spatially-Modulated Imaging Fourier Transform Spectrometers (SMIFTS) for spatially resolved spectral imaging in the visible wavelength region based on work by several authors including Yoshihara and Kitade (1967), Okamoto et al. (1984), Barnes (1985) and Smith and Schempp (1991). Our spectrometers require no moving parts, are compact and enjoy a number of advantages over the other spectral data collection technologies. The unique combination of characteristics define an important niche for astronomical, remote sensing, and reconnaissance spectral data acquisition. Our SMIFTS simultaneously acquires hundreds or thousands of spectral bands for hundreds or thousands of spectral channesl. This type of sensor has been called a "hyperspectral" sensor to emphasize the major quantitative difference between this type of sensor and multispectral imagers which collect only a few spectral bands. The SMIFTS consists of input optics (a telescope), a field limiting aperture, a beamsplitter which divides the input beam into two paths, two mirrors which redirect the split beams through the same path, a collimating lens which forms the interferogram of the input aperture on the detector plane, and a cylindrical imaging lens. Thus on the detector array one axis contains spatial information and the other axis contains the spectral information for each point of the spatial axis. The result of this arrangement is that each row of the detector array contains the interferogram of the corresponding point on the aperture or slit. This slit can be fixed upon the target, or the slit can be scanned across the target to build up a second axis of spatial information resulting in a data set with four dimensions: two spatial, one spectral, and one temporal. We present sample data for both astronomical and remote sensing applications taken with the Malabar SMIFTS. Barnes, T.H. "Photodiode Array Fourier Transform Spectrometer with Improved Dynamic Range", Appl
Single-shot parallel full range complex Fourier-domain optical coherence tomography
NASA Astrophysics Data System (ADS)
Huang, Bingjie; Bu, Peng; Nan, Nan; Wang, Xiangzhao
2011-01-01
We present a method of parallel full range complex Fourier-domain optical coherence tomography (FDOCT) that is capable of acquiring an artifacts-free two-dimensional (2-D) cross-sectional image, i.e. a full range B-scan tomogram, by a single shot of 2-D CCD camera. This method is based on a spatial carrier technique, in which the spatial carrier-frequency is instantaneously introduced into the 2-D spectral interferogram registered in parallel FDOCT by using a grating-generated reference beam. The spatial-carrier-contained 2-D spectral interferogram is processed through Fourier transformation to obtain a complex 2-D spectral interferogram. From the 2-D complex spectral interferomgram, a full range B-scan tomogram is reconstructed. The principle of our method is confirmed by imaging an onion sample.
Fourier and Hadamard transform spectrometers - A limited comparison. II
NASA Technical Reports Server (NTRS)
Harwit, M.; Tai, M. H.
1977-01-01
A mathematical approach was used to compare interferometric spectrometers and Hadamard transform spectrometers. The principle results are reported, noting that the simple Hadamard spectrometer encodes more efficiently than a Michelson interferometer which, in turn, encodes less efficiently than is usually acknowledged. Hirschfeld's (1977) major objections to these findings are discussed, although it is noted that none of his objections is supported by evidence.
Large quantum Fourier transforms are never exactly realized by braiding conformal blocks
Freedman, Michael H.; Wang, Zhenghan
2007-03-15
Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {l_brace}U(2), controlled-NOT{r_brace}, the discrete Fourier transforms F{sub N}=({omega}{sup ij}){sub NxN}, i,j=0,1,...,N-1, {omega}=e{sup 2{pi}}{sup i} at {sup {approx}}{sup sol{approx}} at {sup N}, can be realized exactly by quantum circuits of size O(n{sup 2}), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F{sub N} and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks.
Linear Transformations Performed By An Electro-Optical Processor
NASA Astrophysics Data System (ADS)
Bromley, Keith; Monahan, Michael A.; Saxe, Steven G.
1984-02-01
Abstract. This paper discusses the development of a noncoherent optical signal processing device, termed an electro-optical processor, and its application to performing discrete linear transformations. The device consists of a light-emitting diode (LED), a photographic matrix mask, and an area-array charge-coupled device (CCD). It is capable of performing matrix-vector products at high speed in a small, low-power, and potentially low-cost package. The operation of the processor and a sum-mary of methods for handling bipolar and complex arithmetic are briefly described. Then, consistent with the central theme of this book, em-phasis is placed upon the computation of linear transformations using this optical implementation. The transformations discussed are the cosine, Fourier, proportional-bandwidth spectral analysis, Karhunen-Loeve, sine, Mellin, Waish-Hadamard, Haar, and slant. Examples of the matrix masks for each of these transformations are shown along with a discussion of practical applications.
Megahertz streak-mode Fourier domain optical coherence tomography
Wang, Rui; Yun, Julie X.; Yuan, Xiaocong; Goodwin, Richard; Markwald, Roger R.; Gao, Bruce Z.
2011-01-01
Here we present an ultrahigh-speed Fourier-domain optical coherence tomography (OCT) that records the OCT spectrum in streak mode with a high-speed area scan camera, which allows higher OCT imaging speed than can be achieved with a line-scan camera. Unlike parallel OCT techniques that also use area scan cameras, the conventional single-mode fiber-based point-scanning mechanism is retained to provide a confocal gate that rejects multiply scattered photons from the sample. When using a 1000 Hz resonant scanner as the streak scanner, 1,016,000 A-scans have been obtained in 1 s. This method's effectiveness has been demonstrated by recording in vivo OCT-image sequences of embryonic chick hearts at 1000 frames/s. In addition, 2-megahertz OCT data have been obtained with another high speed camera. PMID:21721817
Watanabe, Yuuki; Itagaki, Toshiki
2009-01-01
Fourier domain optical coherence tomography (FD-OCT) requires resampling of spectrally resolved depth information from wavelength to wave number, and the subsequent application of the inverse Fourier transform. The display rates of OCT images are much slower than the image acquisition rates due to processing speed limitations on most computers. We demonstrate a real-time display of processed OCT images using a linear-in-wave-number (linear-k) spectrometer and a graphics processing unit (GPU). We use the linear-k spectrometer with the combination of a diffractive grating with 1200 lines/mm and a F2 equilateral prism in the 840-nm spectral region to avoid calculating the resampling process. The calculations of the fast Fourier transform (FFT) are accelerated by the GPU with many stream processors, which realizes highly parallel processing. A display rate of 27.9 frames/sec for processed images (2048 FFT size x 1000 lateral A-scans) is achieved in our OCT system using a line scan CCD camera operated at 27.9 kHz. PMID:20059237
NASA Astrophysics Data System (ADS)
Watanabe, Yuuki; Itagaki, Toshiki
2009-11-01
Fourier domain optical coherence tomography (FD-OCT) requires resampling of spectrally resolved depth information from wavelength to wave number, and the subsequent application of the inverse Fourier transform. The display rates of OCT images are much slower than the image acquisition rates due to processing speed limitations on most computers. We demonstrate a real-time display of processed OCT images using a linear-in-wave-number (linear-k) spectrometer and a graphics processing unit (GPU). We use the linear-k spectrometer with the combination of a diffractive grating with 1200 lines/mm and a F2 equilateral prism in the 840-nm spectral region to avoid calculating the resampling process. The calculations of the fast Fourier transform (FFT) are accelerated by the GPU with many stream processors, which realizes highly parallel processing. A display rate of 27.9 frames/sec for processed images (2048 FFT size×1000 lateral A-scans) is achieved in our OCT system using a line scan CCD camera operated at 27.9 kHz.
Grid-Based Fourier Transform Phase Contrast Imaging
NASA Astrophysics Data System (ADS)
Tahir, Sajjad
Low contrast in x-ray attenuation imaging between different materials of low electron density is a limitation of traditional x-ray radiography. Phase contrast imaging offers the potential to improve the contrast between such materials, but due to the requirements on the spatial coherence of the x-ray beam, practical implementation of such systems with tabletop (i.e. non-synchrotron) sources has been limited. One recently developed phase imaging technique employs multiple fine-pitched gratings. However, the strict manufacturing tolerances and precise alignment requirements have limited the widespread adoption of grating-based techniques. In this work, we have investigated a technique recently demonstrated by Bennett et al. that utilizes a single grid of much coarser pitch. Our system consisted of a low power 100 microm spot Mo source, a CCD with 22 microm pixel pitch, and either a focused mammography linear grid or a stainless steel woven mesh. Phase is extracted from a single image by windowing and comparing data localized about harmonics of the grid in the Fourier domain. A Matlab code was written to perform the image processing. For the first time, the effects on the diffraction phase contrast and scattering amplitude images of varying grid types and periods, and of varying the window function type used to separate the harmonics, and the window widths, were investigated. Using the wire mesh, derivatives of the phase along two orthogonal directions were obtained and new methods investigated to form improved phase contrast images.
Products of multiple Fourier series with application to the multiblade transformation
NASA Technical Reports Server (NTRS)
Kunz, D. L.
1981-01-01
A relatively simple and systematic method for forming the products of multiple Fourier series using tensor like operations is demonstrated. This symbolic multiplication can be performed for any arbitrary number of series, and the coefficients of a set of linear differential equations with periodic coefficients from a rotating coordinate system to a nonrotating system is also demonstrated. It is shown that using Fourier operations to perform this transformation make it easily understood, simple to apply, and generally applicable.
Investigation of murine vasodynamics by Fourier domain optical coherence tomography
NASA Astrophysics Data System (ADS)
Meißner, Sven; Müller, Gregor; Walther, Julia; Krüger, Alexander; Cuevas, Maximiliano; Eichhorn, Birgit; Ravens, Ursula; Morawietz, Henning; Koch, Edmund
2007-07-01
In vivo imaging of blood vessels obtain useful insights in characterizing the dynamics of vasoconstriction and vasodilation. Fourier domain optical Coherence Tomography (FD-OCT) imaging technique permits in vivo investigation of blood vessels in their anatomical context without preparation traumata by temporal resolved image stacks. OCT is an optical, contact less imaging technique based on Michelson interferometry of short coherent near infrared light. Particularly by the possibility of a contact-less measurement and the high axial resolution up to 10 microns OCT is superior to an investigation by ultra sound measurement. Furthermore we obtain a high time resolution of vessel dynamic measurements with the used Fourier domain OCT-system by a high A-scan rate [1,22kHz]. In this study the model of saphenous artery was chosen for analyzing function and dynamics. The arteria saphena in the mouse is a suitable blood vessel due to the small inner diameter, a sensitive response to vasoactive stimuli and an advantageous anatomically position. Male wild type mice (C57BL/6) at the age of 8 weeks were fed control or high-fat diet for 10 weeks before analyzing the vasodynamics. The blood vessel was stimulated by dermal application of potassium to induce vasoconstriction or Sodium-Nitroprusside (SNP) to induce vasodilation. The morphology of the a. saphena and vein was determined by 3D image stacks. Time series (72 seconds, 300x512 pixel per frame) of cross-sectional images were analysed using semi automatic image processing software. Time course of dynamic parameters of the vessel was measured.
Portable Fourier Transform Spectroscopy for Analysis of Surface Contamination and Quality Control
NASA Technical Reports Server (NTRS)
Pugel, Diane
2012-01-01
Progress has been made into adapting and enhancing a commercially available infrared spectrometer for the development of a handheld device for in-field measurements of the chemical composition of various samples of materials. The intent is to duplicate the functionality of a benchtop Fourier transform infrared spectrometer (FTIR) within the compactness of a handheld instrument with significantly improved spectral responsivity. Existing commercial technology, like the deuterated L-alanine triglycine sulfide detectors (DLATGS), is capable of sensitive in-field chemical analysis. This proposed approach compares several subsystem elements of the FTIR inside of the commercial, non-benchtop system to the commercial benchtop systems. These subsystem elements are the detector, the preamplifier and associated electronics of the detector, the interferometer, associated readout parameters, and cooling. This effort will examine these different detector subsystem elements to look for limitations in each. These limitations will be explored collaboratively with the commercial provider, and will be prioritized to meet the deliverable objectives. The tool design will be that of a handheld gun containing the IR filament source and associated optics. It will operate in a point-and-shoot manner, pointing the source and optics at the sample under test and capturing the reflected response of the material in the same handheld gun. Data will be captured via the gun and ported to a laptop.
Coherent modeling and stray light in a static Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Etcheto, Pierre; Rosak, Alain; Parant, Philippe; Vigier, Odile
2004-02-01
Atmospheric sounding requires high-resolution spectrometers, such as Fourier transform interferometers. Classical ones need moving mirrors to scan the spectrum, but static interferometers with stepped mirrors can achieve high resolution in within a narrow spectral band. CNES is developing such an instrument for CO2 flow monitoring. The breadboard includes two stepped mirrors, a separating plate, a double imaging system and a detector array. To simulate the actual instrument response, we developed a physically realistic model of the full optical system with ASAP, a software well suited for broad sources, partial coherence and non-sequential propagation. After checking the theoretical interferogram and the resulting instrument spectral response for a point source, we simulated the effects of field, coherence length and chromatism. Then we studied the complex ghost reflections between the mirrors, the separating plate, the optics and the detector, taking coherence into account. Resulting interferograms and spectra were compared to the nominal ones. It appears that the most critical ghosts are not the most intense but the best focused, especially when interfering with the nominal waves. Scatter is tolerable, as it is incoherent and relatively uniform. These results led to design improvements and alignment requirements on the breadboard. This study illustrates how physical modeling can contribute to the early design of complex, non-imaging systems.
Gao, Jingz; Ji, Zhong-Ying; Wang, Zhong-Hou; Cui, Yan
2010-04-01
Spatially modulated imaging Fourier transform spectrometer (SMIFTS) was an instrument that depended on interference, and after calibration, the reconstruction spectrum can quantificationally reflect the diffuse reflection of target under sunshine. On-board calibration of SMIFTS confirmed the change of SMIFTS according to relative spectrum calibration, inspected long-time attenuation of SMIFTS optical system, and corrected export data of SMIFTS. According to the requirement of remote sensor application, it must stay in vacuum environment for a long time. As a radiant standard, the stability of lamp-house in long time is the most important characteristic of on-board calibration system. By calculation and experimentation, analyses of on-board calibration of SMIFTS, and testing spaceflight environment characteristic of on-board calibration, the difficulty in the key parts of on-board calibration of SMIFTS such as lamp-house, spectrum filter and integrating sphere was solved. According to the radiation-time stability testing for lamp-house and optics, particle-radiation testing, environmental-mechanics testing and hot vacuum examination, good result was obtained. By whole-aperture and part-field comparative wavelength calibration, the spectrum curve and before-launch interferogram were obtained. After comparison with reconstruction spectrum under different condition, the stability and credibility of SMIFTS on-board calibration system was proved. PMID:20545151
NASA Astrophysics Data System (ADS)
Kudenov, Michael W.; Banerjee, Bhaskar; Chan, Victoria C.; Dereniak, Eustace L.
2012-09-01
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 and of a rat esophagus, demonstrating the sensor's ability to resolve spectral signatures in both standard outdoor lighting and environmental conditions, as well as in fluorescence spectroscopy.
Data processing pipeline for a time-sampled imaging Fourier transform spectrometer
NASA Astrophysics Data System (ADS)
Naylor, David A.; Fulton, Trevor R.; Davis, Peter W.; Chapman, Ian M.; Gom, Brad G.; Spencer, Locke D.; Lindner, John V.; Nelson-Fitzpatrick, Nathan E.; Tahic, Margaret K.; Davis, Gary R.
2004-10-01
Imaging Fourier transform spectrometers (IFTS) are becoming the preferred systems for remote sensing spectral imaging applications because of their ability to provide, simultaneously, both high spatial and spectral resolution images of a scene. IFTS can be operated in either step-and-integrate or rapid-scan modes, where it is common practice to sample interferograms at equal optical path difference intervals. The step-and-integrate mode requires a translation stage with fast and precise point-to-point motion and additional external trigger circuitry for the detector focal plane array (FPA), and produces uniformly position-sampled interferograms which can be analyzed using standard FFT routines. In the rapid-scan mode, the translation stage is continuously moving and interferograms are often acquired at the frame-rate of the FPA. Since all translation stages have associated velocity errors, the resulting interferograms are sampled at non-uniform intervals of optical path difference, which requires more sophisticated analysis. This paper discusses the processing pipeline which is being developed for the analysis of the non-uniform rapid-scan data produced by the Herschel/SPIRE IFTS.
Yetzbacher, Michael K; Belabas, Nadia; Kitney, Katherine A; Jonas, David M
2007-01-28
Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Deltaomega)w(0) sin(beta)/c](2), where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1). PMID:17286491
NASA Astrophysics Data System (ADS)
Yetzbacher, Michael K.; Belabas, Nadia; Kitney, Katherine A.; Jonas, David M.
2007-01-01
Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of ˜L/λ, where L is the sample thickness and λ is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, Lsin2(β )Δω/(nc), where β is the half angle between beams, n is the refractive index, c is the speed of light, and Δω is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, [(Δω )w0sin(β)/c]2, where w0 is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).
NASA Technical Reports Server (NTRS)
Munoz, R. M. (Inventor)
1974-01-01
An input analog signal to be frequency analyzed is separated into N number of simultaneous analog signal components each identical to the original but delayed relative to the original by a successively larger time delay. The separated and delayed analog components are combined together in a suitable number of adders and attenuators in accordance with at least one component product of the continuous Fourier transform and analog signal matrices to separate the analog input signal into at least one of its continuous analog frequency components of bandwidth 1/N times the bandwidth of the original input signal. The original analog input signal can be reconstituted by combining the separate analog frequency components in accordance with the component products of the continuous Fourier transform and analog frequency component matrices. The continuous Fourier transformation is useful for spectrum analysis, filtering, transfer function synthesis, and communications.
System design of Fourier transform imaging spectrometer using tunable lateral shearing splitter
NASA Astrophysics Data System (ADS)
Meng, Xin; Li, Jianxin; Bai, Caixun; Zhu, Rihong
2015-04-01
The Fourier transform spectrometer without slit has the advantages of high radiation throughput and high spatial resolution. It can be used for detecting more details of the spectral and spatial information. We present the initial structure of the collimator and objective based on the analysis of the principle of the Fourier transform spectrometer. Then the collimator and objective are optimized by Zemax. The MTF of the cut-off frequency is great than 0.7. The tunable lateral shearing splitter is used as the interferometer, which makes the system more compact compared with the system using Sagnac lateral shearing splitter. The method to calculate the geometric dimension of the splitter is presented. Then the complete Fourier transform spectrometer is designed. The MTF of the cut-off frequency is great than 0.6. And the largest RMS of the spot is less than 6μm.
Meng, Xin; Li, Jianxin; Song, Huaqing; Zhu, Rihong
2014-08-20
A Fourier-transform imaging spectropolarimeter is presented and demonstrated. It is composed of a time-division polarization modulator and a high radiation throughput Fourier-transform spectrometer. Four polarization states of the input light are generated by rotating the retarder. Then, the polarized light enters the Fourier-transform spectrometer to create four sets of interferometric images, where we can recover four polarization spectra and calculate the full-Stokes vector in various wavenumber frequency. The method has good performance to resist instrument noise and has the advantage of high spatial resolution. The laboratory setup is described and the noise source is analyzed. Two proven experiments have been carried out in visible light. PMID:25321096
Periodic artifact reduction in Fourier transforms of full field atomic resolution images.
Hovden, Robert; Jiang, Yi; Xin, Huolin L; Kourkoutis, Lena F
2015-04-01
The discrete Fourier transform is among the most routine tools used in high-resolution scanning/transmission electron microscopy (S/TEM). However, when calculating a Fourier transform, periodic boundary conditions are imposed and sharp discontinuities between the edges of an image cause a cross patterned artifact along the reciprocal space axes. This artifact can interfere with the analysis of reciprocal lattice peaks of an atomic resolution image. Here we demonstrate that the recently developed Periodic Plus Smooth Decomposition technique provides a simple, efficient method for reliable removal of artifacts caused by edge discontinuities. In this method, edge artifacts are reduced by subtracting a smooth background that solves Poisson's equation with boundary conditions set by the image's edges. Unlike the traditional windowed Fourier transforms, Periodic Plus Smooth Decomposition maintains sharp reciprocal lattice peaks from the image's entire field of view. PMID:25597865
Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion
NASA Astrophysics Data System (ADS)
Yükçü, Niyazi
2016-03-01
Gaussian type orbitals (GTOs), which are one of the types of exponential type orbitals (ETOs), are used usually as basis functions in the multi-center atomic and molecular integrals to better understand physical and chemical properties of matter. In the Fourier transform method (FTM), basis functions have not simplicity to make mathematical operations, but their Fourier transforms are easier to use. In this work, with the help of FTM, Rayleigh expansion and some properties of unnormalized GTOs, we present new mathematical results for the Fourier transform of GTOs in terms of Laguerre polynomials, hypergeometric and Whittaker functions. Physical and analytical properties of GTOs are discussed and some numerical results have been given in a table. Finally, we compare our mathematical results with the other known literature results by using a computer program and details of evaluation are presented.
Application and sensitivity investigation of Fourier transforms for microwave radiometric inversions
NASA Technical Reports Server (NTRS)
Holmes, J. J.; Balanis, C. A.
1974-01-01
Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature equation, an unstable Fredholm integral equation of the first kind was solved. Fast Fourier Transform techniques were used to invert the integral after it is placed into a cross-correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system were included. The instability of the Fredholm equation was then demonstrated and a restoration procedure was included which smooths the resulting oscillations. With the recent availability and advances of Fast Fourier Transform techniques, the method presented becomes very attractive in the evaluation of large quantities of data. Actual radiometric measurements of sea water are inverted using the restoration method, incorporating the advantages of the Fast Fourier Transform algorithm for computations.
NASA Astrophysics Data System (ADS)
Liu, Jinjun; Haase, Christa; Merkt, Frédéric
2009-06-01
Widely tunable, Fourier-transform-limited pulses of terahertz (THz) radiation have been generated by optical frequency deference using (i) crystals of the highly nonlinear organic salt 4-N,N-dimethylamino-4^'-N^'-methyl stilbazolium tosylate (DAST), (ii) zinc telluride (ZnTe) crystals, and (iii) gallium phosphide (GaP) crystals. Outputs from two narrowband (Δν<1 MHz, λ˜800 nm) cw titanium-doped sapphire (Ti:Sa) ring lasers with a well-controlled frequency difference were shaped into pulses using acousto-optic modulators, coupled into an optical fiber, pulse amplified in Nd:YAG-pumped Ti:Sa crystals and used as optical sources to pump the THz nonlinear crystals. The THz radiation was detected over a broad frequency range and its bandwidth was determined to be ˜10 MHz. Absorption spectra of gas phase molecules including HF and OCS using the THz source will be presented.
Reduction and coding of synthetic aperture radar data with Fourier transforms
NASA Technical Reports Server (NTRS)
Tilley, David G.
1995-01-01
Recently, aboard the Space Radar Laboratory (SRL), the two roles of Fourier Transforms for ocean image synthesis and surface wave analysis have been implemented with a dedicated radar processor to significantly reduce Synthetic Aperture Radar (SAR) ocean data before transmission to the ground. The object was to archive the SAR image spectrum, rather than the SAR image itself, to reduce data volume and capture the essential descriptors of the surface wave field. SAR signal data are usually sampled and coded in the time domain for transmission to the ground where Fourier Transforms are applied both to individual radar pulses and to long sequences of radar pulses to form two-dimensional images. High resolution images of the ocean often contain no striking features and subtle image modulations by wind generated surface waves are only apparent when large ocean regions are studied, with Fourier transforms, to reveal periodic patterns created by wind stress over the surface wave field. Major ocean currents and atmospheric instability in coastal environments are apparent as large scale modulations of SAR imagery. This paper explores the possibility of computing complex Fourier spectrum codes representing SAR images, transmitting the coded spectra to Earth for data archives and creating scenes of surface wave signatures and air-sea interactions via inverse Fourier transformations with ground station processors.
NASA Astrophysics Data System (ADS)
He, Qian; Wang, Guangping; Wu, Jingli; Li, Junwei
2014-11-01
As the impact of the instrument internal error, external interference and other factors, the interferogram measured by Fourier transform spectrometer is asymmetric, result in the complex outcome after Fourier transform. Currently, most radiometric calibration method used for Fourier transform spectrometer is usually based on real spectrums, which is converted from the above complex spectrum by calculating magnitude value or make the phase correction first. Proceed from error sources and mechanisms of the Fourier transform spectrometer, we propose a multi-point radiometric calibration method based on complex spectral data to improve the processing efficiency and accuracy, which is obtained by the original interferogram via Fourier transform. We solving the instrument response function include linear gain and offset by complex spectrum above to calculate complex spectral radiance. Compared with the traditional method based on real spectrum, the present efficient method does not limited to real spectrum and the phase correction is not required. In this paper, we use BOMEM's MR304 Fourier transform infrared spectrometer and the DCN1000N3 blackbody made by HGH Infrared Systems to carry out the radiation calibration experiment in laboratory. The results show that, the amplitude of complex radiance spectrum obtained by this method has a high consistency with the theoretical value, while the extra imaginary spectrum is similar with the difference between results and theoretical value in absolute value and trends. It proved that, this multi-point radiometric calibration method by using the amplitude of complex spectral data is highly reliable; meanwhile, the imaginary spectrum can reflect the calibration error very well and offer a new technical approach for accuracy evaluation research.
A cryogenic scan mechanism for use in Fourier transform spectrometers
NASA Technical Reports Server (NTRS)
Hakun, Claef F.; Blumenstock, Kenneth A.
1995-01-01
This paper describes the requirements, design, assembly and testing of the linear Scan Mechanism (SM) of the Composite Infrared Spectrometer (CIRS) Instrument. The mechanism consists of an over constrained flexible structure, an innovative moving magnet actuator, passive eddy current dampers, a Differential Eddy Current (DEC) sensor, Optical Limit Sensors (OLS), and a launch lock. Although all the components of the mechanism are discussed, the flexible structure and the magnetic components are the primary focus. Several problems encountered and solutions implemented during the development of the scan mechanism are also described.
The Pegg-Barnett phase operator and the discrete Fourier transform
NASA Astrophysics Data System (ADS)
Perez-Leija, Armando; Andrade-Morales, Luis A.; Soto-Eguibar, Francisco; Szameit, Alexander; Moya-Cessa, Héctor M.
2016-04-01
In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg-Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London-Susskind-Glogower phase operator, whose natural logarithm gives rise to the Pegg-Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties.
[Research on spatially modulated Fourier transform imaging spectrometer data processing method].
Huang, Min; Xiangli, Bin; Lü, Qun-Bo; Zhou, Jin-Song; Jing, Juan-Juan; Cui, Yan
2010-03-01
Fourier transform imaging spectrometer is a new technic, and has been developed very rapidly in nearly ten years. The data catched by Fourier transform imaging spectrometer is indirect data, can not be used by user, and need to be processed by various approaches, including data pretreatment, apodization, phase correction, FFT, and spectral radicalization calibration. No paper so far has been found roundly to introduce this method. In the present paper, the author will give an effective method to process the interfering data to spectral data, and with this method we can obtain good result. PMID:20496726
The Los Alamos Fourier-Transform Spectrometer: Applications To Molecular Spectroscopy
NASA Astrophysics Data System (ADS)
Palmer, Byron A.; McDowell, Robert S.
1989-12-01
We outline design considerations and operating characteristics of the Los Alamos Fourier-transform spectrometer, a state-of-the-art instrument operating from 200 nm to 20 μm with a resolution of 0.0026 cm-1 and very high wave number and intensity accuracy. Recent work in molecular spectroscopy carried out with this instrument will be discussed, including N2+ spectra obtained in inductively-coupled plasmas; high-temperature spectra of diatomic molecules of astrophysical interest; high-resolution rovibrational fine structure; and Fourier-transform Raman spectroscopy of species in expansion-cooled gases.
The Los Alamos Fourier-transform spectrometer: Applications to molecular spectroscopy
NASA Astrophysics Data System (ADS)
Palmer, Byron A.; McDowell, Robin S.
The design considerations and operating characteristics are outlined for the Los Alamos Fourier transform spectrometer, a state-of-the-art instrument operating from 200 nm to 20 micrometer with a resolution of 0.0026/cm and very high wave number and intensity accuracy. Recent work in molecular spectroscopy carried out with this instrument is discussed, including N2(+) spectra obtained in inductively-coupled plasmas; high-temperature spectra of diatomic molecules of astrophysical interest; high-resolution rovibrational fine structure; and Fourier transform Raman spectroscopy of species in expansion-cooled gases.
Three-dimensional radiative transfer using a Fourier-transform matrix-operator method
NASA Technical Reports Server (NTRS)
Martonchik, J. V.; Diner, D. J.
1985-01-01
The three-dimensional equation of transfer for a scattering medium with planar geometry is solved by using a spatial Fourier transform and extending matrix-operator techniques developed previously for the one-dimensional equation. Doubling and adding algorithms were derived by means of an interaction principle for computing the Fourier-transformed radiation field. The resulting expressions fully describe the radiative transfer process in a scattering medium, inhomogeneous in the x-, y- and z-directions, illuminated from above by an arbitrarily general intensity field and bounded from below by a surface with completely general reflection properties.
Fast 3D shape measurement using Fourier transform profilometry without phase unwrapping
NASA Astrophysics Data System (ADS)
Song, Kechen; Hu, Shaopeng; Wen, Xin; Yan, Yunhui
2016-09-01
This paper presents a novel, simple, yet fast 3D shape measurement method using Fourier transform profilometry. Different from the conventional Fourier transform profilometry, this proposed method introduces the binocular stereo vision and employs two image pairs (i.e., original image pairs and fringe image pairs) to restructure 3D shape. In this proposed method, instead of phase unwrapping algorithm, a coarse disparity map is adopted as a constraint condition to realize phase matching using wrapped phase. Since the local phase matching and sub-pixel disparity refinement are proposed to obtain high measuring accuracy, high-quality phase is not required. The validity of the proposed method is verified by experiments.
Gridding and fast Fourier transformation on non-uniformly sparse sampled multidimensional NMR data.
Jiang, Bin; Jiang, Xianwang; Xiao, Nan; Zhang, Xu; Jiang, Ling; Mao, Xi-an; Liu, Maili
2010-05-01
For multidimensional NMR method, indirect dimensional non-uniform sparse sampling can dramatically shorten acquisition time of the experiments. However, the non-uniformly sampled NMR data cannot be processed directly using fast Fourier transform (FFT). We show that the non-uniformly sampled NMR data can be reconstructed to Cartesian grid with the gridding method that has been wide applied in MRI, and sequentially be processed using FFT. The proposed gridding-FFT (GFFT) method increases the processing speed sharply compared with the previously proposed non-uniform Fourier Transform, and may speed up application of the non-uniform sparse sampling approaches. PMID:20236843
Gridding and fast Fourier transformation on non-uniformly sparse sampled multidimensional NMR data
NASA Astrophysics Data System (ADS)
Jiang, Bin; Jiang, Xianwang; Xiao, Nan; Zhang, Xu; Jiang, Ling; Mao, Xi-an; Liu, Maili
2010-05-01
For multidimensional NMR method, indirect dimensional non-uniform sparse sampling can dramatically shorten acquisition time of the experiments. However, the non-uniformly sampled NMR data cannot be processed directly using fast Fourier transform (FFT). We show that the non-uniformly sampled NMR data can be reconstructed to Cartesian grid with the gridding method that has been wide applied in MRI, and sequentially be processed using FFT. The proposed gridding-FFT (GFFT) method increases the processing speed sharply compared with the previously proposed non-uniform Fourier Transform, and may speed up application of the non-uniform sparse sampling approaches.
Graphene, plasmons and transformation optics
NASA Astrophysics Data System (ADS)
Huidobro, P. A.; Kraft, M.; Kun, R.; Maier, S. A.; Pendry, J. B.
2016-04-01
Here we study subwavelength gratings for coupling into graphene plasmons by means of an analytical model based on transformation optics that is not limited to very shallow gratings. We consider gratings that consist of a periodic modulation of the charge density in the graphene sheet, and gratings formed by this conductivity modulation together with a dielectric grating placed in close vicinity of the graphene. Explicit expressions for the dispersion relation of the plasmon polaritons supported by the system, and reflectance and transmittance under plane wave illumination are given. We discuss the conditions for maximising the coupling between incident radiation and plasmons in the graphene, finding the optimal modulation strength for a conductivity grating.
NASA Astrophysics Data System (ADS)
Zou, Chun-bo; Hu, Bing-Liang; Li, Li-bo; Bai, Qing-Lan; Sun, Xin; Li, Ran; Yang, Jian-Feng
2014-11-01
A novel dual-band static Fourier transform imaging spectrometer was designed, which was the spatio-temporally modulated imaging Fourier transform spectrometer based on Sagnac interferometer. The approach represented a simplification and mass reduction over the traditional approach. It could obtain two-dimensional spatial images and one dimensional spectral image in two bands simultaneously. The two bands was separated through a dichroic prism and imaging in two detectors. one band was the visible and near infrared band, with the spectral range 400nm-1000nm and spectral resolution 187.5 wave numbers; the other was the short wave infrared band, with the spectral range 1000nm- 2500nm and spectral resolution 150 wave numbers. To reduce the size of the Interferometer, a high aperture compression ratio telescope system was designed before. The optical aperture was compressed to 1/10, and the volume of interferometer was reduced to 1/1000. For the convenience of engineering implementation, the telescope was composed of two no-aberration object lens: fore-lens and Collimating lens. The two band imaging spectrometers shared the primary lens and the second lens of the fore-lens and use their own collimating lens, interferometers and Fourier transform lens. The collimating lens and the Fourier transform lens of each spectrometer could be designed to the same structural style and parameters. The both spectrometers had a focal length of 1000mm, F number of 5, FOV(field of view) of 1°. Moreover, both image qualities were close to the diffraction limit, the distortion was less than 2%. The advantage of the instrument was that dual band spectral image could be acquired at the same time and the interferometer was miniaturized extremely in the case of unchanged technical indicators.
Ground-based Fourier transform infrared spectroscopy in central Mexico
NASA Astrophysics Data System (ADS)
Plaza, Eddy; Stremme, Wolfgang; Bezanilla, Alejandro; Baylon, Jorge; Grutter, Michel; Blumenstock, Thomas; Hase, Frank
2014-05-01
Altzomoni is a high altitude station in central Mexico (19.12 N, 98.65 W, 4000 m a.s.l.) for continuous measurements of various atmospheric parameters. It is located within the Izta-Popo National Park and is operated remotely from the UNAM campus. Since May 2012, high resolution solar absorption spectra have been recorded from this site using a FTIR from Bruker (HR120/5) equipped with MCT, InSb and InGaAs detectors and various optical filters. In this contribution we present a detailed description of the measurement site and the instrumental set-up including a record of the instrumental line-shapes (modulation efficiency and phase error) obtained from cell measurements and analyzed with the LINEFIT code. A preliminary analysis of almost two years of spectra recorded at the Altzomoni site resulting in profile retrievals of four NDACC gases O3, CO, HF and HCl is presented. The retrieval code PROFFIT is used and the Averaging Kernels and an error analysis are used to describe the quality of the measurements. The annual cycles in the time series of O3 and CO are presented and discussed, as well as some examples of anomalies due to volcanic gas emissions of HF and HCl are shown. The presented work is part of an effort to certify this station as part of the NDACC international network.
Addendum to 'A new hybrid algorithm for computing a fast discrete Fourier transform'
NASA Technical Reports Server (NTRS)
Reed, I. S.; Truong, T. K.; Benjauthrit, B.
1981-01-01
The reported investigation represents a continuation of a study conducted by Reed and Truong (1979), who proposed a hybrid algorithm for computing the discrete Fourier transform (DFT). The proposed technique employs a Winograd-type algorithm in conjunction with the Mersenne prime-number theoretic transform to perform a DFT. The implementation of the technique involves a considerable number of additions. The new investigation shows an approach which can reduce the number of additions significantly. It is proposed to use Winograd's algorithm for computing the Mersenne prime-number theoretic transform in the transform portion of the hybrid algorithm.
Fourier-interpolation superresolution optical fluctuation imaging (fSOFi) (Conference Presentation)
NASA Astrophysics Data System (ADS)
Enderlein, Joerg; Stein, Simon C.; Huss, Anja; Hähnel, Dirk; Gregor, Ingo
2016-02-01
Stochastic Optical Fluctuation Imaging (SOFI) is a superresolution fluorescence microscopy technique which allows to enhance the spatial resolution of an image by evaluating the temporal fluctuations of blinking fluorescent emitters. SOFI is not based on the identification and localization of single molecules such as in the widely used Photoactivation Localization Microsopy (PALM) or Stochastic Optical Reconstruction Microscopy (STORM), but computes a superresolved image via temporal cumulants from a recorded movie. A technical challenge hereby is that, when directly applying the SOFI algorithm to a movie of raw images, the pixel size of the final SOFI image is the same as that of the original images, which becomes problematic when the final SOFI resolution is much smaller than this value. In the past, sophisticated cross-correlation schemes have been used for tackling this problem. Here, we present an alternative, exact, straightforward, and simple solution using an interpolation scheme based on Fourier transforms. We exemplify the method on simulated and experimental data.
Gaynor, James D; Courtney, Trevor L; Balasubramanian, Madhumitha; Khalil, Munira
2016-06-15
The development of coherent Fourier transform two-dimensional electronic-vibrational (2D EV) spectroscopy with acousto-optic pulse-shaper-generated near-UV pump pulses and an octave-spanning broadband mid-IR probe pulse is detailed. A 2D EV spectrum of a silicon wafer demonstrates the full experimental capability of this experiment, and a 2D EV spectrum of dissolved hexacyanoferrate establishes the viability of our 2D EV experiment for studying condensed phase molecular ensembles. PMID:27304316
Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov Maxwell system
NASA Astrophysics Data System (ADS)
Eliasson, B.
2007-08-01
A problem with the solution of the Vlasov equation is its tendency to become filamented/oscillatory in velocity space, which in numerical simulations can give rise to unphysical oscillations and recurrence effects. We present a three-dimensional Vlasov-Maxwell solver (three spatial and velocity dimensions, plus time), in which the Vlasov equation is Fourier transformed in velocity space and the resulting equations solved numerically. By designing absorbing outflow boundary conditions in the Fourier transformed velocity space, the highest Fourier modes in velocity space are removed from the numerical solution. This introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced. The well-posedness of the boundary conditions is proved analytically, while the stability of the numerical implementation is assessed by long-time numerical simulations. Well-known wave-modes in magnetized plasmas are shown to be reproduced by the numerical scheme.
Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform
NASA Astrophysics Data System (ADS)
Larsson, Elisabeth; Ahlander, Krister; Hall, Andreas
2008-12-01
We show that the generalized Fourier transform can be used for reducing the computational cost and memory requirements of radial basis function methods for multi-dimensional option pricing. We derive a general algorithm, including a transformation of the Black-Scholes equation into the heat equation, that can be used in any number of dimensions. Numerical experiments in two and three dimensions show that the gain is substantial even for small problem sizes. Furthermore, the gain increases with the number of dimensions.
PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY
Open-path Fourier transform infrared (OP-FT1R) spectroscopy is an accepted technology for measuring gaseous air contaminants. OP-FT1R absorbance spectra acquired during changing aerosols conditions reveal related changes in very broad baseline features. Usually, this shearing of ...
Fourier-transform spectroscopy of O3 in the 3-micron region
NASA Technical Reports Server (NTRS)
Smith, M. A. H.; Rinsland, C. P.; Malathy Devi, V.; Flaud, J.-M.; Camy-Peyret, C.
1989-01-01
Fourier transform spectra of ozone have been recorded in the 2-5-micron region at a resolution of 0.01/cm. Absorption lines belonging to numerous vibration-rotation transitions have been observed in these spectra, and a detailed analysis of the band system centered at 3.6 microns has been completed.
The Use of the Fourier Transform for Solving Linear Elasticity Problems
NASA Astrophysics Data System (ADS)
Kozubek, Tomas; Mocek, Lukas
2011-11-01
This paper deals with solving linear elasticity problems using a modified fictitious domain method and an effective solver based on the discrete Fourier transform and the Schur complement reduction in combination with the null space method. The main goal is to show step by step all ingredients of the numerical solution.
NASA Astrophysics Data System (ADS)
Mocek, Lukas; Kozubek, Tomas
2011-09-01
The paper deals with the numerical solution of elliptic boundary value problems for 2D linear elasticity using the fictitious domain method in combination with the discrete Fourier transform and the FETI domain decomposition. We briefly mention the theoretical background of these methods, introduce resulting solvers, and demonstrate their efficiency on model benchmarks.
Technology Transfer Automated Retrieval System (TEKTRAN)
A new chemometric method based on absorbance ratios from Fourier transform infrared spectra was devised to analyze multicomponent biodegradable plastics. The method uses the BeerLambert law to directly compute individual component concentrations and weight losses before and after biodegradation of c...
ERIC Educational Resources Information Center
Perkins, W. D.
1986-01-01
Discusses: (1) the design of the Fourier Transform-Infrared Spectroscopy (FT-IR) spectrometer; (2) the computation of the spectrum from the interferogram; and (3) the use of apodization. (Part II will discuss advantages of FT-IR over dispersive techniques and show applications of FT-IR to difficult spectroscopic measurements.) (JN)
Refined Fourier-transform method of analysis of full two-dimensional digitized interferograms
NASA Astrophysics Data System (ADS)
Lovrić, Davorin; Vučić, Zlatko; Gladić, Jadranko; Demoli, Nazif; Mitrović, Slobodan; Milas, Mirko
2003-03-01
A refined Fourier-transform method of analysis of interference patterns is presented. The refinements include a method of automatic background subtraction and a way of treating the problem of heterodyning. The method proves particularly useful for analysis of long sequences of interferograms.
NASA Technical Reports Server (NTRS)
Wiedermann, Guenter; Jennings, D. E.; Hanel, R. H.; Kunde, V. G.; Moseley, S. H.
1989-01-01
A postdispersion system for astronomical observations with Fourier transform spectrometers in the thermal infrared has been developed which improves the sensitivity of radiation noise limited observations by reducing the spectral range incident on the detector. Special attention is given to the first-generation blocked impurity band detector. Planetary, solar, and stellar observations are reported.
Nikolay I. Agladz, John Klopf, Gwyn Williams, Albert J. Sievers
2010-06-01
By use of coherent terahertz synchrotron radiation, we experimentally tested a holographic Fourier transform spectrometer coupled to an array detector to determine its viability as a spectral device. Somewhat surprisingly, the overall performance strongly depends on the absorptivity of the birefringent lithium tantalate pixels in the array detector.
Gallery of Datacubes Obtained with the Livermore Imaging Fourier Transform Spectrometer
Wurtz, R; Wishnow, E H; Blais-Ouellette, S; Cook, K H; Holden, B P; Carr, D J; Stubbs, C W
2002-09-12
We have acquired spatial-spectral datacubes of astronomical objects using the Livermore visible-band imaging Fourier transform spectrometer at Apache Point Observatory. Each raw datacube contains hundreds of thousands of spectral interferograms. We present in-progress demonstrations of these observations.
USE OF A FOURIER TRANSFORM SPECTROMETER AS A REMOTE SENSOR AT SUPERFUND SITES
A Fourier transform infrared remote sensor (FTIR-RS) was used to measure chemical emissions at the Shaver's Park Superfund site in northwestern Georgia. he system was bistatic with a source/receiver at one end of a 250 path and a retroreflector at the other end. he source/receive...
Several field tests of a Fourier transform infrared (FTIR) spectrometer have been conducted. he results indicate that effective use of this type of instrument in the field of continuous emissions monitoring (CEM) is possible under the proper conditions, and within limits currentl...
Technology Transfer Automated Retrieval System (TEKTRAN)
This study deals with transferring the near-infrared (NIR) calibration models for quality assessment of barley between two instruments with different resolutions and number of data points, a Fourier transform instrument (master) and a dispersive instrument (slave). A file of spectra from 206 ground ...