Bell’s measure and implementing quantum Fourier transform with orbital angular momentum of classical light

PubMed Central

Song, Xinbing; Sun, Yifan; Li, Pengyun; Qin, Hongwei; Zhang, Xiangdong

2015-01-01

We perform Bell’s measurement for the non-separable correlation between polarization and orbital angular momentum from the same classical vortex beam. The violation of Bell’s inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and non-quantum entanglement between the polarization and the orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally. PMID:26369424

Vesicle sizing by static light scattering: a Fourier cosine transform approach

NASA Astrophysics Data System (ADS)

Wang, Jianhong; Hallett, F. Ross

1995-08-01

A Fourier cosine transform method, based on the Rayleigh-Gans-Debye thin-shell approximation, was developed to retrieve vesicle size distribution directly from the angular dependence of scattered light intensity. Its feasibility for real vesicles was partially tested on scattering data generated by the exact Mie solutions for isotropic vesicles. The noise tolerance of the method in recovering unimodal and biomodal distributions was studied with the simulated data. Applicability of this approach to vesicles with weak anisotropy was examined using Mie theory for anisotropic hollow spheres. A primitive theory about the first four moments of the radius distribution about the origin, excluding the mean radius, was obtained as an alternative to the direct retrieval of size distributions.

Planar metasurface retroreflector

NASA Astrophysics Data System (ADS)

Arbabi, Amir; Arbabi, Ehsan; Horie, Yu; Kamali, Seyedeh Mahsa; Faraon, Andrei

2017-07-01

Metasurfaces are two-dimensional arrangements of subwavelength scatterers that control the propagation of optical waves. Here, we show that cascaded metasurfaces, each performing a predefined mathematical transformation, provide a new optical design framework that enables new functionalities not yet demonstrated with single metasurfaces. Specifically, we demonstrate that retroreflection can be achieved with two vertically stacked planar metasurfaces, the first performing a spatial Fourier transform and its inverse, and the second imparting a spatially varying momentum to the Fourier transform of the incident light. Using this concept, we fabricate and test a planar monolithic near-infrared retroreflector composed of two layers of silicon nanoposts, which reflects light along its incident direction with a normal incidence efficiency of 78% and a large half-power field of view of 60°. The metasurface retroreflector demonstrates the potential of cascaded metasurfaces for implementing novel high-performance components, and enables low-power and low-weight passive optical transmitters.

Metasurface Enabled Wide-Angle Fourier Lens.

PubMed

Liu, Wenwei; Li, Zhancheng; Cheng, Hua; Tang, Chengchun; Li, Junjie; Zhang, Shuang; Chen, Shuqi; Tian, Jianguo

2018-06-01

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goncharov, Vasily V.; Hall, Gregory E., E-mail: gehall@bnl.gov

We demonstrate a method of combining a supercontinuum light source with a commercial Fourier transform spectrometer, using a novel approach to dual-beam balanced detection, implemented with phase-sensitive detection on a single light detector. A 40 dB reduction in the relative intensity noise is achieved for broadband light, analogous to conventional balanced detection methods using two matched photodetectors. Unlike conventional balanced detection, however, this method exploits the time structure of the broadband source to interleave signal and reference pulse trains in the time domain, recording the broadband differential signal at the fundamental pulse repetition frequency of the supercontinuum. The method ismore » capable of real-time correction for instability in the supercontinuum spectral structure over a broad range of wavelengths and is compatible with commercially designed spectrometers. A proof-of-principle experimental setup is demonstrated for weak absorption in the 1500-1600 nm region.« less

Light scattering properties of kidney epithelial cells and nuclei

NASA Astrophysics Data System (ADS)

Vitol, Elina A.; Kurzweg, Timothy P.; Nabet, Bahram

2006-02-01

Enlargement of mammalian cells nuclei due to the cancerous inflammation can be detected early through noninvasive optical techniques. We report on the results of cellular experiments, aimed towards the development of a fiber optic endoscopic probe used for precancerous detection of Barrett's esophagus. We previously presented white light scattering results from tissue phantoms (polystyrene polybead microspheres). In this paper, we discuss light scattering properties of epithelial MDCK (Madine-Darby Canine Kidney) cells and cell nuclei suspensions. A bifurcated optical fiber is used for experimental illumination and signal detection. The resulting scattering spectra from the cells do not exhibit the predicted Mie theory oscillatory behavior inherent to ideally spherical scatterers, such as polystyrene microspheres. However, we are able to demonstrate that the Fourier transform spectra of the cell suspensions are well correlated with the Fourier transform spectra of cell nuclei, concluding that the dominate scatterer in the backscattering region is the nucleus. This correlation experimentally illustrates that in the backscattering region, the cell nuclei are the main scatterer in the cells of the incident light.

2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

NASA Astrophysics Data System (ADS)

Zhao, Liang; Muniraj, Inbarasan; Healy, John J.; Malallah, Ra'ed; Cui, Xiao-Guang; Ryle, James P.; Sheridan, John T.

2017-05-01

The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random- Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.

Scaled nonuniform Fourier transform for image reconstruction in swept source optical coherence tomography

NASA Astrophysics Data System (ADS)

Mezgebo, Biniyam; Nagib, Karim; Fernando, Namal; Kordi, Behzad; Sherif, Sherif

2018-02-01

Swept Source optical coherence tomography (SS-OCT) is an important imaging modality for both medical and industrial diagnostic applications. A cross-sectional SS-OCT image is obtained by applying an inverse discrete Fourier transform (DFT) to axial interferograms measured in the frequency domain (k-space). This inverse DFT is typically implemented as a fast Fourier transform (FFT) that requires the data samples to be equidistant in k-space. As the frequency of light produced by a typical wavelength-swept laser is nonlinear in time, the recorded interferogram samples will not be uniformly spaced in k-space. Many image reconstruction methods have been proposed to overcome this problem. Most such methods rely on oversampling the measured interferogram then use either hardware, e.g., Mach-Zhender interferometer as a frequency clock module, or software, e.g., interpolation in k-space, to obtain equally spaced samples that are suitable for the FFT. To overcome the problem of nonuniform sampling in k-space without any need for interferogram oversampling, an earlier method demonstrated the use of the nonuniform discrete Fourier transform (NDFT) for image reconstruction in SS-OCT. In this paper, we present a more accurate method for SS-OCT image reconstruction from nonuniform samples in k-space using a scaled nonuniform Fourier transform. The result is demonstrated using SS-OCT images of Axolotl salamander eggs.

Depth resolved hyperspectral imaging spectrometer based on structured light illumination and Fourier transform interferometry

PubMed Central

Choi, Heejin; Wadduwage, Dushan; Matsudaira, Paul T.; So, Peter T.C.

2014-01-01

A depth resolved hyperspectral imaging spectrometer can provide depth resolved imaging both in the spatial and the spectral domain. Images acquired through a standard imaging Fourier transform spectrometer do not have the depth-resolution. By post processing the spectral cubes (x, y, λ) obtained through a Sagnac interferometer under uniform illumination and structured illumination, spectrally resolved images with depth resolution can be recovered using structured light illumination algorithms such as the HiLo method. The proposed scheme is validated with in vitro specimens including fluorescent solution and fluorescent beads with known spectra. The system is further demonstrated in quantifying spectra from 3D resolved features in biological specimens. The system has demonstrated depth resolution of 1.8 μm and spectral resolution of 7 nm respectively. PMID:25360367

Coherent field propagation between tilted planes.

PubMed

Stock, Johannes; Worku, Norman Girma; Gross, Herbert

2017-10-01

Propagating electromagnetic light fields between nonparallel planes is of special importance, e.g., within the design of novel computer-generated holograms or the simulation of optical systems. In contrast to the extensively discussed evaluation between parallel planes, the diffraction-based propagation of light onto a tilted plane is more burdensome, since discrete fast Fourier transforms cannot be applied directly. In this work, we propose a quasi-fast algorithm (O(N 3  log N)) that deals with this problem. Based on a proper decomposition into three rotations, the vectorial field distribution is calculated on a tilted plane using the spectrum of plane waves. The algorithm works on equidistant grids, so neither nonuniform Fourier transforms nor an explicit complex interpolation is necessary. The proposed algorithm is discussed in detail and applied to several examples of practical interest.

Fourier transform digital holographic adaptive optics imaging system

PubMed Central

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

Slit Function Measurement of An Imaging Spectrograph Using Fourier Transform Techniques

NASA Technical Reports Server (NTRS)

Park, Hongwoo; Swimyard, Bruce; Jakobsen, Peter; Moseley, Harvey; Greenhouse, Matthew

2004-01-01

Knowledge of a spectrograph slit function is necessary to interpret the unresolved lines in an observed spectrum. A theoretical slit function can be calculated from the sizes of the entrance slit, the detector aperture when it functions as an exit slit, the dispersion characteristic of the disperser, and the point spread function of the spectrograph. A measured slit function is preferred to the theoretical one for the correct interpretation of the spectral data. In a scanning spectrometer with a single exit slit, the slit function is easily measured. In a fixed grating/or disperser spectrograph, illuminating the entrance slit with a near monochromatic light from a pre-monochrmator or a tunable laser and varying the wavelength of the incident light can measure the slit function. Even though the latter technique had been used successfully for the slit function measurements, it had been very laborious and it would be prohibitive to an imaging spectrograph or a multi-object spectrograph that has a large field of view. We explore an alternative technique that is manageable for the measurements. In the proposed technique, the imaging spectrograph is used as a detector of a Fourier transform spectrometer. This method can be applied not only to an IR spectrograph but also has a potential to a visible/UV spectrograph including a wedge filter spectrograph. This technique will require a blackbody source of known temperature and a bolometer to characterize the interferometer part of the Fourier Transform spectrometer. This pa?er will describe the alternative slit function measurement technique using a Fourier transform spectrometer.

Multi-Velocity Component LDV

NASA Technical Reports Server (NTRS)

Johnson, Dennis A. (Inventor)

1996-01-01

A laser doppler velocimeter uses frequency shifting of a laser beam to provide signal information for each velocity component. A composite electrical signal generated by a light detector is digitized and a processor produces a discrete Fourier transform based on the digitized electrical signal. The transform includes two peak frequencies corresponding to the two velocity components.

Joint transform correlators with spatially incoherent illumination

NASA Astrophysics Data System (ADS)

Bykovsky, Yuri A.; Karpiouk, Andrey B.; Markilov, Anatoly A.; Rodin, Vladislav G.; Starikov, Sergey N.

1997-03-01

Two variants of joint transform correlators with monochromatic spatially incoherent illumination are considered. The Fourier-holograms of the reference and recognized images are recorded simultaneously or apart in a time on the same spatial light modulator directly by monochromatic spatially incoherent light. To create the signal of mutual correlation of the images it is necessary to execute nonlinear transformation when the hologram is illuminated by coherent light. In the first scheme of the correlator this aim was achieved by using double pas of a restoring coherent wave through the hologram. In the second variant of the correlator the non-linearity of the characteristic of the spatial light modulator for hologram recording was used. Experimental schemes and results on processing teste images by both variants of joint transform correlators with monochromatic spatially incoherent illumination. The use of spatially incoherent light on the input of joint transform correlators permits to reduce the requirements to optical quality of elements, to reduce accuracy requirements on elements positioning and to expand a number of devices suitable to input images in correlators.

Simultaneous measurement of translation and tilt using digital speckle photography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhaduri, Basanta; Quan, Chenggen; Tay, Cho Jui

2010-06-20

A Michelson-type digital speckle photographic system has been proposed in which one light beam produces a Fourier transform and another beam produces an image at a recording plane, without interfering between themselves. Because the optical Fourier transform is insensitive to translation and the imaging technique is insensitive to tilt, the proposed system is able to simultaneously and independently determine both surface tilt and translation by two separate recordings, one before and another after the surface motion, without the need to obtain solutions for simultaneous equations. Experimental results are presented to verify the theoretical analysis.

Transformation of light double cones in the human retina: the origin of trichromatism, of 4D-spatiotemporal vision, and of patchwise 4D Fourier transformation in Talbot imaging

NASA Astrophysics Data System (ADS)

Lauinger, Norbert

1997-09-01

The interpretation of the 'inverted' retina of primates as an 'optoretina' (a light cones transforming diffractive cellular 3D-phase grating) integrates the functional, structural, and oscillatory aspects of a cortical layer. It is therefore relevant to consider prenatal developments as a basis of the macro- and micro-geometry of the inner eye. This geometry becomes relevant for the postnatal trichromatic synchrony organization (TSO) as well as the adaptive levels of human vision. It is shown that the functional performances, the trichromatism in photopic vision, the monocular spatiotemporal 3D- and 4D-motion detection, as well as the Fourier optical image transformation with extraction of invariances all become possible. To transform light cones into reciprocal gratings especially the spectral phase conditions in the eikonal of the geometrical optical imaging before the retinal 3D-grating become relevant first, then in the von Laue resp. reciprocal von Laue equation for 3D-grating optics inside the grating and finally in the periodicity of Talbot-2/Fresnel-planes in the near-field behind the grating. It is becoming possible to technically realize -- at least in some specific aspects -- such a cortical optoretina sensor element with its typical hexagonal-concentric structure which leads to these visual functions.

Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goncharov, Vasily; Hall, Gregory

Here, we have developed phase-sensitive signal detection and processing algorithms for Fourier transform spectrometers fitted with supercontinuum sources for applications requiring ultimate sensitivity. Similar to well-established approach of source noise cancellation through balanced detection of monochromatic light, our method is capable of reducing the relative intensity noise of polychromatic light by 40 dB. Unlike conventional balanced detection, which relies on differential absorption measured with a well matched pair of photo-detectors, our algorithm utilizes phase-sensitive differential detection on a single photodiode and is capable of the real-time correction for instabilities in supercontinuum spectral structure over a broad range of wavelengths. Inmore » the resulting method is universal in terms of applicable wavelengths and compatible with commercial spectrometers. We present a proof-of-principle experimental« less

Supercontinuum Fourier transform spectrometry with balanced detection on a single photodiode

DOE PAGES

Goncharov, Vasily; Hall, Gregory

2016-08-25

Here, we have developed phase-sensitive signal detection and processing algorithms for Fourier transform spectrometers fitted with supercontinuum sources for applications requiring ultimate sensitivity. Similar to well-established approach of source noise cancellation through balanced detection of monochromatic light, our method is capable of reducing the relative intensity noise of polychromatic light by 40 dB. Unlike conventional balanced detection, which relies on differential absorption measured with a well matched pair of photo-detectors, our algorithm utilizes phase-sensitive differential detection on a single photodiode and is capable of the real-time correction for instabilities in supercontinuum spectral structure over a broad range of wavelengths. Inmore » the resulting method is universal in terms of applicable wavelengths and compatible with commercial spectrometers. We present a proof-of-principle experimental« less

Accurate Transmittance Measurements of Thick, High-Index, High- Dispersion, IR Windows, Using a Fourier Transform IR Spectrometer

NASA Astrophysics Data System (ADS)

Kupferberg, Lenn C.

1996-03-01

Fourier transform IR [FT-IR] spectrometers have virtually replaced scanned grating IR spectrometers in the commercial market. While FTIR spectrometers have been a boon for the chemist, they present problems for the measurement of transmittance of thick, high-index, high-dispersion, IR windows. Reflection and refraction of light by the windows introduce measurement errors. The principles of the FT-IR spectrometer will be briefly reviewed. The origins of the measurement errors will be discussed. Simple modifications to the operation of commercially available instruments will be presented. These include using strategically placed apertures and the use of collimated vs. focused beams at the sample position. They are essential for removing the effects of reflected light entering the interferometer and limiting the divergence angle of light in the interferometer. The latter minimizes refractive effects and insures consistent underfilling of the detector. Data will be shown from FT-IR spectrometers made by four manufactures and compared to measurements from a dispersive spectrometer.

[Application of Fourier transform profilometry in 3D-surface reconstruction].

PubMed

Shi, Bi'er; Lu, Kuan; Wang, Yingting; Li, Zhen'an; Bai, Jing

2011-08-01

With the improvement of system frame and reconstruction methods in fluorescent molecules tomography (FMT), the FMT technology has been widely used as an important experimental tool in biomedical research. It is necessary to get the 3D-surface profile of the experimental object as the boundary constraints of FMT reconstruction algorithms. We proposed a new 3D-surface reconstruction method based on Fourier transform profilometry (FTP) method under the blue-purple light condition. The slice images were reconstructed using proper image processing methods, frequency spectrum analysis and filtering. The results of experiment showed that the method properly reconstructed the 3D-surface of objects and has the mm-level accuracy. Compared to other methods, this one is simple and fast. Besides its well-reconstructed, the proposed method could help monitor the behavior of the object during the experiment to ensure the correspondence of the imaging process. Furthermore, the method chooses blue-purple light section as its light source to avoid the interference towards fluorescence imaging.

In situ characterization of the oxidative degradation of a polymeric light emitting device

NASA Astrophysics Data System (ADS)

Cumpston, B. H.; Parker, I. D.; Jensen, K. F.

1997-04-01

Light-emitting devices with polymeric emissive layers have great promise for the production of large-area, lightweight, flexible color displays, but short lifetimes currently limit applications. We address mechanisms of bulk polymer degradation in these devices and show through in situ Fourier transform infrared characterization of working light-emitting devices with active layers of poly[2-methoxy,5-(2'-ethyl-hexoxy)-1,4-phenylene vinylene] that oxygen is responsible for the degradation of the polymer film. A mechanism is given based on the formation of singlet oxygen from oxygen impurities in the film via energy transfer from a nonradiative exciton. Fourier transform infrared and x-ray photoelectron spectroscopy results are consistent with the mechanism, involving singlet oxygen attack followed by free radical processes. We further show that oxygen readily diffuses into the active polymer layer, changing the electrical characteristics of the film even at low concentrations. Thus, polyphenylene-vinylene-based light-emitting devices will self-destruct during operation if fabricated without special attention to eliminating oxygen contamination during fabrication and device operation.

Study on the algorithm of computational ghost imaging based on discrete fourier transform measurement matrix

NASA Astrophysics Data System (ADS)

Zhang, Leihong; Liang, Dong; Li, Bei; Kang, Yi; Pan, Zilan; Zhang, Dawei; Gao, Xiumin; Ma, Xiuhua

2016-07-01

On the basis of analyzing the cosine light field with determined analytic expression and the pseudo-inverse method, the object is illuminated by a presetting light field with a determined discrete Fourier transform measurement matrix, and the object image is reconstructed by the pseudo-inverse method. The analytic expression of the algorithm of computational ghost imaging based on discrete Fourier transform measurement matrix is deduced theoretically, and compared with the algorithm of compressive computational ghost imaging based on random measurement matrix. The reconstruction process and the reconstruction error are analyzed. On this basis, the simulation is done to verify the theoretical analysis. When the sampling measurement number is similar to the number of object pixel, the rank of discrete Fourier transform matrix is the same as the one of the random measurement matrix, the PSNR of the reconstruction image of FGI algorithm and PGI algorithm are similar, the reconstruction error of the traditional CGI algorithm is lower than that of reconstruction image based on FGI algorithm and PGI algorithm. As the decreasing of the number of sampling measurement, the PSNR of reconstruction image based on FGI algorithm decreases slowly, and the PSNR of reconstruction image based on PGI algorithm and CGI algorithm decreases sharply. The reconstruction time of FGI algorithm is lower than that of other algorithms and is not affected by the number of sampling measurement. The FGI algorithm can effectively filter out the random white noise through a low-pass filter and realize the reconstruction denoising which has a higher denoising capability than that of the CGI algorithm. The FGI algorithm can improve the reconstruction accuracy and the reconstruction speed of computational ghost imaging.

Imaging through ground-level turbulence by Fourier telescopy: Simulations and preliminary experiments

NASA Astrophysics Data System (ADS)

Randunu Pathirannehelage, Nishantha

Fourier telescopy imaging is a recently-developed imaging method that relies on active structured-light illumination of the object. Reflected/scattered light is measured by a large "light bucket" detector; processing of the detected signal yields the magnitude and phase of spatial frequency components of the object reflectance or transmittance function. An inverse Fourier transform results in the image. In 2012 a novel method, known as time-average Fourier telescopy (TAFT), was introduced by William T. Rhodes as a means for diffraction-limited imaging through ground-level atmospheric turbulence. This method, which can be applied to long horizontal-path terrestrial imaging, addresses a need that is not solved by the adaptive optics methods being used in astronomical imaging. Field-experiment verification of the TAFT concept requires instrumentation that is not available at Florida Atlantic University. The objective of this doctoral research program is thus to demonstrate, in the absence of full-scale experimentation, the feasibility of time-average Fourier telescopy through (a) the design, construction, and testing of small-scale laboratory instrumentation capable of exploring basic Fourier telescopy data-gathering operations, and (b) the development of MATLAB-based software capable of demonstrating the effect of kilometer-scale passage of laser beams through ground-level turbulence in a numerical simulation of TAFT.

Binary zone-plate array for a parallel joint transform correlator applied to face recognition.

PubMed

Kodate, K; Hashimoto, A; Thapliya, R

1999-05-10

Taking advantage of small aberrations, high efficiency, and compactness, we developed a new, to our knowledge, design procedure for a binary zone-plate array (BZPA) and applied it to a parallel joint transform correlator for the recognition of the human face. Pairs of reference and unknown images of faces are displayed on a liquid-crystal spatial light modulator (SLM), Fourier transformed by the BZPA, intensity recorded on an optically addressable SLM, and inversely Fourier transformed to obtain correlation signals. Consideration of the bandwidth allows the relations among the channel number, the numerical aperture of the zone plates, and the pattern size to be determined. Experimentally a five-channel parallel correlator was implemented and tested successfully with a 100-person database. The design and the fabrication of a 20-channel BZPA for phonetic character recognition are also included.

Implementation of quantum and classical discrete fractional Fourier transforms.

PubMed

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

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Implementation of quantum and classical discrete fractional Fourier transforms

PubMed Central

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

Principle and analysis of a rotational motion Fourier transform infrared spectrometer

NASA Astrophysics Data System (ADS)

Cai, Qisheng; Min, Huang; Han, Wei; Liu, Yixuan; Qian, Lulu; Lu, Xiangning

2017-09-01

Fourier transform infrared spectroscopy is an important technique in studying molecular energy levels, analyzing material compositions, and environmental pollutants detection. A novel rotational motion Fourier transform infrared spectrometer with high stability and ultra-rapid scanning characteristics is proposed in this paper. The basic principle, the optical path difference (OPD) calculations, and some tolerance analysis are elaborated. The OPD of this spectrometer is obtained by the continuously rotational motion of a pair of parallel mirrors instead of the translational motion in traditional Michelson interferometer. Because of the rotational motion, it avoids the tilt problems occurred in the translational motion Michelson interferometer. There is a cosine function relationship between the OPD and the rotating angle of the parallel mirrors. An optical model is setup in non-sequential mode of the ZEMAX software, and the interferogram of a monochromatic light is simulated using ray tracing method. The simulated interferogram is consistent with the theoretically calculated interferogram. As the rotating mirrors are the only moving elements in this spectrometer, the parallelism of the rotating mirrors and the vibration during the scan are analyzed. The vibration of the parallel mirrors is the main error during the rotation. This high stability and ultra-rapid scanning Fourier transform infrared spectrometer is a suitable candidate for airborne and space-borne remote sensing spectrometer.

Hyperspectral imaging using the single-pixel Fourier transform technique

NASA Astrophysics Data System (ADS)

Jin, Senlin; Hui, Wangwei; Wang, Yunlong; Huang, Kaicheng; Shi, Qiushuai; Ying, Cuifeng; Liu, Dongqi; Ye, Qing; Zhou, Wenyuan; Tian, Jianguo

2017-03-01

Hyperspectral imaging technology is playing an increasingly important role in the fields of food analysis, medicine and biotechnology. To improve the speed of operation and increase the light throughput in a compact equipment structure, a Fourier transform hyperspectral imaging system based on a single-pixel technique is proposed in this study. Compared with current imaging spectrometry approaches, the proposed system has a wider spectral range (400-1100 nm), a better spectral resolution (1 nm) and requires fewer measurement data (a sample rate of 6.25%). The performance of this system was verified by its application to the non-destructive testing of potatoes.

Characterization of plasmonic hole arrays as transparent electrical contacts for organic photovoltaics using high-brightness Fourier transform methods

DOE PAGES

Camino, Fernando E.; Nam, Chang-Yong; Pang, Yutong T.; ...

2014-05-15

Here we present a methodology for probing light-matter interactions in prototype photovoltaic devices consisting of an organic semiconductor active layer with a semitransparent metal electrical contact exhibiting surface plasmon-based enhanced optical transmission. We achieve high-spectral irradiance in a spot size of less than 100 μm using a high-brightness laser-driven light source and appropriate coupling optics. Spatially resolved Fourier transform photocurrent spectroscopy in the visible and near-infrared spectral regions allows us to measure external quantum efficiency with high sensitivity in small-area devices (<1 mm 2). Lastly, this allows for rapid fabrication of variable-pitch sub-wavelength hole arrays in metal films for usemore » as transparent electrical contacts, and evaluation of the evanescent and propagating mode coupling to resonances in the active layer.« less

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

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…

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Optical information processing with transformation of the spatial coherence of light

NASA Astrophysics Data System (ADS)

Bykovskii, Yurii A.; Markilov, A. A.; Rodin, V. G.; Starikov, S. N.

1995-10-01

A description is given of systems with spatially incoherent illumination, intended for spectral and correlation analysis, and for the recording of Fourier holograms. These systems make use of transformation of the degree of the spatial coherence of light. The results are given of the processing of images and signals, including those transmitted by a bundle of fibre-optic waveguides both as monochromatic light and as quasimonochromatic radiation from a cathode-ray tube. The feasibility of spatial frequency filtering and of correlation analysis of images with a bipolar impulse response is considered for systems with spatially incoherent illumination where these tasks are performed by double transformation of the spatial coherence of light. A description is given of experimental systems and the results of image processing are reported.

Monitoring light-induced structural changes of Channelrhodopsin-2 by UV-visible and Fourier transform infrared spectroscopy.

PubMed

Ritter, Eglof; Stehfest, Katja; Berndt, Andre; Hegemann, Peter; Bartl, Franz J

2008-12-12

Channelrhodopsin-2 (ChR2) is a microbial type rhodopsin and a light-gated cation channel that controls phototaxis in Chlamydomonas. We expressed ChR2 in COS-cells, purified it, and subsequently investigated this unusual photoreceptor by flash photolysis and UV-visible and Fourier transform infrared difference spectroscopy. Several transient photoproducts of the wild type ChR2 were identified, and their kinetics and molecular properties were compared with those of the ChR2 mutant E90Q. Based on the spectroscopic data we developed a model of the photocycle comprising six distinguishable intermediates. This photocycle shows similarities to the photocycle of the ChR2-related Channelrhodopsin of Volvox but also displays significant differences. We show that molecular changes include retinal isomerization, changes in hydrogen bonding of carboxylic acids, and large alterations of the protein backbone structure. These alterations are stronger than those observed in the photocycle of other microbial rhodopsins like bacteriorhodopsin and are related to those occurring in animal rhodopsins. UV-visible and Fourier transform infrared difference spectroscopy revealed two late intermediates with different time constants of tau = 6 and 40 s that exist during the recovery of the dark state. The carboxylic side chain of Glu(90) is involved in the slow transition. The molecular changes during the ChR2 photocycle are discussed with respect to other members of the rhodopsin family.

Monitoring Light-induced Structural Changes of Channelrhodopsin-2 by UV-visible and Fourier Transform Infrared Spectroscopy*

PubMed Central

Ritter, Eglof; Stehfest, Katja; Berndt, Andre; Hegemann, Peter; Bartl, Franz J.

2008-01-01

Channelrhodopsin-2 (ChR2) is a microbial type rhodopsin and a light-gated cation channel that controls phototaxis in Chlamydomonas. We expressed ChR2 in COS-cells, purified it, and subsequently investigated this unusual photoreceptor by flash photolysis and UV-visible and Fourier transform infrared difference spectroscopy. Several transient photoproducts of the wild type ChR2 were identified, and their kinetics and molecular properties were compared with those of the ChR2 mutant E90Q. Based on the spectroscopic data we developed a model of the photocycle comprising six distinguishable intermediates. This photocycle shows similarities to the photocycle of the ChR2-related Channelrhodopsin of Volvox but also displays significant differences. We show that molecular changes include retinal isomerization, changes in hydrogen bonding of carboxylic acids, and large alterations of the protein backbone structure. These alterations are stronger than those observed in the photocycle of other microbial rhodopsins like bacteriorhodopsin and are related to those occurring in animal rhodopsins. UV-visible and Fourier transform infrared difference spectroscopy revealed two late intermediates with different time constants of τ = 6 and 40 s that exist during the recovery of the dark state. The carboxylic side chain of Glu90 is involved in the slow transition. The molecular changes during the ChR2 photocycle are discussed with respect to other members of the rhodopsin family. PMID:18927082

Tracking Polymer Cure Via Embedded Optical Fibers

NASA Technical Reports Server (NTRS)

Dean, David L.; Davidson, T. Fred

1993-01-01

Fourier-transform infrared spectroscopy applied in interior of specimen of material by bringing infrared light through specimen in optical fiber. Light interacts with material via evanescent-wave effect. Spectra obtained in this way at various times during curing process also combined with data from ultrasonic, thermographic, and dielectric-impedance monitoring, and other measurement techniques to obtain more complete characterization of progress of curing process.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

Synthesis and characterization of pure and Li⁺ activated Alq₃ complexes for green and blue organic light emitting diodes and display devices.

PubMed

Bhagat, S A; Borghate, S V; Kalyani, N Thejo; Dhoble, S J

2014-08-01

Pure and Li(+)-doped Alq3 complexes were synthesized by simple precipitation method at room temperature, maintaining the stoichiometric ratio. These complexes were characterized by X-ray diffraction, ultraviolet-visible absorption and Fourier transform infrared and photoluminescence (PL) spectra. X-ray diffraction analysis reveals the crystalline nature of the synthesized complexes, while Fourier transform infrared spectroscopy confirm the molecular structure, the completion of quinoline ring formation and presence of quinoline structure in the metal complex. Ultraviolet-visible and PL spectra revealed that Li(+) activated Alq3 complexes exhibit the highest intensity in comparison to pure Alq3 phosphor. Thus, Li(+) enhances PL emission intensity when doped into Alq3 phosphor. The excitation spectra lie in the range of 383-456 nm. All the synthesized complexes other than Liq give green emission, while Liq gives blue emission with enhanced intensity. Thus, he synthesized phosphors are the best suitable candidates for green- and blue-emitting organic light emitting diode, PL liquid-crystal display and solid-state lighting applications. Copyright © 2013 John Wiley & Sons, Ltd.

Photochemistry of Iron and Ruthenium Carbonyl Complexes: Evidence for Light-Induced Loss of Carbon Monoxide and Reductive Elimination of Triethylsilane from cis-mer-HM(SiEt3)(CO)3(PPh3).

DTIC Science & Technology

1983-05-21

JEOL FX9OQ Fourier transform or Bruker 250 or 270 MHz Fourier transform spectrometer. Irradiations. Photochemical reactions were carried out using a...Ph 3 ) 3nd -t-Etin V,- a 313 nm quantum yield of -0.6. The process is photochemically everse if the cis-mer-HM(SiPh 3 )(CO) 3 (PPh 3) is irradiated...process is photochemically reversed if the cis-mer-HM(SiPh 3 )(CO)3 (PPh 3 ) is irradiated in t.e presence of excess Et3SiH. Irradiation of cis-mer-HM

Plant-based Food and Feed Protein Structure Changes Induced by Gene-transformation heating and bio-ethanol processing: A Synchrotron-based Molecular Structure and Nutrition Research Program

DOE Office of Scientific and Technical Information (OSTI.GOV)

P Yu

Unlike traditional 'wet' analytical methods which during processing for analysis often result in destruction or alteration of the intrinsic protein structures, advanced synchrotron radiation-based Fourier transform infrared microspectroscopy has been developed as a rapid and nondestructive and bioanalytical technique. This cutting-edge synchrotron-based bioanalytical technology, taking advantages of synchrotron light brightness (million times brighter than sun), is capable of exploring the molecular chemistry or structure of a biological tissue without destruction inherent structures at ultra-spatial resolutions. In this article, a novel approach is introduced to show the potential of the advanced synchrotron-based analytical technology, which can be used to study plant-basedmore » food or feed protein molecular structure in relation to nutrient utilization and availability. Recent progress was reported on using synchrotron-based bioanalytical technique synchrotron radiation-based Fourier transform infrared microspectroscopy and diffused reflectance infrared Fourier transform spectroscopy to detect the effects of gene-transformation (Application 1), autoclaving (Application 2), and bio-ethanol processing (Application 3) on plant-based food and feed protein structure changes on a molecular basis. The synchrotron-based technology provides a new approach for plant-based protein structure research at ultra-spatial resolutions at cellular and molecular levels.« less

An alternative path to the boundary: The CFT as the Fourier space of AdS

NASA Astrophysics Data System (ADS)

Tolfree, Ian M.

2009-12-01

In this thesis we shed new light on the conjectured duality between an n + 1 dimensional theory of gravity in anti de Sitter space (AdS) and an n dimensional conformal field theory (CFT) by showing that the CFT can be interpreted as the Fourier space of AdS. We then make use of this to gain insight into the nature of black hole entropy. In the first part of this thesis, we give an introduction to the ideas of and review the basics of the AdS/CFT. In the next section we make use of well known integral geometry techniques to derive the Fourier transformation of a function on AdS and see it is a function with compact support on the boundary. Comparing this to the literature, we find that the Green's functions from the literature are actually the Fourier weights of the transformation and that the boundary values of fields appearing in the correspondence are the Fourier coefficients of the transformation. One is thus left to interpret the CFT as the quantized version of a classical theory in AdS and the dual operator as the Fourier coefficients. Group theoretic considerations are discussed in relation to the transformation and its potential use in constructing QCD like theories. In the last section, we then build upon this to study the BTZ black hole. Named after its authors, Banados, Teitelboim and Zanelli, the BTZ black hole is a three dimensional (two space plus one time dimension) black hole in anti de Sitter space. Following standard procedures for modifying Fourier Transformations to accommodate quotient spaces we arrive at a mapping in a black hole background consistent with known results that yields the exact micro-states of a scalar field in a black hole background. We find that the micro-states are the Fourier coefficients on the boundary, which transform under the principal series representation of SL(2, R). Using the knowledge of how to represent a bulk scalar field in the CFT, and knowing how a black hole interacts with a scalar field, we deduce the possible representations of a black hole in the CFT. We find that the black hole micro-states live on the boundary, not on the horizon, and correspond to the possible emission modes of the black hole.

The discrete Fourier transform algorithm for determining decay constants—Implementation using a field programmable gate array

NASA Astrophysics Data System (ADS)

Bostrom, G.; Atkinson, D.; Rice, A.

2015-04-01

Cavity ringdown spectroscopy (CRDS) uses the exponential decay constant of light exiting a high-finesse resonance cavity to determine analyte concentration, typically via absorption. We present a high-throughput data acquisition system that determines the decay constant in near real time using the discrete Fourier transform algorithm on a field programmable gate array (FPGA). A commercially available, high-speed, high-resolution, analog-to-digital converter evaluation board system is used as the platform for the system, after minor hardware and software modifications. The system outputs decay constants at maximum rate of 4.4 kHz using an 8192-point fast Fourier transform by processing the intensity decay signal between ringdown events. We present the details of the system, including the modifications required to adapt the evaluation board to accurately process the exponential waveform. We also demonstrate the performance of the system, both stand-alone and incorporated into our existing CRDS system. Details of FPGA, microcontroller, and circuitry modifications are provided in the Appendix and computer code is available upon request from the authors.

A Short Biography of Joseph Fourier and Historical Development of Fourier Series and Fourier Transforms

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…

Extracting Micro-Doppler Radar Signatures from Rotating Targets Using Fourier-Bessel Transform and Time-Frequency Analysis

DTIC Science & Technology

2014-10-16

Time-Frequency analysis, Short-Time Fourier Transform, Wigner Ville Distribution, Fourier Bessel Transform, Fractional Fourier Transform. I...INTRODUCTION Most widely used time-frequency transforms are short-time Fourier Transform (STFT) and Wigner Ville distribution (WVD). In STFT, time and...frequency resolutions are limited by the size of window function used in calculating STFT. For mono-component signals, WVD gives the best time and frequency

[Study on analysis of copy paper by Fourier transform infrared spectroscopy].

PubMed

Li, Ji-Min; Wang, Yan-Ji; Wang, Jing-Han; Yao, Li-Juan; Zhang, Biao

2009-06-01

A new method of fast identification of copy papers by Fourier transform infrared spectroscopy (FTIR) was developed. The kinds of filler and the cellulosic degree of crystallinity were analyzed by FTIR, and the ageing curves of cellulosic paper were studied with heating and ultraviolet light. The cellulosic degree of crystallinity was showed by the ratio of absorbance at 1 429 cm(-1) to that at 893 cm(-1), the standard deviation of different brands of copy papers was 0.010 7-0.016 0, and the standard deviation of the same brands of copy papers was 0.014 8. The kinds of filler and the cellulosic degree of crystallinity were different in copy papers from different brands of different manufacturing plants, different brands of same manufacturing plants and different manufacturing times of the same brands from the same manufacturing plants, and the curves of ageing were different with heating and ultraviolet light. The results of fast identification of copy papers by FTIR are satisfactory.

Two-Dimensional Fourier Transform Electronic Spectroscopy of Peridinin and Peridinin Analogs

NASA Astrophysics Data System (ADS)

Khosravi, Soroush; Bishop, Michael; Obaid, Razib; Whitelock, Hope; Carroll, Ann Marie; Lafountain, Amy; Frank, Harry; Beck, Warren; Gibson, George; Berrah, Nora

2016-05-01

The peridinin chlorophyll- a protein (PCP) is a light harvesting complex in dinoflagellates that exhibits a carotenoid-to-chlorophyll (Chl) a excitation energy transfer (EET) efficiency of 85-95%. Unlike most light harvesting complexes, where the number of carotenoids is less than Chl, each subunit of PCP contains eight tightly-packed peridinins surrounding two Chl a molecules. The unusual solvent polarity dependence of the lowest excited S1 state of peridinin suggests the presence of an intramolecular charge-transfer (ICT) state. The nature of the ICT state, its coupling to the S1 of peridinin, and whether it enables the high EET efficiency is still unclear. Two-dimensional electronic Fourier transform spectroscopy (2DES) is a powerful method capable of examining these issues. The present work examines the ICT state of peridinin and peridinin analogs that have diminished ICT character. 2DES data adding new insight into the spectral signatures and nature of the ICT state in peridinin will be presented. Funded by the DoE-BES, Grant No. DE-SC0012376.

Reference Interferometer Using a Semiconductor Laser/LED Reference Source in a Cryogenic Fourier-Transform Spectrometer

NASA Technical Reports Server (NTRS)

Martino, Anthony J.; Cornwell, Donald M.

1998-01-01

A combination of a single mode AlGaAs laser diode and broadband LED was used in a Michelson interferometer to provide reference signals in a Fourier transform spectrometer, the Composite Infrared Spectrometer, on the Cassini mission to Saturn. The narrowband light from the laser produced continuous fringes throughout the travel of the interferometer, which were used to control the velocity of the scan mechanism and to trigger data sampling. The broadband light from the LED produced a burst of fringes at zero path difference, which was used as a fixed position reference. The system, including the sources, the interferometer, and the detectors, was designed to work both at room temperature and instrument operating temperature of 170 Kelvin. One major challenge that was overcome was preservation, from room temperature to 170 K, of alignment sufficient for high modulation of fringes from the broadband source. Another was the shift of the source spectra about 30 nm toward shorter wavelengths upon cooldown.

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.

Proposal of AAA-battery-size one-shot ATR Fourier spectroscopic imager for on-site analysis: Simultaneous measurement of multi-components with high accuracy

NASA Astrophysics Data System (ADS)

Hosono, Satsuki; Qi, Wei; Sato, Shun; Suzuki, Yo; Fujiwara, Masaru; Hiramatsu, Hiroyuki; Suzuki, Satoru; Abeygunawardhana, P. K. W.; Wada, Kenji; Nishiyama, Akira; Ishimaru, Ichiro

2015-03-01

For simultaneous measurement of multi-components on-site like factories, the ultra-compact (diameter: 9[mm], length: 45[mm], weight: 200[g]) one-shot ATR (Attenuated Total Reflection) Fourier spectroscopic imager was proposed. Because the proposed one-shot Fourier spectroscopic imaging is based on spatial-phase-shift interferometer, interferograms could be obtained with simple optical configurations. We introduced the transmission-type relativeinclined phase-shifter, that was constructed with a cuboid prism and a wedge prism, onto the optical Fourier transform plane of infinity corrected optical systems. And also, small light-sources and cameras in the mid-infrared light region, whose size are several millimeter on a side, are essential components for the ultra-compact spectroscopic configuration. We selected the Graphite light source (light source area: 1.7×1.7[mm], maker: Hawkeye technologies) whose radiation factor was high. Fortunately, in these days we could apply the cost-effective 2-dimensional light receiving device for smartphone (e.g. product name: LEPTON, maker: FLIR, price: around 400USD). In the case of alcoholic drinks factory, conventionally workers measure glucose and ethanol concentrations by bringing liquid solution back to laboratories every day. The high portable spectroscopy will make it possible to measure multi-components simultaneously on manufacturing scene. But we found experimentally that absorption spectrum of glucose and water and ethanol were overlapped each other in near infrared light region. But for mid-infrared light region, we could distinguish specific absorption peaks of glucose (@10.5[μm]) and ethanol (@11.5[μm]) independently from water absorption. We obtained standard curve between absorption (@9.6[μm]) and ethanol concentration with high correlation coefficient 0.98 successfully by ATR imaging-type 2-dimensional Fourier spectroscopy (wavelength resolution: 0.057[μm]) with the graphite light source (maker: Hawkeye technologies, type: IR-75).

Development of a parallel demodulation system used for extrinsic Fabry-Perot interferometer and fiber Bragg grating sensors.

PubMed

Jiang, Junfeng; Liu, Tiegen; Zhang, Yimo; Liu, Lina; Zha, Ying; Zhang, Fan; Wang, Yunxin; Long, Pin

2006-01-20

A parallel demodulation system for extrinsic Fabry-Perot interferometer (EFPI) and fiber Bragg grating (FBG) sensors is presented, which is based on a Michelson interferometer and combines the methods of low-coherence interference and a Fourier-transform spectrum. The parallel demodulation theory is modeled with Fourier-transform spectrum technology, and a signal separation method with an EFPI and FBG is proposed. The design of an optical path difference scanning and sampling method without a reference light is described. Experiments show that the parallel demodulation system has good spectrum demodulation and low-coherence interference demodulation performance. It can realize simultaneous strain and temperature measurements while keeping the whole system configuration less complex.

Simulation of optical interstellar scintillation

NASA Astrophysics Data System (ADS)

Habibi, F.; Moniez, M.; Ansari, R.; Rahvar, S.

2013-04-01

Aims: Stars twinkle because their light propagates through the atmosphere. The same phenomenon is expected on a longer time scale when the light of remote stars crosses an interstellar turbulent molecular cloud, but it has never been observed at optical wavelengths. The aim of the study described in this paper is to fully simulate the scintillation process, starting from the molecular cloud description as a fractal object, ending with the simulations of fluctuating stellar light curves. Methods: Fast Fourier transforms are first used to simulate fractal clouds. Then, the illumination pattern resulting from the crossing of background star light through these refractive clouds is calculated from a Fresnel integral that also uses fast Fourier transform techniques. Regularisation procedure and computing limitations are discussed, along with the effect of spatial and temporal coherency (source size and wavelength passband). Results: We quantify the expected modulation index of stellar light curves as a function of the turbulence strength - characterised by the diffraction radius Rdiff - and the projected source size, introduce the timing aspects, and establish connections between the light curve observables and the refractive cloud. We extend our discussion to clouds with different structure functions from Kolmogorov-type turbulence. Conclusions: Our study confirms that current telescopes of ~4 m with fast-readout, wide-field detectors have the capability of discovering the first interstellar optical scintillation effects. We also show that this effect should be unambiguously distinguished from any other type of variability through the observation of desynchronised light curves, simultaneously measured by two distant telescopes.

Fourier Transform Infrared (FTIR) Spectroscopy, Ultraviolet Resonance Raman (UVRR) Spectroscopy, and Atomic Force Microscopy (AFM) for Study of the Kinetics of Formation and Structural Characterization of Tau Fibrils.

PubMed

Ramachandran, Gayathri

2017-01-01

Kinetic studies of tau fibril formation in vitro most commonly employ spectroscopic probes such as thioflavinT fluorescence and laser light scattering or negative stain transmission electron microscopy. Here, I describe the use of Fourier transform infrared (FTIR) spectroscopy, ultraviolet resonance Raman (UVRR) spectroscopy, and atomic force microscopy (AFM) as complementary probes for studies of tau aggregation. The sensitivity of vibrational spectroscopic techniques (FTIR and UVRR) to secondary structure content allows for measurement of conformational changes that occur when the intrinsically disordered protein tau transforms into cross-β-core containing fibrils. AFM imaging serves as a gentle probe of structures populated over the time course of tau fibrillization. Together, these assays help further elucidate the structural and mechanistic complexity inherent in tau fibril formation.

Single-pixel non-imaging object recognition by means of Fourier spectrum acquisition

NASA Astrophysics Data System (ADS)

Chen, Huichao; Shi, Jianhong; Liu, Xialin; Niu, Zhouzhou; Zeng, Guihua

2018-04-01

Single-pixel imaging has emerged over recent years as a novel imaging technique, which has significant application prospects. In this paper, we propose and experimentally demonstrate a scheme that can achieve single-pixel non-imaging object recognition by acquiring the Fourier spectrum. In an experiment, a four-step phase-shifting sinusoid illumination light is used to irradiate the object image, the value of the light intensity is measured with a single-pixel detection unit, and the Fourier coefficients of the object image are obtained by a differential measurement. The Fourier coefficients are first cast into binary numbers to obtain the hash value. We propose a new method of perceptual hashing algorithm, which is combined with a discrete Fourier transform to calculate the hash value. The hash distance is obtained by calculating the difference of the hash value between the object image and the contrast images. By setting an appropriate threshold, the object image can be quickly and accurately recognized. The proposed scheme realizes single-pixel non-imaging perceptual hashing object recognition by using fewer measurements. Our result might open a new path for realizing object recognition with non-imaging.

Quantum computation with classical light: Implementation of the Deutsch-Jozsa algorithm

NASA Astrophysics Data System (ADS)

Perez-Garcia, Benjamin; McLaren, Melanie; Goyal, Sandeep K.; Hernandez-Aranda, Raul I.; Forbes, Andrew; Konrad, Thomas

2016-05-01

We propose an optical implementation of the Deutsch-Jozsa Algorithm using classical light in a binary decision-tree scheme. Our approach uses a ring cavity and linear optical devices in order to efficiently query the oracle functional values. In addition, we take advantage of the intrinsic Fourier transforming properties of a lens to read out whether the function given by the oracle is balanced or constant.

The Fourier analysis of biological transients.

PubMed

Harris, C M

1998-08-31

With modern computing technology the digital implementation of the Fourier transform is widely available, mostly in the form of the fast Fourier transform (FFT). Although the FFT has become almost synonymous with the Fourier transform, it is a fast numerical technique for computing the discrete Fourier transform (DFT) of a finite sequence of sampled data. The DFT is not directly equivalent to the continuous Fourier transform of the underlying biological signal, which becomes important when analyzing biological transients. Although this distinction is well known by some, for many it leads to confusion in how to interpret the FFT of biological data, and in how to precondition data so as to yield a more accurate Fourier transform using the FFT. We review here the fundamentals of Fourier analysis with emphasis on the analysis of transient signals. As an example of a transient, we consider the human saccade to illustrate the pitfalls and advantages of various Fourier analyses.

Fourier transform magnitudes are unique pattern recognition templates.

PubMed

Gardenier, P H; McCallum, B C; Bates, R H

1986-01-01

Fourier transform magnitudes are commonly used in the generation of templates in pattern recognition applications. We report on recent advances in Fourier phase retrieval which are relevant to pattern recognition. We emphasise in particular that the intrinsic form of a finite, positive image is, in general, uniquely related to the magnitude of its Fourier transform. We state conditions under which the Fourier phase can be reconstructed from samples of the Fourier magnitude, and describe a method of achieving this. Computational examples of restoration of Fourier phase (and hence, by Fourier transformation, the intrinsic form of the image) from samples of the Fourier magnitude are also presented.

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system.

PubMed

Zhang, Fang; Zhu, Jing; Song, Qiang; Yue, Weirui; Liu, Jingdan; Wang, Jian; Situ, Guohai; Huang, Huijie

2015-10-20

In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

Fourier Transform-Plasmon Waveguide Spectroscopy: A Nondestructive Multifrequency Method for Simultaneously Determining Polymer Thickness and Apparent Index of Refraction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bobbitt, Jonathan M; Weibel, Stephen C; Elshobaki, Moneim

2014-12-16

Fourier transform (FT)-plasmon waveguide resonance (PWR) spectroscopy measures light reflectivity at a waveguide interface as the incident frequency and angle are scanned. Under conditions of total internal reflection, the reflected light intensity is attenuated when the incident frequency and angle satisfy conditions for exciting surface plasmon modes in the metal as well as guided modes within the waveguide. Expanding upon the concept of two-frequency surface plasmon resonance developed by Peterlinz and Georgiadis [ Opt. Commun. 1996, 130, 260], the apparent index of refraction and the thickness of a waveguide can be measured precisely and simultaneously by FT-PWR with an averagemore » percent relative error of 0.4%. Measuring reflectivity for a range of frequencies extends the analysis to a wide variety of sample compositions and thicknesses since frequencies with the maximum attenuation can be selected to optimize the analysis. Additionally, the ability to measure reflectivity curves with both p- and s-polarized light provides anisotropic indices of refraction. FT-PWR is demonstrated using polystyrene waveguides of varying thickness, and the validity of FT-PWR measurements are verified by comparing the results to data from profilometry and atomic force microscopy (AFM).« less

Fourier transform-plasmon waveguide spectroscopy: a nondestructive multifrequency method for simultaneously determining polymer thickness and apparent index of refraction.

PubMed

Bobbitt, Jonathan M; Weibel, Stephen C; Elshobaki, Moneim; Chaudhary, Sumit; Smith, Emily A

2014-12-16

Fourier transform (FT)-plasmon waveguide resonance (PWR) spectroscopy measures light reflectivity at a waveguide interface as the incident frequency and angle are scanned. Under conditions of total internal reflection, the reflected light intensity is attenuated when the incident frequency and angle satisfy conditions for exciting surface plasmon modes in the metal as well as guided modes within the waveguide. Expanding upon the concept of two-frequency surface plasmon resonance developed by Peterlinz and Georgiadis [Opt. Commun. 1996, 130, 260], the apparent index of refraction and the thickness of a waveguide can be measured precisely and simultaneously by FT-PWR with an average percent relative error of 0.4%. Measuring reflectivity for a range of frequencies extends the analysis to a wide variety of sample compositions and thicknesses since frequencies with the maximum attenuation can be selected to optimize the analysis. Additionally, the ability to measure reflectivity curves with both p- and s-polarized light provides anisotropic indices of refraction. FT-PWR is demonstrated using polystyrene waveguides of varying thickness, and the validity of FT-PWR measurements are verified by comparing the results to data from profilometry and atomic force microscopy (AFM).

Fractional finite Fourier transform.

PubMed

Khare, Kedar; George, Nicholas

2004-07-01

We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

Light field measurement based on the single-lens coherent diffraction imaging

NASA Astrophysics Data System (ADS)

Shen, Cheng; Tan, Jiubin; Liu, Zhengjun

2018-01-01

Plenoptic camera and holography are popular light field measurement techniques. However, the low resolution or the complex apparatus hinders their widespread application. In this paper, we put forward a new light field measurement scheme. The lens is introduced into coherent diffraction imaging to operate an optical transform, extended fractional Fourier transform. Combined with the multi-image phase retrieval algorithm, the scheme is proved to hold several advantages. It gets rid of the support requirement and is much easier to implement while keeping a high resolution by making full use of the detector plane. Also, it is verified that our scheme has a superiority over the direct lens focusing imaging in amplitude measurement accuracy and phase retrieval ability.

Topics In Chemical Instrumentation: Fourier Transformations for Chemists Part I. Introduction to the Fourier Transform.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…

Compact Microwave Fourier Spectrum Analyzer

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry

2009-01-01

A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.

Computationally efficient method for Fourier transform of highly chirped pulses for laser and parametric amplifier modeling.

PubMed

Andrianov, Alexey; Szabo, Aron; Sergeev, Alexander; Kim, Arkady; Chvykov, Vladimir; Kalashnikov, Mikhail

2016-11-14

We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

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 τq-Fourier transform: Covariance and uniqueness

NASA Astrophysics Data System (ADS)

Kalogeropoulos, Nikolaos

2018-05-01

We propose an alternative definition for a Tsallis entropy composition-inspired Fourier transform, which we call “τq-Fourier transform”. We comment about the underlying “covariance” on the set of algebraic fields that motivates its introduction. We see that the definition of the τq-Fourier transform is automatically invertible in the proper context. Based on recent results in Fourier analysis, it turns that the τq-Fourier transform is essentially unique under the assumption of the exchange of the point-wise product of functions with their convolution.

[Research of dual-photoelastic-modulator-based beat frequency modulation and Fourier-Bessel transform imaging spectrometer].

PubMed

Wang, Zhi-Bin; Zhang, Rui; Wang, Yao-Li; Huang, Yan-Fei; Chen, You-Hua; Wang, Li-Fu; Yang, Qiang

2014-02-01

As the existing photoelastic-modulator(PEM) modulating frequency in the tens of kHz to hundreds of kHz between, leading to frequency of modulated interference signal is higher, so ordinary array detector cannot effectively caprure interference signal..A new beat frequency modulation method based on dual-photoelastic-modulator (Dual-PEM) and Fourier-Bessel transform is proposed as an key component of dual-photoelastic-modulator-based imaging spectrometer (Dual-PEM-IS) combined with charge coupled device (CCD). The dual-PEM are operated as an electro-optic circular retardance modulator, Operating the PEMs at slightly different resonant frequencies w1 and w2 respectively, generates a differential signal at a much lower heterodyne frequency that modulates the incident light. This method not only retains the advantages of the existing PEM, but also the frequency of modulated photocurrent decreased by 2-3 orders of magnitude (10-500 Hz) and can be detected by common array detector, and the incident light spectra can be obtained by Fourier-Bessel transform of low frequency component in the modulated signal. The method makes the PEM has the dual capability of imaging and spectral measurement. The basic principle is introduced, the basic equations is derived, and the feasibility is verified through the corresponding numerical simulation and experiment. This method has' potential applications in imaging spectrometer technology, and analysis of the effect of deviation of the optical path difference. This work provides the necessary theoretical basis for remote sensing of new Dual-PEM-IS and for engineering implementation of spectra inversion.

Hypercomplex Fourier transforms of color images.

PubMed

Ell, Todd A; Sangwine, Stephen J

2007-01-01

Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed.

Applications of wavelets in interferometry and artificial vision

NASA Astrophysics Data System (ADS)

Escalona Z., Rafael A.

2001-08-01

In this paper we present a different point of view of phase measurements performed in interferometry, image processing and intelligent vision using Wavelet Transform. In standard and white-light interferometry, the phase function is retrieved by using phase-shifting, Fourier-Transform, cosinus-inversion and other known algorithms. Our novel technique presented here is faster, robust and shows excellent accuracy in phase determinations. Finally, in our second application, fringes are no more generate by some light interaction but result from the observation of adapted strip set patterns directly printed on the target of interest. The moving target is simply observed by a conventional vision system and usual phase computation algorithms are adapted to an image processing by wavelet transform, in order to sense target position and displacements with a high accuracy. In general, we have determined that wavelet transform presents properties of robustness, relative speed of calculus and very high accuracy in phase computations.

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

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.

PASSIVELY ESTIMATING INDEX OF REFRACTION FOR SPECULAR REFLECTORS USING POLARIMETRIC HYPERSPECTRAL IMAGING

DTIC Science & Technology

2016-12-22

23 6 Band-averaged radiance image with checkerboard is shown in the upper left. The 2-D Fourier transform of the image is...red is 1) that is multiplied by the Fourier transform of the original image. The inverse Fourier transform is then taken to get the final image with...Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 IFTS Imaging Fourier Transform Spectrometer

Synthesis and luminescent properties of the novel poly(ethylene-co-acrylic acid) films based on surface modification with lanthanide (Eu3+, Tb3+) complexes

NASA Astrophysics Data System (ADS)

Wu, Yuewen; Chu, Yang; Yu, Zhenjiang; Hao, Haixia; Wu, Qingyao; Xie, Hongde

2017-10-01

Two kinds of novel fluorescent films have been successfully synthesized by surface modification on the poly(ethylene-co-acrylic acid) films using the lanthanide (Eu3+, Tb3+) complexes. The process consists of three steps: conversion of carboxylic acid groups on the surface of the poly(ethylene-co-acrylic acid) films to acid chloride groups, synthesis of the lanthanide complexes bearing amino groups, and amidation to form the modified films. To characterize the modified films, Fourier transform infrared, thermogravimetric analysis, static water contact angle measurements and photoluminescence tests have been employed. Fourier transform infrared verifies the successful preparation of the lanthanide complexes and the modified poly(ethylene-co-acrylic acid) films. These films can emit strong characteristic red and green light under UV light excitation. In addition, the films both have short lifetime (1.14 ms and 1.21 ms), high thermal stability (Td = 408 °C and 411 °C) and, compared with unmodified ones, increased hydrophilicity. All these results suggest that the modified films have potential application as luminescent materials under high temperature.

Hyperfine structure measurements of neutral iodine atom (127I) using Fourier Transform Spectrometry

NASA Astrophysics Data System (ADS)

Ashok, Chilukoti; Vishwakarma, S. R.; Bhatt, Himal; Ankush, B. K.; Deo, M. N.

2018-01-01

We report the hyperfine Structure (hfs) splitting observations of neutral iodine atom (II) in the 6000 - 10,000 cm-1 near infrared spectral region. The measurements were carried out using a high-resolution Fourier Transform Spectrometer (FTS), where an electrodeless discharge lamp (EDL), excited using microwaves, was employed as the light source and InGaAs as the light detector. A specially designed setup was used to lower the plasma temperature of the medium so as to reduce the Doppler width and consequently to increase the spectral resolution of hfs components. A total of 183 lines with hfs splitting have been observed, out of which hfs in 53 spectral lines are reported for the first time. On the basis of hfs analysis, we derived the magnetic dipole and electric quadrupole coupling constants, A and B respectively for 30 even and 30 odd energy levels and are compared with the values available in the literature. New hfs values for 5 even and 4 odd levels are also reported here for the first time.

Static and dynamic light scattering of healthy and malaria-parasite invaded red blood cells

NASA Astrophysics Data System (ADS)

Park, Yongkeun; Diez-Silva, Monica; Fu, Dan; Popescu, Gabriel; Choi, Wonshik; Barman, Ishan; Suresh, Subra; Feld, Michael S.

2010-03-01

We present the light scattering of individual Plasmodium falciparum-parasitized human red blood cells (Pf-RBCs), and demonstrate progressive alterations to the scattering signal arising from the development of malaria-inducing parasites. By selectively imaging the electric fields using quantitative phase microscopy and a Fourier transform light scattering technique, we calculate the light scattering maps of individual Pf-RBCs. We show that the onset and progression of pathological states of the Pf-RBCs can be clearly identified by the static scattering maps. Progressive changes to the biophysical properties of the Pf-RBC membrane are captured from dynamic light scattering.

Low-level laser therapy on MCF-7 cells: a micro-Fourier transform infrared spectroscopy study

NASA Astrophysics Data System (ADS)

Magrini, Taciana D.; dos Santos, Nathalia Villa; Milazzotto, Marcella Pecora; Cerchiaro, Giselle; da Silva Martinho, Herculano

2012-10-01

Low-level laser therapy (LLLT) is an emerging therapeutic approach for several clinical conditions. The clinical effects induced by LLLT presumably scale from photobiostimulation/photobioinhibition at the cellular level to the molecular level. The detailed mechanism underlying this effect remains unknown. This study quantifies some relevant aspects of LLLT related to molecular and cellular variations. Malignant breast cells (MCF-7) were exposed to spatially filtered light from a He-Ne laser (633 nm) with fluences of 5, 28.8, and 1000 mJ/cm2. The cell viability was evaluated by optical microscopy using the Trypan Blue viability test. The micro-Fourier transform infrared technique was employed to obtain the vibrational spectra of each experimental group (control and irradiated) and identify the relevant biochemical alterations that occurred due to the process. It was observed that the red light influenced the RNA, phosphate, and serine/threonine/tyrosine bands. We found that light can influence cell metabolism depending on the laser fluence. For 5 mJ/cm2, MCF-7 cells suffer bioinhibition with decreased metabolic rates. In contrast, for the 1 J/cm2 laser fluence, cells present biostimulation accompanied by a metabolic rate elevation. Surprisingly, at the intermediate fluence, 28.8 mJ/cm2, the metabolic rate is increased despite the absence of proliferative results. The data were interpreted within the retrograde signaling pathway mechanism activated with light irradiation.

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",…

Optical calculation of correlation filters for a robotic vision system

NASA Technical Reports Server (NTRS)

Knopp, Jerome

1989-01-01

A method is presented for designing optical correlation filters based on measuring three intensity patterns: the Fourier transform of a filter object, a reference wave and the interference pattern produced by the sum of the object transform and the reference. The method can produce a filter that is well matched to both the object, its transforming optical system and the spatial light modulator used in the correlator input plane. A computer simulation was presented to demonstrate the approach for the special case of a conventional binary phase-only filter. The simulation produced a workable filter with a sharp correlation peak.

A fast algorithm for vertex-frequency representations of signals on graphs

PubMed Central

Jestrović, Iva; Coyle, James L.; Sejdić, Ervin

2016-01-01

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational complexity makes these algorithms impractical. We sought to develop a fast windowed graph Fourier transform and a fast graph S-transform requiring significantly shorter computation time. The proposed schemes have been tested with synthetic test graph signals and real graph signals derived from electroencephalography recordings made during swallowing. The results showed that the proposed schemes provide significantly lower computation time in comparison with the standard windowed graph Fourier transform and the fast graph S-transform. Also, the results showed that noise has no effect on the results of the algorithm for the fast windowed graph Fourier transform or on the graph S-transform. Finally, we showed that graphs can be reconstructed from the vertex-frequency representations obtained with the proposed algorithms. PMID:28479645

Optical information-processing systems and architectures II; Proceedings of the Meeting, San Diego, CA, July 9-13, 1990

NASA Astrophysics Data System (ADS)

Javidi, Bahram

The present conference discusses topics in the fields of neural networks, acoustooptic signal processing, pattern recognition, phase-only processing, nonlinear signal processing, image processing, optical computing, and optical information processing. Attention is given to the optical implementation of an inner-product neural associative memory, optoelectronic associative recall via motionless-head/parallel-readout optical disk, a compact real-time acoustooptic image correlator, a multidimensional synthetic estimation filter, and a light-efficient joint transform optical correlator. Also discussed are a high-resolution spatial light modulator, compact real-time interferometric Fourier-transform processors, a fast decorrelation algorithm for permutation arrays, the optical interconnection of optical modules, and carry-free optical binary adders.

Missing texture reconstruction method based on error reduction algorithm using Fourier transform magnitude estimation scheme.

PubMed

Ogawa, Takahiro; Haseyama, Miki

2013-03-01

A missing texture reconstruction method based on an error reduction (ER) algorithm, including a novel estimation scheme of Fourier transform magnitudes is presented in this brief. In our method, Fourier transform magnitude is estimated for a target patch including missing areas, and the missing intensities are estimated by retrieving its phase based on the ER algorithm. Specifically, by monitoring errors converged in the ER algorithm, known patches whose Fourier transform magnitudes are similar to that of the target patch are selected from the target image. In the second approach, the Fourier transform magnitude of the target patch is estimated from those of the selected known patches and their corresponding errors. Consequently, by using the ER algorithm, we can estimate both the Fourier transform magnitudes and phases to reconstruct the missing areas.

Cotton fiber quality characterization with light scattering and fourier transform infrared techniques.

PubMed

Thomasson, J A; Manickavasagam, S; Mengüç, M P

2009-03-01

Fiber quality measurement is critical to assessing the value of a bale of cotton for various textile purposes. An instrument that could measure numerous cotton quality properties by optical means could be made simpler and faster than current fiber quality measurement instruments, and it might be more amenable to on-line measurement at processing facilities. To that end, a laser system was used to investigate cotton fiber samples with respect to electromagnetic scattering at various wavelengths, polarization angles, and scattering angles. A Fourier transform infrared (FT-IR) instrument was also used to investigate the transmission of electromagnetic energy at various mid-infrared wavelengths. Cotton samples were selected to represent a wide range of micronaire values. Varying the wavelength of the laser at a fixed polarization resulted in little variation in scattered light among the cotton samples. However, varying the polarization at a fixed wavelength produced notable variation, indicating that polarization might be used to differentiate among cotton samples with respect to certain fiber properties. The FT-IR data in the 12 to 22 microm range produced relatively large differences in the amount of scattered light among all samples, and FT-IR data at certain combinations of fixed wavelengths were highly linearly related to certain measures of cotton quality including micronaire.

Partial differential equation transform — Variational formulation and Fourier analysis

PubMed Central

Wang, Yang; Wei, Guo-Wei; Yang, Siyang

2011-01-01

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904

Intelligent Controller for a Compact Wide-Band Compositional Infrared Fourier Transform Spectrometer

NASA Astrophysics Data System (ADS)

Yiu, P.; Keymeulen, D.; Berisford, D. F.; Hand, K. P.; Carlson, R. W.

2013-12-01

This paper presents the design and integration of an intelligent controller for CIRIS (Compositional InfraRed Interferometric Spectrometer) on a stand-alone field programmable gate array (FPGA) architecture. 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. This design eliminates the need for periodically accelerating/decelerating mirrors inherent to canonical Michelson designs and allows for a compact and robust device that is intrinsically radiation-hard, making it ideal for spaceborne measurements in the near-IR to thermal-IR band (2-12 μm) on planetary exploration missions. A traditional Michelson FTS passes a monochromatic light source (incident light from the sample) through a system of refractors/mirrors followed by a mirror moving linearly in the plane of the incident light. This process selectively blocks certain wavelengths and permits measurement of the sample's absorption rates as a function of the wavelengths blocked to produce an 'inteferogram.' This is subsequently processed using a Fourier transform to obtain the sample's spectrum and ascertain the sample's composition. With our prototype CIRIS instrument in development at Design and Prototype Inc. and NASA-JPL, we propose the use of a rotating refractor spinning at a constant velocity to variably phase shift incident light to the detector as an alternative to a linearly moving mirror. This design eliminates sensitivity to vibrations, minimizing path length and non-linear errors due to minor perturbations to the system, in addition to facilitating compact design critical to meeting the strict volume requirements of spacecraft. Further, this is done without sacrificing spectral resolution or throughput when compared to Michelson or diffractive designs. While Michelson designs typically achieve very high wavelength resolution, the intended application of our instrument (spectroscopic investigation of Europa's surface) places higher emphasis on the greater wavelength band sensitivity in the 2-12 μm range provided by a rotating refractor design. The instrument's embedded microcontroller is implemented on a flight-qualified VIRTEX-5 FPGA with the aim of sampling the instrument's detector and optical rotary encoder in order to construct an interferogram. Subsequent signal processing, including a Fast Fourier Transform (FFT), noise reduction/averaging, and spectral calibration techniques are applied in real-time to compose the sample spectrum. Deployment of an FPGA eliminates the instrument's need to share computing resources with the main spacecraft computer and takes advantage of the low power consumption and high-throughput hardware parallelism intrinsic to FPGA applications. This parallelism facilitates the high speed, low latency sampling/signal processing critical to instrument precision with minimal power consumption to achieve highly sensitive spectra within the constraints of available spacecraft resources. The instrument is characterized in simulated space-flight conditions and we demonstrate that this technology is capable of meeting the strict volume, sensitivity, and power consumption requirements for implementation in scientific space systems.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

Anisotropic light scattering of individual sickle red blood cells.

PubMed

Kim, Youngchan; Higgins, John M; Dasari, Ramachandra R; Suresh, Subra; Park, YongKeun

2012-04-01

We present the anisotropic light scattering of individual red blood cells (RBCs) from a patient with sickle cell disease (SCD). To measure light scattering spectra along two independent axes of elongated-shaped sickle RBCs with arbitrary orientation, we introduce the anisotropic Fourier transform light scattering (aFTLS) technique and measured both the static and dynamic anisotropic light scattering. We observed strong anisotropy in light scattering patterns of elongated-shaped sickle RBCs along its major axes using static aFTLS. Dynamic aFTLS analysis reveals the significantly altered biophysical properties in individual sickle RBCs. These results provide evidence that effective viscosity and elasticity of sickle RBCs are significantly different from those of the healthy RBCs.

High-resolution and high-throughput multichannel Fourier transform spectrometer with two-dimensional interferogram warping compensation

NASA Astrophysics Data System (ADS)

Watanabe, A.; Furukawa, H.

2018-04-01

The resolution of multichannel Fourier transform (McFT) spectroscopy is insufficient for many applications despite its extreme advantage of high throughput. We propose an improved configuration to realise both performance using a two-dimensional area sensor. For the spectral resolution, we obtained the interferogram of a larger optical path difference by shifting the area sensor without altering any optical components. The non-linear phase error of the interferometer was successfully corrected using a phase-compensation calculation. Warping compensation was also applied to realise a higher throughput to accumulate the signal between vertical pixels. Our approach significantly improved the resolution and signal-to-noise ratio by factors of 1.7 and 34, respectively. This high-resolution and high-sensitivity McFT spectrometer will be useful for detecting weak light signals such as those in non-invasive diagnosis.

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

PubMed

Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook

2016-09-19

The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 2¹⁰ times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

SITELLE: a wide-field imaging Fourier transform spectrometer for the Canada-France-Hawaii Telescope

NASA Astrophysics Data System (ADS)

Drissen, L.; Bernier, A.-P.; Rousseau-Nepton, L.; Alarie, A.; Robert, C.; Joncas, G.; Thibault, S.; Grandmont, F.

2010-07-01

We describe the concept of a new instrument for the Canada-France-Hawaii telescope (CFHT), SITELLE (Spectromètre Imageur à Transformée de Fourier pour l'Etude en Long et en Large de raies d'Emission), as well as a science case and a technical study of its preliminary design. SITELLE will be an imaging Fourier transform spectrometer capable of obtaining the visible (350 nm - 950 nm) spectrum of every source of light in a field of view of 15 arcminutes, with 100% spatial coverage and a spectral resolution ranging from R = 1 (deep panchromatic image) to R = 104 (for gas dynamics). SITELLE will cover a field of view 100 to 1000 times larger than traditional integral field spectrographs, such as GMOS-IFU on Gemini or the future MUSE on the VLT. It is a legacy from BEAR, the first imaging FTS installed on the CFHT and the direct successor of SpIOMM, a similar instrument attached to the 1.6-m telescope of the Observatoire du Mont-Mégantic in Québec. SITELLE will be used to study the structure and kinematics of HII regions and ejecta around evolved stars in the Milky Way, emission-line stars in clusters, abundances in nearby gas-rich galaxies, and the star formation rate in distant galaxies.

Properties of the Magnitude Terms of Orthogonal Scaling Functions.

PubMed

Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A

2010-09-01

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.

Fully automated corneal endothelial morphometry of images captured by clinical specular microscopy

NASA Astrophysics Data System (ADS)

Bucht, Curry; Söderberg, Per; Manneberg, Göran

2010-02-01

The corneal endothelium serves as the posterior barrier of the cornea. Factors such as clarity and refractive properties of the cornea are in direct relationship to the quality of the endothelium. The endothelial cell density is considered the most important morphological factor of the corneal endothelium. Pathological conditions and physical trauma may threaten the endothelial cell density to such an extent that the optical property of the cornea and thus clear eyesight is threatened. Diagnosis of the corneal endothelium through morphometry is an important part of several clinical applications. Morphometry of the corneal endothelium is presently carried out by semi automated analysis of pictures captured by a Clinical Specular Microscope (CSM). Because of the occasional need of operator involvement, this process can be tedious, having a negative impact on sampling size. This study was dedicated to the development and use of fully automated analysis of a very large range of images of the corneal endothelium, captured by CSM, using Fourier analysis. Software was developed in the mathematical programming language Matlab. Pictures of the corneal endothelium, captured by CSM, were read into the analysis software. The software automatically performed digital enhancement of the images, normalizing lights and contrasts. The digitally enhanced images of the corneal endothelium were Fourier transformed, using the fast Fourier transform (FFT) and stored as new images. Tools were developed and applied for identification and analysis of relevant characteristics of the Fourier transformed images. The data obtained from each Fourier transformed image was used to calculate the mean cell density of its corresponding corneal endothelium. The calculation was based on well known diffraction theory. Results in form of estimated cell density of the corneal endothelium were obtained, using fully automated analysis software on 292 images captured by CSM. The cell density obtained by the fully automated analysis was compared to the cell density obtained from classical, semi-automated analysis and a relatively large correlation was found.

[Study on Differential Optical Absorption Spectroscopy Data Processing Based on Chirp-Z Transformation].

PubMed

Zheng, Hai-ming; Li, Guang-jie; Wu, Hao

2015-06-01

Differential optical absorption spectroscopy (DOAS) is a commonly used atmospheric pollution monitoring method. Denoising of monitoring spectral data will improve the inversion accuracy. Fourier transform filtering method is effectively capable of filtering out the noise in the spectral data. But the algorithm itself can introduce errors. In this paper, a chirp-z transform method is put forward. By means of the local thinning of Fourier transform spectrum, it can retain the denoising effect of Fourier transform and compensate the error of the algorithm, which will further improve the inversion accuracy. The paper study on the concentration retrieving of SO2 and NO2. The results show that simple division causes bigger error and is not very stable. Chirp-z transform is proved to be more accurate than Fourier transform. Results of the frequency spectrum analysis show that Fourier transform cannot solve the distortion and weakening problems of characteristic absorption spectrum. Chirp-z transform shows ability in fine refactoring of specific frequency spectrum.

Fourier removal of stripe artifacts in IRAS images

NASA Technical Reports Server (NTRS)

Van Buren, Dave

1987-01-01

By working in the Fourier plane, approximate removal of stripe artifacts in IRAS images can be effected. The image of interest is smoothed and subtracted from the original, giving the high-spatial-frequency part. This 'filtered' image is then clipped to remove point sources and then Fourier transformed. Subtracting the Fourier components contributing to the stripes in this image from the Fourier transform of the original and transforming back to the image plane yields substantial removal of the stripes.

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Optical signal-processing systems based on anisotropic media

NASA Astrophysics Data System (ADS)

Kiyashko, B. V.

1995-10-01

Partially coherent optical systems for signal processing are considered. The transfer functions are formed in these systems by interference of polarised light transmitted by an anisotropic medium. It is shown that such systems can perform various integral transformations of both optical and electric signals, in particular, two-dimensional Fourier and Fresnel transformations, as well as spectral analysis of weak light sources. It is demonstrated that such systems have the highest luminosity and vibration immunity among the systems with interference formation of transfer functions. An experimental investigation is reported of the application of these systems in the processing of signals from a linear hydroacoustic antenna array, and in measurements of the optical spectrum and of the intrinsic noise.

Low-level laser therapy on MCF-7 cells: a micro-Fourier transform infrared spectroscopy study.

PubMed

Magrini, Taciana D; dos Santos, Nathalia Villa; Milazzotto, Marcella Pecora; Cerchiaro, Giselle; da Silva Martinho, Herculano

2012-10-01

Low-level laser therapy (LLLT) is an emerging therapeutic approach for several clinical conditions. The clinical effects induced by LLLT presumably scale from photobiostimulation/photobioinhibition at the cellular level to the molecular level. The detailed mechanism underlying this effect remains unknown. This study quantifies some relevant aspects of LLLT related to molecular and cellular variations. Malignant breast cells (MCF-7) were exposed to spatially filtered light from a He-Ne laser (633 nm) with fluences of 5, 28.8, and 1000  mJ/cm². The cell viability was evaluated by optical microscopy using the Trypan Blue viability test. The micro-Fourier transform infrared technique was employed to obtain the vibrational spectra of each experimental group (control and irradiated) and identify the relevant biochemical alterations that occurred due to the process. It was observed that the red light influenced the RNA, phosphate, and serine/threonine/tyrosine bands. We found that light can influence cell metabolism depending on the laser fluence. For 5  mJ/cm², MCF-7 cells suffer bioinhibition with decreased metabolic rates. In contrast, for the 1  J/cm² laser fluence, cells present biostimulation accompanied by a metabolic rate elevation. Surprisingly, at the intermediate fluence, 28.8  mJ/cm², the metabolic rate is increased despite the absence of proliferative results. The data were interpreted within the retrograde signaling pathway mechanism activated with light irradiation.

[The investigation and simulation of a novel spatially modulated micro-Fourier transform spectrometer].

PubMed

Kong, Yan-mei; Liang, Jing-qiu; Wang, Bo; Liang, Zhong-zhu; Xu, Da-wei; Zhang, Jun

2009-04-01

Fourier transform spectrometer (FTS) is widely used in science and industry for the measurement of electromagnetic spectra, and it's trend of minimization is particularly pronounced in many applications. A novel model of a micro FTS with no moving parts is proposed and analyzed. During the analysis, the gradients which mainly introduce the phase error are accounted for in details. Based on these assumptions and the improved Mertz phase correcting method, the spectrum of the signal is simulated, given the real extended light source. The resolution can reach 3.43 nm@800 nm, with high SNR limiting resolving ability 6.8 dB. The novel micro FTS could be made by MOEMS technology, which has some advantages over the conventional micro dispersive spectrometers based on the traditional technology, and this method can also afford some new concepts on the design of spectrometers. The research work is underway to demonstrate the theory.

Ceramic femoral component fracture in total knee arthroplasty: an analysis using fractography, fourier-transform infrared microscopy, contact radiography and histology.

PubMed

Krueger, Alexander P; Singh, Gurpal; Beil, Frank Timo; Feuerstein, Bernd; Ruether, Wolfgang; Lohmann, Christoph H

2014-05-01

Ceramic components in total knee arthroplasty (TKA) are evolving. We analyze the first case of BIOLOX delta ceramic femoral component fracture. A longitudinal midline fracture in the patellar groove was present, with an intact cement mantle and no bony defects. Fractographic analysis with laser scanning microscopy and white light interferometry showed no evidence of arrest lines, hackles, wake hackles, material flaws, fatigue or crack propagation. Analysis of periprosthetic tissues with Fourier-transform infrared (FT-IR) microscopy, contact radiography, histology, and subsequent digestion and high-speed centrifugation did not show ceramic debris. A macrophage-dominated response was present around polyethylene debris. We conclude that ceramic femoral component failure in this case was related to a traumatic event. Further research is needed to determine the suitability of ceramic components in TKA. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

Security analysis of quadratic phase based cryptography

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

2016-09-01

The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

Choice of optical system is critical for the security of double random phase encryption systems

NASA Astrophysics Data System (ADS)

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Cassidy, Derek; Zhao, Liang; Ryle, James P.; Healy, John J.; Sheridan, John T.

2017-06-01

The linear canonical transform (LCT) is used in modeling a coherent light-field propagation through first-order optical systems. Recently, a generic optical system, known as the quadratic phase encoding system (QPES), for encrypting a two-dimensional image has been reported. In such systems, two random phase keys and the individual LCT parameters (α,β,γ) serve as secret keys of the cryptosystem. It is important that such encryption systems also satisfy some dynamic security properties. We, therefore, examine such systems using two cryptographic evaluation methods, the avalanche effect and bit independence criterion, which indicate the degree of security of the cryptographic algorithms using QPES. We compared our simulation results with the conventional Fourier and the Fresnel transform-based double random phase encryption (DRPE) systems. The results show that the LCT-based DRPE has an excellent avalanche and bit independence characteristics compared to the conventional Fourier and Fresnel-based encryption systems.

Preparation and characterization of novel carbon dioxide adsorbents based on polyethylenimine-modified Halloysite nanotubes.

PubMed

Cai, Haohao; Bao, Feng; Gao, Jie; Chen, Tao; Wang, Si; Ma, Rui

2015-01-01

New nano-sized carbon dioxide (CO2) adsorbents based on Halloysite nanotubes impregnated with polyethylenimine (PEI) were designed and synthesized, which were excellent adsorbents for the capture of CO2 at room temperature and had relatively high CO2 adsorption capacity. The prepared adsorbents were characterized by various techniques such as Fourier transform infrared spectrometry, gel permeation chromatography, dynamic light scattering, thermogravimetry, thermogravimetry-Fourier transform-infrared spectrometry, scanning electron microscopy and transmission electron microscopy. The adsorption characteristics and capacity were studied at room temperature, the highest CO2 adsorption capacity of 156.6 mg/g-PEI was obtained and the optimal adsorption capacity can reach a maximum value of 54.8 mg/g-adsorbent. The experiment indicated that this kind of adsorbent has a high stability at 80°C and PEI-impregnated adsorbents showed good reversibility and stability during cyclic adsorption-regeneration tests.

High-resolution Fourier transform infrared synchrotron spectroscopy of the NO2 in-plane rock band of nitromethane

NASA Astrophysics Data System (ADS)

Dawadi, Mahesh B.; Twagirayezu, Sylvestre; Perry, David S.; Billinghurst, Brant E.

2015-09-01

The high-resolution rotationally resolved Fourier-transform infrared spectrum of the NO2 in-plane rock band (440-510 cm-1) of nitromethane (CH3NO2) has been recorded using the Far-Infrared Beamline at the Canadian Light Source, with a resolution of 0.00096 cm-1. About 1773 transitions reaching the upper state levels m‧ = 0; Ka‧ ⩽ 7;J‧ ⩽ 50 have been assigned using an automated ground-state combination difference program together with the traditional Loomis-Wood approach. These data from the lowest torsional state, m‧ = 0, were fit using the six-fold torsion-rotation program developed by Ilyushin et al. (2010). The analysis reveals that the rotational energy level structure in the upper vibrational state is similar to that of the ground vibrational state, but the sign and magnitude of high-order constants are significantly changed suggesting the presence of multiple perturbations.

Synchrotron-based far-infrared spectroscopy of furan: Rotational analysis of the ν 14 , ν 11 , ν 18 and ν 19 vibrational levels

NASA Astrophysics Data System (ADS)

Tokaryk, D. W.; Culligan, S. D.; Billinghurst, B. E.; van Wijngaarden, J. A.

2011-11-01

Four vibrational levels of the five-membered ring molecule furan (C 4H 4O) have been rotationally analyzed from far-infrared Fourier transform spectra obtained at the Canadian Light Source synchrotron. We found that the low-lying ν14 and ν11 levels at 602.9 and 599.6 cm -1 interact through a second-order Coriolis resonance. This perturbation was characterized through a coupled analysis of the ν14 and ν18 fundamental spectra and the ν18- ν11 band. The ν19 fundamental spectrum was analyzed as well, and the data for all observed bands were combined with previously reported microwave transitions to produce the final fit. The spectra are an excellent demonstration of the high quality of data that can be obtained when far-infrared synchrotron radiation is used as the radiation source in Fourier transform spectroscopy experiments.

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.

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.

An Introduction to Fast Fourier Transforms through the Study of Oscillating Reactions.

ERIC Educational Resources Information Center

Eastman, M. P.; And Others

1986-01-01

Discusses an experiment designed to introduce students to the basic principles of the fast Fourier transform and Fourier smoothing through transformation of time-dependent optical absorption data from an oscillating reaction. Uses the Belousov-Zhabotinskii reaction. Describes the experimental setup and data analysis techniques.

Fourier Transforms for Chemists Part III. Fourier Transforms in Data Treatment.

ERIC Educational Resources Information Center

Glasser, L.

1987-01-01

Discusses the factors affecting the behavior of a spectral function. Lists some important properties of Fourier transform (FT) pairs that are helpful when using the FT. Notes that these properties of the mathematical formulation have identical counterparts in the physical behavior of FT systems. (TW)

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)

The application and improvement of Fourier transform spectrometer experiment

NASA Astrophysics Data System (ADS)

Liu, Zhi-min; Gao, En-duo; Zhou, Feng-qi; Wang, Lan-lan; Feng, Xiao-hua; Qi, Jin-quan; Ji, Cheng; Wang, Luning

2017-08-01

According to teaching and experimental requirements of Optoelectronic information science and Engineering, in order to consolidate theoretical knowledge and improve the students practical ability, the Fourier transform spectrometer ( FTS) experiment, its design, application and improvement are discussed in this paper. The measurement principle and instrument structure of Fourier transform spectrometer are introduced, and the spectrums of several common Laser devices are measured. Based on the analysis of spectrum and test, several possible improvement methods are proposed. It also helps students to understand the application of Fourier transform in physics.

Validating data analysis of broadband laser ranging

NASA Astrophysics Data System (ADS)

Rhodes, M.; Catenacci, J.; Howard, M.; La Lone, B.; Kostinski, N.; Perry, D.; Bennett, C.; Patterson, J.

2018-03-01

Broadband laser ranging combines spectral interferometry and a dispersive Fourier transform to achieve high-repetition-rate measurements of the position of a moving surface. Telecommunications fiber is a convenient tool for generating the large linear dispersions required for a dispersive Fourier transform, but standard fiber also has higher-order dispersion that distorts the Fourier transform. Imperfections in the dispersive Fourier transform significantly complicate the ranging signal and must be dealt with to make high-precision measurements. We describe in detail an analysis process for interpreting ranging data when standard telecommunications fiber is used to perform an imperfect dispersive Fourier transform. This analysis process is experimentally validated over a 27-cm scan of static positions, showing an accuracy of 50 μm and a root-mean-square precision of 4.7 μm.

The morphing of geographical features by Fourier transformation.

PubMed

Li, Jingzhong; Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features' continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable.

Fast Implicit Methods For Elliptic Moving Interface Problems

DTIC Science & Technology

2015-12-11

analyzed, and tested for the Fourier transform of piecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. These transforms...evaluation, and one to three orders of magnitude slower than the classical uniform Fast Fourier Transform. Second, bilinear quadratures ---which...a fast algorithm was derived, analyzed, and tested for the Fourier transform of pi ecewise polynomials given on d-dimensional simplices in D

The scale of the Fourier transform: a point of view of the fractional Fourier transform

NASA Astrophysics Data System (ADS)

Jimenez, C. J.; Vilardy, J. M.; Salinas, S.; Mattos, L.; Torres, C. O.

2017-01-01

In this paper using the Fourier transform of order fractional, the ray transfer matrix for the symmetrical optical systems type ABCD and the formulae by Collins for the diffraction, we obtain explicitly the expression for scaled Fourier transform conventional; this result is the great importance in optical signal processing because it offers the possibility of scaling the size of output the Fourier distribution of the system, only by manipulating the distance of the diffraction object toward the thin lens, this research also emphasizes on practical limits when a finite spherical converging lens aperture is used. Digital simulation was carried out using the numerical platform of Matlab 7.1.

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

PubMed

Oktem, Figen S; Ozaktas, Haldun M

2010-08-01

Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

Enhanced Photocatalytic Property of Cu Doped Sodium Niobate

DOE PAGES

Xu, Jianbin; Zhang, Feng; Sun, Bingyang; ...

2015-01-01

Here, we investigate the photocatalytic activity of Cu doped NaNbO 3 powder sample prepared by the modified polymer complex method. The photocatalytic activity of hydrogen evolution from methanol aqueous solution was improved by Cu 2.6 at% doping. The photocatalytic degradation of rhodamine B (RhB) under visible light irradiation was enhanced in comparison with pristine NaNbO 3. Cu introduction improved the adsorption property of NaNbO 3, judging from the Fourier transform infrared spectra. Moreover, the ultraviolet light excitation in Cu doped sample would accelerate the mineralized process.

Droplet characteristic measurement in Fourier interferometry imaging and behavior at the rainbow angle.

PubMed

Briard, Paul; Saengkaew, Sawitree; Wu, Xuecheng; Meunier-Guttin-Cluzel, Siegfried; Chen, Linghong; Cen, Kefa; Gréhan, Gérard

2013-01-01

This paper presents the possibility of measuring the three-dimensional (3D) relative locations and diameters of a set of spherical particles and discusses the behavior of the light recorded around the rainbow angle, an essential step toward refractive index measurements. When a set of particles is illuminated by a pulsed incident wave, the particles act as spherical light wave sources. When the pulse duration is short enough to fix the particle location (typically about 10 ns), interference fringes between these different spherical waves can be recorded. The Fourier transform of the fringes divides the complex fringe systems into a series of spots, with each spot characterizing the interference between a pair of particles. The analyses of these spots (in position and shape) potentially allow the measurement of particle characteristics (3D relative position, particle diameter, and particle refractive index value).

Techniques of noninvasive optical tomographic imaging

NASA Astrophysics Data System (ADS)

Rosen, Joseph; Abookasis, David; Gokhler, Mark

2006-01-01

Recently invented methods of optical tomographic imaging through scattering and absorbing media are presented. In one method, the three-dimensional structure of an object hidden between two biological tissues is recovered from many noisy speckle pictures obtained on the output of a multi-channeled optical imaging system. Objects are recovered from many speckled images observed by a digital camera through two stereoscopic microlens arrays. Each microlens in each array generates a speckle image of the object buried between the layers. In the computer each image is Fourier transformed jointly with an image of the speckled point-like source captured under the same conditions. A set of the squared magnitudes of the Fourier-transformed pictures is accumulated to form a single average picture. This final picture is again Fourier transformed, resulting in the three-dimensional reconstruction of the hidden object. In the other method, the effect of spatial longitudinal coherence is used for imaging through an absorbing layer with different thickness, or different index of refraction, along the layer. The technique is based on synthesis of multiple peak spatial degree of coherence. This degree of coherence enables us to scan simultaneously different sample points on different altitudes, and thus decreases the acquisition time. The same multi peak degree of coherence is also used for imaging through the absorbing layer. Our entire experiments are performed with a quasi-monochromatic light source. Therefore problems of dispersion and inhomogeneous absorption are avoided.

Coherence Conversion for Optimized Resolution in Optical Measurements - Example of Femtosecond Time Resolution Using the Transverse Coherence of 100-Picosecond X-Rays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, Bernhard W.

2015-01-01

A way is proposed to obtain a femtosecond time resolution over a picosecond range in x-ray spectroscopic measurements where the light source and the detector are much slower than that. It is based on the invariance of the modulus of the Fourier transform to object translations. The method geometrically correlates time in the sample with x-ray amplitudes over a spatial coordinate, and then takes the optical Fourier transform through far-field diffraction. Thus, explicitly time-invariant intensities that encode the time evolution of the sample can be measured with a slow detector. This corresponds to a phase-space transformation that converts the transversemore » coherence to become effective in the longitudinal direction. Because synchrotron-radiation sources have highly anisotropic coherence properties with about $10^5$ longitudinal electromagnetic-field modes at 1 eV bandwidth, but only tens to hundreds transverse modes, coherence conversion can drastically improve the time resolution. Reconstruction of the femtosecond time evolution in the sample from the Fourier intensities is subject to a phase ambiguity that is well-known in crystallography. However, a way is presented to resolve it that is not available in that discipline. Finally, data from a demonstration experiment are presented. The same concept can be used to obtain attosecond time resolution with an x-ray free-electron laser.« less

Research about vibration characteristics of timing chain system based on short-time Fourier transform

NASA Astrophysics Data System (ADS)

Xi, Jiaxin; Liu, Ning

2017-09-01

Vibration characteristic of timing chain system is very important for an engine. In this study, we used a bush roller chain drive system as an example to explain how to use mulitybody dynamic techniques and short-time Fourier transform to investigate vibration characteristics of timing chain system. Multibody dynamic simulation data as chain tension force and external excitation sources curves were provided for short-time Fourier transform study. The study results of short-time Fourier transform illustrate that there are two main vibration frequency domain of timing chain system, one is the low frequency vibration caused by crankshaft sprocket velocity and camshaft sprocket torque. Another is vibration around 1000Hz lead by hydraulic tensioner. Hence, short-time Fourier transform method is useful for basic research of vibration characteristics for timing chain system.

Fourier transform mass spectrometry.

PubMed

Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander

2011-07-01

This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.

Fourier Transform Mass Spectrometry

PubMed Central

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

The morphing of geographical features by Fourier transformation

PubMed Central

Liu, Pengcheng; Yu, Wenhao; Cheng, Xiaoqiang

2018-01-01

This paper presents a morphing model of vector geographical data based on Fourier transformation. This model involves three main steps. They are conversion from vector data to Fourier series, generation of intermediate function by combination of the two Fourier series concerning a large scale and a small scale, and reverse conversion from combination function to vector data. By mirror processing, the model can also be used for morphing of linear features. Experimental results show that this method is sensitive to scale variations and it can be used for vector map features’ continuous scale transformation. The efficiency of this model is linearly related to the point number of shape boundary and the interceptive value n of Fourier expansion. The effect of morphing by Fourier transformation is plausible and the efficiency of the algorithm is acceptable. PMID:29351344

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.

Representation of Complex Spectra in Auditory Cortex

DTIC Science & Technology

1997-01-01

predict the response to any broadband dynamic sound. Fourier Transform Inverse Transform ∫ [.] exp(±2πjΩx±2πjwt) 2 1 2 / 1 1 a 2 1 2 / 1 1 a...Systems Research University of Maryland Spectro-Temporal Transform Ω wx = log f t w = “ripple velocity” Ω = “ripple frequency” Fourier Transform Inverse ... Transform ∫ [.] exp(±2πjΩx±2πjwt) Real functions in the spectro-temporal domain give rise to complex conjugate symmetric functions in the Fourier

Symmetric Phase-Only Filtering in Particle-Image Velocimetry

NASA Technical Reports Server (NTRS)

Wemet, Mark P.

2008-01-01

Symmetrical phase-only filtering (SPOF) can be exploited to obtain substantial improvements in the results of data processing in particle-image velocimetry (PIV). In comparison with traditional PIV data processing, SPOF PIV data processing yields narrower and larger amplitude correlation peaks, thereby providing more-accurate velocity estimates. The higher signal-to-noise ratios associated with the higher amplitude correlation peaks afford greater robustness and reliability of processing. SPOF also affords superior performance in the presence of surface flare light and/or background light. SPOF algorithms can readily be incorporated into pre-existing algorithms used to process digitized image data in PIV, without significantly increasing processing times. A summary of PIV and traditional PIV data processing is prerequisite to a meaningful description of SPOF PIV processing. In PIV, a pulsed laser is used to illuminate a substantially planar region of a flowing fluid in which particles are entrained. An electronic camera records digital images of the particles at two instants of time. The components of velocity of the fluid in the illuminated plane can be obtained by determining the displacements of particles between the two illumination pulses. The objective in PIV data processing is to compute the particle displacements from the digital image data. In traditional PIV data processing, to which the present innovation applies, the two images are divided into a grid of subregions and the displacements determined from cross-correlations between the corresponding sub-regions in the first and second images. The cross-correlation process begins with the calculation of the Fourier transforms (or fast Fourier transforms) of the subregion portions of the images. The Fourier transforms from the corresponding subregions are multiplied, and this product is inverse Fourier transformed, yielding the cross-correlation intensity distribution. The average displacement of the particles across a subregion results in a displacement of the correlation peak from the center of the correlation plane. The velocity is then computed from the displacement of the correlation peak and the time between the recording of the two images. The process as described thus far is performed for all the subregions. The resulting set of velocities in grid cells amounts to a velocity vector map of the flow field recorded on the image plane. In traditional PIV processing, surface flare light and bright background light give rise to a large, broad correlation peak, at the center of the correlation plane, that can overwhelm the true particle- displacement correlation peak. This has made it necessary to resort to tedious image-masking and background-subtraction procedures to recover the relatively small amplitude particle-displacement correlation peak. SPOF is a variant of phase-only filtering (POF), which, in turn, is a variant of matched spatial filtering (MSF). In MSF, one projects a first image (denoted the input image) onto a second image (denoted the filter) as part of a computation to determine how much and what part of the filter is present in the input image. MSF is equivalent to cross-correlation. In POF, the frequency-domain content of the MSF filter is modified to produce a unitamplitude (phase-only) object. POF is implemented by normalizing the Fourier transform of the filter by its magnitude. The advantage of POFs is that they yield correlation peaks that are sharper and have higher signal-to-noise ratios than those obtained through traditional MSF. In the SPOF, these benefits of POF can be extended to PIV data processing. The SPOF yields even better performance than the POF approach, which is uniquely applicable to PIV type image data. In SPOF as now applied to PIV data processing, a subregion of the first image is treated as the input image and the corresponding subregion of the second image is treated as the filter. The Fourier transforms from both the firs and second- image subregions are normalized by the square roots of their respective magnitudes. This scheme yields optimal performance because the amounts of normalization applied to the spatial-frequency contents of the input and filter scenes are just enough to enhance their high-spatial-frequency contents while reducing their spurious low-spatial-frequency content. As a result, in SPOF PIV processing, particle-displacement correlation peaks can readily be detected above spurious background peaks, without need for masking or background subtraction.

Noninterferometric Two-Dimensional Fourier-Transform Spectroscopy of Multilevel Systems

NASA Astrophysics Data System (ADS)

Davis, J. A.; Dao, L. V.; Do, M. T.; Hannaford, P.; Nugent, K. A.; Quiney, H. M.

2008-06-01

We demonstrate a technique that determines the phase of the photon-echo emission from spectrally resolved intensity data without requiring phase-stabilized input pulses. The full complex polarization of the emission is determined from spectral intensity measurements. The validity of this technique is demonstrated using simulated data, and is then applied to the analysis of two-color data obtained from the light-harvesting molecule lycopene.

[Optical-fiber Fourier transform spectrometer].

PubMed

Liu, Yong; Li, Bao-sheng; Liu, Yan; Zhai, Yu-feng; Wang, An

2006-10-01

A novel Fourier transform spectrum analyzer based on a single mode fiber Mach-Zehnder interferometer is reported. An optical fiber Fourier transform spectrometer, with bulk optics components replaced by fiber optical components and with the moving mirror replaced by a piezoelectric element fiber stretcher was constructed. The output spectrum of a LD below threshold was measured. Experiment result agrees with that by using grating spectrum analyzer, showing the feasibility of the optic fiber Fourier transform spectrometer for practical spectrum measurement. Spectrum resolution -7 cm(-1) was obtained in our experiment. The resolution can be further improved by increasing the maximum optical path difference.

Stripe artifact elimination based on nonsubsampled contourlet transform for light sheet fluorescence microscopy

NASA Astrophysics Data System (ADS)

Liang, Xiao; Zang, Yali; Dong, Di; Zhang, Liwen; Fang, Mengjie; Yang, Xin; Arranz, Alicia; Ripoll, Jorge; Hui, Hui; Tian, Jie

2016-10-01

Stripe artifacts, caused by high-absorption or high-scattering structures in the illumination light path, are a common drawback in both unidirectional and multidirectional light sheet fluorescence microscopy (LSFM), significantly deteriorating image quality. To circumvent this problem, we present an effective multidirectional stripe remover (MDSR) method based on nonsubsampled contourlet transform (NSCT), which can be used for both unidirectional and multidirectional LSFM. In MDSR, a fast Fourier transform (FFT) filter is designed in the NSCT domain to shrink the stripe components and eliminate the noise. Benefiting from the properties of being multiscale and multidirectional, MDSR succeeds in eliminating stripe artifacts in both unidirectional and multidirectional LSFM. To validate the method, MDSR has been tested on images from a custom-made unidirectional LSFM system and a commercial multidirectional LSFM system, clearly demonstrating that MDSR effectively removes most of the stripe artifacts. Moreover, we performed a comparative experiment with the variational stationary noise remover and the wavelet-FFT methods and quantitatively analyzed the results with a peak signal-to-noise ratio, showing an improved noise removal when using the MDSR method.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

PubMed

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.

A cascade method for TFT-LCD defect detection

NASA Astrophysics Data System (ADS)

Yi, Songsong; Wu, Xiaojun; Yu, Zhiyang; Mo, Zhuoya

2017-07-01

In this paper, we propose a novel cascade detection algorithm which focuses on point and line defects on TFT-LCD. At the first step of the algorithm, we use the gray level difference of su-bimage to segment the abnormal area. The second step is based on phase only transform (POT) which corresponds to the Discrete Fourier Transform (DFT), normalized by the magnitude. It can remove regularities like texture and noise. After that, we improve the method of setting regions of interest (ROI) with the method of edge segmentation and polar transformation. The algorithm has outstanding performance in both computation speed and accuracy. It can solve most of the defect detections including dark point, light point, dark line, etc.

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.

A Simple Approach to Fourier Aliasing

ERIC Educational Resources Information Center

Foadi, James

2007-01-01

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and…

A general spectral transformation simultaneously including a Fourier transformation and a Laplace transformation

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.

Fourier Analysis and Structure Determination: Part I: Fourier Transforms.

ERIC Educational Resources Information Center

Chesick, John P.

1989-01-01

Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)

Fourier transform of delayed fluorescence as an indicator of herbicide concentration.

PubMed

Guo, Ya; Tan, Jinglu

2014-12-21

It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Lightweight multi-carrier modulation for IoT

NASA Astrophysics Data System (ADS)

Hussein, Ahmed F.; Elgala, Hany

2018-01-01

Visible light communications (VLC) based on intensity-modulation with direct-detection (IM/DD) is a promising technology to offer broadband wireless Internet access. A VLC system based on the well-known multi-carrier orthogonal frequency-division multiplexing (OFDM) modulation has the potential to coexist with radio frequency (RF) technologies such as WiFi. Recently, the VLC technology is considered to enable wireless connectivity of resource limited devices, thus enabling the Internet-of-Things (IoT) vision. This paper presents a novel concept for modulating multiple light sources to realize a lightweight version of OFDM communication chain suitable for resource limited IoT devices. In such proposed system, different sinusoidal streams from an array of light sources are carrying the encoded OFDM time-domain samples, thus enabling the realization of the Fourier transformation in the optical domain. Accordingly, the fast Fourier transform (FFT) operation required for the demodulation at the receiver side is eliminated, which is crucial for resource limited IoT devices. In addition, the proposed concept, (1) offers the same spectral efficiency as the well-known asymmetrically clipped optical OFDM (ACO-OFDM), (2) reduces the bandwidth requirement from individual light sources, (3) reduces the peak-to-average power ratio (PAPR) of the signal formed and transmitted over the optical channel, and (4) supports simultaneous sensing applications using the different sinusoidal streams that are acting as unique beaconing signals. The proposed concept is numerically evaluated and compared with ACO-OFDM. The obtained results reveal a clear reduction in the PAPR with ˜ 5dB at a complementary cumulative distribution function (CCDF) of 10-2 and remarkable enhancement in bit-error performance.

Study on sampling of continuous linear system based on generalized Fourier transform

NASA Astrophysics Data System (ADS)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

White light Sagnac interferometer—a common (path) tale of light

NASA Astrophysics Data System (ADS)

Schwartz, Eyal

2017-11-01

White or polychromatic light sources are vastly abundant in nature and lie in our most basic understanding of the theory of light, beginning from stars like our Sun and extending to every common household light bulb or street lamp. In this paper, I present concepts of white light interferometery using a common-path Sagnac interferometer, manifested in a straightforward laboratory experiment. I further show the use of this as a Fourier transform spectrometer while presenting a basic overview of the theoretical concepts and spectrum of different light sources obtained experimentally. This work, both experimentally and analytically, is suitable for upper-level undergraduate physics or engineering courses where electromagnetic theory and optics are discussed. The experiment and theory presents important deep concepts and aspects in modern optics and physics that every science student should acquire.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. G.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates

PubMed Central

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

Performance of the Wavelet Decomposition on Massively Parallel Architectures

NASA Technical Reports Server (NTRS)

El-Ghazawi, Tarek A.; LeMoigne, Jacqueline; Zukor, Dorothy (Technical Monitor)

2001-01-01

Traditionally, Fourier Transforms have been utilized for performing signal analysis and representation. But although it is straightforward to reconstruct a signal from its Fourier transform, no local description of the signal is included in its Fourier representation. To alleviate this problem, Windowed Fourier transforms and then wavelet transforms have been introduced, and it has been proven that wavelets give a better localization than traditional Fourier transforms, as well as a better division of the time- or space-frequency plane than Windowed Fourier transforms. Because of these properties and after the development of several fast algorithms for computing the wavelet representation of any signal, in particular the Multi-Resolution Analysis (MRA) developed by Mallat, wavelet transforms have increasingly been applied to signal analysis problems, especially real-life problems, in which speed is critical. In this paper we present and compare efficient wavelet decomposition algorithms on different parallel architectures. We report and analyze experimental measurements, using NASA remotely sensed images. Results show that our algorithms achieve significant performance gains on current high performance parallel systems, and meet scientific applications and multimedia requirements. The extensive performance measurements collected over a number of high-performance computer systems have revealed important architectural characteristics of these systems, in relation to the processing demands of the wavelet decomposition of digital images.

Realistic Analytical Polyhedral MRI Phantoms

PubMed Central

Ngo, Tri M.; Fung, George S. K.; Han, Shuo; Chen, Min; Prince, Jerry L.; Tsui, Benjamin M. W.; McVeigh, Elliot R.; Herzka, Daniel A.

2015-01-01

Purpose Analytical phantoms have closed form Fourier transform expressions and are used to simulate MRI acquisitions. Existing 3D analytical phantoms are unable to accurately model shapes of biomedical interest. It is demonstrated that polyhedral analytical phantoms have closed form Fourier transform expressions and can accurately represent 3D biomedical shapes. Theory The derivations of the Fourier transform of a polygon and polyhedron are presented. Methods The Fourier transform of a polyhedron was implemented and its accuracy in representing faceted and smooth surfaces was characterized. Realistic anthropomorphic polyhedral brain and torso phantoms were constructed and their use in simulated 3D/2D MRI acquisitions was described. Results Using polyhedra, the Fourier transform of faceted shapes can be computed to within machine precision. Smooth surfaces can be approximated with increasing accuracy by increasing the number of facets in the polyhedron; the additional accumulated numerical imprecision of the Fourier transform of polyhedra with many faces remained small. Simulations of 3D/2D brain and 2D torso cine acquisitions produced realistic reconstructions free of high frequency edge aliasing as compared to equivalent voxelized/rasterized phantoms. Conclusion Analytical polyhedral phantoms are easy to construct and can accurately simulate shapes of biomedical interest. PMID:26479724

A Comparison of Optical versus Hardware Fourier Transforms.

DTIC Science & Technology

1983-10-31

AD- R136 223 A COMPRISON’OF OPTICAL ERSUS HARDWARE FOURIER i/i.TRANSFORMS(U) VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF PHYSICS S P...transform and its inverse filtered Fourier transform obtained with the Digital Image Processing (DIP) hardware system located at the School of Aerospace...transparencies, and provided to us by Dr. Ralph G. Allen, Director of the Laser Effects Branch (Division of Radiation Sciences). The DIP system consisted of: an

Fourier analysis and signal processing by use of the Moebius inversion formula

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Yu, Xiaoli; Shih, Ming-Tang; Tufts, Donald W.; Truong, T. K.

1990-01-01

A novel Fourier technique for digital signal processing is developed. This approach to Fourier analysis is based on the number-theoretic method of the Moebius inversion of series. The Fourier transform method developed is shown also to yield the convolution of two signals. A computer simulation shows that this method for finding Fourier coefficients is quite suitable for digital signal processing. It competes with the classical FFT (fast Fourier transform) approach in terms of accuracy, complexity, and speed.

Exploring Algorithms for Stellar Light Curves With TESS

NASA Astrophysics Data System (ADS)

Buzasi, Derek

2018-01-01

The Kepler and K2 missions have produced tens of thousands of stellar light curves, which have been used to measure rotation periods, characterize photometric activity levels, and explore phenomena such as differential rotation. The quasi-periodic nature of rotational light curves, combined with the potential presence of additional periodicities not due to rotation, complicates the analysis of these time series and makes characterization of uncertainties difficult. A variety of algorithms have been used for the extraction of rotational signals, including autocorrelation functions, discrete Fourier transforms, Lomb-Scargle periodograms, wavelet transforms, and the Hilbert-Huang transform. In addition, in the case of K2 a number of different pipelines have been used to produce initial detrended light curves from the raw image frames.In the near future, TESS photometry, particularly that deriving from the full-frame images, will dramatically further expand the number of such light curves, but details of the pipeline to be used to produce photometry from the FFIs remain under development. K2 data offers us an opportunity to explore the utility of different reduction and analysis tool combinations applied to these astrophysically important tasks. In this work, we apply a wide range of algorithms to light curves produced by a number of popular K2 pipeline products to better understand the advantages and limitations of each approach and provide guidance for the most reliable and most efficient analysis of TESS stellar data.

Image Reconstruction from Data Collected with an Imaging Interferometer

NASA Astrophysics Data System (ADS)

DeSantis, Z. J.; Thurman, S. T.; Hix, T. T.; Ogden, C. E.

The intensity distribution of an incoherent source and the spatial coherence function at some distance away are related by a Fourier transform, via the Van Cittert-Zernike theorem. Imaging interferometers measure the spatial coherence of light propagated from the incoherently illuminated object by combining light from spatially separated points to measure interference fringes. The contrast and phase of the fringe are the amplitude and phase of a Fourier component of the source’s intensity distribution. The Fiber-Coupled Interferometer (FCI) testbed is a visible light, lab-based imaging interferometer designed to test aspects of an envisioned ground-based interferometer for imaging geosynchronous satellites. The front half of the FCI testbed consists of the scene projection optics, which includes an incoherently backlit scene, located at the focus of a 1 m aperture f/100 telescope. The projected light was collected by the back half of the FCI testbed. The collection optics consisted of three 11 mm aperture fiber-coupled telescopes. Light in the fibers was combined pairwise and dispersed onto a sensor to measure the interference fringe as a function of wavelength, which produces a radial spoke of measurements in the Fourier domain. The visibility function was sampled throughout the Fourier domain by recording fringe data at many different scene rotations and collection telescope separations. Our image reconstruction algorithm successfully produced images for the three scenes we tested: asymmetric pair of pinholes, U.S. Air Force resolution bar target, and satellite scene. The bar target reconstruction shows detail and resolution near the predicted resolution limit. This research was developed with funding from the Defense Advanced Research Projects Agency (DARPA). The views, opinions and/or findings expressed are those of the author(s) and should not be interpreted as reflecting the official views or policies of the Department of Defense or the U.S. Government.

Double Fourier analysis for Emotion Identification in Voiced Speech

NASA Astrophysics Data System (ADS)

Sierra-Sosa, D.; Bastidas, M.; Ortiz P., D.; Quintero, O. L.

2016-04-01

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech. Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions. A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds. Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions. Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it. Finally features related with emotions in voiced speech are extracted and presented.

Rapid update of discrete Fourier transform for real-time signal processing

NASA Astrophysics Data System (ADS)

Sherlock, Barry G.; Kakad, Yogendra P.

2001-10-01

In many identification and target recognition applications, the incoming signal will have properties that render it amenable to analysis or processing in the Fourier domain. In such applications, however, it is usually essential that the identification or target recognition be performed in real time. An important constraint upon real-time processing in the Fourier domain is the time taken to perform the Discrete Fourier Transform (DFT). Ideally, a new Fourier transform should be obtained after the arrival of every new data point. However, the Fast Fourier Transform (FFT) algorithm requires on the order of N log2 N operations, where N is the length of the transform, and this usually makes calculation of the transform for every new data point computationally prohibitive. In this paper, we develop an algorithm to update the existing DFT to represent the new data series that results when a new signal point is received. Updating the DFT in this way uses less computational order by a factor of log2 N. The algorithm can be modified to work in the presence of data window functions. This is a considerable advantage, because windowing is often necessary to reduce edge effects that occur because the implicit periodicity of the Fourier transform is not exhibited by the real-world signal. Versions are developed in this paper for use with the boxcar window, the split triangular, Hanning, Hamming, and Blackman windows. Generalization of these results to 2D is also presented.

Built-in hyperspectral camera for smartphone in visible, near-infrared and middle-infrared lights region (second report): sensitivity improvement of Fourier-spectroscopic imaging to detect diffuse reflection lights from internal human tissues for healthcare sensors

NASA Astrophysics Data System (ADS)

Kawashima, Natsumi; Hosono, Satsuki; Ishimaru, Ichiro

2016-05-01

We proposed the snapshot-type Fourier spectroscopic imaging for smartphone that was mentioned in 1st. report in this conference. For spectroscopic components analysis, such as non-invasive blood glucose sensors, the diffuse reflection lights from internal human skins are very weak for conventional hyperspectral cameras, such as AOTF (Acousto-Optic Tunable Filter) type. Furthermore, it is well known that the spectral absorption of mid-infrared lights or Raman spectroscopy especially in long wavelength region is effective to distinguish specific biomedical components quantitatively, such as glucose concentration. But the main issue was that photon energies of middle infrared lights and light intensities of Raman scattering are extremely weak. For improving sensitivity of our spectroscopic imager, the wide-field-stop & beam-expansion method was proposed. Our line spectroscopic imager introduced a single slit for field stop on the conjugate objective plane. Obviously to increase detected light intensities, the wider slit width of the field stop makes light intensities higher, regardless of deterioration of spatial resolutions. Because our method is based on wavefront-division interferometry, it becomes problems that the wider width of single slit makes the diffraction angle narrower. This means that the narrower diameter of collimated objective beams deteriorates visibilities of interferograms. By installing the relative inclined phaseshifter onto optical Fourier transform plane of infinity corrected optical systems, the collimated half flux of objective beams derived from single-bright points on objective surface penetrate through the wedge prism and the cuboid glass respectively. These two beams interfere each other and form the infererogram as spatial fringe patterns. Thus, we installed concave-cylindrical lens between the wider slit and objective lens as a beam expander. We successfully obtained the spectroscopic characters of hemoglobin from reflected lights from human fingers.

Investigation of hidden periodic structures on SEM images of opal-like materials using FFT and IFFT.

PubMed

Stephant, Nicolas; Rondeau, Benjamin; Gauthier, Jean-Pierre; Cody, Jason A; Fritsch, Emmanuel

2014-01-01

We have developed a method to use fast Fourier transformation (FFT) and inverse fast Fourier transformation (IFFT) to investigate hidden periodic structures on SEM images. We focused on samples of natural, play-of-color opals that diffract visible light and hence are periodically structured. Conventional sample preparation by hydrofluoric acid etch was not used; untreated, freshly broken surfaces were examined at low magnification relative to the expected period of the structural features, and, the SEM was adjusted to get a very high number of pixels in the images. These SEM images were treated by software to calculate autocorrelation, FFT, and IFFT. We present how we adjusted SEM acquisition parameters for best results. We first applied our procedure on an SEM image on which the structure was obvious. Then, we applied the same procedure on a sample that must contain a periodic structure because it diffracts visible light, but on which no structure was visible on the SEM image. In both cases, we obtained clearly periodic patterns that allowed measurements of structural parameters. We also investigated how the irregularly broken surface interfered with the periodic structure to produce additional periodicity. We tested the limits of our methodology with the help of simulated images. © 2014 Wiley Periodicals, Inc.

Fourier transform-wavefront reconstruction for the pyramid wavefront sensor

NASA Astrophysics Data System (ADS)

Quirós-Pacheco, Fernando; Correia, Carlos; Esposito, Simone

The application of Fourier-transform reconstruction techniques to the pyramid wavefront sensor has been investigated. A preliminary study based on end-to-end simulations of an adaptive optics system with ≈40x40 subapertures and actuators shows that the performance of the Fourier-transform reconstructor (FTR) is of the same order of magnitude than the one obtained with a conventional matrix-vector multiply (MVM) method.

Polarization Ratio Determination with Two Identical Linearly Polarized Antennas

DTIC Science & Technology

2017-01-17

Fourier transform analysis of 21 measurements with one of the antennas rotating about its axis a circular polarization ratio is derived which can be...deter- mined directly from a discrete Fourier transform (DFT) of (5). However, leakage between closely spaced DFT bins requires improving the... Fourier transform and a mechanical antenna rotation to separate the principal and opposite circular polarization components followed by a basis

Laboratory demonstration of image reconstruction for coherent optical system of modular imaging collectors (COSMIC)

NASA Technical Reports Server (NTRS)

Traub, W. A.

1984-01-01

The first physical demonstration of the principle of image reconstruction using a set of images from a diffraction-blurred elongated aperture is reported. This is an optical validation of previous theoretical and numerical simulations of the COSMIC telescope array (coherent optical system of modular imaging collectors). The present experiment utilizes 17 diffraction blurred exposures of a laboratory light source, as imaged by a lens covered by a narrow-slit aperture; the aperture is rotated 10 degrees between each exposure. The images are recorded in digitized form by a CCD camera, Fourier transformed, numerically filtered, and added; the sum is then filtered and inverse Fourier transformed to form the final image. The image reconstruction process is found to be stable with respect to uncertainties in values of all physical parameters such as effective wavelength, rotation angle, pointing jitter, and aperture shape. Future experiments will explore the effects of low counting rates, autoguiding on the image, various aperture configurations, and separated optics.

Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

PubMed

Pei, Soo-Chang; Ding, Jian-Jiun

2005-03-01

Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

Theory and operational rules for the discrete Hankel transform.

PubMed

Baddour, Natalie; Chouinard, Ugo

2015-04-01

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

Thermal effects in light scattering from ultracold bosons in an optical lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lakomy, Kazimierz; Idziaszek, Zbigniew; Trippenbach, Marek

2009-10-15

We study the scattering of a weak and far-detuned light from a system of ultracold bosons in one-dimensional and three-dimensional optical lattices. We show the connection between angular distributions of the scattered light and statistical properties of a Bose gas in a periodic potential. The angular patterns are determined by the Fourier transform of the second-order correlation function, and thus they can be used to retrieve information on particle number fluctuations and correlations. We consider superfluid and Mott-insulator phases of the Bose gas in a lattice and we analyze in detail how the scattering depends on the system dimensionality, temperature,more » and atom-atom interactions.« less

Sequential measurement of conjugate variables as an alternative quantum state tomography.

PubMed

Di Lorenzo, Antonio

2013-01-04

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by sequentially measuring two conjugate variables. The procedure relies on the quasicharacteristic function, the Fourier transform of the Wigner quasiprobability. The proper characteristic function obtained by Fourier transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasicharacteristic function of the two detectors and that unknown of the quantum system. This allows state reconstruction through the sequence (1) data collection, (2) Fourier transform, (3) algebraic operation, and (4) inverse Fourier transform. The strength of the measurement should be intermediate for the procedure to work.

Photonic fractional Fourier transformer with a single dispersive device.

PubMed

Cuadrado-Laborde, C; Carrascosa, A; Díez, A; Cruz, J L; Andres, M V

2013-04-08

In this work we used the temporal analog of spatial Fresnel diffraction to design a temporal fractional Fourier transformer with a single dispersive device, in this way avoiding the use of quadratic phase modulators. We demonstrate that a single dispersive passive device inherently provides the fractional Fourier transform of an incident optical pulse. The relationships linking the fractional Fourier transform order and scaling factor with the dispersion parameters are derived. We first provide some numerical results in order to prove the validity of our proposal, using a fiber Bragg grating as the dispersive device. Next, we experimentally demonstrate the feasibility of this proposal by using a spool of a standard optical fiber as the dispersive device.

Algorithm for Wavefront Sensing Using an Extended Scene

NASA Technical Reports Server (NTRS)

Sidick, Erkin; Green, Joseph; Ohara, Catherine

2008-01-01

A recently conceived algorithm for processing image data acquired by a Shack-Hartmann (SH) wavefront sensor is not subject to the restriction, previously applicable in SH wavefront sensing, that the image be formed from a distant star or other equivalent of a point light source. That is to say, the image could be of an extended scene. (One still has the option of using a point source.) The algorithm can be implemented in commercially available software on ordinary computers. The steps of the algorithm are the following: 1. Suppose that the image comprises M sub-images. Determine the x,y Cartesian coordinates of the centers of these sub-images and store them in a 2xM matrix. 2. Within each sub-image, choose an NxN-pixel cell centered at the coordinates determined in step 1. For the ith sub-image, let this cell be denoted as si(x,y). Let the cell of another subimage (preferably near the center of the whole extended-scene image) be designated a reference cell, denoted r(x,y). 3. Calculate the fast Fourier transforms of the sub-sub-images in the central NxN portions (where N < N and both are preferably powers of 2) of r(x,y) and si(x,y). 4. Multiply the two transforms to obtain a cross-correlation function Ci(u,v), in the Fourier domain. Then let the phase of Ci(u, v) constitute a phase function, phi(u,v). 5. Fit u and v slopes to phi (u,v) over a small u,v subdomain. 6. Compute the fast Fourier transform, Si(u,v) of the full NxN cell si(x,y). Multiply this transform by the u and phase slopes obtained in step 4. Then compute the inverse fast Fourier transform of the product. 7. Repeat steps 4 through 6 in an iteration loop, cumulating the u and slopes, until a maximum iteration number is reached or the change in image shift becomes smaller than a predetermined tolerance. 8. Repeat steps 4 through 7 for the cells of all other sub-images.

Teaching Fourier optics through ray matrices

NASA Astrophysics Data System (ADS)

Moreno, I.; Sánchez-López, M. M.; Ferreira, C.; Davis, J. A.; Mateos, F.

2005-03-01

In this work we examine the use of ray-transfer matrices for teaching and for deriving some topics in a Fourier optics course, exploiting the mathematical simplicity of ray matrices compared to diffraction integrals. A simple analysis of the physical meaning of the elements of the ray matrix provides a fast derivation of the conditions to obtain the optical Fourier transform. We extend this derivation to fractional Fourier transform optical systems, and derive the order of the transform from the ray matrix. Some examples are provided to stress this point of view, both with classical and with graded index lenses. This formulation cannot replace the complete explanation of Fourier optics provided by the wave theory, but it is a complementary tool useful to simplify many aspects of Fourier optics and to relate them to geometrical optics.

Signal processing applications of massively parallel charge domain computing devices

NASA Technical Reports Server (NTRS)

Fijany, Amir (Inventor); Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor)

1999-01-01

The present invention is embodied in a charge coupled device (CCD)/charge injection device (CID) architecture capable of performing a Fourier transform by simultaneous matrix vector multiplication (MVM) operations in respective plural CCD/CID arrays in parallel in O(1) steps. For example, in one embodiment, a first CCD/CID array stores charge packets representing a first matrix operator based upon permutations of a Hartley transform and computes the Fourier transform of an incoming vector. A second CCD/CID array stores charge packets representing a second matrix operator based upon different permutations of a Hartley transform and computes the Fourier transform of an incoming vector. The incoming vector is applied to the inputs of the two CCD/CID arrays simultaneously, and the real and imaginary parts of the Fourier transform are produced simultaneously in the time required to perform a single MVM operation in a CCD/CID array.

Apparatus for direct-to-digital spatially-heterodyned holography

DOEpatents

Thomas, Clarence E.; Hanson, Gregory R.

2006-12-12

An apparatus operable to record a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis includes: a laser; a beamsplitter optically coupled to the laser; an object optically coupled to the beamsplitter; a focusing lens optically coupled to both the beamsplitter and the object; a digital recorder optically coupled to the focusing lens; and a computer that performs a Fourier transform, applies a digital filter, and performs an inverse Fourier transform. A reference beam and an object beam are focused by the focusing lens at a focal plane of the digital recorder to form a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis which is recorded by the digital recorder, and the computer transforms the recorded spatially low-frequency heterodyne hologram including spatially heterodyne fringes and shifts axes in Fourier space to sit on top of a heterodyne carrier frequency defined by an angle between the reference beam and the object beam and cuts off signals around an original origin before performing the inverse Fourier transform.

Practical Sub-Nyquist Sampling via Array-Based Compressed Sensing Receiver Architecture

DTIC Science & Technology

2016-07-10

different array ele- ments at different sub-Nyquist sampling rates. Signal processing inspired by the sparse fast Fourier transform allows for signal...reconstruction algorithms can be computationally demanding (REF). The related sparse Fourier transform algorithms aim to reduce the processing time nec- essary to...compute the DFT of frequency-sparse signals [7]. In particular, the sparse fast Fourier transform (sFFT) achieves processing time better than the

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.

Molecular Characterization of Thiols in Fossil Fuels by Michael Addition Reaction Derivatization and Electrospray Ionization Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

PubMed

Wang, Meng; Zhao, Suoqi; Liu, Xuxia; Shi, Quan

2016-10-04

Thiols widely occur in sediments and fossil fuels. However, the molecular composition of these compounds is unclear due to the lack of appropriate analytical methods. In this work, a characterization method for thiols in fossil fuels was developed on the basis of Michael addition reaction derivatization followed by electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI FT-ICR MS). Model thiol compound studies showed that thiols were selectively reacted with phenylvinylsulfone and transformed to sulfones with greater than 98% conversions. This method was applied to a coker naphtha, light and heavy gas oils, and crude oils from various geological sources. The results showed that long alkyl chain thiols are readily present in petroleum, which have up to 30 carbon atoms. Large DBE dispersity of thiols indicates that naphthenic and aromatic thiols are also present in the petroleum. This method is capable of detecting thiol compounds in the part per million range by weight. This method allows characterization of thiols in a complex hydrocarbon matrix, which is complementary to the comprehensive analysis of sulfur compounds in fossil fuels.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA.

PubMed

Scargle, Jeffrey D; Way, M J; Gazis, P R

2017-04-10

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

STRUCTURE IN THE 3D GALAXY DISTRIBUTION: III. FOURIER TRANSFORMING THE UNIVERSE: PHASE AND POWER SPECTRA

PubMed Central

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys. PMID:29628519

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R.

2017-01-01

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Core-shell magnetite-silica composite nanoparticles enhancing DNA damage induced by a photoactive platinum-diimine complex in red light.

PubMed

Zhang, Zhigang; Chai, Aiyun

2012-12-01

Lack of solubility under physiological conditions poses an additional risk for toxicity and side effects for intravenous delivery of the photodynamic therapeutic agent in vivo. Employing magnetite-silica composite nanoparticles as carriers of the photodynamic therapeutic agents may be a promising way to solve the problem. In this study, core-shell magnetite-silica composite nanoparticles were prepared by a sol-gel method, and characterized by X-ray diffraction, Fourier transform infrared spectroscopy, transmission electron microscopy and dynamic light scattering, then they were used as carriers of a photoactive platinum diimine complex. The interactions of the photosensitizer-loaded magnetic composite nanoparticles with DNA in red light were monitored by agarose-gel electrophoresis. The results suggest that high doses of magnetite-silica composite nanoparticles might facilitate the transformation of covalently closed circular (ccc)-DNA band to open circular (oc)-DNA band though they are harmless to DNA at their low concentrations, therefore enhancing the extent of DNA damage caused by the metal complex in red light. Copyright © 2012 Elsevier Inc. All rights reserved.

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

NASA Astrophysics Data System (ADS)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

Treatment Characteristics of Polysaccharides and Endotoxin Using Oxygen Plasma Produced by RF Discharge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kitazaki, Satoshi; Hayashi, Nobuya; Goto, Masaaki

Treatment of polysaccharides and endotoxin were attempted using oxygen plasma produced by RF discharge. Oxygen radicals observed by optical light emission spectra are factors of decomposition of polysaccharides and endotoxin. Fourier transform infrared spectra indicate that most of chemical bonds in the polysaccharides are dissociated after irradiation of the oxygen plasma. Also, the decomposition rate of endotoxin was approximately 90% after irradiation of the oxygen plasma for 180 min.

Treatment Characteristics of Polysaccharides and Endotoxin Using Oxygen Plasma Produced by RF Discharge

NASA Astrophysics Data System (ADS)

Kitazaki, Satoshi; Hayashi, Nobuya; Goto, Masaaki

2010-10-01

Treatment of polysaccharides and endotoxin were attempted using oxygen plasma produced by RF discharge. Oxygen radicals observed by optical light emission spectra are factors of decomposition of polysaccharides and endotoxin. Fourier transform infrared spectra indicate that most of chemical bonds in the polysaccharides are dissociated after irradiation of the oxygen plasma. Also, the decomposition rate of endotoxin was approximately 90% after irradiation of the oxygen plasma for 180 min.

Singular-value demodulation of phase-shifted holograms.

PubMed

Lopes, Fernando; Atlan, Michael

2015-06-01

We report on phase-shifted holographic interferogram demodulation by singular-value decomposition. Numerical processing of optically acquired interferograms over several modulation periods was performed in two steps: (1) rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; and (2) eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.

An Investigation into the Use of Spatially-Filtered Fourier Transforms to Classify Mammary Lesions.

DTIC Science & Technology

difference in Fourier space between lesioned breast tissue which would enable accurate computer classification of benign and malignant lesions. Low...separate benign and malignant breast tissue. However, no success was achieved when using two-dimensional Fourier transform and power spectrum analysis. (Author)

Detection of Fast Moving and Accelerating Targets Compensating Range and Doppler Migration

DTIC Science & Technology

2014-06-01

Radon -Fourier transform has been introduced to realize long- term coherent integration of the moving targets with range migration [8, 9]. Radon ...2010) Long-time coherent integration for radar target detection base on Radon -Fourier transform, in Proceedings of the IEEE Radar Conference, pp...432–436. 9. Xu, J., Yu, J., Peng, Y. & Xia, X. (2011) Radon -Fourier transform for radar target detection, I: Generalized Doppler filter bank, IEEE

Understanding the Physical Optics Phenomena by Using a Digital Application for Light Propagation

NASA Astrophysics Data System (ADS)

Sierra-Sosa, Daniel-Esteban; Ángel-Toro, Luciano

2011-01-01

Understanding the light propagation on the basis of the Huygens-Fresnel principle stands for a fundamental factor for deeper comprehension of different physical optics related phenomena like diffraction, self-imaging, image formation, Fourier analysis and spatial filtering. This constitutes the physical approach of the Fourier optics whose principles and applications have been developed since the 1950's. Both for analytical and digital applications purposes, light propagation can be formulated in terms of the Fresnel Integral Transform. In this work, a digital optics application based on the implementation of the Discrete Fresnel Transform (DFT), and addressed to serve as a tool for applications in didactics of optics is presented. This tool allows, at a basic and intermediate learning level, exercising with the identification of basic phenomena, and observing changes associated with modifications of physical parameters. This is achieved by using a friendly graphic user interface (GUI). It also assists the user in the development of his capacity for abstracting and predicting the characteristics of more complicated phenomena. At an upper level of learning, the application could be used to favor a deeper comprehension of involved physics and models, and experimenting with new models and configurations. To achieve this, two characteristics of the didactic tool were taken into account when designing it. First, all physical operations, ranging from simple diffraction experiments to digital holography and interferometry, were developed on the basis of the more fundamental concept of light propagation. Second, the algorithm was conceived to be easily upgradable due its modular architecture based in MATLAB® software environment. Typical results are presented and briefly discussed in connection with didactics of optics.

Mosaicking Techniques for Deep Submergence Vehicle Video Imagery - Applications to Ridge2000 Science

NASA Astrophysics Data System (ADS)

Mayer, L.; Rzhanov, Y.; Fornari, D. J.; Soule, A.; Shank, T. M.; Beaulieu, S. E.; Schouten, H.; Tivey, M.

2004-12-01

Severe attenuation of visible light and limited power capabilities of many submersible vehicles require acquisition of imagery from short ranges, rarely exceeding 8-10 meters. Although modern video- and photo-equipment makes high-resolution video surveying possible, the field of view of each image remains relatively narrow. To compensate for the deficiencies in light and field of view researchers have been developing techniques allowing for combining images into larger composite images i.e., mosaicking. A properly constructed, accurate mosaic has a number of well-known advantages in comparison with the original sequence of images, the most notable being improved situational awareness. We have developed software strategies for PC-based computers that permit conversion of video imagery acquired from any underwater vehicle, operated within both absolute (e.g. LBL or USBL) or relative (e.g. Doppler Velocity Log-DVL) navigation networks, to quickly produce a set of geo-referenced photomosaics which can then be directly incorporated into a Geographic Information System (GIS) data base. The timescale of processing is rapid enough to permit analysis of the resulting mosaics between submersible dives thus enhancing the efficiency of deep-sea research. Commercial imaging processing packages usually handle cases where there is no or little parallax - an unlikely situation for undersea world where terrain has pronounced 3D content and imagery is acquired from moving platforms. The approach we have taken is optimized for situations in which there is significant relief and thus parallax in the imagery (e.g. seafloor fault scarps or constructional volcanic escarpments and flow fronts). The basis of all mosaicking techniques is a pair-wise image registration method that finds a transformation relating pixels of two consecutive image frames. We utilize a "rigid affine model" with four degrees of freedom for image registration that allows for camera translation in all directions and camera rotation about its optical axis. The coefficients of the transformation can be determined robustly using the well-established and powerful "featureless Fourier domain-based technique" (FFDT), which is an extension of the FFT-based correlation approach. While calculation of cross-correlation allows the recovery of only two parameters of the transformation (translation in 2D), FFDT uses the "Phase shift" theorem of the Fourier Transform as well as a log-polar transform of the Fourier magnitude spectrum to recover all four transformation coefficients required for the rigid affine model. Examples of results of our video mosaicking data processing for the East Pacific Rise ISS will be presented.

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)

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.

Sparsity guided empirical wavelet transform for fault diagnosis of rolling element bearings

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yi, Cai; Tsui, Kwok-Leung; Lin, Jianhui

2018-02-01

Rolling element bearings are widely used in various industrial machines, such as electric motors, generators, pumps, gearboxes, railway axles, turbines, and helicopter transmissions. Fault diagnosis of rolling element bearings is beneficial to preventing any unexpected accident and reducing economic loss. In the past years, many bearing fault detection methods have been developed. Recently, a new adaptive signal processing method called empirical wavelet transform attracts much attention from readers and engineers and its applications to bearing fault diagnosis have been reported. The main problem of empirical wavelet transform is that Fourier segments required in empirical wavelet transform are strongly dependent on the local maxima of the amplitudes of the Fourier spectrum of a signal, which connotes that Fourier segments are not always reliable and effective if the Fourier spectrum of the signal is complicated and overwhelmed by heavy noises and other strong vibration components. In this paper, sparsity guided empirical wavelet transform is proposed to automatically establish Fourier segments required in empirical wavelet transform for fault diagnosis of rolling element bearings. Industrial bearing fault signals caused by single and multiple railway axle bearing defects are used to verify the effectiveness of the proposed sparsity guided empirical wavelet transform. Results show that the proposed method can automatically discover Fourier segments required in empirical wavelet transform and reveal single and multiple railway axle bearing defects. Besides, some comparisons with three popular signal processing methods including ensemble empirical mode decomposition, the fast kurtogram and the fast spectral correlation are conducted to highlight the superiority of the proposed method.

Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 resultedmore » 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.« less

A Short-Segment Fourier Transform Methodology

DTIC Science & Technology

2009-03-01

defined sampling of the continuous-valued discrete-time Fourier transform, superresolution in the frequency domain and allowance of Dirac delta functions associated with pure sinusoidal input data components.

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

40 CFR 98.414 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... appropriate detector, infrared (IR), fourier transform infrared (FTIR), and nuclear magnetic resonance (NMR... Compounds by Extractive Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by...

Pseudo and true visible light photocatalytic activity of nanotube titanic acid/graphene composites

NASA Astrophysics Data System (ADS)

Wang, Xiaodong; Liu, Xiaogang; Xue, Xiaoxiao; Pan, Hui; Zhang, Min; Li, Qiuye; Yu, Laigui; Yang, Jianjun; Zhang, Zhijun

2013-09-01

Nanotube titanic acid/graphene (NTA/Gr) composites were prepared by an easy hydrothermal treatment of graphene oxide (GO) and NTA in a mixed solvent of ethanol-water. As-prepared NTA/Gr composites and GO were characterized by means of Fourier transform infrared spectrometry, X-ray diffraction, diffuse-reflection spectrometry, thermal analysis, and transmission electron microscopy. Besides, the photocatalytic activities of as-prepared NTA/Gr composites were evaluated by monitoring the degradation of methyl orange (MO) under visible light irradiation. It has been found that extending hydrothermal reaction time (24 h instead of 3 h) leads to great changes in the morphology and crystal structure of as-prepared composites. Namely, the orthorhombic NTA (ca. 10 nm in diameter) in the composite transformed to anatase TiO2 particle (ca. 20-30 nm in diameter) while the Gr sheets (with micrometers-long wrinkles) in it transformed to a few Gr fragments (ca. 50 nm in diameter). Correspondingly, the NTA/Gr composite transformed to titanium dioxide/graphene (TiO2/Gr) composite. In the meantime, pure GO only has adsorption effect but it has no photocatalytic activity in the visible light region. Nevertheless, increasing Gr ratio results in enhanced visible light absorption capability and photocatalytic activity of NTA/Gr composites as well as the TiO2/Gr composites. This demonstrates that the true visible light photocatalytic activity of NTA/Gr composites as well as the TiO2/Gr composites for the degradation of MO is not as excellent as expected, and their high apparent activity is attributed to the strong adsorption of MO on the composites.

Effects of N precursor on the agglomeration and visible light photocatalytic activity of N-doped TiO2 nanocrystalline powder.

PubMed

Hu, Yulong; Liu, Hongfang; Rao, Qiuhua; Kong, Xiaodong; Sun, Wei; Guo, Xingpeng

2011-04-01

N-doped TiO2 nanocrystalline powders were prepared by the sol-gel method using various N precursors, including triethylamine, hydrazine hydrate, ethylenediamine, ammonium hydroxide, and urea. The samples were characterized by X-ray diffraction, N2 adsorption isotherms, transmission electron microscopy, ultraviolet-visible diffuse reflectance spectroscopy, Fourier transform infrared spectroscopy, and X-ray photoelectron spectroscopy. The photocatalytic activities of as-prepared samples under irradiation of visible light (lambda > 405 nm) were evaluated by photodecomposition of methyl orange. The alkalinity of N precursor was found to play a key role in the gel process. The N precursor with moderate alkalinity causes TiO2 nanoparticles to be sol-transformed into a loosely agglomerated gel. This transformation facilitates the preparation of an N-doped TiO2 powder with small nanocrystal size, large specific surface area, and high N doping level and results in high visible light photocatalytic activity. The N in TiO2 with N is binding energy at 399-400 eV may be assigned to the N-H species located in interstitial sites of TiO2 lattice which is the active N species responsible for the visible light photocatalytic activity. The N species of N 1s peak at 402 and 405 eV are ineffective to the visible light photocatalytic activity and may inhibit the photocatalytic activity. Moreover, a TiO2 nanoparticle powder with large specific area can be achieved by using urea as a template and then by using ammonium hydroxide to transform the sol into gel.

Analysis and application of Fourier transform spectroscopy in atmospheric remote sensing

NASA Technical Reports Server (NTRS)

Park, J. H.

1984-01-01

An analysis method for Fourier transform spectroscopy is summarized with applications to various types of distortion in atmospheric absorption spectra. This analysis method includes the fast Fourier transform method for simulating the interferometric spectrum and the nonlinear least-squares method for retrieving the information from a measured spectrum. It is shown that spectral distortions can be simulated quite well and that the correct information can be retrieved from a distorted spectrum by this analysis technique.

Robust alignment of chromatograms by statistically analyzing the shifts matrix generated by moving window fast Fourier transform cross-correlation.

PubMed

Zhang, Mingjing; Wen, Ming; Zhang, Zhi-Min; Lu, Hongmei; Liang, Yizeng; Zhan, Dejian

2015-03-01

Retention time shift is one of the most challenging problems during the preprocessing of massive chromatographic datasets. Here, an improved version of the moving window fast Fourier transform cross-correlation algorithm is presented to perform nonlinear and robust alignment of chromatograms by analyzing the shifts matrix generated by moving window procedure. The shifts matrix in retention time can be estimated by fast Fourier transform cross-correlation with a moving window procedure. The refined shift of each scan point can be obtained by calculating the mode of corresponding column of the shifts matrix. This version is simple, but more effective and robust than the previously published moving window fast Fourier transform cross-correlation method. It can handle nonlinear retention time shift robustly if proper window size has been selected. The window size is the only one parameter needed to adjust and optimize. The properties of the proposed method are investigated by comparison with the previous moving window fast Fourier transform cross-correlation and recursive alignment by fast Fourier transform using chromatographic datasets. The pattern recognition results of a gas chromatography mass spectrometry dataset of metabolic syndrome can be improved significantly after preprocessing by this method. Furthermore, the proposed method is available as an open source package at https://github.com/zmzhang/MWFFT2. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Implementation of the semiclassical quantum Fourier transform in a scalable system.

PubMed

Chiaverini, J; Britton, J; Leibfried, D; Knill, E; Barrett, M D; Blakestad, R B; Itano, W M; Jost, J D; Langer, C; Ozeri, R; Schaetz, T; Wineland, D J

2005-05-13

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

[Using 2-DCOS to identify the molecular spectrum peaks for the isomer in the multi-component mixture gases Fourier transform infrared analysis].

PubMed

Zhao, An-Xin; Tang, Xiao-Jun; Zhang, Zhong-Hua; Liu, Jun-Hua

2014-10-01

The generalized two-dimensional correlation spectroscopy and Fourier transform infrared were used to identify hydrocarbon isomers in the mixed gases for absorption spectra resolution enhancement. The Fourier transform infrared spectrum of n-butane and iso-butane and the two-dimensional correlation infrared spectrum of concentration perturbation were used for analysis as an example. The all band and the main absorption peak wavelengths of Fourier transform infrared spectrum for single component gas showed that the spectra are similar, and if they were mixed together, absorption peaks overlap and peak is difficult to identify. The synchronous and asynchronous spectrum of two-dimensional correlation spectrum can clearly identify the iso-butane and normal butane and their respective characteristic absorption peak intensity. Iso-butane has strong absorption characteristics spectrum lines at 2,893, 2,954 and 2,893 cm(-1), and n-butane at 2,895 and 2,965 cm(-1). The analysis result in this paper preliminary verified that the two-dimensional infrared correlation spectroscopy can be used for resolution enhancement in Fourier transform infrared spectrum quantitative analysis.

Statistical optics

NASA Astrophysics Data System (ADS)

Goodman, J. W.

This book is based on the thesis that some training in the area of statistical optics should be included as a standard part of any advanced optics curriculum. Random variables are discussed, taking into account definitions of probability and random variables, distribution functions and density functions, an extension to two or more random variables, statistical averages, transformations of random variables, sums of real random variables, Gaussian random variables, complex-valued random variables, and random phasor sums. Other subjects examined are related to random processes, some first-order properties of light waves, the coherence of optical waves, some problems involving high-order coherence, effects of partial coherence on imaging systems, imaging in the presence of randomly inhomogeneous media, and fundamental limits in photoelectric detection of light. Attention is given to deterministic versus statistical phenomena and models, the Fourier transform, and the fourth-order moment of the spectrum of a detected speckle image.

A BASIC program for the removal of noise from reaction traces using Fourier filtering.

PubMed

Brittain, T

1989-04-01

Software for the removal of noise from reaction curves using the principle of Fourier filtering has been written in BASIC to execute on a PC. The program inputs reaction traces which are subjected to a rotation-inversion process, to produce functions suitable for Fourier analysis. Fourier transformation into the frequency domain is followed by multiplication of the transform by a rectangular filter function, to remove the noise frequencies. Inverse transformation then yields a noise-reduced reaction trace suitable for further analysis. The program is interactive at each stage and could easily be modified to remove noise from a range of input data types.

Photodegradation of methyl red under visible light by mesoporous carbon nitride

NASA Astrophysics Data System (ADS)

Hu, Yueyue; Zhang, Min; Xiao, Zaozao; Jiang, Tao; Yan, Bing; Li, Jian

2018-02-01

Mesoporous carbon nitride (mpg-C3N4) with tunable microstructure has been successfully prepared through a simple polymerization reaction of cyanamide by a nano hard-templating approach. The obtained materials have been characterized using X-ray diffraction (XRD), N2 adsorption, and Fourier transform infrared (FT-IR) spectroscopy. The results show that the pore diameter of the mpg-C3N4 materials can be easily tuned from 3.8 to 10.5 nm. The mpg-C3N4 materials are demonstrated to exhibit much higher visible light photocatalytic activity than that of g-C3N4 for the degradation of aqueous methyl red (MR). The high surface areas and large pore volume contributed to the efficient visible light photocatalytic activity.

Simultaneous retrieval of atmospheric CO2 and light path modification from space-based spectroscopic observations of greenhouse gases: methodology and application to GOSAT measurements over TCCON sites.

PubMed

Oshchepkov, Sergey; Bril, Andrey; Yokota, Tatsuya; Yoshida, Yukio; Blumenstock, Thomas; Deutscher, Nicholas M; Dohe, Susanne; Macatangay, Ronald; Morino, Isamu; Notholt, Justus; Rettinger, Markus; Petri, Christof; Schneider, Matthias; Sussman, Ralf; Uchino, Osamu; Velazco, Voltaire; Wunch, Debra; Belikov, Dmitry

2013-02-20

This paper presents an improved photon path length probability density function method that permits simultaneous retrievals of column-average greenhouse gas mole fractions and light path modifications through the atmosphere when processing high-resolution radiance spectra acquired from space. We primarily describe the methodology and retrieval setup and then apply them to the processing of spectra measured by the Greenhouse gases Observing SATellite (GOSAT). We have demonstrated substantial improvements of the data processing with simultaneous carbon dioxide and light path retrievals and reasonable agreement of the satellite-based retrievals against ground-based Fourier transform spectrometer measurements provided by the Total Carbon Column Observing Network (TCCON).

Green-light-emitting electroluminescent device based on a new cadmium complex

NASA Astrophysics Data System (ADS)

Kumar, Rahul; Srivastava, Ritu; Kumar, Akshay; Kamalasanan, M. N.; Singh, K.

2010-06-01

A new cadmium complex is synthesized to investigate its stability and applicability for a luminescent device. The as-prepared Cd(Bpy)q sample is characterized by Fourier-transformed infra-red spectroscopy (FTIR), thermal gravimetric analyzer (TGA) and photoluminescence (PL). The prepared sample shows excellent thermal stability up to 380 °C. A maximum is observed at 240 nm in absorption spectra which is attributed to the π-π* transition. An organic-light-emitting diode (OLED) has been fabricated using this material. The fundamental structures of the device exhibit ITO/α-NPD/Cd(Bpy)q/BCP/Alq3/LiF/Al. The electroluminescence (EL) device emits bright green light with maximum luminescence 1683 cd/m2 at 20 V.

Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

NASA Astrophysics Data System (ADS)

Saksida, Pavle

2018-01-01

We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

40 CFR 98.224 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy. (2) ASTM D6348-03 Standard Test Method for Determination of Gaseous Compounds by Extractive Direct Interface Fourier Transform...

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.

Vibrational analysis of carbonyl modes in different stages of light-induced cyclopyrimidine dimer repair reactions

NASA Astrophysics Data System (ADS)

Schmitz, Matthias; Tavan, Paul; Nonella, Marco

2001-11-01

The formation of cyclopyrimidine dimers is a DNA defect, which is repaired by the enzyme DNA photolyase in a light-induced reaction. Radical anions of the dimers have been suggested to occur as short-lived intermediates during repair. For their identification time-resolved Fourier-transform infrared (FTIR) spectroscopy will be a method of choice. To support and guide such spectroscopic studies we have calculated the vibrational spectra of various pyrimidine compounds using density functional methods. Our results suggest that the carbonyl vibrations of these molecules can serve as marker modes to identify and distinguish intermediates of the repair reaction.

Three Dimensional Imaging of the Nucleon

NASA Astrophysics Data System (ADS)

More, Jai; Mukherjee, Asmita; Nair, Sreeraj

2018-05-01

We study the Wigner distributions of quarks and gluons in light-front dressed quark model using the overlap of light front wave functions (LFWFs). We take the target to be a dressed quark, this is a composite spin -1/2 state of quark dressed with a gluon. This state allows us to calculate the quark and gluon Wigner distributions analytically in terms of LFWFs using Hamiltonian perturbation theory. We analyze numerically the Wigner distributions of quark and gluon and report their nature in the contour plots. We use an improved numerical technique to remove the cutoff dependence of the Fourier transformed integral over \\varvec{Δ}_\\perp.

Ultrafast Dephasing and Incoherent Light Photon Echoes in Organic Amorphous Systems

NASA Astrophysics Data System (ADS)

Yano, Ryuzi; Matsumoto, Yoshinori; Tani, Toshiro; Nakatsuka, Hiroki

1989-10-01

Incoherent light photon echoes were observed in organic amorphous systems (cresyl violet in polyvinyl alcohol and 1,4-dihydroxyanthraquinone in polymethacrylic acid) by using temporally-incoherent nanosecond laser pulses. It was found that an echo decay curve of an organic amorphous system is composed of a sharp peak which decays very rapidly and a slowly decaying wing at the tail. We show that the persistent hole burning (PHB) spectra were reproduced by the Fourier-cosine transforms of the echo decay curves. We claim that in general, we must take into account the multi-level feature of the system in order to explain ultrafast dephasing at very low temperatures.

Development of a diffraction imaging flow cytometer

PubMed Central

Jacobs, Kenneth M.; Lu, Jun Q.

2013-01-01

Diffraction images record angle-resolved distribution of scattered light from a particle excited by coherent light and can correlate highly with the 3D morphology of a particle. We present a jet-in-fluid design of flow chamber for acquisition of clear diffraction images in a laminar flow. Diffraction images of polystyrene spheres of different diameters were acquired and found to correlate highly with the calculated ones based on the Mie theory. Fast Fourier transform analysis indicated that the measured images can be used to extract sphere diameter values. These results demonstrate the significant potentials of high-throughput diffraction imaging flow cytometry for extracting 3D morphological features of cells. PMID:19794790

Use of the fractional Fourier transform in {pi}/2 converters of laser modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Malyutin, A A

2004-02-28

The possibility of using the fractional Fourier transform (FrFT) in optical schemes for astigmatic {pi}/2 converters of Hermite-Gaussian modes to donut Laguerre-Gaussian modes is considered. Several schemes of converters based on the FrFT of the half-integer and irrational orders are presented. The lowest FrFT order than can be used in astigmatic mode converters is found. The properties of converters based on the fractional and ordinary Fourier transforms are compared. (laser beams)

Restoration algorithms for imaging through atmospheric turbulence

DTIC Science & Technology

2017-02-18

the Fourier spectrum of each frame. The reconstructed image is then obtained by taking the inverse Fourier transform of the average of all processed...with wipξq “ Gσp|Fpviqpξq|pq řM j“1Gσp|Fpvjqpξq|pq , where F denotes the Fourier transform (ξ are the frequencies) and Gσ is a Gaussian filter of...a combination of SIFT [26] and ORSA [14] algorithms) in order to remove affine transformations (translations, rotations and homothety). The authors

Tomography: Three Dimensional Image Construction. Applications of Analysis to Medical Radiology. [and] Genetic Counseling. Applications of Probability to Medicine. [and] The Design of Honeycombs. Applications of Differential Equations to Biology. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 318, 456, 502.

ERIC Educational Resources Information Center

Solomon, Frederick; And Others.

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

A laboratory demonstration of high-resolution hard X-ray and gamma-ray imaging using Fourier-transform techniques

NASA Technical Reports Server (NTRS)

Palmer, David; Prince, Thomas A.

1987-01-01

A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard X-ray and gamma-ray imaging, with particular emphasis on possible applications to high-energy astronomy. Considerations for the design of a Fourier-transform imager and the instrumentation used in the laboratory studies is described. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented.

Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.

PubMed

Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene

2017-08-01

Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.

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.

VLSI Implementation of Digital Fourier Transforms.

DTIC Science & Technology

1982-11-01

If we use this lemna and the identities (29) and (30) to expand (34). we arrive at ",)(l., , )BR l - ) • • , ,, - - , (36) :.:"s "’" n -( 01)/(L...moving potential wells, that travel along the surface of the silicon crystal. Information is contained as a packet of minority carriers in these moving...drain areas (figure 29). Charge coupled devices on the other hand move minority carriers through lightly doped substrate regions close to the surface. The

Apparatus and Method for Measuring Strain in Optical Fibers using Rayleigh Scatter

NASA Technical Reports Server (NTRS)

Froggatt, Mark E. (Inventor); Moore, Jason P. (Inventor)

2003-01-01

An apparatus and method for measuring strain in an optical fiber using the spectral shift of Rayleigh scattered light. The interference pattern produced by an air gap reflector and backscattered radiation is measured. Using Fourier Transforms, the spectrum of any section of fiber can be extracted. Cross correlation with an unstrained measurement produces a correlation peak. The location of the correlation peak indicates the strain level in the selected portion of optical fiber.

Evaluation of photostability of solid-state nicardipine hydrochloride polymorphs by using Fourier-transformed reflection-absorption infrared spectroscopy - effect of grinding on the photostability of crystal form.

PubMed

Teraoka, Reiko; Otsuka, Makoto; Matsuda, Yoshihisa

2004-11-22

Photostability and physicochemical properties of nicardipine hydrochloride polymorphs (alpha- and beta-form) were studied by using Fourier-transformed reflection-absorption infrared spectroscopy (FT-IR-RAS) of the tablets, X-ray powder diffraction analysis, differential scanning calorimetry (DSC), and color difference measurement. It was clear from the results of FT-IR-RAS spectra after irradiation that nicardipine hydrochloride in the solid state decomposed to its pyridine derivative when exposed to light. The photostability of the ground samples of two forms was also measured in the same manner. The two crystalline forms of the drug changed to nearly amorphous form after 150 min grinding in a mixer mill. X-ray powder diffraction patterns of those ground samples showed almost halo patterns. The nicardipine hydrochloride content on the surface of the tablet was determined based on the absorbance at 1700 cm(-1) attributable to the C=O stretch vibration in FT-IR-RAS spectra before and after irradiation by fluorescent lamp (3500 lx). The photodegradation followed apparently the first-order kinetics for any sample. The apparent photodegradation rate constant of beta-form was greater than that of alpha-form. The ground samples decomposed rapidly under the same light irradiation as compared with the intact crystalline forms. The photodegradation rate constant decreased with increase of the heat of fusion. copyright 2004 Elsevier B.V.

A Fourier-Transform Infrared Study of Biochar Aging in Soils

PubMed Central

Singh, B.; Fang, Y.; Johnston, C.T.

2018-01-01

We used diffuse reflectance Fourier-transform infrared (DR-FTIR) spectroscopy, X-ray diffraction (XRD), and chemical and isotopic analyses to characterize the light fraction of four contrasting soils (control and biocharamended soils) to determine changes in biochar properties after aging. Two Eucalyptus saligna Sm. wood biochars, produced at 450°C (B450) and 550°C (B550), were incubated separately in each of the four soils for up to 12 mo at 20, 40, and 60°C. Total C and isotopic (δ13C) methods were used to quantify the amounts of biochar C and native C mineralized during incubation. The DR-FTIR spectra of the light fraction showed distinct absorption bands representing native soil organic C, biochar C, and mineral constituents present in the soils; the mineral bands were consistent with XRD data of the clay fraction of the four soils. Analysis of the DR-FTIR spectra in the ν(C–H) bands showed that the ratio of the aromatic ν(C–H) bands systematically increased relative to the aliphatic ν(C–H) bands with increasing mineralization of biochar C in the B550 amended soils, and this relationship was unique for each soil type. In contrast, this relationship was not observed for the B450 amended soils that contained a relatively smaller proportion of aromatic C. PMID:29657354

Effects of light wavelengths on extracellular and capsular polysaccharide production by Nostoc flagelliforme.

PubMed

Han, Pei-pei; Sun, Ying; Jia, Shi-ru; Zhong, Cheng; Tan, Zhi-lei

2014-05-25

The influences of different wavelengths of light (red 660nm, yellow 590nm, green 520nm, blue 460nm, purple 400nm) and white light on extracellular polysaccharide (EPS) and capsular polysaccharide (CPS) production by Nostoc flagelliforme in liquid culture were demonstrated in this study. The results showed that, compared with white light, red and blue lights significantly increased both EPS and CPS production while yellow light reduced their production; purple and green lights stimulated EPS production but inhibited CPS formation. Nine constituent monosaccharides and one uronic acid were detected in both EPS and CPS, and their ratios showed significant differences among treatment with different light wavelengths. However, the advanced structure of EPS and CPS from various light conditions did not present obvious difference through Fourier transform infrared spectroscopy and X-ray diffraction characterization. These findings establish a basis for development of high-yielding polysaccharide production process and understanding their regulation. Copyright © 2014 Elsevier Ltd. All rights reserved.

Extremely simple holographic projection of color images

NASA Astrophysics Data System (ADS)

Makowski, Michal; Ducin, Izabela; Kakarenko, Karol; Suszek, Jaroslaw; Kolodziejczyk, Andrzej; Sypek, Maciej

2012-03-01

A very simple scheme of holographic projection is presented with some experimental results showing good quality image projection without any imaging lens. This technique can be regarded as an alternative to classic projection methods. It is based on the reconstruction real images from three phase iterated Fourier holograms. The illumination is performed with three laser beams of primary colors. A divergent wavefront geometry is used to achieve an increased throw angle of the projection, compared to plane wave illumination. Light fibers are used as light guidance in order to keep the setup as simple as possible and to provide point-like sources of high quality divergent wave-fronts at optimized position against the light modulator. Absorbing spectral filters are implemented to multiplex three holograms on a single phase-only spatial light modulator. Hence color mixing occurs without any time-division methods, which cause rainbow effects and color flicker. The zero diffractive order with divergent illumination is practically invisible and speckle field is effectively suppressed with phase optimization and time averaging techniques. The main advantages of the proposed concept are: a very simple and highly miniaturizable configuration; lack of lens; a single LCoS (Liquid Crystal on Silicon) modulator; a strong resistance to imperfections and obstructions of the spatial light modulator like dead pixels, dust, mud, fingerprints etc.; simple calculations based on Fast Fourier Transform (FFT) easily processed in real time mode with GPU (Graphic Programming).

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2013 CFR

2013-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR 98.54 - Monitoring and QA/QC requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

... Inorganic Emissions by Extractive Fourier Transform Infrared (FTIR) Spectroscopy in 40 CFR part 63, Appendix... Direct Interface Fourier Transform Infrared (FTIR) Spectroscopy (incorporated by reference, see § 98.7...

40 CFR Appendix B to Subpart Uuuuu... - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2014 CFR

2014-07-01

... extractive Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novales-Sanchez, H.; Toscano, J. J.

A five-dimensional pure Yang-Mills theory, with the fifth coordinate compactified on the orbifold S{sup 1}/Z{sub 2} of radius R, leads to a four-dimensional theory which is governed by two types of infinitesimal gauge transformations, namely, the well-known standard gauge transformations (SGT) dictated by the SU{sub 4}(N) group under which the zero Fourier modes A{sub {mu}}{sup (0)a} transform as gauge fields, and a set of nonstandard gauge transformations (NSGT) determining the gauge nature of the Kaluza-Klein (KK) excitations A{sub {mu}}{sup (m)a}. By using a SGT-covariant gauge-fixing procedure for removing the degeneration associated with the NSGT, we integrate out the KK excitationsmore » and obtain a low-energy effective Lagrangian expansion involving all of the independent canonical-dimension-six operators that are invariant under the SGT of the SU{sub 4}(N) group and that are constituted by light gauge fields, A{sub {mu}}{sup (0)a}, exclusively. It is shown that this effective Lagrangian is invariant under the SGT, but it depends on the gauge-fixing of the gauge KK excitations. Our result shows explicitly that the one-loop contributions of the KK excitations to light (standard) Green's functions are renormalizable.« less

High Accuracy Evaluation of the Finite Fourier Transform Using Sampled Data

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

1997-01-01

Many system identification and signal processing procedures can be done advantageously in the frequency domain. A required preliminary step for this approach is the transformation of sampled time domain data into the frequency domain. The analytical tool used for this transformation is the finite Fourier transform. Inaccuracy in the transformation can degrade system identification and signal processing results. This work presents a method for evaluating the finite Fourier transform using cubic interpolation of sampled time domain data for high accuracy, and the chirp Zeta-transform for arbitrary frequency resolution. The accuracy of the technique is demonstrated in example cases where the transformation can be evaluated analytically. Arbitrary frequency resolution is shown to be important for capturing details of the data in the frequency domain. The technique is demonstrated using flight test data from a longitudinal maneuver of the F-18 High Alpha Research Vehicle.

3-D surface profilometry based on modulation measurement by applying wavelet transform method

NASA Astrophysics Data System (ADS)

Zhong, Min; Chen, Feng; Xiao, Chao; Wei, Yongchao

2017-01-01

A new analysis of 3-D surface profilometry based on modulation measurement technique by the application of Wavelet Transform method is proposed. As a tool excelling for its multi-resolution and localization in the time and frequency domains, Wavelet Transform method with good localized time-frequency analysis ability and effective de-noizing capacity can extract the modulation distribution more accurately than Fourier Transform method. Especially for the analysis of complex object, more details of the measured object can be well remained. In this paper, the theoretical derivation of Wavelet Transform method that obtains the modulation values from a captured fringe pattern is given. Both computer simulation and elementary experiment are used to show the validity of the proposed method by making a comparison with the results of Fourier Transform method. The results show that the Wavelet Transform method has a better performance than the Fourier Transform method in modulation values retrieval.

40 CFR Appendix B to Subpart Uuuuu - -HCl and HF Monitoring Provisions

Code of Federal Regulations, 2012 CFR

2012-07-01

... Fourier Transform Infrared Spectroscopy (FTIR) continuous emissions monitoring systems in appendix B to... Fourier Transform Infrared (FTIR) Spectroscopy” (incorporated by reference, see § 63.14), each applied...

An Evaluation of the Environmental Fate and Behavior of Munitions Materiel (Tetryl and Polar Metabolites of TNT) in Soil and Plant Systems. Environmental Fate and Behavior of Tetryl

DTIC Science & Technology

1992-03-01

attempted to verify product identity and purity by GC with either Fourier transform infrared spectro.icopy (FTIR) or mass spectroscopy (MS) detection...ýl0 5 In-1 z U)-’i0oo -3g’i o -6o0 626o a i60 ito1 2i oo I ’ o [JfnVENUII8ER (cm- FIGURE 3,9. Fourier Transform Infrared Spectroscopy Spectrum of...Fourier Transform Infrared Spectroscopy Spectrum of Tetryl I-I F1U~IGUR Fourier Utransformlfret Spcrop S ectrum of TeasomtinPoutrl 0 , -39 i : : : -. . i

All-photonic drying and sintering process via flash white light combined with deep-UV and near-infrared irradiation for highly conductive copper nano-ink

PubMed Central

Hwang, Hyun-Jun; Oh, Kyung-Hwan; Kim, Hak-Sung

2016-01-01

We developed an ultra-high speed photonic sintering method involving flash white light (FWL) combined with near infrared (NIR) and deep UV light irradiation to produce highly conductive copper nano-ink film. Flash white light irradiation energy and the power of NIR/deep UV were optimized to obtain high conductivity Cu films. Several microscopic and spectroscopic characterization techniques such as scanning electron microscopy (SEM), a x-ray diffraction (XRD), and Fourier-transform infrared (FT-IR) spectroscopy were employed to characterize the Cu nano-films. Optimally sintered Cu nano-ink films produced using a deep UV-assisted flash white light sintering technique had the lowest resistivity (7.62 μΩ·cm), which was only 4.5-fold higher than that of bulk Cu film (1.68 μΩ•cm). PMID:26806215

All-photonic drying and sintering process via flash white light combined with deep-UV and near-infrared irradiation for highly conductive copper nano-ink.

PubMed

Hwang, Hyun-Jun; Oh, Kyung-Hwan; Kim, Hak-Sung

2016-01-25

We developed an ultra-high speed photonic sintering method involving flash white light (FWL) combined with near infrared (NIR) and deep UV light irradiation to produce highly conductive copper nano-ink film. Flash white light irradiation energy and the power of NIR/deep UV were optimized to obtain high conductivity Cu films. Several microscopic and spectroscopic characterization techniques such as scanning electron microscopy (SEM), a x-ray diffraction (XRD), and Fourier-transform infrared (FT-IR) spectroscopy were employed to characterize the Cu nano-films. Optimally sintered Cu nano-ink films produced using a deep UV-assisted flash white light sintering technique had the lowest resistivity (7.62 μΩ·cm), which was only 4.5-fold higher than that of bulk Cu film (1.68 μΩ•cm).

Adaptive DFT-Based Interferometer Fringe Tracking

NASA Astrophysics Data System (ADS)

Wilson, Edward; Pedretti, Ettore; Bregman, Jesse; Mah, Robert W.; Traub, Wesley A.

An automatic interferometer fringe tracking system has been developed, implemented, and tested at the Infrared Optical Telescope Array (IOTA) Observatory at Mount Hopkins, Arizona. The system can minimize the optical path differences (OPDs) for all three baselines of the Michelson stellar interferometer at IOTA. Based on sliding window discrete Fourier-transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on offline data. Implemented in ANSI C on the 266 MHz PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately 2.0 milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. The adaptive DFT-based tracking algorithm should be applicable to other systems where there is a need to detect or track a signal with an approximately constant-frequency carrier pulse. One example of such an application might be to the field of thin-film measurement by ellipsometry, using a broadband light source and a Fourier-transform spectrometer to detect the resulting fringe patterns.

Image encryption based on fractal-structured phase mask in fractional Fourier transform domain

NASA Astrophysics Data System (ADS)

Zhao, Meng-Dan; Gao, Xu-Zhen; Pan, Yue; Zhang, Guan-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-04-01

We present an optical encryption approach based on the combination of fractal Fresnel lens (FFL) and fractional Fourier transform (FrFT). Our encryption approach is in fact a four-fold encryption scheme, including the random phase encoding produced by the Gerchberg–Saxton algorithm, a FFL, and two FrFTs. A FFL is composed of a Sierpinski carpet fractal plate and a Fresnel zone plate. In our encryption approach, the security is enhanced due to the more expandable key spaces and the use of FFL overcomes the alignment problem of the optical axis in optical system. Only using the perfectly matched parameters of the FFL and the FrFT, the plaintext can be recovered well. We present an image encryption algorithm that from the ciphertext we can get two original images by the FrFT with two different phase distribution keys, obtained by performing 100 iterations between the two plaintext and ciphertext, respectively. We test the sensitivity of our approach to various parameters such as the wavelength of light, the focal length of FFL, and the fractional orders of FrFT. Our approach can resist various attacks.

Research of transmissive near infrared spectroscopy for non-invasive blood glucose measurement

NASA Astrophysics Data System (ADS)

Yang, Wenming; Liao, Ningfang; Li, Yasheng; Shao, Liwei; Huang, Dehuang

2016-10-01

Near infrared (NIR) has prospectively applied in non-invasive blood glucose measurement due to glucose absorption among the 1.0-2.5m spectral bands. However, this significant technology is hard to be developed because of other blood components and low signal-to-noise ratio (SNR). In this work, we presented a non-invasive glucose measurement system using Fourier transform spectrometer which will work in fingertips or other human body tissues. A refrigerated InGaAs detector with high quantum efficiency performing well in the range of 1.0-1.7μm wavelength is used to acquire transmissive radiation. Preliminary experiment investigations were set up to test glucose levels of aqueous solutions with different concentrations. The analytical modeling of the interferogram data is based on arithmetic Fourier transform and supported by the curvilineal characterization. Experimental results show the variation of light intensity among different glucose concentrations and emphasize the obvious absorption of glucose in NIR wave-range. This study confirms the suitability that NIR can be developed in non-invasive glucose measurement.

Fast precalculated triangular mesh algorithm for 3D binary computer-generated holograms.

PubMed

Yang, Fan; Kaczorowski, Andrzej; Wilkinson, Tim D

2014-12-10

A new method for constructing computer-generated holograms using a precalculated triangular mesh is presented. The speed of calculation can be increased dramatically by exploiting both the precalculated base triangle and GPU parallel computing. Unlike algorithms using point-based sources, this method can reconstruct a more vivid 3D object instead of a "hollow image." In addition, there is no need to do a fast Fourier transform for each 3D element every time. A ferroelectric liquid crystal spatial light modulator is used to display the binary hologram within our experiment and the hologram of a base right triangle is produced by utilizing just a one-step Fourier transform in the 2D case, which can be expanded to the 3D case by multiplying by a suitable Fresnel phase plane. All 3D holograms generated in this paper are based on Fresnel propagation; thus, the Fresnel plane is treated as a vital element in producing the hologram. A GeForce GTX 770 graphics card with 2 GB memory is used to achieve parallel computing.

Evaluation of parameters of a plankton community's biological rhythms under the natural environment of the Black Sea using the Fourier transform method.

PubMed

Mel'nikova, Ye B

2017-05-01

Night-time changes in bioluminescence intensity in the coastal area of the Black Sea were recorded. It was noted that the biomass of luminous organisms is closely correlated with the biomass of plankton and other pelagic organisms, including commercial pelagic fish. The parameters of plankton communities' basic biological rhythms were determined using the discrete Fourier transform method. These rhythms were manifest as spatial and temporal changes in the bioluminescence intensity. It was shown that changes in the bioluminescence intensity over a 14.0-h period were due to the duration of the light/dark cycles. By contrast, changes in bioluminescence intensity with periods of 4.7 and 2.8 h were due to the endogenous rhythms of the plankton community (feeding and cell division). An original method for evaluating of errors in the calculated periods of the biological rhythms was proposed. A strong correlation (r = 0.906) was observed between the measured and calculated values for the bioluminescence intensity, which provided support for the assumptions made. Copyright © 2016 John Wiley & Sons, Ltd.

Adaptive DFT-Based Interferometer Fringe Tracking

NASA Astrophysics Data System (ADS)

Wilson, Edward; Pedretti, Ettore; Bregman, Jesse; Mah, Robert W.; Traub, Wesley A.

2005-12-01

An automatic interferometer fringe tracking system has been developed, implemented, and tested at the Infrared Optical Telescope Array (IOTA) Observatory at Mount Hopkins, Arizona. The system can minimize the optical path differences (OPDs) for all three baselines of the Michelson stellar interferometer at IOTA. Based on sliding window discrete Fourier-transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on offline data. Implemented in ANSI C on the 266 MHz PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately [InlineEquation not available: see fulltext.] milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. The adaptive DFT-based tracking algorithm should be applicable to other systems where there is a need to detect or track a signal with an approximately constant-frequency carrier pulse. One example of such an application might be to the field of thin-film measurement by ellipsometry, using a broadband light source and a Fourier-transform spectrometer to detect the resulting fringe patterns.

Quest for secondary μSR signals for Fe3O4 using MaxEnt: a Verwey phase transition study.

NASA Astrophysics Data System (ADS)

Boekema, C.; Colebaugh, A.; Lee, A.-L.; Lin, I.; Cabot, A.; Morante, C.

Most muon-spin rotation (μSR) time series for magnetite (Fe3O4) have been interpreted in terms of one μSR frequency signal. Its Fourier transform appears to confirm this internal magnetic field. Yet many time series show a beat pattern, strongly suggesting a second signal with a close-by frequency. We are searching for secondary signals in zero-field Fe3O4 μ SR data using Maximum Entropy, a recently developed technique more sensitive than curve fitting and/or Fourier transformation. There is also another dilemma namely: the upper signal found for Fe3O4 has a local magnetic field larger than the maximum allowable vectorial sum of external and internal contributions. However, the (non)occurrence of secondary signals may shed light on the nature of the Verwey phase transition and its precursors in the Fe3O4 Mott-Wigner glass between Tv (123 K) and twice Tv (247 K). Research supported by LANL-DOE, SETI-NASA, SJSU & AFC.

Hydrogen and Nitrogen Broadened Ethane and Propane Absorption Cross Sections

NASA Astrophysics Data System (ADS)

Hargreaves, Robert J.; Appadoo, Dominique; Billinghurst, Brant E.; Bernath, Peter F.

2015-06-01

High-resolution infrared absorption cross sections are presented for the ν9 band of ethane (C2H6) at 823 cm-1. These cross sections make use of spectra recorded at the Australian Synchrotron using a Fourier transform infrared spectrometer with maximum resolution of 0.00096 cm-1. The spectra have been recorded at 150, 120 and 90 K for hydrogen and nitrogen broadened C2H6. They cover appropriate temperatures, pressures and broadening gases associated with the atmospheres of the Outer Planets and Titan, and will improve atmospheric retrievals. The THz/Far-IR beamline at the Australian Synchrotron is unique in combining a high-resolution Fourier transform spectrometer with an 'enclosive flow cooling' (EFC) cell designed to study molecules at low temperatures. The EFC cell is advantageous at temperatures for which the vapor pressure is very low, such as C2H6 at 90 K. Hydrogen broadened absorption cross sections of propane between 700 and 1200 cm-1 will also be presented based on spectra obtained at the Canadian Light Source.

A general purpose wideband optical spatial frequency spectrum analyzer

NASA Technical Reports Server (NTRS)

Ballard, G. S.; Mellor, F. A.

1972-01-01

The light scattered at various angles by a transparent media is studied. An example of these applications is the optical Fourier spectrum measurement resulting from various spatial frequencies which were recorded on a photographic emulsion. A method for obtaining these measurements consists of illuminating the test object with parallel monochromatic light. A stationary lens, placed in the resulting wavefield at a distance of one focal length from the object, will focus parallel waves emanating from the test object at a point lying in the focal plane of the lens. A light detector with a small filtering aperture is then used to measure the intensity variation of the light in the focal or transform plane of the lens. Such measurements require the use of a lens which is highly corrected for all of the common aberrations except chromatic aberration.

Secure Image Transmission over DFT-precoded OFDM-VLC systems based on Chebyshev Chaos scrambling

NASA Astrophysics Data System (ADS)

Wang, Zhongpeng; Qiu, Weiwei

2017-08-01

This paper proposes a physical layer image secure transmission scheme for discrete Fourier transform (DFT) precoded OFDM-based visible light communication systems by using Chebyshev chaos maps. In the proposed scheme, 256 subcarriers and QPSK modulation are employed. The transmitted digital signal of the image is encrypted with a Chebyshev chaos sequence. The encrypted signal is then transformed by a DFT precoding matrix to reduce the PAPR of the OFDM signal. After that, the encrypted and DFT-precoded OFDM are transmitted over a VLC channel. The simulation results show that the proposed image security transmission scheme can not only protect the DFT-precoded OFDM-based VLC from eavesdroppers but also improve BER performance.

Spectral ballistic imaging: a novel technique for viewing through turbid or obstructing media.

PubMed

Granot, Er'el; Sternklar, Shmuel

2003-08-01

We propose a new method for viewing through turbid or obstructing media. The medium is illuminated with a modulated cw laser and the amplitude and phase of the transmitted (or reflected) signal is measured. This process takes place for a set of wavelengths in a certain wide band. In this way we acquire the Fourier transform of the temporal output. With this information we can reconstruct the temporal shape of the transmitted signal by computing the inverse transform. The proposed method benefits from the advantages of the first-light technique: high resolution, simple algorithms, insensitivity to boundary condition, etc., without suffering from its main deficiencies: complex and expensive equipment.

Method for extracting long-equivalent wavelength interferometric information

NASA Technical Reports Server (NTRS)

Hochberg, Eric B. (Inventor)

1991-01-01

A process for extracting long-equivalent wavelength interferometric information from a two-wavelength polychromatic or achromatic interferometer. The process comprises the steps of simultaneously recording a non-linear sum of two different frequency visible light interferograms on a high resolution film and then placing the developed film in an optical train for Fourier transformation, low pass spatial filtering and inverse transformation of the film image to produce low spatial frequency fringes corresponding to a long-equivalent wavelength interferogram. The recorded non-linear sum irradiance derived from the two-wavelength interferometer is obtained by controlling the exposure so that the average interferogram irradiance is set at either the noise level threshold or the saturation level threshold of the film.

High-resolution Fourier transform synchrotron spectroscopy of the C-S stretching band of methyl mercaptan, CH332SH

NASA Astrophysics Data System (ADS)

Lees, R. M.; Xu, Li-Hong; Billinghurst, B. E.

2016-01-01

The C-S stretching fundamental band of 12CH332SH, the principal isotopologue of methyl mercaptan, has been investigated by Fourier transform infrared spectroscopy on the Far-Infrared beamline at the Canadian Light Source synchrotron. The band is centered around 710 cm-1 and shows well-resolved a-type parallel structure. Most of the A and E spectral sub-bands have been assigned up to K = 12 for the vt = 0 torsional state and K = 9 for the vt = 1 state, along with a smaller variety of sub-bands for vt = 2. C-S stretching energy term values have been determined employing known ground-state energies, and have been fitted to series expansions in powers of J(J + 1) to determine the substate origins. The origins have in turn been fitted to a Fourier model to characterize the oscillatory torsional energy structure of the C-S stretching state. The amplitude of oscillation of the vt = 0 torsional curves is significantly larger for the C-S stretch state compared to the ground state. A strategy devised to relate this amplitude to an effective torsional barrier height indicates a decrease of about 7% in the effective V3 for the C-S stretch. The vibrational frequency determined for the stretching fundamental from the Fourier fit is 710.3 cm-1. The C-S stretching manifold is crossed by excited vt = 4 torsional levels of the ground state, and strong torsion-vibrational resonant coupling is observed via perturbations in the spectrum together with forbidden sub-bands induced by mixing and intensity borrowing.

Synthesis, Analysis, and Processing of Fractal Signals

DTIC Science & Technology

1991-10-01

coordinator in hockey, squash, volleyball, and softball, but also for reminding me periodically that 1/f noise can exist outside a computer. More...similar signals as Fourier-based representations are for stationary and periodic signals. Furthermore, because wave- let transformations can be...and periodic signals. Furthermore, just as the discovery of fast Fourier transform (FFT) algorithms dramatically increased the viability the Fourier

Wavelets

NASA Astrophysics Data System (ADS)

Strang, Gilbert

1994-06-01

Several methods are compared that are used to analyze and synthesize a signal. Three ways are mentioned to transform a symphony: into cosine waves (Fourier transform), into pieces of cosines (short-time Fourier transform), and into wavelets (little waves that start and stop). Choosing the best basis, higher dimensions, fast wavelet transform, and Daubechies wavelets are discussed. High-definition television is described. The use of wavelets in identifying fingerprints in the future is related.

Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.

PubMed

Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing

2016-10-01

The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.

Applying wavelet transforms to analyse aircraft-measured turbulence and turbulent fluxes in the atmospheric boundary layer over eastern Siberia

NASA Astrophysics Data System (ADS)

Strunin, M. A.; Hiyama, T.

2004-11-01

The wavelet spectral method was applied to aircraft-based measurements of atmospheric turbulence obtained during joint Russian-Japanese research on the atmospheric boundary layer near Yakutsk (eastern Siberia) in April-June 2000. Practical ways to apply Fourier and wavelet methods for aircraft-based turbulence data are described. Comparisons between Fourier and wavelet transform results are shown and they demonstrate, in conjunction with theoretical and experimental restrictions, that the Fourier transform method is not useful for studying non-homogeneous turbulence. The wavelet method is free from many disadvantages of Fourier analysis and can yield more informative results. Comparison of Fourier and Morlet wavelet spectra showed good agreement at high frequencies (small scales). The quality of the wavelet transform and corresponding software was estimated by comparing the original data with restored data constructed with an inverse wavelet transform. A Haar wavelet basis was inappropriate for the turbulence data; the mother wavelet function recommended in this study is the Morlet wavelet. Good agreement was also shown between variances and covariances estimated with different mathematical techniques, i.e. through non-orthogonal wavelet spectra and through eddy correlation methods.

A Comparison of FTNMR and FTIR Techniques.

ERIC Educational Resources Information Center

Ahn, Myong-Ku

1989-01-01

Nuclear magnetic resonance and infrared are two spectroscopic methods that commonly use the Fourier transform technique. Discussed are the similarities and differences in the use of the Fourier transform in these two spectroscopic techniques. (CW)

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.

Novel hybrid optical correlator: theory and optical simulation.

PubMed

Casasent, D; Herold, R L

1975-02-01

The inverse transform of the product of two Fourier transform holograms is analyzed and shown to contain the correlation of the two images from which the holograms were formed. The theory, analysis, and initial experimental demonstration of the feasibility of a novel correlation scheme using this multiplied Fourier transform hologram system are presented.

Fast algorithm for chirp transforms with zooming-in ability and its applications.

PubMed

Deng, X; Bihari, B; Gan, J; Zhao, F; Chen, R T

2000-04-01

A general fast numerical algorithm for chirp transforms is developed by using two fast Fourier transforms and employing an analytical kernel. This new algorithm unifies the calculations of arbitrary real-order fractional Fourier transforms and Fresnel diffraction. Its computational complexity is better than a fast convolution method using Fourier transforms. Furthermore, one can freely choose the sampling resolutions in both x and u space and zoom in on any portion of the data of interest. Computational results are compared with analytical ones. The errors are essentially limited by the accuracy of the fast Fourier transforms and are higher than the order 10(-12) for most cases. As an example of its application to scalar diffraction, this algorithm can be used to calculate near-field patterns directly behind the aperture, 0 < or = z < d2/lambda. It compensates another algorithm for Fresnel diffraction that is limited to z > d2/lambdaN [J. Opt. Soc. Am. A 15, 2111 (1998)]. Experimental results from waveguide-output microcoupler diffraction are in good agreement with the calculations.

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

PubMed

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

3D Imaging with Holographic Tomography

NASA Astrophysics Data System (ADS)

Sheppard, Colin J. R.; Kou, Shan Shan

2010-04-01

There are two main types of tomography that enable the 3D internal structures of objects to be reconstructed from scattered data. The commonly known computerized tomography (CT) give good results in the x-ray wavelength range where the filtered back-projection theorem and Radon transform can be used. These techniques rely on the Fourier projection-slice theorem where rays are considered to propagate straight through the object. Another type of tomography called `diffraction tomography' applies in applications in optics and acoustics where diffraction and scattering effects must be taken into account. The latter proves to be a more difficult problem, as light no longer travels straight through the sample. Holographic tomography is a popular way of performing diffraction tomography and there has been active experimental research on reconstructing complex refractive index data using this approach recently. However, there are two distinct ways of doing tomography: either by rotation of the object or by rotation of the illumination while fixing the detector. The difference between these two setups is intuitive but needs to be quantified. From Fourier optics and information transformation point of view, we use 3D transfer function analysis to quantitatively describe how spatial frequencies of the object are mapped to the Fourier domain. We first employ a paraxial treatment by calculating the Fourier transform of the defocused OTF. The shape of the calculated 3D CTF for tomography, by scanning the illumination in one direction only, takes on a form that we might call a 'peanut,' compared to the case of object rotation, where a diablo is formed, the peanut exhibiting significant differences and non-isotropy. In particular, there is a line singularity along one transverse direction. Under high numerical aperture conditions, the paraxial treatment is not accurate, and so we make use of 3D analytical geometry to calculate the behaviour in the non-paraxial case. This time, we obtain a similar peanut, but without the line singularity.

Experimental image alignment system

NASA Technical Reports Server (NTRS)

Moyer, A. L.; Kowel, S. T.; Kornreich, P. G.

1980-01-01

A microcomputer-based instrument for image alignment with respect to a reference image is described which uses the DEFT sensor (Direct Electronic Fourier Transform) for image sensing and preprocessing. The instrument alignment algorithm which uses the two-dimensional Fourier transform as input is also described. It generates signals used to steer the stage carrying the test image into the correct orientation. This algorithm has computational advantages over algorithms which use image intensity data as input and is suitable for a microcomputer-based instrument since the two-dimensional Fourier transform is provided by the DEFT sensor.

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 and global contrast interferometer alignment methods

DOEpatents

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.

A fast D.F.T. algorithm using complex integer transforms

NASA Technical Reports Server (NTRS)

Reed, I. S.; Truong, T. K.

1978-01-01

Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.

A High Resolution Fourier-Transform Spectrometer for the Measurement of Atmospheric Column Abundances

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).

Technique for the metrology calibration of a Fourier transform spectrometer

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.

Atomic Gaussian type orbitals and their Fourier transforms via the Rayleigh expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yükçü, Niyazi

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 propertiesmore » 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.« less

Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

PubMed

van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

2015-12-01

Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

Component analyses of urinary nanocrystallites of uric acid stone formers by combination of high-resolution transmission electron microscopy, fast Fourier transformation, energy dispersive X-ray spectroscopy, X-ray diffraction and Fourier transform infrared spectroscopy.

PubMed

Sun, Xin-Yuan; Xue, Jun-Fa; Xia, Zhi-Yue; Ouyang, Jian-Ming

2015-06-01

This study aimed to analyse the components of nanocrystallites in urines of patients with uric acid (UA) stones. X-ray diffraction (XRD), Fourier transform infrared spectroscopy, high-resolution transmission electron microscopy (HRTEM), fast Fourier transformation (FFT) of HRTEM, and energy dispersive X-ray spectroscopy (EDS) were performed to analyse the components of these nanocrystallites. XRD and FFT showed that the main component of urinary nanocrystallites was UA, which contains a small amount of calcium oxalate monohydrate and phosphates. EDS showed the characteristic absorption peaks of C, O, Ca and P. The formation of UA stones was closely related to a large number of UA nanocrystallites in urine. A combination of HRTEM, FFT, EDS and XRD analyses could be performed accurately to analyse the components of urinary nanocrystallites.

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.

Single Channel Quantum Color Image Encryption Algorithm Based on HSI Model and Quantum Fourier Transform

NASA Astrophysics Data System (ADS)

Gong, Li-Hua; He, Xiang-Tao; Tan, Ru-Chao; Zhou, Zhi-Hong

2018-01-01

In order to obtain high-quality color images, it is important to keep the hue component unchanged while emphasize the intensity or saturation component. As a public color model, Hue-Saturation Intensity (HSI) model is commonly used in image processing. A new single channel quantum color image encryption algorithm based on HSI model and quantum Fourier transform (QFT) is investigated, where the color components of the original color image are converted to HSI and the logistic map is employed to diffuse the relationship of pixels in color components. Subsequently, quantum Fourier transform is exploited to fulfill the encryption. The cipher-text is a combination of a gray image and a phase matrix. Simulations and theoretical analyses demonstrate that the proposed single channel quantum color image encryption scheme based on the HSI model and quantum Fourier transform is secure and effective.

Method and apparatus for aerosol particle absorption spectroscopy

DOEpatents

Campillo, Anthony J.; Lin, Horn-Bond

1983-11-15

A method and apparatus for determining the absorption spectra, and other properties, of aerosol particles. A heating beam source provides a beam of electromagnetic energy which is scanned through the region of the spectrum which is of interest. Particles exposed to the heating beam which have absorption bands within the band width of the heating beam absorb energy from the beam. The particles are also illuminated by light of a wave length such that the light is scattered by the particles. The absorption spectra of the particles can thus be determined from an analysis of the scattered light since the absorption of energy by the particles will affect the way the light is scattered. Preferably the heating beam is modulated to simplify the analysis of the scattered light. In one embodiment the heating beam is intensity modulated so that the scattered light will also be intensity modulated when the particles absorb energy. In another embodiment the heating beam passes through an interferometer and the scattered light reflects the Fourier Transform of the absorption spectra.

Coherent optical processing using noncoherent light after source masking.

PubMed

Boopathi, V; Vasu, R M

1992-01-10

Coherent optical processing starting with spatially noncoherent illumination is described. Good spatial coherence is introduced in the far field by modulating a noncoherent source when masks with sharp autocorrelation are used. The far-field mutual coherence function of light is measured and it is seen that, for the masks and the source size used here, we get a fairly large area over which the mutual coherence function is high and flat. We demonstrate traditional coherent processing operations such as Fourier transformation and image deblurring when coherent light that is produced in the above fashion is used. A coherence-redundancy merit function is defined for this type of processing system. It is experimentally demonstrated that the processing system introduced here has superior blemish tolerance compared with a traditional processor that uses coherent illumination.

Differences between time domain and Fourier domain optical coherence tomography in imaging tissues.

PubMed

Gao, W; Wu, X

2017-11-01

It has been numerously demonstrated that both time domain and Fourier domain optical coherence tomography (OCT) can generate high-resolution depth-resolved images of living tissues and cells. In this work, we compare the common points and differences between two methods when the continuous and random properties of live tissue are taken into account. It is found that when relationships that exist between the scattered light and tissue structures are taken into account, spectral interference measurements in Fourier domain OCT (FDOCT) is more advantageous than interference fringe envelope measurements in time domain OCT (TDOCT) in the cases where continuous property of tissue is taken into account. It is also demonstrated that when random property of tissue is taken into account FDOCT measures the Fourier transform of the spatial correlation function of the refractive index and speckle phenomena will limit the effective limiting imaging resolution in both TDOCT and FDOCT. Finally, the effective limiting resolution of both TDOCT and FDOCT are given which can be used to estimate the effective limiting resolution in various practical applications. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

Real-time processing for full-range Fourier-domain optical-coherence tomography with zero-filling interpolation using multiple graphic processing units.

PubMed

Watanabe, Yuuki; Maeno, Seiya; Aoshima, Kenji; Hasegawa, Haruyuki; Koseki, Hitoshi

2010-09-01

The real-time display of full-range, 2048?axial pixelx1024?lateral pixel, Fourier-domain optical-coherence tomography (FD-OCT) images is demonstrated. The required speed was achieved by using dual graphic processing units (GPUs) with many stream processors to realize highly parallel processing. We used a zero-filling technique, including a forward Fourier transform, a zero padding to increase the axial data-array size to 8192, an inverse-Fourier transform back to the spectral domain, a linear interpolation from wavelength to wavenumber, a lateral Hilbert transform to obtain the complex spectrum, a Fourier transform to obtain the axial profiles, and a log scaling. The data-transfer time of the frame grabber was 15.73?ms, and the processing time, which includes the data transfer between the GPU memory and the host computer, was 14.75?ms, for a total time shorter than the 36.70?ms frame-interval time using a line-scan CCD camera operated at 27.9?kHz. That is, our OCT system achieved a processed-image display rate of 27.23 frames/s.

A new Fourier transform based CBIR scheme for mammographic mass classification: a preliminary invariance assessment

NASA Astrophysics Data System (ADS)

Gundreddy, Rohith Reddy; Tan, Maxine; Qui, Yuchen; Zheng, Bin

2015-03-01

The purpose of this study is to develop and test a new content-based image retrieval (CBIR) scheme that enables to achieve higher reproducibility when it is implemented in an interactive computer-aided diagnosis (CAD) system without significantly reducing lesion classification performance. This is a new Fourier transform based CBIR algorithm that determines image similarity of two regions of interest (ROI) based on the difference of average regional image pixel value distribution in two Fourier transform mapped images under comparison. A reference image database involving 227 ROIs depicting the verified soft-tissue breast lesions was used. For each testing ROI, the queried lesion center was systematically shifted from 10 to 50 pixels to simulate inter-user variation of querying suspicious lesion center when using an interactive CAD system. The lesion classification performance and reproducibility as the queried lesion center shift were assessed and compared among the three CBIR schemes based on Fourier transform, mutual information and Pearson correlation. Each CBIR scheme retrieved 10 most similar reference ROIs and computed a likelihood score of the queried ROI depicting a malignant lesion. The experimental results shown that three CBIR schemes yielded very comparable lesion classification performance as measured by the areas under ROC curves with the p-value greater than 0.498. However, the CBIR scheme using Fourier transform yielded the highest invariance to both queried lesion center shift and lesion size change. This study demonstrated the feasibility of improving robustness of the interactive CAD systems by adding a new Fourier transform based image feature to CBIR schemes.

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.

Instrument Line Shape Modeling and Correction for Off-Axis Detectors in Fourier Transform Spectrometry

NASA Technical Reports Server (NTRS)

Bowman, K.; Worden, H.; Beer, R.

1999-01-01

Spectra measured by off-axis detectors in a high-resolution Fourier transform spectrometer (FTS) are characterized by frequency scaling, asymmetry and broadening of their line shape, and self-apodization in the corresponding interferogram.

Fourier Transform 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)

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)

A fast Karhunen-Loeve transform for a class of random processes

NASA Technical Reports Server (NTRS)

Jain, A. K.

1976-01-01

It is shown that for a class of finite first-order Markov signals, the Karhunen-Loeve (KL) transform for data compression is a set of periodic sine functions if the boundary values of the signal are fixed or known. These sine functions are shown to be related to the Fourier transform so that a fast Fourier transform algorithm can be used to implement the KL transform. Extension to two dimensions with reference to images with separable contravariance function is shown.

The Fresnel Diffraction: A Story of Light and Darkness

NASA Astrophysics Data System (ADS)

Aime, C.; Aristidi, É.; Rabbia, Y.

2013-03-01

In a first part of the paper we give a simple introduction to the free space propagation of light at the level of a Master degree in Physics. The presentation promotes linear filtering aspects at the expense of fundamental physics. Following the Huygens-Fresnel approach, the propagation of the wave writes as a convolution relationship, the impulse response being a quadratic phase factor. We give the corresponding filter in the Fourier plane. As an illustration, we describe the propagation of wave with a spatial sinusoidal amplitude, introduce lenses as quadratic phase transmissions, discuss their Fourier transform properties and give some properties of Soret screens. Classical diffractions of rectangular diaphragms are also given here. In a second part of the paper, the presentation turns into the use of external occulters in coronagraphy for the detection of exoplanets and the study of the solar corona. Making use of Lommel series expansions, we obtain the analytical expression for the diffraction of a circular opaque screen, giving thereby the complete formalism for the Arago-Poisson spot. We include there shaped occulters. The paper ends up with a brief application to incoherent imaging in astronomy.

360-degrees profilometry using strip-light projection coupled to Fourier phase-demodulation.

PubMed

Servin, Manuel; Padilla, Moises; Garnica, Guillermo

2016-01-11

360 degrees (360°) digitalization of three dimensional (3D) solids using a projected light-strip is a well-established technique in academic and commercial profilometers. These profilometers project a light-strip over the digitizing solid while the solid is rotated a full revolution or 360-degrees. Then, a computer program typically extracts the centroid of this light-strip, and by triangulation one obtains the shape of the solid. Here instead of using intensity-based light-strip centroid estimation, we propose to use Fourier phase-demodulation for 360° solid digitalization. The advantage of Fourier demodulation over strip-centroid estimation is that the accuracy of phase-demodulation linearly-increases with the fringe density, while in strip-light the centroid-estimation errors are independent. Here we proposed first to construct a carrier-frequency fringe-pattern by closely adding the individual light-strip images recorded while the solid is being rotated. Next, this high-density fringe-pattern is phase-demodulated using the standard Fourier technique. To test the feasibility of this Fourier demodulation approach, we have digitized two solids with increasing topographic complexity: a Rubik's cube and a plastic model of a human-skull. According to our results, phase demodulation based on the Fourier technique is less noisy than triangulation based on centroid light-strip estimation. Moreover, Fourier demodulation also provides the amplitude of the analytic signal which is a valuable information for the visualization of surface details.

Modulated near-field spectral extraction of broadband mid-infrared signals with a ceramic light source.

PubMed

Ishikawa, Michio; Katsura, Makoto; Nakashima, Satoru; Aizawa, Kento; Inoue, Tsutomu; Okamura, Hidekazu; Ikemoto, Yuka

2011-06-20

In order to obtain broadband near-field infrared (IR) spectra, a Fourier-transform IR spectrometer (FT-IR) and a ceramic light source were used with a scattering-type scanning near-field optical microscope (s-SNOM). To suppress the background (far-field) scattering, the distance between the scattering probe and the sample was modulated with frequency Ω by a piezo-electric actuator, and the Ω component was extracted from the signal with a lock-in detection. With Ω=30 kHz, a peak-to-peak modulation amplitude of 198 nm, and a probe with smooth surface near the tip, broadband near-field IR spectra could be obtained in the 1200-2500 cm(-1).

Demodulation of micro fiber-optic Fabry-Perot interferometer using subcarrier and dual-wavelength method

NASA Astrophysics Data System (ADS)

Lu, En; Ran, Zengling; Peng, Fei; Liu, Zhiwei; Xu, Fuguo

2012-03-01

Subcarrier technology and dual-wavelength demodulation method are combined for tracking the cavity length variation of a micro fiber-optic Fabry-Perot (F-P). Compared with conventional dual-wavelength demodulation method, two operation wavelengths for demodulation are modulated with two different carrier frequencies, respectively, and then injected into optical link connected with the F-P cavity. Light power reflected for the two wavelengths is obtained by interrogating the powers of Fast Fourier Transform (FFT) spectrum at their carrier frequencies. Because the light at the two wavelengths experiences the same optical and electrical routes, measurement deviation resulting from the drift of optical and electrical links can be entirely eliminated.

Demodulation of micro fiber-optic Fabry-Perot interferometer using subcarrier and dual-wavelength method

NASA Astrophysics Data System (ADS)

Ran, Zengling; Rao, Yunjiang; Liu, Zhiwei; Xu, Fuguo

2011-05-01

Subcarrier technology and dual-wavelength demodulation method are combined for tracking the cavity length variation of a micro fiber-optic fabry-periot (F-P). Compared with conventional dual-wavelength demodulation method, two operation wavelengths for demodulation are modulated with two different carrier frequencies, respectively, and then injected into optical link connected with the F-P cavity. Light power reflected for the two wavelengths is obtained by interrogating the powers of Fast Fourier Transform (FFT) spectrum at their carrier frequencies. Because the light at the two wavelengths experiences the same optical and electrical routes, measurement deviation resulting from the drift of optical and electrical links can be entirely eliminated.

Photographic film image enhancement

NASA Technical Reports Server (NTRS)

Horner, J. L.

1975-01-01

A series of experiments were undertaken to assess the feasibility of defogging color film by the techniques of optical spatial filtering. A coherent optical processor was built using red, blue, and green laser light input and specially designed Fourier transformation lenses. An array of spatial filters was fabricated on black and white emulsion slides using the coherent optical processor. The technique was first applied to laboratory white light fogged film, and the results were successful. However, when the same technique was applied to some original Apollo X radiation fogged color negatives, the results showed no similar restoration. Examples of each experiment are presented and possible reasons for the lack of restoration in the Apollo films are discussed.

A Scattered Light Correction to Color Images Taken of Europa by the Galileo Spacecraft: Initial Results

NASA Astrophysics Data System (ADS)

Phillips, C. B.; Valenti, M.

2009-12-01

Jupiter's moon Europa likely possesses an ocean of liquid water beneath its icy surface, but estimates of the thickness of the surface ice shell vary from a few kilometers to tens of kilometers. Color images of Europa reveal the existence of a reddish, non-ice component associated with a variety of geological features. The composition and origin of this material is uncertain, as is its relationship to Europa's various landforms. Published analyses of Galileo Near Infrared Mapping Spectrometer (NIMS) observations indicate the presence of highly hydrated sulfate compounds. This non-ice material may also bear biosignatures or other signs of biotic material. Additional spectral information from the Galileo Solid State Imager (SSI) could further elucidate the nature of the surface deposits, particularly when combined with information from the NIMS. However, little effort has been focused on this approach because proper calibration of the color image data is challenging, requiring both skill and patience to process the data and incorporate the appropriate scattered light correction. We are currently working to properly calibrate the color SSI data. The most important and most difficult issue to address in the analysis of multispectral SSI data entails using thorough calibrations and a correction for scattered light. Early in the Galileo mission, studies of the Galileo SSI data for the moon revealed discrepancies of up to 10% in relative reflectance between images containing scattered light and images corrected for scattered light. Scattered light adds a wavelength-dependent low-intensity brightness factor to pixels across an image. For example, a large bright geological feature located just outside the field of view of an image will scatter extra light onto neighboring pixels within the field of view. Scattered light can be seen as a dim halo surrounding an image that includes a bright limb, and can also come from light scattered inside the camera by dirt, edges, and the interfaces of lenses. Because of the wavelength dependence of this effect, a scattered light correction must be performed on any SSI multispectral dataset before quantitative spectral analysis can be done. The process involves using a point-spread function for each filter that helps determine the amount of scattered light expected for a given pixel based on its location and the model attenuation factor for that pixel. To remove scattered light for a particular image taken through a particular filter, the Fourier transform of the attenuation function, which is the point spread function for that filter, is convolved with the Fourier transform of the image at the same wavelength. The result is then filtered for noise in the frequency domain, and then transformed back to the spatial domain. This results in a version of the original image that would have been taken without the scattered light contribution. We will report on our initial results from this calibration.

Sources, compositions, and optical properties of humic-like substances in Beijing during the 2014 APEC summit: Results from dual carbon isotope and Fourier-transform ion cyclotron resonance mass spectrometry analyses.

PubMed

Mo, Yangzhi; Li, Jun; Jiang, Bin; Su, Tao; Geng, Xiaofei; Liu, Junwen; Jiang, Haoyu; Shen, Chengde; Ding, Ping; Zhong, Guangcai; Cheng, Zhineng; Liao, Yuhong; Tian, Chongguo; Chen, Yingjun; Zhang, Gan

2018-08-01

Humic-like substances (HULIS) are a class of high molecular weight, light-absorbing compounds that are highly related to brown carbon (BrC). In this study, the sources and compositions of HULIS isolated from fine particles collected in Beijing, China during the 2014 Asia-Pacific Economic Cooperation (APEC) summit were characterized based on carbon isotope ( 13 C and 14 C) and Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR MS) analyses, respectively. HULIS were the main light-absorbing components of water-soluble organic carbon (WSOC), accounting for 80.2 ± 6.1% of the WSOC absorption capacity at 365 nm. The carbon isotope data showed that HULIS had a lower non-fossil contribution (53 ± 4%) and were less enriched with 13 C (-24.2 ± 0.6‰) relative to non-HULIS (62 ± 8% and -20.8 ± 0.3‰, respectively). The higher relative intensity fraction of sulfur-containing compounds in HULIS before and after APEC was attributed to higher sulfur dioxide levels emitted from fossil fuel combustion, whereas the higher fraction of nitrogen-containing compounds during APEC may have been due to the relatively greater contribution of non-fossil compounds or the influence of nitrate radical chemistry. The results of investigating the relationships among the sources, elemental compositions, and optical properties of HULIS demonstrated that the light absorption of HULIS appeared to increase with increasing unsaturation degree, but decrease with increasing oxidation level. The unsaturation of HULIS was affected by both sources and aging level. Copyright © 2018 Elsevier Ltd. All rights reserved.

KAM Tori Construction Algorithms

NASA Astrophysics Data System (ADS)

Wiesel, W.

In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.

Generalized fiber Fourier optics.

PubMed

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.

QUANTITATIVE FOURIER TRANSFORM INFRARED SPECTROSCOPIC INVESTIGATION OF HUMIC SUBSTANCE FUNCTIONAL GROUP COMPOSITION

EPA Science Inventory

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,...

Fast Fourier Transform Spectral Analysis Program

NASA Technical Reports Server (NTRS)

Daniel, J. A., Jr.; Graves, M. L.; Hovey, N. M.

1969-01-01

Fast Fourier Transform Spectral Analysis Program is used in frequency spectrum analysis of postflight, space vehicle telemetered trajectory data. This computer program with a digital algorithm can calculate power spectrum rms amplitudes and cross spectrum of sampled parameters at even time increments.

[Research on spatially modulated Fourier transform imaging spectrometer data processing method].

PubMed

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.

Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.

PubMed

Ran, Qiwen; Zhang, Haiying; Zhang, Jin; Tan, Liying; Ma, Jing

2009-06-01

Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process. (c) 2009 Optical Society of America.

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.

Discovery of Peculiar Periodic Spectral Modulations in a Small Fraction of Solar-type Stars

NASA Astrophysics Data System (ADS)

Borra, Ermanno F.; Trottier, Eric

2016-11-01

A Fourier transform analysis of 2.5 million spectra in the Sloan Digital Sky Survey was carried out to detect periodic spectral modulations. Signals having the same period were found in only 234 stars overwhelmingly in the F2 to K1 spectral range. The signals cannot be caused by instrumental or data analysis effects because they are present in only a very small fraction of stars within a narrow spectral range and because signal-to-noise ratio considerations predict that the signal should mostly be detected in the brightest objects, while this is not the case. We consider several possibilities, such as rotational transitions in molecules, rapid pulsations, Fourier transform of spectral lines, and signals generated by extraterrestrial intelligence (ETI). They cannot be generated by molecules or rapid pulsations. It is highly unlikely that they come from the Fourier transform of spectral lines because too many strong lines located at nearly periodic frequencies are needed. Finally, we consider the possibility, predicted in a previous published paper, that the signals are caused by light pulses generated by ETI to makes us aware of their existence. We find that the detected signals have exactly the shape of an ETI signal predicted in the previous publication and are therefore in agreement with this hypothesis. The fact that they are only found in a very small fraction of stars within a narrow spectral range centered near the spectral type of the Sun is also in agreement with the ETI hypothesis. However, at this stage, this hypothesis needs to be confirmed with further work. Although unlikely, there is also a possibility that the signals are due to highly peculiar chemical compositions in a small fraction of galactic halo stars.

Modified solvothermal synthesis of cobalt ferrite (CoFe2O4) magnetic nanoparticles photocatalysts for degradation of methylene blue with H2O2/visible light

NASA Astrophysics Data System (ADS)

Kalam, Abul; Al-Sehemi, Abdullah G.; Assiri, Mohammed; Du, Gaohui; Ahmad, Tokeer; Ahmad, Irfan; Pannipara, M.

2018-03-01

Different grads of magnetic nano-scaled cobalt ferrites (CoFe2O4) photocatalysts were synthesized by modified Solvothermal (MST) process with and without polysaccharide. The indigenously synthesized photocatalysts were characterized by means of X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), thermo gravimetric analysis (TGA), Fourier transform infrared (FT-IR), UV-visible (UV-vis) spectroscopy and N2 adsorption-desorption isotherm method. The Fourier transform infrared spectroscopy study showed the Fe-O stretching vibration 590-619 cm-1, confirming the formation of metal oxide. The crystallite size of the synthesized photocatalysts was found in the range between 20.0 and 30.0 nm. The surface area of obtained magnetic nanoparticles is found to be reasonably high in the range of 63.0-76.0 m2/g. The results shown that only MST-2 is the most active catalyst for photo-Fenton like scheme for fast photodegradation action of methylene blue dye, this is possible due to optical band gap estimated of 2.65 eV. Captivatingly the percentage of degradation efficiency increases up to 80% after 140 min by using MST-2 photocatalyst. Photocatalytic degradation of methylene blue (MB) dye under visible light irradiation with cobalt ferrite magnetic nanoparticles followed first order kinetic constant and rate constant of MST-2 is almost 2.0 times greater than MST-1 photocatalyst.

A 2D Fourier tool for the analysis of photo-elastic effect in large granular assemblies

NASA Astrophysics Data System (ADS)

Leśniewska, Danuta

2017-06-01

Fourier transforms are the basic tool in constructing different types of image filters, mainly those reducing optical noise. Some DIC or PIV software also uses frequency space to obtain displacement fields from a series of digital images of a deforming body. The paper presents series of 2D Fourier transforms of photo-elastic transmission images, representing large pseudo 2D granular assembly, deforming under varying boundary conditions. The images related to different scales were acquired using the same image resolution, but taken at different distance from the sample. Fourier transforms of images, representing different stages of deformation, reveal characteristic features at the three (`macro-`, `meso-` and `micro-`) scales, which can serve as a data to study internal order-disorder transition within granular materials.

Bessel function expansion to reduce the calculation time and memory usage for cylindrical computer-generated holograms.

PubMed

Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko

2017-07-10

This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.

Fourier Phase Domain Steganography: Phase Bin Encoding Via Interpolation

NASA Astrophysics Data System (ADS)

Rivas, Edward

2007-04-01

In recent years there has been an increased interest in audio steganography and watermarking. This is due primarily to two reasons. First, an acute need to improve our national security capabilities in light of terrorist and criminal activity has driven new ideas and experimentation. Secondly, the explosive proliferation of digital media has forced the music industry to rethink how they will protect their intellectual property. Various techniques have been implemented but the phase domain remains a fertile ground for improvement due to the relative robustness to many types of distortion and immunity to the Human Auditory System. A new method for embedding data in the phase domain of the Discrete Fourier Transform of an audio signal is proposed. Focus is given to robustness and low perceptibility, while maintaining a relatively high capacity rate of up to 172 bits/s.

Enhancement of Signal-to-noise Ratio in Natural-source Transient Magnetotelluric Data with Wavelet Transform

NASA Astrophysics Data System (ADS)

Zhang, Y.; Paulson, K. V.

For audio-frequency magnetotelluric surveys where the signals are lightning-stroke transients, the conventional Fourier transform method often fails to produce a high quality impedance tensor. An alternative approach is to use the wavelet transform method which is capable of localizing target information simultaneously in both the temporal and frequency domains. Unlike Fourier analysis that yields an average amplitude and phase, the wavelet transform produces an instantaneous estimate of the amplitude and phase of a signal. In this paper a complex well-localized wavelet, the Morlet wavelet, has been used to transform and analyze audio-frequency magnetotelluric data. With the Morlet wavelet, the magnetotelluric impedance tensor can be computed directly in the wavelet transform domain. The lightning-stroke transients are easily identified on the dilation-translation plane. Choosing those wavelet transform values where the signals are located, a higher signal-to-noise ratio estimation of the impedance tensor can be obtained. In a test using real data, the wavelet transform showed a significant improvement in the signal-to-noise ratio over the conventional 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)

ENVIRONMENTAL ANALYSIS BY AB INITIO QUANTUM MECHANICAL COMPUTATION AND GAS CHROMATOGRAPHY/FOURIER TRANSFORM INFRARED SPECTROMETRY.

EPA Science Inventory

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...

A method to perform a fast fourier transform with primitive image transformations.

PubMed

Sheridan, Phil

2007-05-01

The Fourier transform is one of the most important transformations in image processing. A major component of this influence comes from the ability to implement it efficiently on a digital computer. This paper describes a new methodology to perform a fast Fourier transform (FFT). This methodology emerges from considerations of the natural physical constraints imposed by image capture devices (camera/eye). The novel aspects of the specific FFT method described include: 1) a bit-wise reversal re-grouping operation of the conventional FFT is replaced by the use of lossless image rotation and scaling and 2) the usual arithmetic operations of complex multiplication are replaced with integer addition. The significance of the FFT presented in this paper is introduced by extending a discrete and finite image algebra, named Spiral Honeycomb Image Algebra (SHIA), to a continuous version, named SHIAC.

Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scargle, Jeffrey D.; Way, M. J.; Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fouriermore » transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.« less

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

PubMed

Pünschel, Markus; Rötteler, Martin

2007-06-01

We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper.

Applications of the diffraction and interference of light and electronic waves

NASA Astrophysics Data System (ADS)

Bahrim, Cristian; Lanning, Robert

2010-10-01

As part of a NSF sponsored program, called STAIRSTEP, at Lamar University we work on improving the basic knowledge of our physics majors in topics with broader impact in various areas of science and engineering [1]. The purpose is to facilitate a deeper understanding of some fundamental concepts in the field of optics through hands-on experience [2]. We choose to study the interference/diffraction of light and matter waves, because of its fundamental importance in physics with many applications. We target multiple goals in our field of study such as to understand the formation of electronic waves (wave packets) and their interaction with atoms in crystals (electron diffraction); the Fourier analysis of light with applications in spectroscopy, etc. We can show that a crystal lattice Fourier transforms the sinusoidal waves associated to free electrons fired toward the crystal. Our studies led to a simple and instructive recipe for discovering the arrangement of atoms in crystals from the analysis of the diffraction patterns produced by radiation or by electrons transmitted through crystals. [1] Doerschuk P. et al., 39th ASEE/IEEE Frontiers in Education Conference, San Antonio 2009, M3F-1. [2] Bahrim C, Innovation 2006 -- World Innovations in Engineering Education and Research, Chapter 17, iNEER Innovation Series, ISBN 0-9741252-5-3.

Nonlinear Optical Image Processing with Bacteriorhodopsin Films

NASA Technical Reports Server (NTRS)

Downie, John D.; Deiss, Ron (Technical Monitor)

1994-01-01

The transmission properties of some bacteriorhodopsin film spatial light modulators are uniquely suited to allow nonlinear optical image processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude transmission feature of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. The bacteriorhodopsin film displays the logarithmic amplitude response for write beam intensities spanning a dynamic range greater than 2.0 orders of magnitude. We present experimental results demonstrating the principle and capability for several different image and noise situations, including deterministic noise and speckle. Using the bacteriorhodopsin film, we successfully filter out image noise from the transformed image that cannot be removed from the original image.

Three-dimensional rearrangement of single atoms using actively controlled optical microtraps.

PubMed

Lee, Woojun; Kim, Hyosub; Ahn, Jaewook

2016-05-02

We propose and demonstrate three-dimensional rearrangements of single atoms. In experiments performed with single ⁸⁷Rb atoms in optical microtraps actively controlled by a spatial light modulator, we demonstrate various dynamic rearrangements of up to N = 9 atoms including rotation, 2D vacancy filling, guiding, compactification, and 3D shuffling. With the capability of a phase-only Fourier mask to generate arbitrary shapes of the holographic microtraps, it was possible to place single atoms at arbitrary geometries of a few μm size and even continuously reconfigure them by conveying each atom. For this purpose, we loaded a series of computer-generated phase masks in the full frame rate of 60 Hz of the spatial light modulator, so the animation of phase mask transformed the holographic microtraps in real time, driving each atom along the assigned trajectory. Possible applications of this method of transformation of single atoms include preparation of scalable quantum platforms for quantum computation, quantum simulation, and quantum many-body physics.

Development of a High-Throughput Microwave Imaging System for Concealed Weapons Detection

DTIC Science & Technology

2016-07-15

hardware. Index Terms—Microwave imaging, multistatic radar, Fast Fourier Transform (FFT). I. INTRODUCTION Near-field microwave imaging is a non-ionizing...configuration, but its computational demands are extreme. Fast Fourier Transform (FFT) imaging has long been used to efficiently construct images sampled with...Simulated image of 25 point scatterers imaged at range 1.5m, with array layout depicted in Fig. 3. Left: image formed with Equation (5) ( Fourier

Formulation of the rotational transformation of wave fields and their application to digital holography.

PubMed

Matsushima, Kyoji

2008-07-01

Rotational transformation based on coordinate rotation in Fourier space is a useful technique for simulating wave field propagation between nonparallel planes. This technique is characterized by fast computation because the transformation only requires executing a fast Fourier transform twice and a single interpolation. It is proved that the formula of the rotational transformation mathematically satisfies the Helmholtz equation. Moreover, to verify the formulation and its usefulness in wave optics, it is also demonstrated that the transformation makes it possible to reconstruct an image on arbitrarily tilted planes from a wave field captured experimentally by using digital holography.

A Method to Compute the Force Signature of a Body Impacting on a Linear Elastic Structure Using Fourier Analysis

DTIC Science & Technology

1982-09-17

FK * 1PK (2) The convolution of two transforms in time domain is the inverse transform of the product in frequency domain. Thus Rp(s) - Fgc() Ipg(*) (3...its inverse transform by: R,(r)- R,(a.)e’’ do. (5)2w In order to nuke use f a very accurate numerical method to ompute Fourier "ke and coil...taorm. When the inverse transform it tken by using Eq. (15), the cosine transform, because it converges faster than the sine transform refu-ft the

EVALUATION OF A PORTABLE FOURIER TRANSFORM INFRARED GAS ANALYZER FOR MEASUREMENTS OF AIR TOXICS IN POLLUTION PREVENTION RESEARCH

EPA Science Inventory

A portable Fourier transform infrared gas analyzer with a photoacoustic detector performed reliably during pollution prevention research at two industrial facilities. It exhibited good agreement (within approximately 6%) with other analytical instruments (dispersive infrared and ...

PARTICULATE MATTER MEASUREMENTS USING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROSCOPY

EPA Science Inventory

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 ...

Gravity data inversion to determine 3D topographycal density contrast of Banten area, Indonesia based on fast Fourier transform

NASA Astrophysics Data System (ADS)

Windhari, Ayuty; Handayani, Gunawan

2015-04-01

The 3D inversion gravity anomaly to estimate topographical density using a matlab source code from gridded data provided by Parker Oldenburg algorithm based on fast Fourier transform was computed. We extend and improved the source code of 3DINVERT.M invented by Gomez Ortiz and Agarwal (2005) using the relationship between Fourier transform of the gravity anomaly and the sum of the Fourier transform from the topography density. We gave density contrast between the two media to apply the inversion. FFT routine was implemented to construct amplitude spectrum to the given mean depth. The results were presented as new graphics of inverted topography density, the gravity anomaly due to the inverted topography and the difference between the input gravity data and the computed ones. It terminates when the RMS error is lower than pre-assigned value used as convergence criterion or until maximum of iterations is reached. As an example, we used the matlab program on gravity data of Banten region, Indonesia.

Construction of high frame rate images with Fourier transform

NASA Astrophysics Data System (ADS)

Peng, Hu; Lu, Jian-Yu

2002-05-01

Traditionally, images are constructed with a delay-and-sum method that adjusts the phases of received signals (echoes) scattered from the same point in space so that they are summed in phase. Recently, the relationship between the delay-and-sum method and the Fourier transform is investigated [Jian-yu Lu, Anjun Liu, and Hu Peng, ``High frame rate and delay-and-sum imaging methods,'' IEEE Trans. Ultrason. Ferroelectr. Freq. Control (submitted)]. In this study, a generic Fourier transform method is developed. Two-dimensional (2-D) or three-dimensional (3-D) high frame rate images can be constructed using the Fourier transform with a single transmission of an ultrasound pulse from an array as long as the transmission field of the array is known. To verify our theory, computer simulations have been performed with a linear array, a 2-D array, a convex curved array, and a spherical 2-D array. The simulation results are consistent with our theory. [Work supported in part by Grant 5RO1 HL60301 from NIH.

Wavelength-encoded tomography based on optical temporal Fourier transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Chi; Wong, Kenneth K. Y., E-mail: kywong@eee.hku.hk

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,more » 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.« less

The limit distribution in the q-CLT for q\\,\\geqslant \\,1 is unique and can not have a compact support

NASA Astrophysics Data System (ADS)

Umarov, Sabir; Tsallis, Constantino

2016-10-01

In a paper by Umarov et al (2008 Milan J. Math. 76 307-28), a generalization of the Fourier transform, called the q-Fourier transform, was introduced and applied for the proof of a q-generalized central limit theorem (q-CLT). Subsequently, Hilhorst illustrated (2009 Braz. J. Phys. 39 371-9 2010 J. Stat. Mech. P10023) that the q-Fourier transform for q\\gt 1, is not invertible in the space of density functions. Indeed, using an invariance principle, he constructed a family of densities with the same q-Fourier transform and noted that ‘as a consequence, the q-CLT falls short of achieving its stated goal’. The distributions constructed there have compact support. We prove now that the limit distribution in the q-CLT is unique and can not have a compact support. This result excludes all the possible counterexamples which can be constructed using the invariance principle and fills the gap mentioned by Hilhorst.

Application of the fractional Fourier transform to image reconstruction in MRI.

PubMed

Parot, Vicente; Sing-Long, Carlos; Lizama, Carlos; Tejos, Cristian; Uribe, Sergio; Irarrazaval, Pablo

2012-07-01

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding. Copyright © 2011 Wiley Periodicals, Inc.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

PubMed

Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

2009-05-01

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

Angular acceptance analysis of an infrared focal plane array with a built-in stationary Fourier transform spectrometer.

PubMed

Gillard, Frédéric; Ferrec, Yann; Guérineau, Nicolas; Rommeluère, Sylvain; Taboury, Jean; Chavel, Pierre

2012-06-01

Stationary Fourier transform spectrometry is an interesting concept for building reliable field or embedded spectroradiometers, especially for the mid- and far- IR. Here, a very compact configuration of a cryogenic stationary Fourier transform IR (FTIR) spectrometer is investigated, where the interferometer is directly integrated in the focal plane array (FPA). We present a theoretical analysis to explain and describe the fringe formation inside the FTIR-FPA structure when illuminated by an extended source positioned at a finite distance from the detection plane. The results are then exploited to propose a simple front lens design compatible with a handheld package.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Direct generation of abruptly focusing vortex beams using a 3/2 radial phase-only pattern.

PubMed

Davis, Jeffrey A; Cottrell, Don M; Zinn, Jonathan M

2013-03-20

Abruptly focusing Airy beams have previously been generated using a radial cubic phase pattern that represents the Fourier transform of the Airy beam. The Fourier transform of this pattern is formed using a system length of 2f, where f is the focal length of the Fourier transform lens. In this work, we directly generate these abruptly focusing Airy beams using a 3/2 radial phase pattern encoded onto a liquid crystal display. The resulting optical system is much shorter. In addition, we can easily produce vortex patterns at the focal point of these beams. Experimental results match theoretical predictions.

Determination of Structural Parameters from EXAFS (Extended X-Ray Absorption Fine Structure): Application to Solutions and Catalysts.

DTIC Science & Technology

1984-05-23

the disorder was accurately known. Inverse Transform To isolate the EAFS contribution due to a single feature in the Fourier transform, the inverse ...is associated with setting the "fold" components to 27 zero in r-space. An inverse transform (real part) of the major feature of the Fig. 4 Fourier...phase of the resulting inverse transform represents only any differences between the material being studied and the reference. This residual is

Fourier-transform imaging of cotton and botanical and field trash mixtures

USDA-ARS?s Scientific Manuscript database

Botanical and field cotton trash comingled with cotton lint can greatly reduce the marketability and quality of cotton. Trash can be found comingled with cotton lint during harvesting, ginning, and processing, thus this study is of interest. Attenuated Total Reflectance-Fourier Transform Infrared (A...

Detection and classification of salmonella serotypes using spectral signatures collected by fourier transform infrared (FT-IR) spectroscopy

USDA-ARS?s Scientific Manuscript database

Spectral signatures of Salmonella serotypes namely Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky were collected using Fourier transform infrared spectroscopy (FT-IR). About 5-10 µL of Salmonella suspensions with concentrations of 1...

Identification and characterization of salmonella serotypes using DNA spectral characteristics by fourier transform infrared (FT-IR) spectroscopy

USDA-ARS?s Scientific Manuscript database

Analysis of DNA samples of Salmonella serotypes (Salmonella Typhimurium, Salmonella Enteritidis, Salmonella Infantis, Salmonella Heidelberg and Salmonella Kentucky) were performed using Fourier transform infrared spectroscopy (FT-IR) spectrometer by placing directly in contact with a diamond attenua...

Phase in Optical Image Processing

NASA Astrophysics Data System (ADS)

Naughton, Thomas J.

2010-04-01

The use of phase has a long standing history in optical image processing, with early milestones being in the field of pattern recognition, such as VanderLugt's practical construction technique for matched filters, and (implicitly) Goodman's joint Fourier transform correlator. In recent years, the flexibility afforded by phase-only spatial light modulators and digital holography, for example, has enabled many processing techniques based on the explicit encoding and decoding of phase. One application area concerns efficient numerical computations. Pushing phase measurement to its physical limits, designs employing the physical properties of phase have ranged from the sensible to the wonderful, in some cases making computationally easy problems easier to solve and in other cases addressing mathematics' most challenging computationally hard problems. Another application area is optical image encryption, in which, typically, a phase mask modulates the fractional Fourier transformed coefficients of a perturbed input image, and the phase of the inverse transform is then sensed as the encrypted image. The inherent linearity that makes the system so elegant mitigates against its use as an effective encryption technique, but we show how a combination of optical and digital techniques can restore confidence in that security. We conclude with the concept of digital hologram image processing, and applications of same that are uniquely suited to optical implementation, where the processing, recognition, or encryption step operates on full field information, such as that emanating from a coherently illuminated real-world three-dimensional object.

Is Fourier analysis performed by the visual system or by the visual investigator.

PubMed

Ochs, A L

1979-01-01

A numerical Fourier transform was made of the pincushion grid illusion and the spectral components orthogonal to the illusory lines were isolated. Their inverse transform creates a picture of the illusion. The spatial-frequency response of cortical, simple receptive field neurons similarly filters the grid. A complete set of these neurons thus approximates a two-dimensional Fourier analyzer. One cannot conclude, however, that the brain actually uses frequency-domain information to interpret visual images.

Probing specific molecular processes and intermediates by time-resolved Fourier transform infrared spectroscopy: application to the bacteriorhodopsin photocycle.

PubMed

Lórenz-Fonfría, Víctor A; Kandori, Hideki; Padrós, Esteve

2011-06-23

We present a general approach for probing the kinetics of specific molecular processes in proteins by time-resolved Fourier transform infrared (IR) spectroscopy. Using bacteriorhodopsin (bR) as a model we demonstrate that by appropriately monitoring some selected IR bands it is possible obtaining the kinetics of the most important events occurring in the photocycle, namely changes in the chromophore and the protein backbone conformation, and changes in the protonation state of the key residues implicated in the proton transfers. Besides confirming widely accepted views of the bR photocycle, our analysis also sheds light into some disputed issues: the degree of retinal torsion in the L intermediate to respect the ground state; the possibility of a proton transfer from Asp85 to Asp212; the relationship between the protonation/deprotonation of Asp85 and the proton release complex; and the timing of the protein backbone dynamics. By providing a direct way to estimate the kinetics of photocycle intermediates the present approach opens new prospects for a robust quantitative kinetic analysis of the bR photocycle, which could also benefit the study of other proteins involved in photosynthesis, in phototaxis, or in respiratory chains.

Speckle techniques for determining stresses in moving objects

NASA Technical Reports Server (NTRS)

Murphree, E. A.; Wilson, T. F.; Ranson, W. F.; Swinson, W. F.

1978-01-01

Laser speckle interferometry is a relatively new experimental technique which shows promise of alleviating many difficult problems in experimental mechanics. The method utilizes simple high-resolution photographs of the surface which is illuminated by coherent light. The result is a real-time or permanently stored whole-field record of interference fringes which yields a map of displacements in the object. In this thesis, the time-average theory using the Fourier transform is developed to present the application of this technique to measurement of in-plane displacement induced by the vibration of an object.

Onion cell imaging by using Talbot/self-imaging effect

NASA Astrophysics Data System (ADS)

Agarwal, Shilpi; Kumar, Varun; Shakher, Chandra

2017-08-01

This paper presents the amplitude and phase imaging of onion epidermis cell using the self-imaging capabilities of a grating (Talbot effect) in visible light region. In proposed method, the Fresnel diffraction pattern from the first grating and object is recorded at self-image plane. Fast Fourier Transform (FFT) is used for extracting the 3D amplitude and phase image of onion epidermis cell. The stability of the proposed system, from environmental perturbation as well as its compactness and portability give the proposed system a high potential for several clinical applications.

Spatially-Heterodyned Holography

DOEpatents

Thomas, Clarence E [Knoxville, TN; Hanson, Gregory R [Clinton, TN

2006-02-21

A method of recording a spatially low-frequency heterodyne hologram, including spatially heterodyne fringes for Fourier analysis, includes: splitting a laser beam into a reference beam and an object beam; interacting the object beam with an object; focusing the reference beam and the object beam at a focal plane of a digital recorder to form a spatially low-frequency heterodyne hologram including spatially heterodyne fringes for Fourier analysis; digital recording the spatially low-frequency heterodyne hologram; Fourier transforming axes of the recorded spatially low-frequency heterodyne hologram including spatially heterodyne fringes in Fourier space to sit on top of a heterodyne carrier frequency defined by an angle between the reference beam and the object beam; cutting off signals around an origin; and performing an inverse Fourier transform.

Application of space periodic variation of light polarization in imaging polarimetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Drobczynski, Slawomir; Kasprzak, Henryk

The application of space periodic variation of light polarization for measurement and calculation of the distribution of the phase retardation between two eigenwaves propagating inside a linearly birefringent media and the distribution of the azimuth angle of the first eigenvector is described. The measuring method proposed does not require any mechanical movements or rotations of any optical elements. Application of a liquid crystal (LC) modulator instead of a quarter-wave plate gives an opportunity to introduce the required phase shift. The space periodic modulation of the polarization of light is achieved by the use of a Wollaston prism placed inside themore » path of the light beam. Then a fast Fourier transform is used for further calculations. The number of measurements of the light intensity at the output of the system is minimized to two. These assumptions make the proposed method very fast, which is especially important in measurements of the objects with optical anisotropy that is changing in time.« less

Photocatalytic activity of Fe-doped CaTiO₃ under UV-visible light.

PubMed

Yang, He; Han, Chong; Xue, Xiangxin

2014-07-01

The photocatalytic degradation of methylene blue (MB) over Fe-doped CaTiO₃ under UV-visible light was investigated. The as-prepared samples were characterized using X-ray diffraction (XRD), scanning electron microscope (SEM) equipped with an energy dispersive spectrometer (EDS) system, Fourier transform infrared spectra (FT-IR), and UV-visible diffuse reflectance spectroscopy (DRS). The results show that the doping with Fe significantly promoted the light absorption ability of CaTiO₃ in the visible light region. The Fe-doped CaTiO₃ exhibited higher photocatalytic activity than CaTiO₃ for the degradation of MB. However, the photocatalytic activity of the Fe-doped CaTiO₃ was greatly influenced by the calcination temperature during the preparation process. The Fe-doped CaTiO₃ prepared at 500°C exhibited the best photocatalytic activity, with degradation of almost 100% MB (10ppm) under UV-visible light for 180 min. Copyright © 2014. Published by Elsevier B.V.

Investigation of thermomechanical effects of lighting conditions on canvas paintings by laser shearography

NASA Astrophysics Data System (ADS)

Meybodi, M. K.; Dobrev, I.; Klausmeyer, P.; Harrington, E. J.; Furlong, C.

Quantitative techniques to characterize thermomechanical effects of light on canvas paintings are necessary in order to better understand the deleterious effects that light has on precious art collections in museum exhibitions. In this paper, we present advances in the development of a customized laser shearography system for temporal characterization of inplane displacements of canvas paintings when subjected to specific lighting conditions. The shearography system is synchronized with a thermal IR camera and concomitant measurements of derivatives of displacements along two orthogonal shearing directions as well as thermal fields are performed. Due to the nature of the measurements, we have developed real-time temporal phase unwrapping algorithms and high-resolution Fast Fourier Transform (FFT) methods to calibrate applied shearing levels. In addition, we are developing methods to isolate thermally-induced components from randomly-induced mechanical vibrations that occur in museum environments by application of IR imaging data. Representative examples are shown, which illustrate capabilities to measure, detect, and map crack propagation as a function of lighting conditions and time.

Feature Extraction for Bearing Prognostics and Health Management (PHM) - A Survey (Preprint)

DTIC Science & Technology

2008-05-01

Envelope analysis • Cepstrum analysis • Higher order spectrum • Short-time Fourier Transform (STFT) • Wigner - Ville distribution ( WVD ) • Empirical mode...techniques are the short-time Fourier transform (STFT), the Wigner - Ville distribution , and the wavelet transform. In this paper we categorize wavelets...diagnosis have shown in many publications, for example, [22]. b) Wigner – Ville distribution : The afore-mentioned STFT is conceptually simple. However

Physicochemcial characteristic of CdS-anchored porous WS2 hybrid in the photocatalytic degradation of crystal violet under UV and visible light irradiation

NASA Astrophysics Data System (ADS)

Vattikuti, S. V. Prabhakar; Ngo, Ich-Long; Byon, Chan

2016-11-01

In this work, we report the synthesis of CdS-incorporated porous WS2 by a simple hydrothermal method. The structural, morphological, and optical properties of the samples were examined by X-ray diffraction (XRD), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), Fourier transform infrared spectroscopy (FTIR), high resolution X-ray photoelectron spectroscopy (XPS) and UV-visible spectrometry. The photocatalytic activities were established for degradation of crystal violet (CV) under UV and visible light irradiation. The CdS-incorporated porous WS2 hybrid demonstrated high photocatalytic activity for degradation of CV pollutant compared to pure CdS nanoparticles and porous WS2 sheets. This result implies that the CdS-incorporated porous WS2 promoted more electron-hole pair transformation under UV and visible light irradiation. This significant enhancement of photocatalytic efficiency of CdS-incorporated porous WS2 photocatalyst under visible light can be ascribed to the presence of CdS nanospheres on the meshed-like WS2 sheets which potentially improves absorption in the visible range enabled by surface plasmon resonance effect of CdS nanospheres. The photostability and reusability of the CdS-porous WS2 were examined through recycling experiments.

Limitations and potential of spectral subtractions in fourier-transform infrared (FTIR) spectroscopy of soil samples

USDA-ARS?s Scientific Manuscript database

Soil science research is increasingly applying Fourier transform infrared (FTIR) spectroscopy for analysis of soil organic matter (SOM). However, the compositional complexity of soils and the dominance of the mineral component can limit spectroscopic resolution of SOM and other minor components. The...

Detection of starch adulteration in onion powder by FT-NIR and FT-IR spectroscopy

USDA-ARS?s Scientific Manuscript database

Adulteration of onion powder with cornstarch was identified by Fourier transform near-infrared (FT-NIR) and Fourier transform infrared (FT-IR) spectroscopy. The reflectance spectra of 180 pure and adulterated samples (1–35 wt% starch) were collected and preprocessed to generate calibration and predi...

Coordinate axes, location of origin, and redundancy for the one and two-dimensional discrete Fourier transform

NASA Technical Reports Server (NTRS)

Ioup, G. E.; Ioup, J. W.

1985-01-01

Appendix 4 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer discusses coordinate axes, location of origin, and redundancy for the one- and two-dimensional Fourier transform for complex and real data.

3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography

Treesearch

Michael C. Martin; Charlotte Dabat-Blondeau; Miriam Unger; Julia Sedlmair; Dilworth Y. Parkinson; Hans A. Bechtel; Barbara Illman; Jonathan M. Castro; Marco Keiluweit; David Buschke; Brenda Ogle; Michael J. Nasse; Carol J. Hirschmugl

2013-01-01

We report Fourier transform infrared spectro-microtomography, a nondestructive three-dimensional imaging approach that reveals the distribution of distinctive chemical compositions throughout an intact biological or materials sample. The method combines mid-infrared absorption contrast with computed tomographic data acquisition and reconstruction to enhance chemical...

Chemometric Analysis of Multicomponent Biodegradable Plastics by Fourier Transform Infrared Spectrometry: The R-Matrix Method

USDA-ARS?s Scientific Manuscript database

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...

Applications of Fourier transform infrared spectroscopy to quality control of the epoxy matrix

NASA Technical Reports Server (NTRS)

Antoon, M. K.; Starkey, K. M.; Koenig, J. L.

1979-01-01

The object of the paper is to demonstrate the utility of Fourier transform infrared (FT-IR) difference spectra for investigating the composition of a neat epoxy resin, hardener, and catalysts. The composition and degree of cross-linking of the cured matrix is also considered.

The Kinetics of Mo(Co)6 Substitution Monitored by Fourier Transform Infrared Spectrophotometry.

ERIC Educational Resources Information Center

Suslick, Kenneth S.; And Others

1987-01-01

Describes a physical chemistry experiment that uses Fourier transform (FTIR) spectrometers and microcomputers as a way of introducing students to the spectral storage and manipulation techniques associated with digitized data. It can be used to illustrate FTIR spectroscopy, simple kinetics, inorganic mechanisms, and Beer's Law. (TW)

A statistical evaluation of spectral fingerprinting methods using analysis of variance and principal component analysis

USDA-ARS?s Scientific Manuscript database

Six methods were compared with respect to spectral fingerprinting of a well-characterized series of broccoli samples. Spectral fingerprints were acquired for finely-powdered solid samples using Fourier transform-infrared (IR) and Fourier transform-near infrared (NIR) spectrometry and for aqueous met...

Machine Learning-Aided, Robust Wideband Spectrum Sensing for Cognitive Radios

DTIC Science & Technology

2015-06-12

to even Approved for public release; distribution is unlimited. 2 on the order of a giga -Hertz (GHz). Due to wide bandwidth and noncontiguous...Frequency Band CS Compressive Sampling DFT Discrete Fourier Transform EMI Electro Magnetic Interference FFT Fast Fourier Transform GHz Giga Hertz Hz Hertz

Blue light emitting diesel soot for photonic applications

NASA Astrophysics Data System (ADS)

Swapna, M. S.; Sankararaman, S.

2018-01-01

The present work is the first report of producing blue light emission from phosphor free and low-cost material—the diesel soot from the internal combustion engines (ICEs). The structural morphology is analyzed by field emission scanning electron microscopy and high-resolution transmission electron microscopy. The optical characterization is done by recording UV-visible spectrum and photoluminescent Spectrum. The CIE plot and the power spectrum for the sample show blue emission. This is further verified by collecting diesel soot from the ICE of different year of make. A visual confirmation of blue emission is obtained by exciting the sample with UV laser. The presence of various allotropic forms of carbon in the sample is identified by x-ray diffraction, Fourier transform infrared and Raman spectroscopic analysis.

The Effect of Substrate Emissivity on the Spectral Emission of a Hot-Gas Overlayer

DTIC Science & Technology

2015-12-30

unlimited. Unclassified Unlimited Unclassified Unlimited Unclassified Unlimited Unclassified Unlimited 19 Harold D. Ladouceur (202) 767-3558 Fourier ...13 REFERENCES………………………………………………………………………………….………..14 E-1 EXECUTIVE SUMMARY Fourier transform infrared...Raman spectroscopy, ambient x-ray photoelectron spectroscopy, near- infrared thermal imaging, and Fourier transform infrared emission spectroscopy

Fourier Deconvolution Methods for Resolution Enhancement in Continuous-Wave EPR Spectroscopy.

PubMed

Reed, George H; Poyner, Russell R

2015-01-01

An overview of resolution enhancement of conventional, field-swept, continuous-wave electron paramagnetic resonance spectra using Fourier transform-based deconvolution methods is presented. Basic steps that are involved in resolution enhancement of calculated spectra using an implementation based on complex discrete Fourier transform algorithms are illustrated. Advantages and limitations of the method are discussed. An application to an experimentally obtained spectrum is provided to illustrate the power of the method for resolving overlapped transitions. © 2015 Elsevier Inc. All rights reserved.

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.

Diffraction Theory and Almost Periodic Distributions

NASA Astrophysics Data System (ADS)

Strungaru, Nicolae; Terauds, Venta

2016-09-01

We introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distribution. We further introduce the spaces of weakly, strongly and null weakly almost periodic tempered distributions and show that for weakly almost periodic tempered distributions the Eberlein decomposition holds. For translation bounded measures all these notions coincide with the classical ones. We show that tempered distributions with measure Fourier transform are weakly almost periodic and that for this class, the Eberlein decomposition is exactly the Fourier dual of the Lebesgue decomposition, with the Fourier-Bohr coefficients specifying the pure point part of the Fourier transform. We complete the project by looking at few interesting examples.

MRS3D: 3D Spherical Wavelet Transform on the Sphere

NASA Astrophysics Data System (ADS)

Lanusse, F.; Rassat, A.; Starck, J.-L.

2011-12-01

Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D Spherical Fourier-Bessel (SFB) analysis is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. We present a new fast Discrete Spherical Fourier-Bessel Transform (DSFBT) based on both a discrete Bessel Transform and the HEALPIX angular pixelisation scheme. We tested the 3D wavelet transform and as a toy-application, applied a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and found we can successfully remove noise without much loss to the large scale structure. The new spherical 3D isotropic wavelet transform, called MRS3D, is ideally suited to analysing and denoising future 3D spherical cosmological surveys; it uses a novel discrete spherical Fourier-Bessel Transform. MRS3D is based on two packages, IDL and Healpix and can be used only if these two packages have been installed.

Wavelet based detection of manatee vocalizations

NASA Astrophysics Data System (ADS)

Gur, Berke M.; Niezrecki, Christopher

2005-04-01

The West Indian manatee (Trichechus manatus latirostris) has become endangered partly because of watercraft collisions in Florida's coastal waterways. Several boater warning systems, based upon manatee vocalizations, have been proposed to reduce the number of collisions. Three detection methods based on the Fourier transform (threshold, harmonic content and autocorrelation methods) were previously suggested and tested. In the last decade, the wavelet transform has emerged as an alternative to the Fourier transform and has been successfully applied in various fields of science and engineering including the acoustic detection of dolphin vocalizations. As of yet, no prior research has been conducted in analyzing manatee vocalizations using the wavelet transform. Within this study, the wavelet transform is used as an alternative to the Fourier transform in detecting manatee vocalizations. The wavelet coefficients are analyzed and tested against a specified criterion to determine the existence of a manatee call. The performance of the method presented is tested on the same data previously used in the prior studies, and the results are compared. Preliminary results indicate that using the wavelet transform as a signal processing technique to detect manatee vocalizations shows great promise.

A Sagnac Fourier spectrometer

DOE PAGES

Lenzner, Matthias; Diels, Jean -Claude

2017-03-09

A spectrometer based on a Sagnac interferometer, where one of the mirrors is replaced by a transmission grating, is introduced. Since the action of a transmission grating is reversible, both directions experience the same diffraction at a given wavelength. At the output, the crossed wavefronts are imaged onto a camera, where their Fizeau fringe pattern is recorded. Each spectral element produces a unique spatial frequency, hence the Fourier transform of the recorded interferogram contains the spectrum. Since the grating is tuned to place zero spatial frequency at a selected wavelength, the adjoining spectrum is heterodyned with respect to this wavelength.more » This spectrum can then be discriminated at a high spectral resolution from relatively low spatial frequencies. The spectrometer can be designed without moving parts for a relatively narrow spectral range or with a rotatable grating. As a result, the latter version bears the potential to be calibrated without a calibrated light source.« less

A Sagnac Fourier spectrometer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lenzner, Matthias; Diels, Jean -Claude

A spectrometer based on a Sagnac interferometer, where one of the mirrors is replaced by a transmission grating, is introduced. Since the action of a transmission grating is reversible, both directions experience the same diffraction at a given wavelength. At the output, the crossed wavefronts are imaged onto a camera, where their Fizeau fringe pattern is recorded. Each spectral element produces a unique spatial frequency, hence the Fourier transform of the recorded interferogram contains the spectrum. Since the grating is tuned to place zero spatial frequency at a selected wavelength, the adjoining spectrum is heterodyned with respect to this wavelength.more » This spectrum can then be discriminated at a high spectral resolution from relatively low spatial frequencies. The spectrometer can be designed without moving parts for a relatively narrow spectral range or with a rotatable grating. As a result, the latter version bears the potential to be calibrated without a calibrated light source.« less

The Use of Continuous Wavelet Transform Based on the Fast Fourier Transform in the Analysis of Multi-channel Electrogastrography Recordings.

PubMed

Komorowski, Dariusz; Pietraszek, Stanislaw

2016-01-01

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal.

Analytical properties of time-of-flight PET data.

PubMed

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M

2008-06-07

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the 'bow-tie' property of the 2D Radon transform to the time-of-flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data.

Analytical properties of time-of-flight PET data

NASA Astrophysics Data System (ADS)

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M.

2008-06-01

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the 'bow-tie' property of the 2D Radon transform to the time-of-flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data.

Improving Spectral Results Using Row-by-Row Fourier Transform of Spatial Heterodyne Raman Spectrometer Interferogram.

PubMed

Barnett, Patrick D; Strange, K Alicia; Angel, S Michael

2017-06-01

This work describes a method of applying the Fourier transform to the two-dimensional Fizeau fringe patterns generated by the spatial heterodyne Raman spectrometer (SHRS), a dispersive interferometer, to correct the effects of certain types of optical alignment errors. In the SHRS, certain types of optical misalignments result in wavelength-dependent and wavelength-independent rotations of the fringe pattern on the detector. We describe here a simple correction technique that can be used in post-processing, by applying the Fourier transform in a row-by-row manner. This allows the user to be more forgiving of fringe alignment and allows for a reduction in the mechanical complexity of the SHRS.

The application of digital signal processing techniques to a teleoperator radar system

NASA Technical Reports Server (NTRS)

Pujol, A.

1982-01-01

A digital signal processing system was studied for the determination of the spectral frequency distribution of echo signals from a teleoperator radar system. The system consisted of a sample and hold circuit, an analog to digital converter, a digital filter, and a Fast Fourier Transform. The system is interfaced to a 16 bit microprocessor. The microprocessor is programmed to control the complete digital signal processing. The digital filtering and Fast Fourier Transform functions are implemented by a S2815 digital filter/utility peripheral chip and a S2814A Fast Fourier Transform chip. The S2815 initially simulates a low-pass Butterworth filter with later expansion to complete filter circuit (bandpass and highpass) synthesizing.

Color image cryptosystem using Fresnel diffraction and phase modulation in an expanded fractional Fourier transform domain

NASA Astrophysics Data System (ADS)

Chen, Hang; Liu, Zhengjun; Chen, Qi; Blondel, Walter; Varis, Pierre

2018-05-01

In this letter, what we believe is a new technique for optical color image encryption by using Fresnel diffraction and a phase modulation in an extended fractional Fourier transform domain is proposed. Different from the RGB component separation based method, the color image is converted into one component by improved Chirikov mapping. The encryption system is addressed with Fresnel diffraction and phase modulation. A pair of lenses is placed into the fractional Fourier transform system for the modulation of beam propagation. The structure parameters of the optical system and parameters in Chirikov mapping serve as extra keys. Some numerical simulations are given to test the validity of the proposed cryptosystem.

Ultra-Wideband Radar Transient Detection using Time-Frequency and Wavelet Transforms.

DTIC Science & Technology

1992-12-01

if p==2, mesh(flipud(abs(spdatamatrix).A2)) end 2. Wigner - Ville Distribution function P = wvd (data,winlenstep,begintheendp) % Filename: wvd.m % Title...short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution , and time-scale methods, such as the a trous...such as the short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution [1], and time-scale methods, such

SAR image formation with azimuth interpolation after azimuth transform

DOEpatents

Doerry,; Armin W. , Martin; Grant D. , Holzrichter; Michael, W [Albuquerque, NM

2008-07-08

Two-dimensional SAR data can be processed into a rectangular grid format by subjecting the SAR data to a Fourier transform operation, and thereafter to a corresponding interpolation operation. Because the interpolation operation follows the Fourier transform operation, the interpolation operation can be simplified, and the effect of interpolation errors can be diminished. This provides for the possibility of both reducing the re-grid processing time, and improving the image quality.

Delineation of First-Order Elastic Property Closures for Hexagonal Metals Using Fast Fourier Transforms

PubMed Central

Landry, Nicholas W.; Knezevic, Marko

2015-01-01

Property closures are envelopes representing the complete set of theoretically feasible macroscopic property combinations for a given material system. In this paper, we present a computational procedure based on fast Fourier transforms (FFTs) for delineation of elastic property closures for hexagonal close packed (HCP) metals. The procedure consists of building a database of non-zero Fourier transforms for each component of the elastic stiffness tensor, calculating the Fourier transforms of orientation distribution functions (ODFs), and calculating the ODF-to-elastic property bounds in the Fourier space. In earlier studies, HCP closures were computed using the generalized spherical harmonics (GSH) representation and an assumption of orthotropic sample symmetry; here, the FFT approach allowed us to successfully calculate the closures for a range of HCP metals without invoking any sample symmetry assumption. The methodology presented here facilitates for the first time computation of property closures involving normal-shear coupling stiffness coefficients. We found that the representation of these property linkages using FFTs need more terms compared to GSH representations. However, the use of FFT representations reduces the computational time involved in producing the property closures due to the use of fast FFT algorithms. Moreover, FFT algorithms are readily available as opposed to GSH codes. PMID:28793566

Accurate determination of the diffusion coefficient of proteins by Fourier analysis with whole column imaging detection.

PubMed

Zarabadi, Atefeh S; Pawliszyn, Janusz

2015-02-17

Analysis in the frequency domain is considered a powerful tool to elicit precise information from spectroscopic signals. In this study, the Fourier transformation technique is employed to determine the diffusion coefficient (D) of a number of proteins in the frequency domain. Analytical approaches are investigated for determination of D from both experimental and data treatment viewpoints. The diffusion process is modeled to calculate diffusion coefficients based on the Fourier transformation solution to Fick's law equation, and its results are compared to time domain results. The simulations characterize optimum spatial and temporal conditions and demonstrate the noise tolerance of the method. The proposed model is validated by its application for the electropherograms from the diffusion path of a set of proteins. Real-time dynamic scanning is conducted to monitor dispersion by employing whole column imaging detection technology in combination with capillary isoelectric focusing (CIEF) and the imaging plug flow (iPF) experiment. These experimental techniques provide different peak shapes, which are utilized to demonstrate the Fourier transformation ability in extracting diffusion coefficients out of irregular shape signals. Experimental results confirmed that the Fourier transformation procedure substantially enhanced the accuracy of the determined values compared to those obtained in the time domain.

Optical joint transform correlation on the DMD. [deformable mirror device

NASA Technical Reports Server (NTRS)

Knopp, Jerome; Juday, Richard D.

1989-01-01

Initial experimental investigation of the deformable mirror device (DMD) in a joint optical transform correlation is reported. The inverted cloverleaf version of the DMD, in which form the DMD is phase-mostly but of limited phase range, is used. Binarized joint Fourier transforms were calculated for similar and dissimilar objects and written onto the DMD. Inverse Fourier transform was done in a diffraction order for which the DMD shows phase-mostly modulation. Matched test objects produced sharp correlation, distinct objects did not. Further studies are warranted and they are outlined.

Innovative design method of automobile profile based on Fourier descriptor

NASA Astrophysics Data System (ADS)

Gao, Shuyong; Fu, Chaoxing; Xia, Fan; Shen, Wei

2017-10-01

Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.

Fourier transform wavefront control with adaptive prediction of the atmosphere.

PubMed

Poyneer, Lisa A; Macintosh, Bruce A; Véran, Jean-Pierre

2007-09-01

Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.

PLANE-INTEGRATED OPEN-PATH FOURIER TRANSFORM INFRARED SPECTROMETRY METHODOLOGY FOR ANAEROBIC SWINE LAGOON EMISSION MEASUREMENTS

EPA Science Inventory

Emissions of ammonia and methane from an anaerobic lagoon at a swine animal feeding operation were evaluated five times over a period of two years. The plane-integrated (PI) open-path Fourier transform infrared spectrometry (OP-FTIR) methodology was used to transect the plume at ...

Turbulence excited frequency domain damping measurement and truncation effects

NASA Technical Reports Server (NTRS)

Soovere, J.

1976-01-01

Existing frequency domain modal frequency and damping analysis methods are discussed. The effects of truncation in the Laplace and Fourier transform data analysis methods are described. Methods for eliminating truncation errors from measured damping are presented. Implications of truncation effects in fast Fourier transform analysis are discussed. Limited comparison with test data is presented.

Comparison and validation of Fourier transform infrared spectroscopic methods for monitoring secondary cell wall cellulose from cotton fibers

USDA-ARS?s Scientific Manuscript database

The amount of secondary cell wall (SCW) cellulose in the fiber affects the quality and commercial value of cotton. Accurate assessments of SCW cellulose are essential for improving cotton fibers. Fourier Transform Infrared (FT-IR) spectroscopy enables distinguishing SCW from other cell wall componen...

CHARACTERIZATION OF AMBIENT PM2.5 AEROSOL AT A SOUTHEASTERN US SITE: FOURIER TRANSFORM INFRARED ANALYSIS OR PARTICLE PHASE

EPA Science Inventory

During a field study in the summer of 2000 in the Research Triangle Park (RTP), aerosol samples were collected using a five stage cascade impactor and subsequently analyzed using Fourier Transform Infrared Spectroscopy (FTIR). The impaction surfaces were stainless steel disks....

Abel inversion using fast Fourier transforms.

PubMed

Kalal, M; Nugent, K A

1988-05-15

A fast Fourier transform based Abel inversion technique is proposed. The method is faster than previously used techniques, potentially very accurate (even for a relatively small number of points), and capable of handling large data sets. The technique is discussed in the context of its use with 2-D digital interferogram analysis algorithms. Several examples are given.

Topics in Chemical Instrumentation: Fourier Transform-Infrared Spectroscopy: Part I. Instrumentation.

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)

Diffuse-reflectance fourier-transform mid-infrared spectroscopy as a method of characterizing changes in soil organic matter

USDA-ARS?s Scientific Manuscript database

Diffuse-Reflectance Fourier-Transform Mid-Infrared Spectroscopy (MidIR) can identify the presence of important organic functional groups in soil organic matter (SOM). Soils contain myriad organic and inorganic components that absorb in the MidIR so spectral interpretation needs to be validated in or...

Secondary cell wall development in cotton fibers as examined with attenuated total reflection Fourier transform infrared spectroscopy

USDA-ARS?s Scientific Manuscript database

Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-IR) spectroscopy. The selected harvesting points coincide with secondary cell wall (SCW) development in the fibers. Progressive but moderat...

Development of secondary cell wall in cotton fibers as examined with Fourier transform-infrared spectroscopy

USDA-ARS?s Scientific Manuscript database

Our presentation will focus on continuing efforts to examine secondary cell wall development in cotton fibers using infrared Spectroscopy. Cotton fibers harvested at 18, 20, 24, 28, 32, 36 and 40 days after flowering were examined using attenuated total reflection Fourier transform-infrared (ATR FT-...

INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections

NASA Astrophysics Data System (ADS)

Caliari, Marco; Zuccher, Simone

2017-04-01

Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of arbitrary points are quite rare, especially in MATLAB language. Here we employ the Nonequispaced Fast Fourier Transform (NFFT, by J. Keiner, S. Kunis, and D. Potts), a C library designed for this purpose, and provide a Matlab® and GNU Octave interface that makes NFFT easily available to the Numerical Analysis community. We test the effectiveness of our package in the framework of quantum vortex reconnections, where pseudospectral Fourier methods are commonly used and local high resolution is required in the post-processing stage. We show that the efficient evaluation of a truncated Fourier series at arbitrary points provides excellent results at a computational cost much smaller than carrying out a numerical simulation of the problem on a sufficiently fine regular grid that can reproduce comparable details of the reconnecting vortices.

Vibrational spectroscopy and DFT calculations of flavonoid derriobtusone A

NASA Astrophysics Data System (ADS)

Marques, A. N. L.; Mendes Filho, J.; Freire, P. T. C.; Santos, H. S.; Albuquerque, M. R. J. R.; Bandeira, P. N.; Leite, R. V.; Braz-Filho, R.; Gusmão, G. O. M.; Nogueira, C. E. S.; Teixeira, A. M. R.

2017-02-01

Flavonoids are secondary metabolites of plants which perform various functions. One subclass of flavonoid is auronol that can present immunostimulating activity. In this work Fourier-Transform Infrared with Attenuated Total Reflectance (FTIR-ATR) and Fourier-Transform Raman (FT-Raman) spectra of an auronol, derriobtusone A (C18H12O4), were obtained at room temperature. Theoretical calculations using Density Functional Theory (DFT) were performed in order to assign the normal modes and to interpret the spectra of the derriobtusone A molecule. The FTIR-ATR and FT-Raman spectra of the crystal, were recorded at room temperature in the regions 600 cm-1 to 4000 cm-1 and 40 cm-1 to 4000 cm-1, respectively. The normal modes of vibrations were obtained using Density Functional Theory with B3LYP functional and 6-31G+ (d,p) basis set. The calculated frequencies are in good agreement with those obtained experimentally. Detailed assignments of the normal modes present in both the Fourier-Transform infrared and the Fourier-Transform Raman spectra of the crystal are given.

PISCES High Contrast Integral Field Spectrograph Simulations and Data Reduction Pipeline

NASA Technical Reports Server (NTRS)

Llop Sayson, Jorge Domingo; Memarsadeghi, Nargess; McElwain, Michael W.; Gong, Qian; Perrin, Marshall; Brandt, Timothy; Grammer, Bryan; Greeley, Bradford; Hilton, George; Marx, Catherine

2015-01-01

The PISCES (Prototype Imaging Spectrograph for Coronagraphic Exoplanet Studies) is a lenslet array based integral field spectrograph (IFS) designed to advance the technology readiness of the WFIRST (Wide Field Infrared Survey Telescope)-AFTA (Astrophysics Focused Telescope Assets) high contrast Coronagraph Instrument. We present the end to end optical simulator and plans for the data reduction pipeline (DRP). The optical simulator was created with a combination of the IDL (Interactive Data Language)-based PROPER (optical propagation) library and Zemax (a MatLab script), while the data reduction pipeline is a modified version of the Gemini Planet Imager's (GPI) IDL pipeline. The simulations of the propagation of light through the instrument are based on Fourier transform algorithms. The DRP enables transformation of the PISCES IFS data to calibrated spectral data cubes.

Zeroth-order phase-contrast technique.

PubMed

Pizolato, José Carlos; Cirino, Giuseppe Antonio; Gonçalves, Cristhiane; Neto, Luiz Gonçalves

2007-11-01

What we believe to be a new phase-contrast technique is proposed to recover intensity distributions from phase distributions modulated by spatial light modulators (SLMs) and binary diffractive optical elements (DOEs). The phase distribution is directly transformed into intensity distributions using a 4f optical correlator and an iris centered in the frequency plane as a spatial filter. No phase-changing plates or phase dielectric dots are used as a filter. This method allows the use of twisted nematic liquid-crystal televisions (LCTVs) operating in the real-time phase-mostly regime mode between 0 and p to generate high-intensity multiple beams for optical trap applications. It is also possible to use these LCTVs as input SLMs for optical correlators to obtain high-intensity Fourier transform distributions of input amplitude objects.

Production and characterization of activated carbon from wood wastes

NASA Astrophysics Data System (ADS)

Ramirez, A. P.; Giraldo, S.; Ulloa, M.; Flórez, E.; Y Acelas, N.

2017-12-01

Cedarwood (Cedrela Angustifolia) and teak (Tectona Grandis) woods are typically used for furniture manufacture because they have high durability, are light and easy to work. During these manufacturing process, large amount of these wastes is generated causing disposal environmental problems. In this paper, the residual wastes (sawdust) of Cedar (C) and Teak (T) are transformed into an activated material. The chemical composition of both biomass (C and T) was determinate by TGA (Thermogravimetric Analysis). Activated materials were characterized in surface area following the BET (Brunauer, Emmett and Teller) method, morphology using SEM (Scanning Electron Microscopy) and to know their functional groups a FTIR (Fourier Transform Infrared Spectroscopy) analysis was done. Their adsorption capacity was evaluated by removal of Methylene Blue (MB) and Congo Red (CR) from aqueous solutions.

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans.

PubMed

Magnes, Jenny; Hastings, Harold M; Raley-Susman, Kathleen M; Alivisatos, Clara; Warner, Adam; Hulsey-Vincent, Miranda

2017-09-13

This manuscript describes how to classify nematodes using temporal far-field diffraction signatures. A single C. elegans is suspended in a water column inside an optical cuvette. A 632 nm continuous wave HeNe laser is directed through the cuvette using front surface mirrors. A significant distance of at least 20-30 cm traveled after the light passes through the cuvette ensures a useful far-field (Fraunhofer) diffraction pattern. The diffraction pattern changes in real time as the nematode swims within the laser beam. The photodiode is placed off-center in the diffraction pattern. The voltage signal from the photodiode is observed in real time and recorded using a digital oscilloscope. This process is repeated for 139 wild type and 108 "roller" C. elegans. Wild type worms exhibit a rapid oscillation pattern in solution. The "roller" worms have a mutation in a key component of the cuticle that interferes with smooth locomotion. Time intervals that are not free of saturation and inactivity are discarded. It is practical to divide each average by its maximum to compare relative intensities. The signal for each worm is Fourier transformed so that the frequency pattern for each worm emerges. The signal for each type of worm is averaged. The averaged Fourier spectra for the wild type and the "roller" C. elegans are distinctly different and reveal that the dynamic worm shapes of the two different worm strains can be distinguished using Fourier analysis. The Fourier spectra of each worm strain match an approximate model using two different binary worm shapes that correspond to locomotory moments. The envelope of the averaged frequency distribution for actual and modeled worms confirms the model matches the data. This method can serve as a baseline for Fourier analysis for many microscopic species, as every microorganism will have its unique Fourier spectrum.

Three-dimensional Fourier transform evaluation of sequences of spatially and temporally modulated speckle interferograms.

PubMed

Trillo, C; Doval, A F; López-Vázquez, J C

2010-07-05

Phase evaluation methods based on the 2D spatial Fourier transform of a speckle interferogram with spatial carrier usually assume that the Fourier spectrum of the interferogram has a trimodal distribution, i. e. that the side lobes corresponding to the interferential terms do not overlap the other two spectral terms, which are related to the intensity of the object and reference beams, respectively. Otherwise, part of the spectrum of the object beam is inside the inverse-transform window of the selected interference lobe and induces an error in the resultant phase map. We present a technique for the acquisition and processing of speckle interferogram sequences that separates the interference lobes from the other spectral terms when the aforementioned assumption does not apply and regardless of the temporal bandwidth of the phase signal. It requires the recording of a sequence of interferograms with spatial and temporal carriers, and their processing with a 3D Fourier transform. In the resultant 3D spectrum, the spatial and temporal carriers separate the conjugate interferential terms from each other and from the term related to the object beam. Experimental corroboration is provided through the measurement of the amplitude of surface acoustic waves in plates with a double-pulsed TV holography setup. The results obtained with the proposed method are compared to those obtained with the processing of individual interferograms with the regular spatial-carrier 2D Fourier transform method.

Structures of aspartic acid-96 in the L and N intermediates of bacteriorhodopsin: analysis by Fourier transform infrared spectroscopy

NASA Technical Reports Server (NTRS)

Maeda, A.; Sasaki, J.; Shichida, Y.; Yoshizawa, T.; Chang, M.; Ni, B.; Needleman, R.; Lanyi, J. K.

1992-01-01

The light-induced difference Fourier transform infrared spectrum between the L or N intermediate minus light-adapted bacteriorhodopsin (BR) was measured in order to examine the protonated states and the changes in the interactions of carboxylic acids of Asp-96 and Asp-115 in these intermediates. Vibrational bands due to the protonated and unprotonated carboxylic acid were identified by isotope shift and band depletion upon substitution of Asp-96 or -115 by asparagine. While the signal due to the deprotonation of Asp-96 was clearly observed in the N intermediate, this residue remained protonated in L. Asp-115 was partially deprotonated in L. The C = O stretching vibration of protonated Asp-96 of L showed almost no shift upon 2H2O substitution, in contrast to the corresponding band of Asp-96 or Asp-115 of BR, which shifted by 9-12 cm-1 under the same conditions. In the model system of acetic acid in organic solvents, such an absence of the shift of the C = O stretching vibration of the protonated carboxylic acid upon 2H2O substitution was seen only when the O-H of acetic acid is hydrogen-bonded. The non-hydrogen-bonded monomer showed the 2H2O-dependent shift. Thus, the O-H bond of Asp-96 enters into hydrogen bonding upon conversion of BR to L. Its increased hydrogen bonding in L is consistent with the observed downshift of the O-H stretching vibration of the carboxylic acid of Asp-96.

Solid perception mechanism by a shading pattern: spatial frequency components in a corrugated wave pattern.

PubMed

Nameda, N

1988-01-01

Illumination allows solid object perception to be obtained and depicted by a shading pattern produced by lighting. The shading cue, as one of solid perception cues (Gibson 1979), was investigated in regard to a white corrugated wave shape, using computer graphic device: Tospix-2. The reason the corrugated wave was chosen, is that an alternately bright and dark pattern, produced by shading, can be conveniently analyzed into contained spatial frequencies. This paper reports spatial frequency properties contained in the shading pattern. The shading patterns, input into the computer graphic device, are analyzed by Fourier Transformation by the same device. After the filtration by various spatial frequency low and high pass filters, Inverse Fourier Transformation is carried out for the residual components. The result of the analysis indicates that the third through higher harmonics components are important in regard to presenting a solid reality feeling in solid perception. Sakata (1983) also reported that an edged pattern, superimposed onto a lower sinusoidal pattern, was important in solid perception. The third through higher harmonics components express the changing position of luminance on the pattern, and a slanted plane relating to the light direction. Detection of a solid shape, constructed with flat planes, is assumed to be on the bottom of the perfect curved solid perception mechanism. Apparent evidence for this assumption, in difficult visual conditions, is that a flat paneled solid is seen before the curved solid. This mechanism is explained by two spatial frequency neural network systems, assumed as having correspondence with higher spatial frequency detection and lower spatial frequency detection.

Identification of carbonates as additives in pressure-sensitive adhesive tape substrate with Fourier transform infrared spectroscopy (FTIR) and its application in three explosive cases.

PubMed

Lv, Jungang; Feng, Jimin; Zhang, Wen; Shi, Rongguang; Liu, Yong; Wang, Zhaohong; Zhao, Meng

2013-01-01

Pressure-sensitive tape is often used to bind explosive devices. It can become important trace evidence in many cases. Three types of calcium carbonate (heavy, light, and active CaCO(3)), which were widely used as additives in pressure-sensitive tape substrate, were analyzed with Fourier transform infrared spectroscopy (FTIR) in this study. A Spectrum GX 2000 system with a diamond anvil cell and a deuterated triglycine sulfate detector was employed for IR observation. Background was subtracted for every measurement, and triplicate tests were performed. Differences in positions of main peaks and the corresponding functional groups were investigated. Heavy CaCO(3) could be identified from the two absorptions near 873 and 855/cm, while light CaCO(3) only has one peak near 873/cm because of the low content of aragonite. Active CaCO(3) could be identified from the absorptions in the 2800-2900/cm region because of the existence of organic compounds. Tiny but indicative changes in the 878-853/cm region were found in the spectra of CaCO(3) with different content of aragonite and calcite. CaCO(3) in pressure-sensitive tape, which cannot be differentiated by scanning electron microscope/energy dispersive X-ray spectrometer and thermal analysis, can be easily identified using FTIR. The findings were successfully applied to three specific explosive cases and would be helpful in finding the possible source of explosive devices in future cases. © 2012 American Academy of Forensic Sciences.

Investigations of the functional states of dendritic cells under different conditioned microenvironments by Fourier transformed infrared spectroscopy.

PubMed

Dong, Rong; Long, Jinhua; Xu, Xiaoli; Zhang, Chunlin; Wen, Zongyao; Li, Long; Yao, Weijuan; Zeng, Zhu

2014-01-10

Dendritic cells are potent and specialized antigen presenting cells, which play a crucial role in initiating and amplifying both the innate and adaptive immune responses. The dendritic cell-based vaccination against cancer has been clinically achieved promising successes. But there are still many challenges in its clinical application, especially for how to identify the functional states. The CD14+ monocytes were isolated from human peripheral blood after plastic adherence and purified to approximately 98% with cocktail immunomagnetic beads. The immature dendritic cells and mature dendritic cells were induced by traditional protocols. The resulting dendritic cells were cocultured with normal cells and cancer cells. The functional state of dendritic cells including immature dendritic cells (imDCs) and mature dendritic cells (mDCs) under different conditioned microenvironments were investigated by Fourier transformed infrared spectroscopy (FTIR) and molecular biological methods. The results of Fourier transformed infrared spectroscopy showed that the gene transcription activity and energy states of dendritic cells were specifically suppressed by tumor cells (P < 0.05 or 0.01). The expression levels of NF-kappa B (NF-κB) in dendritic cells were also specifically inhibited by tumor-derived factors (P < 0.05 or 0.01). Moreover, the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were closely correlated with the expression levels of NF-κB (R2:0.69 and R2:0.81, respectively). Our results confirmed that the ratios of absorption intensities of Fourier transformed infrared spectroscopy at given wave numbers were positively correlated with the expression levels of NF-κB, suggesting that Fourier transformed infrared spectroscopy technology could be clinically applied to identify the functional states of dendritic cell when performing dendritic cell-based vaccination. It's significant for the simplification and standardization of dendritic cell-based vaccination clinical preparation protocols.

Visible-Light Initiated Free-Radical/Cationic Ring-Opening Hybrid Photopolymerization of Methacrylate/Epoxy: Polymerization Kinetics, Crosslinking Structure, and Dynamic Mechanical Properties.

PubMed

Ge, Xueping; Ye, Qiang; Song, Linyong; Misra, Anil; Spencer, Paulette

2015-04-01

The effects of polymerization kinetics and chemical miscibility on the crosslinking structure and mechanical properties of polymers cured by visible-light initiated free-radical/cationic ring-opening hybrid photopolymerization are determined. A three-component initiator system is used and the monomer system contains methacrylates and epoxides. The photopolymerization kinetics is monitored in situ by Fourier transform infrared-attenuated total reflectance. The crosslinking structure is studied by modulated differential scanning calorimetry and dynamic mechanical analysis. X-ray microcomputed tomography is used to evaluate microphase separation. The mechanical properties of polymers formed by hybrid formed by free-radical polymerization. These investigations mark the first time that the benefits of the chain transfer reaction between epoxy and hydroxyl groups of methacrylate, on the crosslinking network and microphase separation during hybrid visible-light initiated photopolymerization, have been determined.

Synthesis of a ternary Ag/RGO/ZnO nanocomposite via microwave irradiation and its application for the degradation of Rhodamine B under visible light.

PubMed

Surendran, Divya Kollikkara; Xavier, Marilyn Mary; Viswanathan, Vandana Parakkal; Mathew, Suresh

2017-06-01

Reduced graphene oxide supporting plasmonic photocatalyst (Ag) on ZnO has been synthesized via a facile two-step microwave synthesis using RGO/ZnO and AgNO 3 . First step involves fabrication of RGO/ZnO via microwave irradiation. The nanocomposites were characterized by X-ray diffraction analysis, transmission electron microscopy, Fourier transform infrared spectroscopy, and Raman spectroscopy. Ag/RGO/ZnO shows enhanced photoactivity under visible light for the degradation of Rhodamine B. Enhanced charge separation and migration have been assigned using UV-vis diffuse reflectance spectra, photoluminescence spectra, electrochemical impedance spectra, and TCSPC analysis. The improved photoactivity of Ag/RGO/ZnO can be ascribed to the prolonged lifetime of photogenerated electron-hole pairs and effective interfacial hybridization between RGO and Ag with ZnO nanoparticles. Ag nanoparticles can absorb visible light via surface plasmon resonance to enhance photocatalytic activity.

Characterising laser beams with liquid crystal displays

NASA Astrophysics Data System (ADS)

Dudley, Angela; Naidoo, Darryl; Forbes, Andrew

2016-02-01

We show how one can determine the various properties of light, from the modal content of laser beams to decoding the information stored in optical fields carrying orbital angular momentum, by performing a modal decomposition. Although the modal decomposition of light has been known for a long time, applied mostly to pattern recognition, we illustrate how this technique can be implemented with the use of liquid-crystal displays. We show experimentally how liquid crystal displays can be used to infer the intensity, phase, wavefront, Poynting vector, and orbital angular momentum density of unknown optical fields. This measurement technique makes use of a single spatial light modulator (liquid crystal display), a Fourier transforming lens and detector (CCD or photo-diode). Such a diagnostic tool is extremely relevant to the real-time analysis of solid-state and fibre laser systems as well as mode division multiplexing as an emerging technology in optical communication.

Equations for solar tracking.

PubMed

Merlaud, Alexis; De Mazière, Martine; Hermans, Christian; Cornet, Alain

2012-01-01

Direct sunlight absorption by trace gases can be used to quantify them and investigate atmospheric chemistry. In such experiments, the main optical apparatus is often a grating or a Fourier transform spectrometer. A solar tracker based on motorized rotating mirrors is commonly used to direct the light along the spectrometer axis, correcting for the apparent rotation of the Sun. Calculating the Sun azimuth and altitude for a given time and location can be achieved with high accuracy but different sources of angular offsets appear in practice when positioning the mirrors. A feedback on the motors, using a light position sensor close to the spectrometer, is almost always needed. This paper aims to gather the main geometrical formulas necessary for the use of a widely used kind of solar tracker, based on two 45° mirrors in altazimuthal set-up with a light sensor on the spectrometer, and to illustrate them with a tracker developed by our group for atmospheric research.

Equations for Solar Tracking

PubMed Central

Merlaud, Alexis; De Mazière, Martine; Hermans, Christian; Cornet, Alain

2012-01-01

Direct sunlight absorption by trace gases can be used to quantify them and investigate atmospheric chemistry. In such experiments, the main optical apparatus is often a grating or a Fourier transform spectrometer. A solar tracker based on motorized rotating mirrors is commonly used to direct the light along the spectrometer axis, correcting for the apparent rotation of the Sun. Calculating the Sun azimuth and altitude for a given time and location can be achieved with high accuracy but different sources of angular offsets appear in practice when positioning the mirrors. A feedback on the motors, using a light position sensor close to the spectrometer, is almost always needed. This paper aims to gather the main geometrical formulas necessary for the use of a widely used kind of solar tracker, based on two 45° mirrors in altazimuthal set-up with a light sensor on the spectrometer, and to illustrate them with a tracker developed by our group for atmospheric research. PMID:22666019

Development of online NIR urine analyzing system based on AOTF

NASA Astrophysics Data System (ADS)

Wan, Feng; Sun, Zhendong; Li, Xiaoxia

2006-09-01

In this paper, some key techniques on development of on-line MR urine analyzing system based on AOTF (Acousto - Optics Tunable Filter) are introduced. Problems about designing the optical system including collimation of incident light and working distance (the shortest distance for separating incident light and diffracted light) are analyzed and researched. DDS (Direct Digital Synthesizer) controlled by microprocessor is used to realize the wavelength scan. The experiment results show that this MR urine analyzing system based on. AOTF has 10000 - 4000cm -1 wavelength range and O.3ms wavelength transfer rate. Compare with the conventional Fourier Transform NIP. spectrophotometer for analyzing multi-components in urine, this system features low cost, small volume and on-line measurement function. Unscrambler software (multivariate statistical software by CAMO Inc. Norway) is selected as the software for processing the data. This system can realize on line quantitative analysis of protein, urea and creatinine in urine.

Enhanced photocatalytic activity of ZnO/CuO nanocomposite for the degradation of textile dye on visible light illumination.

PubMed

Saravanan, R; Karthikeyan, S; Gupta, V K; Sekaran, G; Narayanan, V; Stephen, A

2013-01-01

The photocatalytic degradation of organic dyes such as methylene blue and methyl orange in the presence of various percentages of composite catalyst under visible light irradiation was carried out. The catalyst ZnO nanorods and ZnO/CuO nanocomposites of different weight ratios were prepared by new thermal decomposition method, which is simple and cost effective. The prepared catalysts were characterized by different techniques such as X-ray diffraction, transmission electron microscopy, field emission scanning electron microscopy, Fourier transform infrared spectroscopy and UV-visible absorption spectroscopy. Further, the most photocatalytically active composite material was used for degradation of real textile waste water under visible light illumination. The irradiated samples were analysed by total organic carbon and chemical oxygen demand. The efficiency of the catalyst and their photocatalytic mechanism has been discussed in detail. Copyright © 2012 Elsevier B.V. All rights reserved.

Light-Cone Effect of Radiation Fields in Cosmological Radiative Transfer Simulations

NASA Astrophysics Data System (ADS)

Ahn, Kyungjin

2015-02-01

We present a novel method to implement time-delayed propagation of radiation fields in cosmo-logical radiative transfer simulations. Time-delayed propagation of radiation fields requires construction of retarded-time fields by tracking the location and lifetime of radiation sources along the corresponding light-cones. Cosmological radiative transfer simulations have, until now, ignored this "light-cone effect" or implemented ray-tracing methods that are computationally demanding. We show that radiative trans-fer calculation of the time-delayed fields can be easily achieved in numerical simulations when periodic boundary conditions are used, by calculating the time-discretized retarded-time Green's function using the Fast Fourier Transform (FFT) method and convolving it with the source distribution. We also present a direct application of this method to the long-range radiation field of Lyman-Werner band photons, which is important in the high-redshift astrophysics with first stars.

Theory of Wavelet-Based Coarse-Graining Hierarchies for Molecular Dynamics

DTIC Science & Technology

2017-04-01

resolution. ............................................... 15 Fig. 6 Fourier transform of the y-component of 1,000 atoms in crystalline PE (100,800 atoms...of magnitude of optimal representation. . 16 Fig. 7 Top row: Fourier transform of the y-component of a 100,800 atom crystalline PE sampled at 1 fs. 3... transform of the z-component of alanine dipeptide in vacuum excluding zero frequency to allow detail at other frequencies. MD at 500 K and 1 atm. Left

Fast space-varying convolution using matrix source coding with applications to camera stray light reduction.

PubMed

Wei, Jianing; Bouman, Charles A; Allebach, Jan P

2014-05-01

Many imaging applications require the implementation of space-varying convolution for accurate restoration and reconstruction of images. Here, we use the term space-varying convolution to refer to linear operators whose impulse response has slow spatial variation. In addition, these space-varying convolution operators are often dense, so direct implementation of the convolution operator is typically computationally impractical. One such example is the problem of stray light reduction in digital cameras, which requires the implementation of a dense space-varying deconvolution operator. However, other inverse problems, such as iterative tomographic reconstruction, can also depend on the implementation of dense space-varying convolution. While space-invariant convolution can be efficiently implemented with the fast Fourier transform, this approach does not work for space-varying operators. So direct convolution is often the only option for implementing space-varying convolution. In this paper, we develop a general approach to the efficient implementation of space-varying convolution, and demonstrate its use in the application of stray light reduction. Our approach, which we call matrix source coding, is based on lossy source coding of the dense space-varying convolution matrix. Importantly, by coding the transformation matrix, we not only reduce the memory required to store it; we also dramatically reduce the computation required to implement matrix-vector products. Our algorithm is able to reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. Experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy.

Remote microscopy and volumetric imaging on the surface of icy satellites

NASA Astrophysics Data System (ADS)

Soto, Alejandro; Nowicki, Keith; Howett, Carly; Feldkhun, Daniel; Retherford, Kurt D.

2017-10-01

With NASA PIDDP support we have applied recent advancements in Fourier-domain microscopy to develop an instrument capable of microscopic imaging from meter-scale distances for use on a planetary lander on the surface of an icy satellite or other planetary bodies. Without moving parts, our instrument projects dynamic patterns of laser light onto a distant target using a lightweight large-aperture reflector, which then collects the light scattered or fluoresced by the target on a fast photon-bucket detector. Using Fourier Transform based techniques, we reconstruct an image from the detected light. The remote microscope has been demonstrated to produce 2D images with better than 15 micron lateral resolution for targets at a distance of 5 meters and is capable of linearly proportionally higher resolution at shorter distances. The remote microscope is also capable of providing three-dimensional (3D) microscopic imaging capabilities, allowing future surface scientists to explore the morphology of microscopic features in surface ices, for example. The instrument enables microscopic in-situ imaging during day or night without the use of a robotic arm, greatly facilitating the surface operations for a lander or rover while expanding the area of investigation near a landing site for improved science targeting. We are developing this remote microscope for in-situ planetary exploration as a collaboration between the Southwest Research Institute, LambdaMetrics, and the University of Colorado.

If EM waves don't interfere, what causes interferograms?

NASA Astrophysics Data System (ADS)

Wellard, Stanley J.

2012-10-01

Photonics engineers involved in designing and operating Fourier transform spectrometers (FTS) often rely on Maxwell's wave equations and time-frequency (distance-wavenumber) Fourier theory as models to understand and predict the conversion of optical energy to electrical signals in their instruments. Dr. Chandrasekhar Roychoudhuri and his colleagues, at last year's conference, presented three significant concepts that might completely change the way we comprehend the interaction of light and matter and the way interference information is generated. The first concept is his non-interaction of waves (NIW) formulation, which puts in place an optical wave description that more accurately describe the properties of the finite time and spatial signals of an optical system. The second is a new description for the cosmic EM environment that recognizes that space is really filled with the ether of classical electromagnetics. The third concept is a new metaphysics or metaphotonics that compares the photon as a particle in a void against the photon as a wave in a medium to see which best explain the twelve different aspects of light. Dr. Henry Lindner presents a compelling case that photons are waves in a medium and particles (electrons, protons, atoms) are wave-structures embedded in the new ether. Discussion of the three new principles is intended to increase the curiosity of photonics engineers to investigate these changes in the nature of light and matter.

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.

Use of Fourier transforms for asynoptic mapping: Applications to the Upper Atmosphere Research Satellite microwave limb sounder

NASA Technical Reports Server (NTRS)

Elson, Lee S.; Froidevaux, Lucien

1993-01-01

Fourier analysis has been applied to data obtained from limb viewing instruments on the Upper Atmosphere Research Satellite. A coordinate system rotation facilitates the efficient computation of Fourier transforms in the temporal and longitudinal domains. Fields such as ozone (O3), chlorine monoxide (ClO), temperature, and water vapor have been transformed by this process. The transforms have been inverted to provide maps of these quantities at selected times, providing a method of accurate time interpolation. Maps obtained by this process show evidence of both horizontal and vertical transport of important trace species such as O3 and ClO. An examination of the polar regions indicates that large-scale planetary variations are likely to play a significant role in transporting midstratospheric O3 into the polar regions. There is also evidence that downward transport occurs, providing a means of moving O3 into the polar vortex at lower altitudes. The transforms themselves show the structure and propagation characteristics of wave variations.

Geometry and dynamics in the fractional discrete Fourier transform.

PubMed

Wolf, Kurt Bernardo; Krötzsch, Guillermo

2007-03-01

The N x N Fourier matrix is one distinguished element within the group U(N) of all N x N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N-->infinity contraction limit for the integral Fourier transform and its fractional powers. In the finite-N case, several options have been considered in the literature. We compare their fidelity in reproducing the classical harmonic motion of discrete coherent states.

A novel recursive Fourier transform for nonuniform sampled signals: application to heart rate variability spectrum estimation.

PubMed

Holland, Alexander; Aboy, Mateo

2009-07-01

We present a novel method to iteratively calculate discrete Fourier transforms for discrete time signals with sample time intervals that may be widely nonuniform. The proposed recursive Fourier transform (RFT) does not require interpolation of the samples to uniform time intervals, and each iterative transform update of N frequencies has computational order N. Because of the inherent non-uniformity in the time between successive heart beats, an application particularly well suited for this transform is power spectral density (PSD) estimation for heart rate variability. We compare RFT based spectrum estimation with Lomb-Scargle Transform (LST) based estimation. PSD estimation based on the LST also does not require uniform time samples, but the LST has a computational order greater than Nlog(N). We conducted an assessment study involving the analysis of quasi-stationary signals with various levels of randomly missing heart beats. Our results indicate that the RFT leads to comparable estimation performance to the LST with significantly less computational overhead and complexity for applications requiring iterative spectrum estimations.

Computing the Power-Density Spectrum for an Engineering Model

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1982-01-01

Computer program for calculating of power-density spectrum (PDS) from data base generated by Advanced Continuous Simulation Language (ACSL) uses algorithm that employs fast Fourier transform (FFT) to calculate PDS of variable. Accomplished by first estimating autocovariance function of variable and then taking FFT of smoothed autocovariance function to obtain PDS. Fast-Fourier-transform technique conserves computer resources.

Using Mathematical Software to Introduce Fourier Transforms in Physical Chemistry to Develop Improved Understanding of Their Applications in Analytical Chemistry

ERIC Educational Resources Information Center

Miller, Tierney C.; Richardson, John N.; Kegerreis, Jeb S.

2016-01-01

This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…

Teaching Stable Two-Mirror Resonators through the Fractional Fourier Transform

ERIC Educational Resources Information Center

Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

2010-01-01

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

Rapid identification and classification of Listeria spp. and serotype assignment of Listeria monocytogenes using fourier transform-infrared spectroscopy and artificial neural network analysis

USDA-ARS?s Scientific Manuscript database

The use of Fourier Transform-Infrared Spectroscopy (FT-IR) in conjunction with Artificial Neural Network software, NeuroDeveloper™ was examined for the rapid identification and classification of Listeria species and serotyping of Listeria monocytogenes. A spectral library was created for 245 strains...

COMPARISON OF AN INNOVATIVE NONLINEAR ALGORITHM TO CLASSICAL LEAST SQUARES FOR ANALYZING OPEN-PATH FOURIER TRANSFORM INFRARED SPECTRA COLLECTED AT A CONCENTRATED SWINE PRODUCTION FACILITY

EPA Science Inventory

Open-path Fourier transform infrared (OP/FTIR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric gases at an integrated swine production facility. The concentration-pathlength products of the target gases at this site often exceeded th...

APPLICATION OF STANDARDIZED QUALITY CONTROL PROCEDURES TO OPEN-PATH FOURIER TRANSFORM INFRARED DATA COLLECTED AT A CONCENTRATED SWINE PRODUCTION FACILITY

EPA Science Inventory

Open-path Fourier transform infrared (OP/FT-IR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric eases at a concentrated swine production facility. A total of 2200 OP/FT-IR spectra were acquired along nine different monitoring paths d...

“Self-absorption” phenomenon in near-infrared Fourier transform Raman spectroscopy of cellulosic and lignocellulosic materials

Treesearch

Umesh P. Agarwal; Nancy Kawai

2005-01-01

While cellulosic and lignocellulosic materials have been studied using conventional Raman spectroscopy, availability of near-infrared (NIR) Fourier transform (FT) Raman instrumentation has made studying these materials much more convenient. This is especially true because the problem of laser-induced fluorescence can be avoided or minimized in FT- Raman (NIR Raman)...

Propagation Characteristics Of Weakly Guiding Optical Fibers

NASA Technical Reports Server (NTRS)

Manshadi, Farzin

1992-01-01

Report discusses electromagnetic propagation characteristics of weakly guiding optical-fiber structures having complicated shapes with cross-sectional dimensions of order of wavelength. Coupling, power-dividing, and transition dielectric-waveguide structures analyzed. Basic data computed by scalar-wave, fast-Fourier-transform (SW-FFT) technique, based on numerical solution of scalar version of wave equation by forward-marching fast-Fourier-transform method.

Analytical Properties of Time-of-Flight PET Data

PubMed Central

Cho, Sanghee; Ahn, Sangtae; Li, Quanzheng; Leahy, Richard M.

2015-01-01

We investigate the analytical properties of time-of-flight (TOF) positron emission tomography (PET) sinograms, where the data are modeled as line integrals weighted by a spatially invariant TOF kernel. First, we investigate the Fourier transform properties of 2D TOF data and extend the “bow-tie” property of the 2D Radon transform to the time of flight case. Second, we describe a new exact Fourier rebinning method, TOF-FOREX, based on the Fourier transform in the time-of-flight variable. We then combine TOF-FOREX rebinning with a direct extension of the projection slice theorem to TOF data, to perform fast 3D TOF PET image reconstruction. Finally, we illustrate these properties using simulated data. PMID:18460746

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.

Application of Fourier transforms for microwave radiometric inversions

NASA Technical Reports Server (NTRS)

Holmes, J. J.; Balanis, C. A.; Truman, W. M.

1975-01-01

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, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are 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 are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

Fourier transform infrared microspectroscopy for the analysis of the biochemical composition of C. elegans worms.

PubMed

Sheng, Ming; Gorzsás, András; Tuck, Simon

2016-01-01

Changes in intermediary metabolism have profound effects on many aspects of C. elegans biology including growth, development and behavior. However, many traditional biochemical techniques for analyzing chemical composition require relatively large amounts of starting material precluding the analysis of mutants that cannot be grown in large amounts as homozygotes. Here we describe a technique for detecting changes in the chemical compositions of C. elegans worms by Fourier transform infrared microspectroscopy. We demonstrate that the technique can be used to detect changes in the relative levels of carbohydrates, proteins and lipids in one and the same worm. We suggest that Fourier transform infrared microspectroscopy represents a useful addition to the arsenal of techniques for metabolic studies of C. elegans worms.

The short time Fourier transform and local signals

NASA Astrophysics Data System (ADS)

Okumura, Shuhei

In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT's modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross-covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.

The extended Fourier transform for 2D spectral estimation.

PubMed

Armstrong, G S; Mandelshtam, V A

2001-11-01

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to infinity one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals. Copyright 2001 Academic Press.

Replica Fourier Tansforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

NASA Astrophysics Data System (ADS)

de Dominicis, C.; Carlucci, D. M.; Temesvári, T.

1997-01-01

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices M^{α β;γ^δ}, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work. On montre que l'analyse d'objets vivant sur un arbre ultramétrique, en particulier, la diagonalisation par blocs d'une matrice M^{α β;γ^δ} dépendant de 4-répliques, se simplifie de façon dramatique si l'on introduit les opérations appropriées sur ces objets. Ce sont les Transformées de Fourier de Répliques sur un arbre ultramétrique. Ces transformations sont définies et utilisées dans le présent travail.

Intelligent Automatic Classification of True and Counterfeit Notes Based on Spectrum Analysis

NASA Astrophysics Data System (ADS)

Matsunaga, Shohei; Omatu, Sigeru; Kosaka, Toshohisa

The purpose of this paper is to classify bank notes into “true” or “counterfeit” ones faster and more precisely compared with a conventional method. We note that thin lines are represented by direct lines in the images of true notes while they are represented in the counterfeit notes by dotted lines. This is due to properties of dot printers or scanner levels. To use the properties, we propose two method to classify a note into true or counterfeited one by checking whether there exist thin lines or dotted lines of the note. First, we use Fourier transform of the note to find quantity of features for classification and we classify a note into true or counterfeit one by using the features by Fourier transform. Then we propose a classification method by using wavelet transform in place of Fourier transform. Finally, some classification results are illustrated to show the effectiveness of the proposed methods.

On the action of Heisenberg's uncertainty principle in discrete linear methods for calculating the components of the deflection of the vertical

NASA Astrophysics Data System (ADS)

Mazurova, Elena; Lapshin, Aleksey

2013-04-01

The method of discrete linear transformations that can be implemented through the algorithms of the Standard Fourier Transform (SFT), Short-Time Fourier Transform (STFT) or Wavelet transform (WT) is effective for calculating the components of the deflection of the vertical from discrete values of gravity anomaly. The SFT due to the action of Heisenberg's uncertainty principle indicates weak spatial localization that manifests in the following: firstly, it is necessary to know the initial digital signal on the complete number line (in case of one-dimensional transform) or in the whole two-dimensional space (if a two-dimensional transform is performed) in order to find the SFT. Secondly, the localization and values of the "peaks" of the initial function cannot be derived from its Fourier transform as the coefficients of the Fourier transform are formed by taking into account all the values of the initial function. Thus, the SFT gives the global information on all frequencies available in the digital signal throughout the whole time period. To overcome this peculiarity it is necessary to localize the signal in time and apply the Fourier transform only to a small portion of the signal; the STFT that differs from the SFT only by the presence of an additional factor (window) is used for this purpose. A narrow enough window is chosen to localize the signal in time and, according to Heisenberg's uncertainty principle, it results in have significant enough uncertainty in frequency. If one chooses a wide enough window it, according to the same principle, will increase time uncertainty. Thus, if the signal is narrowly localized in time its spectrum, on the contrary, is spread on the complete axis of frequencies, and vice versa. The STFT makes it possible to improve spatial localization, that is, it allows one to define the presence of any frequency in the signal and the interval of its presence. However, owing to Heisenberg's uncertainty principle, it is impossible to tell precisely, what frequency is present in the signal at the current moment of time: it is possible to speak only about the range of frequencies. Besides, it is impossible to specify precisely the time moment of the presence of this or that frequency: it is possible to speak only about the time frame. It is this feature that imposes major constrains on the applicability of the STFT. In spite of the fact that the problems of resolution in time and frequency result from a physical phenomenon (Heisenberg's uncertainty principle) and exist independent of the transform applied, there is a possibility to analyze any signal, using the alternative approach - the multiresolutional analysis (MRA). The wavelet-transform is one of the methods for making a MRA-type analysis. Thanks to it, low frequencies can be shown in a more detailed form with respect to time, and high ones - with respect to frequency. The paper presents the results of calculating of the components of the deflection of the vertical, done by the SFT, STFT and WT. The results are presented in the form of 3-d models that visually show the action of Heisenberg's uncertainty principle in the specified algorithms. The research conducted allows us to recommend the application of wavelet-transform to calculate of the components of the deflection of the vertical in the near-field zone. Keywords: Standard Fourier Transform, Short-Time Fourier Transform, Wavelet Transform, Heisenberg's uncertainty principle.

The Contradiction Between the Measurement Theory of Quantum Mechanics and the Theory that the Velocity of Any Particle Can Not be Larger than the Velocity of Light

NASA Technical Reports Server (NTRS)

Shen, Y.; Shen, Z. J.; Shen, G. T.; Yang, B. C.

1996-01-01

By the measurement theory of quantum mechanics and the method of Fourier transform,we proved that the wave function psi(x,y,z,t)= (8/((2(pi)(2L(exp (1/2)))(exp 3))(Phi(L,t,x)Phi(L,t,y)Phi(L,t,z)). According to the theory that the velocity of any particle can not be larger than the velocity of light and the Born interpretation, when absolute value of delta greater than (ct+ L),Phi(L,t,delta) = 0. But according to the calculation, we proved that for some delta, even if absolute value of delta is greater than (ct+L), Phi(L,t,delta) is not equal to 0.

Differential dynamic microscopy to characterize Brownian motion and bacteria motility

NASA Astrophysics Data System (ADS)

Germain, David; Leocmach, Mathieu; Gibaud, Thomas

2016-03-01

We have developed a lab module for undergraduate students, which involves the process of quantifying the dynamics of a suspension of microscopic particles using Differential Dynamic Microscopy (DDM). DDM is a relatively new technique that constitutes an alternative method to more classical techniques such as dynamic light scattering (DLS) or video particle tracking (VPT). The technique consists of imaging a particle dispersion with a standard light microscope and a camera and analyzing the images using a digital Fourier transform to obtain the intermediate scattering function, an autocorrelation function that characterizes the dynamics of the dispersion. We first illustrate DDM in the textbook case of colloids under Brownian motion, where we measure the diffusion coefficient. Then we show that DDM is a pertinent tool to characterize biological systems such as motile bacteria.

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

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.

Experimental research of adaptive OFDM and OCT precoding with a high SE for VLLC system

NASA Astrophysics Data System (ADS)

Liu, Shuang-ao; He, Jing; Chen, Qinghui; Deng, Rui; Zhou, Zhihua; Chen, Shenghai; Chen, Lin

2017-09-01

In this paper, an adaptive orthogonal frequency division multiplexing (OFDM) modulation scheme with 128/64/32/16-quadrature amplitude modulation (QAM) and orthogonal circulant matrix transform (OCT) precoding is proposed and experimentally demonstrated for a visible laser light communication (VLLC) system with a cost-effective 450-nm blue-light laser diode (LD). The performance of OCT precoding is compared with conventional the adaptive Discrete Fourier Transform-spread (DFT-spread) OFDM scheme, 32 QAM OCT precoding OFDM scheme, 64 QAM OCT precoding OFDM scheme and adaptive OCT precoding OFDM scheme. The experimental results show that OCT precoding can achieve a relatively flat signal-to-noise ratio (SNR) curve, and it can provide performance improvement in bit error rate (BER). Furthermore, the BER of the proposed OFDM signal with a raw bit rate 5.04 Gb/s after 5-m free space transmission is less than 20% of soft-decision forward error correlation (SD-FEC) threshold of 2.4 × 10-2, and the spectral efficiency (SE) of 4.2 bit/s/Hz can be successfully achieved.

Three Dimensional Imaging with Multiple Wavelength Speckle Interferometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernacki, Bruce E.; Cannon, Bret D.; Schiffern, John T.

2014-05-28

We present the design, modeling, construction, and results of a three-dimensional imager based upon multiple-wavelength speckle interferometry. A surface under test is illuminated with tunable laser light in a Michelson interferometer configuration while a speckled image is acquired at each laser frequency step. The resulting hypercube is Fourier transformed in the frequency dimension and the beat frequencies that result map the relative offsets of surface features. Synthetic wavelengths resulting from the laser tuning can probe features ranging from 18 microns to hundreds of millimeters. Three dimensional images will be presented along with modeling results.

Absorbing metasurface created by diffractionless disordered arrays of nanoantennas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chevalier, Paul; Minao, Laboratoire de Photonique et Nanostructures; Bouchon, Patrick, E-mail: patrick.bouchon@onera.fr

2015-12-21

We study disordered arrays of metal-insulator-metal nanoantenna in order to create a diffractionless metasurface able to absorb light in the 3–5 μm spectral range. This study is conducted with angle-resolved reflectivity measurements obtained with a Fourier transform infrared spectrometer. A first design is based on a perturbation of a periodic arrangement, leading to a significant reduction of the radiative losses. Then, a random assembly of nanoantennas is built following a Poisson-disk distribution of given density, in order to obtain a nearly perfect cluttered assembly with optical properties of a homogeneous material.

Effects of atomic oxygen and ultraviolet radiation on candidate elastomeric materials for long duration missions. Test series no.1

NASA Technical Reports Server (NTRS)

Linton, R. C.; Finckenor, M. M.; Kamenetzky, R. R.; Gray, P.

1993-01-01

Research was conducted at MSFC on the behavior of elastomeric materials after exposure to simulated space environment. Silicone S383 and Viton V747 samples were exposed to thermal vacuum, ultraviolet radiation, and atomic oxygen and then evaluated for changes in material properties. Characterization of the elastomeric materials included weight, hardness, optical inspection under normal and black light, spectrofluorescence, solar absorptance and emittance, Fourier transform infrared spectroscopy, and permeability. These results indicate a degree of sensitivity to exposure and provided some evidence of UV and atomic oxygen synergism.

Infrared absorption cross sections of propane broadened by hydrogen

NASA Astrophysics Data System (ADS)

Wong, A.; Hargreaves, R. J.; Billinghurst, B.; Bernath, P. F.

2017-09-01

Fourier transform infrared absorption cross-sections of pure propane (C3H8) and propane broadened with H2 have been calculated from transmittance spectra recorded at temperatures from 292 K to 205 K. Transmittance spectra were recorded at the Canadian Light Source (CLS) Far-Infrared beamline, utilizing both the synchrotron source and the internal glowbar source. The absorption cross-sections have been calibrated to Pacific Northwest National Laboratory (PNNL) reference cross-sections of propane and can be used to interpret astronomical observations of giant planets such as Jupiter and Saturn as well as exoplanets.

Coherent time-stretch transformation for real-time capture of wideband signals.

PubMed

Buckley, Brandon W; Madni, Asad M; Jalali, Bahram

2013-09-09

Time stretch transformation of wideband waveforms boosts the performance of analog-to-digital converters and digital signal processors by slowing down analog electrical signals before digitization. The transform is based on dispersive Fourier transformation implemented in the optical domain. A coherent receiver would be ideal for capturing the time-stretched optical signal. Coherent receivers offer improved sensitivity, allow for digital cancellation of dispersion-induced impairments and optical nonlinearities, and enable decoding of phase-modulated optical data formats. Because time-stretch uses a chirped broadband (>1 THz) optical carrier, a new coherent detection technique is required. In this paper, we introduce and demonstrate coherent time stretch transformation; a technique that combines dispersive Fourier transform with optically broadband coherent detection.

Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

NASA Astrophysics Data System (ADS)

Stupin, Daniil D.; Koniakhin, Sergei V.; Verlov, Nikolay A.; Dubina, Michael V.

2017-05-01

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

Kinetics and Product Branching Fractions of Reactions between a Cation and a Radical: Ar+ + CH3 and O2+ + CH3 (Postprint)

DTIC Science & Technology

2015-01-13

Gross group using a Chen nozzle coupled to a Fourier transform ion cyclotron reso- nance (FT-ICR) mass spectrometer for reactions of the benzyl radical...reactions: A Fourier transform ion cyclotron resonance study of allyl radical reacting with aromatic radical cations. Int. J. Mass Spectrom. 2009, 287, 8

Introduction to Flight Test Engineering (Introduction aux techniques des essais en vol)

DTIC Science & Technology

2005-07-01

or aircraft parameters • Calculations in the frequency domain ( Fast Fourier Transform) • Data analysis with dedicated software for: • Signal...density Fast Fourier Transform Transfer function analysis Frequency response analysis Etc. PRESENTATION Color/black & white Display screen...envelope by operating the airplane at increasing ranges - representing increasing risk - of engine operation, airspeeds both fast and slow, altitude

Color and surface chemistry changes of extracted wood flour after heating at 120 °C

Treesearch

Yao Chen; Mandla A. Tshabalala; Jianmin Gao; Nicole M. Stark

2013-01-01

To investigate the effect of heat on color and surface chemistry of wood flour (WF), unextracted, extracted and delignified samples of commercial WF were heated at 120 °C for 24 h and analyzed by colorimetry, diffuse reflectance visible (DRV), attenuated total reflectance Fourier transform infrared (ATR-FTIR) and Fourier transform Raman (FT-Raman) spectroscopies....

Characterization of southern yellow pine bark layers by Attenuated Total Reflectance (ATR) and Fourier Transform Infrared (FT-IR) Spectroscopy

Treesearch

Thomas L. Eberhardt

2009-01-01

The outer bark (rhytidome) of the southern yellow pines is a complex structure comprised of alternating layers of obliterated phloem and periderm tissues, with the latter comprised of three layers, those being phellem, phellogen, and phelloderm. An attenuated total reflectance (ATR) sampling accessory, coupled with a Fourier transform infrared (FTIR) spectrometer,...

Determination of diosmin in pharmaceutical formulations using Fourier transform infrared spectrophotometry

PubMed Central

Bunaciu, Andrei A.; Udristioiu, Gabriela Elena; Ruţă, Lavinia L.; Fleschin, Şerban; Aboul-Enein, Hassan Y.

2009-01-01

A Fourier transform infrared (FT-IR) spectrometric method was developed for the rapid, direct measurement of diosmin in different pharmaceutical drugs. Conventional KBr-spectra were compared for best determination of active substance in commercial preparations. The Beer–Lambert law and two chemometric approaches, partial least squares (PLS) and principal component regression (PCR+) methods, were tried in data processing. PMID:23960715

Molecular Isotopic Distribution Analysis (MIDAs) with Adjustable Mass Accuracy

NASA Astrophysics Data System (ADS)

Alves, Gelio; Ogurtsov, Aleksey Y.; Yu, Yi-Kuo

2014-01-01

In this paper, we present Molecular Isotopic Distribution Analysis (MIDAs), a new software tool designed to compute molecular isotopic distributions with adjustable accuracies. MIDAs offers two algorithms, one polynomial-based and one Fourier-transform-based, both of which compute molecular isotopic distributions accurately and efficiently. The polynomial-based algorithm contains few novel aspects, whereas the Fourier-transform-based algorithm consists mainly of improvements to other existing Fourier-transform-based algorithms. We have benchmarked the performance of the two algorithms implemented in MIDAs with that of eight software packages (BRAIN, Emass, Mercury, Mercury5, NeutronCluster, Qmass, JFC, IC) using a consensus set of benchmark molecules. Under the proposed evaluation criteria, MIDAs's algorithms, JFC, and Emass compute with comparable accuracy the coarse-grained (low-resolution) isotopic distributions and are more accurate than the other software packages. For fine-grained isotopic distributions, we compared IC, MIDAs's polynomial algorithm, and MIDAs's Fourier transform algorithm. Among the three, IC and MIDAs's polynomial algorithm compute isotopic distributions that better resemble their corresponding exact fine-grained (high-resolution) isotopic distributions. MIDAs can be accessed freely through a user-friendly web-interface at http://www.ncbi.nlm.nih.gov/CBBresearch/Yu/midas/index.html.

GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography.

PubMed

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).

Determination of Spectroscopic Properties of Atmospheric Molecules from High Resolution Vacuum Ultraviolet Cross Section and Wavelength Measurements

NASA Technical Reports Server (NTRS)

Parkinson, W. H.; Yoshino, K.

1997-01-01

An account is given of progress during the period 8/l/96-7/31/97 on work on (a) cross section measurements of O2 S-R using a Fourier transform spectrometer (FTS) at the Photon Factory in Japan; (b) the determination of the predissociation linewidths of the Schumann-Runge bands (S-R) of 02; (c) cross section measurements of 02 Herzberg bands using a Fourier transform spectrometer (FTS) at Imperial College; and (d) cross section measurements of H2O in the wavelength region 120-188 nm. The experimental investigations are effected at high resolution with a 6.65 m scanning spectrometer and with the Fourier transform spectrometer. Below 175 nm, synchrotron radiation is most suitable for cross section measurements in combination with spectrometers at the Photon Factory Japan. Cross section measurements of the Doppler limited bands depend on using the very high resolution, available with the Fourier transform spectrometer, (0.025/cm resolution). All of these spectroscopic measurements are needed for accurate calculations of the production of atomic oxygen, the penetration of solar radiation into the Earth's atmosphere, and photochemistry of minor molecules.

Molecular Isotopic Distribution Analysis (MIDAs) with adjustable mass accuracy.

PubMed

Alves, Gelio; Ogurtsov, Aleksey Y; Yu, Yi-Kuo

2014-01-01

In this paper, we present Molecular Isotopic Distribution Analysis (MIDAs), a new software tool designed to compute molecular isotopic distributions with adjustable accuracies. MIDAs offers two algorithms, one polynomial-based and one Fourier-transform-based, both of which compute molecular isotopic distributions accurately and efficiently. The polynomial-based algorithm contains few novel aspects, whereas the Fourier-transform-based algorithm consists mainly of improvements to other existing Fourier-transform-based algorithms. We have benchmarked the performance of the two algorithms implemented in MIDAs with that of eight software packages (BRAIN, Emass, Mercury, Mercury5, NeutronCluster, Qmass, JFC, IC) using a consensus set of benchmark molecules. Under the proposed evaluation criteria, MIDAs's algorithms, JFC, and Emass compute with comparable accuracy the coarse-grained (low-resolution) isotopic distributions and are more accurate than the other software packages. For fine-grained isotopic distributions, we compared IC, MIDAs's polynomial algorithm, and MIDAs's Fourier transform algorithm. Among the three, IC and MIDAs's polynomial algorithm compute isotopic distributions that better resemble their corresponding exact fine-grained (high-resolution) isotopic distributions. MIDAs can be accessed freely through a user-friendly web-interface at http://www.ncbi.nlm.nih.gov/CBBresearch/Yu/midas/index.html.

Airborne measurements in the infrared using FTIR-based imaging hyperspectral sensors

NASA Astrophysics Data System (ADS)

Puckrin, E.; Turcotte, C. S.; Lahaie, P.; Dubé, D.; Lagueux, P.; Farley, V.; Marcotte, F.; Chamberland, M.

2009-09-01

Hyperspectral ground mapping is being used in an ever-increasing extent for numerous applications in the military, geology and environmental fields. The different regions of the electromagnetic spectrum help produce information of differing nature. The visible, near-infrared and short-wave infrared radiation (400 nm to 2.5 μm) has been mostly used to analyze reflected solar light, while the mid-wave (3 to 5 μm) and long-wave (8 to 12 μm or thermal) infrared senses the self-emission of molecules directly, enabling the acquisition of data during night time. Push-broom dispersive sensors have been typically used for airborne hyperspectral mapping. However, extending the spectral range towards the mid-wave and long-wave infrared brings performance limitations due to the self emission of the sensor itself. The Fourier-transform spectrometer technology has been extensively used in the infrared spectral range due to its high transmittance as well as throughput and multiplex advantages, thereby reducing the sensor self-emission problem. Telops has developed the Hyper-Cam, a rugged and compact infrared hyperspectral imager. The Hyper-Cam is based on the Fourier-transform technology yielding high spectral resolution and enabling high accuracy radiometric calibration. It provides passive signature measurement capability, with up to 320x256 pixels at spectral resolutions of up to 0.25 cm-1. The Hyper-Cam has been used on the ground in several field campaigns, including the demonstration of standoff chemical agent detection. More recently, the Hyper-Cam has been integrated into an airplane to provide airborne measurement capabilities. A special pointing module was designed to compensate for airplane attitude and forward motion. To our knowledge, the Hyper-Cam is the first commercial airborne hyperspectral imaging sensor based on Fourier-transform infrared technology. The first airborne measurements and some preliminary performance criteria for the Hyper-Cam are presented in this paper.

Airborne measurements in the infrared using FTIR-based imaging hyperspectral sensors

NASA Astrophysics Data System (ADS)

Puckrin, E.; Turcotte, C. S.; Lahaie, P.; Dubé, D.; Farley, V.; Lagueux, P.; Marcotte, F.; Chamberland, M.

2009-05-01

Hyperspectral ground mapping is being used in an ever-increasing extent for numerous applications in the military, geology and environmental fields. The different regions of the electromagnetic spectrum help produce information of differing nature. The visible, near-infrared and short-wave infrared radiation (400 nm to 2.5 μm) has been mostly used to analyze reflected solar light, while the mid-wave (3 to 5 μm) and long-wave (8 to 12 μm or thermal) infrared senses the self-emission of molecules directly, enabling the acquisition of data during night time. Push-broom dispersive sensors have been typically used for airborne hyperspectral mapping. However, extending the spectral range towards the mid-wave and long-wave infrared brings performance limitations due to the self emission of the sensor itself. The Fourier-transform spectrometer technology has been extensively used in the infrared spectral range due to its high transmittance as well as throughput and multiplex advantages, thereby reducing the sensor self-emission problem. Telops has developed the Hyper-Cam, a rugged and compact infrared hyperspectral imager. The Hyper-Cam is based on the Fourier-transform technology yielding high spectral resolution and enabling high accuracy radiometric calibration. It provides passive signature measurement capability, with up to 320x256 pixels at spectral resolutions of up to 0.25 cm-1. The Hyper-Cam has been used on the ground in several field campaigns, including the demonstration of standoff chemical agent detection. More recently, the Hyper-Cam has been integrated into an airplane to provide airborne measurement capabilities. A special pointing module was designed to compensate for airplane attitude and forward motion. To our knowledge, the Hyper-Cam is the first commercial airborne hyperspectral imaging sensor based on Fourier-transform infrared technology. The first airborne measurements and some preliminary performance criteria for the Hyper-Cam are presented in this paper.

Detection of aflatoxin and surface mould contaminated figs by using Fourier transform near-infrared reflectance spectroscopy.

PubMed

Durmuş, Efkan; Güneş, Ali; Kalkan, Habil

2017-01-01

Aflatoxins are toxic metabolites that are mainly produced by members of the Aspergillus section Flavi on many agricultural products. Certain agricultural products such as figs are known to be high risk products for aflatoxin contamination. Aflatoxin contaminated figs may show a bright greenish yellow fluorescence (BGYF) under ultraviolet (UV) light at a wavelength of 365 nm. Traditionally, BGYF positive figs are manually selected by workers. However, manual selection depends on the expertise level of the workers and it may cause them skin-related health problems due to UV radiation. In this study, we propose a non-invasive approach to detect aflatoxin and surface mould contaminated figs by using Fourier transform near-infrared (FT-NIR) reflectance spectroscopy. A classification accuracy of 100% is achieved for classifying the figs into aflatoxin contaminated/uncontaminated and surface mould contaminated/uncontaminated categories. In addition, a strong correlation has been found between aflatoxin and surface mould. Combined with pattern classification methods, the NIR spectroscopy can be used to detect aflatoxin contaminated figs non-invasively. Furthermore, a positive correlation between surface mould and aflatoxin contamination leads to a promising alternative indicator for the detection of aflatoxin-contaminated figs. © 2016 Society of Chemical Industry. © 2016 Society of Chemical Industry.

Structural analysis of an intact monoclonal antibody by online electrochemical reduction of disulfide bonds and Fourier transform ion cyclotron resonance mass spectrometry.

PubMed

Nicolardi, Simone; Deelder, André M; Palmblad, Magnus; van der Burgt, Yuri E M

2014-06-03

Structural confirmation and quality control of recombinant monoclonal antibodies (mAbs) by top-down mass spectrometry is still challenging due to the size of the proteins, disulfide content, and post-translational modifications such as glycosylation. In this study we have applied electrochemistry (EC) to overcome disulfide bridge complexity in top-down analysis of mAbs. To this end, an electrochemical cell was coupled directly to an electrospray ionization (ESI) source and a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer (MS) equipped with a 15 T magnet. By performing online EC-assisted reduction of interchain disulfide bonds in an intact mAb, the released light chains could be selected for tandem mass spectrometry (MS/MS) analysis without interference from heavy-chain fragments. Moreover, the acquisition of full MS scans under denaturing conditions allowed profiling of all abundant mAb glycoforms. Ultrahigh-resolution FTICR-MS measurements provided fully resolved isotopic distributions of intact mAb and enabled the identification of the most abundant adducts and other interfering species. Furthermore, it was found that reduction of interchain disulfide bonds occurs in the ESI source dependent on capillary voltage and solvent composition. This phenomenon was systematically evaluated and compared with the results obtained from reduction in the electrochemical cell.

Structural and magnetic properties of multi-core nanoparticles analysed using a generalised numerical inversion method

PubMed Central

Bender, P.; Bogart, L. K.; Posth, O.; Szczerba, W.; Rogers, S. E.; Castro, A.; Nilsson, L.; Zeng, L. J.; Sugunan, A.; Sommertune, J.; Fornara, A.; González-Alonso, D.; Barquín, L. Fernández; Johansson, C.

2017-01-01

The structural and magnetic properties of magnetic multi-core particles were determined by numerical inversion of small angle scattering and isothermal magnetisation data. The investigated particles consist of iron oxide nanoparticle cores (9 nm) embedded in poly(styrene) spheres (160 nm). A thorough physical characterisation of the particles included transmission electron microscopy, X-ray diffraction and asymmetrical flow field-flow fractionation. Their structure was ultimately disclosed by an indirect Fourier transform of static light scattering, small angle X-ray scattering and small angle neutron scattering data of the colloidal dispersion. The extracted pair distance distribution functions clearly indicated that the cores were mostly accumulated in the outer surface layers of the poly(styrene) spheres. To investigate the magnetic properties, the isothermal magnetisation curves of the multi-core particles (immobilised and dispersed in water) were analysed. The study stands out by applying the same numerical approach to extract the apparent moment distributions of the particles as for the indirect Fourier transform. It could be shown that the main peak of the apparent moment distributions correlated to the expected intrinsic moment distribution of the cores. Additional peaks were observed which signaled deviations of the isothermal magnetisation behavior from the non-interacting case, indicating weak dipolar interactions. PMID:28397851

Fourier transform synchrotron spectroscopy of torsional and CO-stretching bands of CH 3 17 OH

NASA Astrophysics Data System (ADS)

Moruzzi, G.; Murphy, R. J.; Vos, J.; Lees, R. M.; Predoi-Cross, A.; Billinghurst, B. E.

2011-07-01

The Fourier transform spectrum of the CH 317OH isotopologue of methanol has been recorded in the 65-1200 cm -1 spectral region at a resolution of 0.00096 cm -1 using synchrotron source radiation at the Canadian Light Source. Here we present an extension to higher torsional states of our investigation of the torsion-rotation transitions within the small-amplitude vibrational ground state, now including assignments of more than 16 500 lines involving quantum numbers in the ranges v t ⩽ 3, J ⩽ 30 and | K| ⩽ 12, as well as a study of the strong CO-stretching band centered at 1020 cm -1. Energy term values have been determined for assigned ground and CO-stretching levels by use of the Ritz program, and have been fitted to series expansions in powers of J( J + 1) to determine substate origins and effective B values. Several Fermi anharmonic and Coriolis level-crossing resonances coupling the CO stretch with high torsional ground-state levels have been identified and characterized. The study is motivated by astrophysical applications, with a principal aim being the compilation of an extensive set of energy term values to permit prediction of astronomically observable sub-millimetre transitions to within an uncertainty of a few MHz.

A Discussion of the Discrete Fourier Transform Execution on a Typical Desktop PC

NASA Technical Reports Server (NTRS)

White, Michael J.

2006-01-01

This paper will discuss and compare the execution times of three examples of the Discrete Fourier Transform (DFT). The first two examples will demonstrate the direct implementation of the algorithm. In the first example, the Fourier coefficients are generated at the execution of the DFT. In the second example, the coefficients are generated prior to execution and the DFT coefficients are indexed at execution. The last example will demonstrate the Cooley- Tukey algorithm, better known as the Fast Fourier Transform. All examples were written in C executed on a PC using a Pentium 4 running at 1.7 Ghz. As a function of N, the total complex data size, the direct implementation DFT executes, as expected at order of N2 and the FFT executes at order of N log2 N. At N=16K, there is an increase in processing time beyond what is expected. This is not caused by implementation but is a consequence of the effect that machine architecture and memory hierarchy has on implementation. This paper will include a brief overview of digital signal processing, along with a discussion of contemporary work with discrete Fourier processing.

Stress wave calculations in composite plates using the fast Fourier transform.

NASA Technical Reports Server (NTRS)

Moon, F. C.

1973-01-01

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform

PubMed Central

Chan, Kenny K. H.; Tang, Shuo

2010-01-01

The useful imaging range in spectral domain optical coherence tomography (SD-OCT) is often limited by the depth dependent sensitivity fall-off. Processing SD-OCT data with the non-uniform fast Fourier transform (NFFT) can improve the sensitivity fall-off at maximum depth by greater than 5dB concurrently with a 30 fold decrease in processing time compared to the fast Fourier transform with cubic spline interpolation method. NFFT can also improve local signal to noise ratio (SNR) and reduce image artifacts introduced in post-processing. Combined with parallel processing, NFFT is shown to have the ability to process up to 90k A-lines per second. High-speed SD-OCT imaging is demonstrated at camera-limited 100 frames per second on an ex-vivo squid eye. PMID:21258551

Multichannel Dynamic Fourier-Transform IR Spectrometer

NASA Astrophysics Data System (ADS)

Balashov, A. A.; Vaguine, V. A.; Golyak, Il. S.; Morozov, A. N.; Khorokhorin, A. I.

2017-09-01

A design of a multichannel continuous scan Fourier-transform IR spectrometer for simultaneous recording and analysis of the spectral characteristics of several objects is proposed. For implementing the design, a multi-probe fiber is used, constructed from several optical fibers connected into a single optical connector and attached at the output of the interferometer. The Fourier-transform spectrometer is used as a signal modulator. Each fiber is individually mated with an investigated sample and a dedicated radiation detector. For the developed system, the radiation intensity of the spectrometer is calculated from the condition of the minimum spectral resolution and parameters of the optical fibers. Using the proposed design, emission spectra of a gas-discharge neon lamp have been recorded using a single fiber 1 mm in diameter with a numerical aperture NA = 0.22.

The angular difference function and its application to image registration.

PubMed

Keller, Yosi; Shkolnisky, Yoel; Averbuch, Amir

2005-06-01

The estimation of large motions without prior knowledge is an important problem in image registration. In this paper, we present the angular difference function (ADF) and demonstrate its applicability to rotation estimation. The ADF of two functions is defined as the integral of their spectral difference along the radial direction. It is efficiently computed using the pseudopolar Fourier transform, which computes the discrete Fourier transform of an image on a near spherical grid. Unlike other Fourier-based registration schemes, the suggested approach does not require any interpolation. Thus, it is more accurate and significantly faster.

Application of Fourier analysis to multispectral/spatial recognition

NASA Technical Reports Server (NTRS)

Hornung, R. J.; Smith, J. A.

1973-01-01

One approach for investigating spectral response from materials is to consider spatial features of the response. This might be accomplished by considering the Fourier spectrum of the spatial response. The Fourier Transform may be used in a one-dimensional to multidimensional analysis of more than one channel of data. The two-dimensional transform represents the Fraunhofer diffraction pattern of the image in optics and has certain invariant features. Physically the diffraction pattern contains spatial features which are possibly unique to a given configuration or classification type. Different sampling strategies may be used to either enhance geometrical differences or extract additional features.

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…

Fourier Spectroscopy: A Simple Analysis Technique

ERIC Educational Resources Information Center

Oelfke, William C.

1975-01-01

Presents a simple method of analysis in which the student can integrate, point by point, any interferogram to obtain its Fourier transform. The manual technique requires no special equipment and is based on relationships that most undergraduate physics students can derive from the Fourier integral equations. (Author/MLH)

Two-window heterodyne methods to characterize light fields

NASA Astrophysics Data System (ADS)

Reil, Frank

In this dissertation, I develop a novel Two-Window heterodyne technique for measuring the time-resolved Wigner function of light fields, which allows their complete characterization. A Wigner function is a quasi-probability density that describes the transverse position and transverse momentum of a light field and is Fourier-transform related to its mutual coherence function. It obeys rigorous transport equations and therefore provides an ideal way to characterize a light field and its propagation through various media. I first present the experimental setup of our Two-Window technique, which is based on a heterodyne scheme involving two phase-coupled Local Oscillator beams we call the Dual-LO. The Dual-LO consists of a focused beam ('SLO') which sets the spatial resolution, and a collimated beam ('BLO') which sets the momental resolution. The resolution in transverse position and transverse momentum can be adjusted individually by the size of the SLO and BLO, which enables a measurement resolution surpassing the uncertainty principle associated with Fourier-transform pairs which limits the resolution when just a single LO is used. We first use our technique to determine the beam size, transverse coherence length and radius of curvature of a Gaussian-Schell beam, as well as its longitudinal characteristics, which are related to its optical spectrum. We then examine Enhanced Backscattering at various path-lengths in the turbid medium. For the first time ever, we demonstrate the phase-conjugating properties of a turbid medium by observing the change in sign of the radius of curvature for a non-collimated field incident on the medium. We also perform time-resolved measurements in the transmission regime. In tenuous media we observe two peaks in phase-space confined by a hyperbola which are due to low-order scattering. Their distance depends on the chosen path-delay. Some coherence and even spatial properties of the incident field are preserved in those peaks as measurements with our Two-Window technique show. Various other applications are presented in less detail, such as the Wigner function of the field inside a speckle produced by a piece of glass containing air bubbles.

Frequency division multiplexed multi-color fluorescence microscope system

NASA Astrophysics Data System (ADS)

Le, Vu Nam; Yang, Huai Dong; Zhang, Si Chun; Zhang, Xin Rong; Jin, Guo Fan

2017-10-01

Grayscale camera can only obtain gray scale image of object, while the multicolor imaging technology can obtain the color information to distinguish the sample structures which have the same shapes but in different colors. In fluorescence microscopy, the current method of multicolor imaging are flawed. Problem of these method is affecting the efficiency of fluorescence imaging, reducing the sampling rate of CCD etc. In this paper, we propose a novel multiple color fluorescence microscopy imaging method which based on the Frequency division multiplexing (FDM) technology, by modulating the excitation lights and demodulating the fluorescence signal in frequency domain. This method uses periodic functions with different frequency to modulate amplitude of each excitation lights, and then combine these beams for illumination in a fluorescence microscopy imaging system. The imaging system will detect a multicolor fluorescence image by a grayscale camera. During the data processing, the signal obtained by each pixel of the camera will be processed with discrete Fourier transform, decomposed by color in the frequency domain and then used inverse discrete Fourier transform. After using this process for signals from all of the pixels, monochrome images of each color on the image plane can be obtained and multicolor image is also acquired. Based on this method, this paper has constructed and set up a two-color fluorescence microscope system with two excitation wavelengths of 488 nm and 639 nm. By using this system to observe the linearly movement of two kinds of fluorescent microspheres, after the data processing, we obtain a two-color fluorescence dynamic video which is consistent with the original image. This experiment shows that the dynamic phenomenon of multicolor fluorescent biological samples can be generally observed by this method. Compared with the current methods, this method can obtain the image signals of each color at the same time, and the color video's frame rate is consistent with the frame rate of the camera. The optical system is simpler and does not need extra color separation element. In addition, this method has a good filtering effect on the ambient light or other light signals which are not affected by the modulation process.

Linking SOM Content, Chemistry, and Decomposition: Complex Responses to Input Manipulation and Long-term Incubation

NASA Astrophysics Data System (ADS)

Bridgham, S. D.; Reynolds, L. L.; Tfaily, M.; Roscioli, K.; Lajtha, K.; Bowden, R.; Johnson, B. R.

2014-12-01

The mechanisms of soil organic matter (SOM) protection and their relationship with carbon inputs and decomposition are poorly understood. We used Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) and Fourier transform infrared spectroscopy (FTIR) to characterize SOM in soils exposed to litter-input exclusion or addition for 20 years, and subsequently incubated for more than a year. Our aim was to describe shifts in SOM content and chemical composition due to the input manipulation and degree of decomposition, particularly in the light (i.e., free particulate, younger) versus the heavy (mineral-adsorbed, older) fractions of SOM, and to link these shifts to carbon mineralization rates. The soils were collected from a deciduous hardwood forest in Meadville, PA, one of the Detritus and Input Removal Treatment (DIRT) sites. They were subjected to either litter and root exclusion (NI), double litter (DL), or ambient inputs (CO) for 20 years and subsequently incubated at 35oC for 525 days. Soils from the beginning and end of the incubation were divided into light and heavy fractions using 1.8 g cm-3 sodium polytungstate. Bulk CO soils and heavy fractions of NI, DL, and CO soil were analyzed with FTICR-MS, while light and heavy fractions were analyzed with FTIR. Twenty years of input exclusion decreased the mineralization rate, the total carbon respired, and total carbon content, though litter addition had no significant effect (NI < CO = DL). The FTICR-MS and FTIR data reveal substantial differences in SOM chemistry among DIRT treatments, fractions, and before and after incubation. CO contained several classes of compounds, including alcohols and phenols, not detected in either DL or NI soils, and all samples showed an enrichment in aromatics between the light and heavy fractions. The heavy fraction DL soils were proportionally enriched in lipids compared to NI and CO soils, and these lipids were preferentially mineralized during incubation. Heavy fraction CO and NI soils were similar initially, though CO soil lost primarily lipids, while NI soil lost unsaturated hydrocarbons and proteins. These results indicate the complex interrelationships between litter inputs and soil carbon content, chemistry, and SOM decomposition.

Optical correlator method and apparatus for particle image velocimetry processing

NASA Technical Reports Server (NTRS)

Farrell, Patrick V. (Inventor)

1991-01-01

Young's fringes are produced from a double exposure image of particles in a flowing fluid by passing laser light through the film and projecting the light onto a screen. A video camera receives the image from the screen and controls a spatial light modulator. The spatial modulator has a two dimensional array of cells the transmissiveness of which are controlled in relation to the brightness of the corresponding pixel of the video camera image of the screen. A collimated beam of laser light is passed through the spatial light modulator to produce a diffraction pattern which is focused onto another video camera, with the output of the camera being digitized and provided to a microcomputer. The diffraction pattern formed when the laser light is passed through the spatial light modulator and is focused to a point corresponds to the two dimensional Fourier transform of the Young's fringe pattern projected onto the screen. The data obtained fro This invention was made with U.S. Government support awarded by the Department of the Army (DOD) and NASA grand number(s): DOD #DAAL03-86-K0174 and NASA #NAG3-718. The U.S. Government has certain rights in this invention.

Dynamic light absorption of biomass burning organic carbon photochemically aged under natural sunlight

NASA Astrophysics Data System (ADS)

Zhong, M.; Jang, M.

2013-08-01

Wood burning aerosol produced under smoldering conditions was photochemically aged with different relative humidity (RH) and NOx conditions using a 104 m3 dual outdoor chamber under natural sunlight. Light absorption of organic carbon (OC) was measured over the course of photooxidation using a UV-visible spectrometer connected to an integrating sphere. At high RH, the color decayed rapidly. NOx slightly prolonged the color of wood smoke, suggesting that NOx promotes the formation of chromophores via secondary processes. Overall, the mass absorption cross-section (integrated between 280 nm and 600 nm) of OC increased by 11-54% (except high RH) in the morning and then gradually decreased by 19-68% in the afternoon. This dynamic change in light absorption of wood burning OC can be explained by two mechanisms: chromophore formation and sunlight bleaching. To investigate the effect of chemical transformation on light absorption, wood smoke particles were characterized using various spectrometers. The intensity of fluorescence, which is mainly related to polycyclic aromatic hydrocarbons (PAHs), rapidly decreased with time indicating the potential bleaching of PAHs. A decline of levoglucosan concentrations evinced the change of POA with time. The aerosol water content measured by Fourier transform infrared spectroscopy showed that wood burning aerosol became less hygroscopic as photooxidation proceeded. A similar trend in light absorption changes has been observed in ambient smoke aerosol originating from the 2012 County Line Wildfire in Florida. We conclude that the biomass burning OC becomes less light absorbing after 8-9 h sunlight exposure compared to fresh wood burning OC.

Dynamic light absorption of biomass-burning organic carbon photochemically aged under natural sunlight

NASA Astrophysics Data System (ADS)

Zhong, M.; Jang, M.

2014-02-01

Wood-burning aerosol produced under smoldering conditions was photochemically aged with different relative humidity (RH) and NOx conditions using a 104 m3 dual outdoor chamber under natural sunlight. Light absorption of organic carbon (OC) was measured over the course of photooxidation using a UV-visible spectrometer connected to an integrating sphere. At high RH, the color decayed rapidly. NOx slightly prolonged the color of wood smoke, suggesting that NOx promotes the formation of chromophores via secondary processes. Overall, the mass absorption cross section (integrated between 280 and 600 nm) of OC increased by 11-54% (except high RH) in the morning and then gradually decreased by 19-68% in the afternoon. This dynamic change in light absorption of wood-burning OC can be explained by two mechanisms: chromophore formation and sunlight bleaching. To investigate the effect of chemical transformation on light absorption, wood smoke particles were characterized using various spectrometers. The intensity of fluorescence, which is mainly related to polycyclic aromatic hydrocarbons (PAHs), rapidly decreased with time, indicating the potential bleaching of PAHs. A decline of levoglucosan concentrations evinced the change of primary organic aerosol with time. The aerosol water content measured by Fourier transform infrared spectroscopy showed that wood-burning aerosol became less hygroscopic as photooxidation proceeded. A similar trend in light absorption changes has been observed in ambient smoke aerosol originating from the 2012 County Line wildfire in Florida. We conclude that the biomass-burning OC becomes less light absorbing after 8-9 h sunlight exposure compared to fresh wood-burning OC.

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

NASA Technical Reports Server (NTRS)

Wong, J. S. L.; Truong, T. K.; Benjauthrit, B.; Mulhall, B. D. L.; Reed, I. S.

1977-01-01

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding.

Determination of Carbon Dioxide, Carbon Monoxide, and Methane Concentrations in Cigarette Smoke by Fourier Transform Infrared Spectroscopy

ERIC Educational Resources Information Center

Tan, T. L.; Lebron, G. B.

2012-01-01

The integrated absorbance areas of vibrational bands of CO[subscript 2], CO, and CH[subscript 4] gases in cigarette smoke were measured from Fourier transform infrared (FTIR) spectra to derive the partial pressures of these gases at different smoke times. The quantity of the three gas-phase components of cigarette smoke at different smoke times…

To See the World in a Grain of Sand: Recognizing the Origin of Sand Specimens by Diffuse Reflectance Infrared Fourier Transform Spectroscopy and Multivariate Exploratory Data Analysis

ERIC Educational Resources Information Center

Pezzolo, Alessandra De Lorenzi

2011-01-01

The diffuse reflectance infrared Fourier transform (DRIFT) spectra of sand samples exhibit features reflecting their composition. Basic multivariate analysis (MVA) can be used to effectively sort subsets of homogeneous specimens collected from nearby locations, as well as pointing out similarities in composition among sands of different origins.…

Double Fourier Series Solution of Poisson’s Equation on a Sphere.

DTIC Science & Technology

1980-10-29

algebraic systems, the solution of these systems, and the inverse transform of the solution in Fourier space back to physi- cal space. 6. Yee, S. Y. K...Multiply each count in steps (2) through (5) by K] 7. Inverse transform um(0j j = 1, J - 1, to obtain u k; set u(P) = u 0 (P). [K(J - 1) log 2 K

Using multiple calibration sets to improve the quantitative accuracy of partial least squares (PLS) regression on open-path fourier transform infrared (OP/FT-IR) spectra of ammonia over wide concentration ranges

USDA-ARS?s Scientific Manuscript database

A technique of using multiple calibration sets in partial least squares regression (PLS) was proposed to improve the quantitative determination of ammonia from open-path Fourier transform infrared spectra. The spectra were measured near animal farms, and the path-integrated concentration of ammonia...

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.

A two-dimensional time domain near zone to far zone transformation

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Ryan, Deirdre; Beggs, John H.; Kunz, Karl S.

1991-01-01

A time domain transformation useful for extrapolating three dimensional near zone finite difference time domain (FDTD) results to the far zone was presented. Here, the corresponding two dimensional transform is outlined. While the three dimensional transformation produced a physically observable far zone time domain field, this is not convenient to do directly in two dimensions, since a convolution would be required. However, a representative two dimensional far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required, it can be obtained by inverse Fourier transform of the final frequency domain result.

A two-dimensional time domain near zone to far zone transformation

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Ryan, Deirdre; Beggs, John H.; Kunz, Karl S.

1991-01-01

In a previous paper, a time domain transformation useful for extrapolating 3-D near zone finite difference time domain (FDTD) results to the far zone was presented. In this paper, the corresponding 2-D transform is outlined. While the 3-D transformation produced a physically observable far zone time domain field, this is not convenient to do directly in 2-D, since a convolution would be required. However, a representative 2-D far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required it can be obtained by inverse Fourier transform of the final frequency domain result.

A Review of Maximum Entropy Spectral Analysis and Applications to Fourier Spectroscopy.

DTIC Science & Technology

1985-04-03

1 From Pythagoras to Fourier 3 2. 2 The Periodogram as Introduced by Sir Arthur Schuster 6 2. 3 The Slutzky Effect and the Work of Yule 7 2.4 The...Transform 27 4. 2 The Z-Transform Convolution Theorem 29 4. 3 The Wiener -Khintchmne , Theorem 31 4.4 The Z-Transform of el. 3 5. A COMPARISON BETWEEN...the Convolution I’heoreni, the Wiene i-Khintrbitte Theorem , aind the conventional ;pp roach of Il1ac km in and Tuke-,. Finally, it should he

On Weak and Strong 2k- bent Boolean Functions

DTIC Science & Technology

2016-01-01

U.S.A. Email: pstanica@nps.edu Abstract—In this paper we introduce a sequence of discrete Fourier transforms and define new versions of bent...denotes the complex conjugate of z. An important tool in our analysis is the discrete Fourier transform , known in Boolean functions literature, as Walsh...Hadamard, or Walsh–Hadamard transform , which is the func- tion Wf : Fn2 → C, defined by Wf (u) = 2− n 2 ∑ x∈Vn (−1)f(x)⊕u·x. Any f ∈ Bn can be

Fractional Fourier transform of truncated elliptical Gaussian beams.

PubMed

Du, Xinyue; Zhao, Daomu

2006-12-20

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

A pipeline design of a fast prime factor DFT on a finite field

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, In-Shek; Shao, H. M.; Reed, Irving S.; Shyu, Hsuen-Chyun

1988-01-01

A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented.

pH-Dependent Regulation of the Relaxation Rate of the Radical Anion of the Secondary Quinone Electron Acceptor QB in Photosystem II As Revealed by Fourier Transform Infrared Spectroscopy.

PubMed

Nozawa, Yosuke; Noguchi, Takumi

2018-05-15

Photosystem II (PSII) is a protein complex that performs water oxidation using light energy during photosynthesis. In PSII, electrons abstracted from water are eventually transferred to the secondary quinone electron acceptor, Q B , and upon double reduction, Q B is converted to quinol by binding two protons. Thus, excess electron transfer in PSII increases the pH of the stroma. In this study, to investigate the pH-dependent regulation of the electron flow in PSII, we have estimated the relaxation rate of the Q B - radical anion in the pH region between 5 and 8 by direct monitoring of its population using light-induced Fourier transform infrared difference spectroscopy. The decay of Q B - by charge recombination with the S 2 state of the water oxidation center in PSII membranes was shown to be accelerated at higher pH, whereas that of Q A - examined in the presence of a herbicide was virtually unaffected at pH ≤7.5 and slightly slowed at pH 8. These observations were consistent with the previous studies that included rather indirect monitoring of the Q B - and Q A - decays using fluorescence detection. The accelerated relaxation of Q B - was explained by the shift of a redox equilibrium between Q A - and Q B - to the Q A - side due to the decrease in the redox potential of Q B at higher pH, which is induced by deprotonation of a single amino acid residue near Q B . It is proposed that this pH-dependent Q B - relaxation is one of the mechanisms of electron flow regulation in PSII for its photoprotection.

Determination of NIR informative wavebands for transmission non-invasive blood glucose measurement using a Fourier transform spectrometer

NASA Astrophysics Data System (ADS)

Yang, Wenming; Liao, Ningfang; Cheng, Haobo; Li, Yasheng; Bai, Xueqiong; Deng, Chengyang

2018-03-01

Non-invasive blood glucose measurement using near infrared (NIR) spectroscopy relies on wavebands that provide reliable information about spectral absorption. In this study, we investigated wavebands which are informative for blood glucose in the NIR shortwave band (900˜1450 nm) and the first overtone band (1450˜1700 nm) through a specially designed NIR Fourier transform spectrometer (FTS), which featured a test fixture (where a sample or subject's finger could be placed) and all-reflective optics, except for a Michelson structure. Different concentrations of glucose solution and seven volunteers who had undergone oral glucose tolerance tests (OGTT) were studied to acquire transmission spectra in the shortwave band and the first overtone band. Characteristic peaks of glucose absorption were identified from the spectra of glucose aqueous solution by second-order derivative processing. The wavebands linked to blood glucose were successfully estimated through spectra of the middle fingertip of OGTT participants by a simple linear regression and correlation coefficient. The light intensity difference showed that glucose absorption in the first overtone band was much more prominent than it was in the shortwave band. The results of the SLR model established from seven OGTTs in total on seven participants enabled a positive estimation of the glucose-linked wavelength. It is suggested that wavebands with prominent characteristic peaks, a high correlation coefficient between blood glucose and light intensity difference and a relatively low standard deviation of predicted values will be the most informative wavebands for transmission non-invasive blood glucose measurement methods. This work provides a guidance for waveband selection for the development of non-invasive NIR blood glucose measurement.

Induction and quantification of collagen fiber alignment in a three-dimensional hydroxyapatite-collagen composite scaffold.

PubMed

Banglmaier, Richard F; Sander, Edward A; VandeVord, Pamela J

2015-04-01

Hydroxyapatite-collagen composite scaffolds are designed to serve as a regenerative load bearing replacement that mimics bone. However, the material properties of these scaffolds are at least an order of magnitude less than that of bone and subject to fail under physiological loading conditions. These scaffolds compositionally resemble bone but they do not possess important structural attributes such as an ordered arrangement of collagen fibers, which is a correlate to the mechanical properties in bone. Furthermore, it is unclear how much ordering of structure is satisfactory to mimic bone. Therefore, quantitative methods are needed to characterize collagen fiber alignment in these scaffolds for better correlation between the scaffold structure and the mechanical properties. A combination of extrusion and compaction was used to induce collagen fiber alignment in composite scaffolds. Collagen fiber alignment, due to extrusion and compaction, was quantified from polarized light microscopy images with a Fourier transform image processing algorithm. The Fourier transform method was capable of resolving the degree of collagen alignment from polarized light images. Anisotropy indices of the image planes ranged from 0.08 to 0.45. Increases in the degree of fiber alignment induced solely by extrusion (0.08-0.25) or compaction (0.25-0.44) were not as great as those by the combination of extrusion and compaction (0.35-0.45). Additional measures of randomness and fiber direction corroborate these anisotropy findings. This increased degree of collagen fiber alignment was induced in a preferred direction that is consistent with the extrusion direction and parallel with the compacted plane. Copyright © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

An intrinsically disordered photosystem II subunit, PsbO, provides a structural template and a sensor of the hydrogen-bonding network in photosynthetic water oxidation.

PubMed

Offenbacher, Adam R; Polander, Brandon C; Barry, Bridgette A

2013-10-04

Photosystem II (PSII) is a membrane-bound enzyme that utilizes solar energy to catalyze the photooxidation of water. Molecular oxygen is evolved after four sequential light-driven oxidation reactions at the Mn4CaO5 oxygen-evolving complex, producing five sequentially oxidized states, Sn. PSII is composed of 17 membrane-spanning subunits and three extrinsic subunits, PsbP, PsbQ, and PsbO. PsbO is intrinsically disordered and plays a role in facilitation of the water oxidizing cycle. Native PsbO can be removed and substituted with recombinant PsbO, thereby restoring steady-state activity. In this report, we used reaction-induced Fourier transform infrared spectroscopy to obtain information concerning the role of PsbP, PsbQ, and PsbO during the S state cycle. Light-minus-dark difference spectra were acquired, monitoring structural changes associated with each accessible flash-induced S state transition in a highly purified plant PSII preparation (Triton X-100, octylthioglucoside). A comparison of S2 minus S1 spectra revealed that removal of PsbP and PsbQ had no significant effect on the data, whereas amide frequency and intensity changes were associated with PsbO removal. These data suggest that PsbO acts as an organizational template for the PSII reaction center. To identify any coupled conformational changes arising directly from PsbO, global (13)C-PsbO isotope editing was employed. The reaction-induced Fourier transform infrared spectra of accessible S states provide evidence that PsbO spectral contributions are temperature (263 and 277 K) and S state dependent. These experiments show that PsbO undergoes catalytically relevant structural dynamics, which are coupled over long distance to hydrogen-bonding changes at the Mn4CaO5 cluster.

Qualitative and semiquantitative Fourier transformation using a noncoherent system.

PubMed

Rogers, G L

1979-09-15

A number of authors have pointed out that a system of zone plates combined with a diffuse source, transparent input, lens, and focusing screen will display on the output screen the Fourier transform of the input. Strictly speaking, the transform normally displayed is the cosine transform, and the bipolar output is superimposed on a dc gray level to give a positive-only intensity variation. By phase-shifting one zone plate the sine transform is obtained. Temporal modulation is possible. It is also possible to redesign the system to accept a diffusely reflecting input at the cost of introducing a phase gradient in the output. Results are given of the sine and cosine transforms of a small circular aperture. As expected, the sine transform is a uniform gray. Both transforms show unwanted artifacts beyond 0.1 rad off-axis. An analysis shows this is due to unwanted circularly symmetrical moire patterns between the zone plates.

New Substrate-Guided Method of Predicting Slow Conducting Isthmuses of Ventricular Tachycardia: Preliminary Analysis to the Combined Use of Voltage Limit Adjustment and Fast-Fourier Transform Analysis.

PubMed

Kuroki, Kenji; Nogami, Akihiko; Igarashi, Miyako; Masuda, Keita; Kowase, Shinya; Kurosaki, Kenji; Komatsu, Yuki; Naruse, Yoshihisa; Machino, Takeshi; Yamasaki, Hiro; Xu, Dongzhu; Murakoshi, Nobuyuki; Sekiguchi, Yukio; Aonuma, Kazutaka

2018-04-01

Several conducting channels of ventricular tachycardia (VT) can be identified using voltage limit adjustment (VLA) of substrate mapping. However, the sensitivity or specificity to predict a VT isthmus is not high by using VLA alone. This study aimed to evaluate the efficacy of the combined use of VLA and fast-Fourier transform analysis to predict VT isthmuses. VLA and fast-Fourier transform analyses of local ventricular bipolar electrograms during sinus rhythm were performed in 9 postinfarction patients who underwent catheter ablation for a total of 13 monomorphic VTs. Relatively higher voltage areas on an electroanatomical map were defined as high voltage channels (HVCs), and relatively higher fast-Fourier transform areas were defined as high-frequency channels (HFCs). HVCs were classified into full or partial HVCs (the entire or >30% of HVC can be detectable, respectively). Twelve full HVCs were identified in 7 of 9 patients. HFCs were located on 7 of 12 full HVCs. Five VT isthmuses (71%) were included in the 7 full HVC+/HFC+ sites, whereas no VT isthmus was found in the 5 full HVC+/HFC- sites. HFCs were identical to 9 of 16 partial HVCs. Eight VT isthmuses (89%) were included in the 9 partial HVC+/HFC+ sites, whereas no VT isthmus was found in the 7 partial HVC+/HFC- sites. All HVC+/HFC+ sites predicted VT isthmus with a sensitivity of 100% and a specificity of 80%. Combined use of VLA and fast-Fourier transform analysis may be a useful method to detect VT isthmuses. © 2018 American Heart Association, Inc.

Criteria for confirming sequence periodicity identified by Fourier transform analysis: application to GCR2, a candidate plant GPCR?

PubMed

Illingworth, Christopher J R; Parkes, Kevin E; Snell, Christopher R; Mullineaux, Philip M; Reynolds, Christopher A

2008-03-01

Methods to determine periodicity in protein sequences are useful for inferring function. Fourier transformation is one approach but care is required to ensure the periodicity is genuine. Here we have shown that empirically-derived statistical tables can be used as a measure of significance. Genuine protein sequences data rather than randomly generated sequences were used as the statistical backdrop. The method has been applied to G-protein coupled receptor (GPCR) sequences, by Fourier transformation of hydrophobicity values, codon frequencies and the extent of over-representation of codon pairs; the latter being related to translational step times. Genuine periodicity was observed in the hydrophobicity whereas the apparent periodicity (as inferred from previously reported measures) in the translation step times was not validated statistically. GCR2 has recently been proposed as the plant GPCR receptor for the hormone abscisic acid. It has homology to the Lanthionine synthetase C-like family of proteins, an observation confirmed by fold recognition. Application of the Fourier transform algorithm to the GCR2 family revealed strongly predicted seven fold periodicity in hydrophobicity, suggesting why GCR2 has been reported to be a GPCR, despite negative indications in most transmembrane prediction algorithms. The underlying multiple sequence alignment, also required for the Fourier transform analysis of periodicity, indicated that the hydrophobic regions around the 7 GXXG motifs commence near the C-terminal end of each of the 7 inner helices of the alpha-toroid and continue to the N-terminal region of the helix. The results clearly explain why GCR2 has been understandably but erroneously predicted to be a GPCR.

[Spatial domain display for interference image dataset].

PubMed

Wang, Cai-Ling; Li, Yu-Shan; Liu, Xue-Bin; Hu, Bing-Liang; Jing, Juan-Juan; Wen, Jia

2011-11-01

The requirements of imaging interferometer visualization is imminent for the user of image interpretation and information extraction. However, the conventional researches on visualization only focus on the spectral image dataset in spectral domain. Hence, the quick show of interference spectral image dataset display is one of the nodes in interference image processing. The conventional visualization of interference dataset chooses classical spectral image dataset display method after Fourier transformation. In the present paper, the problem of quick view of interferometer imager in image domain is addressed and the algorithm is proposed which simplifies the matter. The Fourier transformation is an obstacle since its computation time is very large and the complexion would be even deteriorated with the size of dataset increasing. The algorithm proposed, named interference weighted envelopes, makes the dataset divorced from transformation. The authors choose three interference weighted envelopes respectively based on the Fourier transformation, features of interference data and human visual system. After comparing the proposed with the conventional methods, the results show the huge difference in display time.

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS

PubMed Central

BAJAJ, CHANDRAJIT; BAUER, BENEDIKT; BETTADAPURA, RADHAKRISHNA; VOLLRATH, ANTJE

2013-01-01

The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ∈ SO(3), t ∈ ℝ3 that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup either with respect to the sought translation or rotation. We present PFcorr, a new exhaustive solution, based on the non-equispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PFcorr can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogs of the above problems in which the flexibility of the protein is relevant. PMID:24379643

Hypothesis on human eye perceiving optical spectrum rather than an image

NASA Astrophysics Data System (ADS)

Zheng, Yufeng; Szu, Harold

2015-05-01

It is a common knowledge that we see the world because our eyes can perceive an optical image. A digital camera seems a good example of simulating the eye imaging system. However, the signal sensing and imaging on human retina is very complicated. There are at least five layers (of neurons) along the signal pathway: photoreceptors (cones and rods), bipolar, horizontal, amacrine and ganglion cells. To sense an optical image, it seems that photoreceptors (as sensors) plus ganglion cells (converting to electrical signals for transmission) are good enough. Image sensing does not require ununiformed distribution of photoreceptors like fovea. There are some challenging questions, for example, why don't we feel the "blind spots" (never fibers exiting the eyes)? Similar situation happens to glaucoma patients who do not feel their vision loss until 50% or more nerves died. Now our hypothesis is that human retina initially senses optical (i.e., Fourier) spectrum rather than optical image. Due to the symmetric property of Fourier spectrum the signal loss from a blind spot or the dead nerves (for glaucoma patients) can be recovered. Eye logarithmic response to input light intensity much likes displaying Fourier magnitude. The optics and structures of human eyes satisfy the needs of optical Fourier spectrum sampling. It is unsure that where and how inverse Fourier transform is performed in human vision system to obtain an optical image. Phase retrieval technique in compressive sensing domain enables image reconstruction even without phase inputs. The spectrum-based imaging system can potentially tolerate up to 50% of bad sensors (pixels), adapt to large dynamic range (with logarithmic response), etc.